papers/2409.01700v2.json

{
    "title": "Cosmic-ray induced sputtering of interstellar formaldehyde ices",
    "abstract": "Context. In the cold and dense regions of the interstellar medium (ISM), for example in prestellar cores, gas-phase chemical abundances undergo a steep decrease due to the freeze-out of molecules onto the dust grain surfaces. While the depletion of many species would bring molecular abundances to undetected levels within short timescales, non-thermal desorption mechanisms such as UV photodesorption or cosmic-ray sputtering allows the return of a fraction of the ice mantle species back to the gas phase and prevents a complete freeze-out in the densest regions. In the last decade much effort has been devoted to understanding the microphysics of desorption and quantifying molecular desorption yields.",
    "sections": [
        {
            "section_id": "1",
            "parent_section_id": null,
            "section_name": "Introduction",
            "text": "The chemistry of prestellar cores is characterised by high amounts of molecular depletion due to the freeze-out of gas-phase molecules onto interstellar dust grains. At the high densities prevailing in prestellar cores, molecules from the gas phase collide and stick to the grains, building up an ice mantle. Millimetre wave observations of rotational transitions indeed show a molecular abundance decrease for most species towards the core centres (e.g. Willacy et al., 1998  ###reference_b82###; Caselli et al., 1999  ###reference_b16###; Bacmann et al., 2002  ###reference_b4###) where the densities are highest. Additionally, infrared observations have established the presence of several species in the solid phase of the dense interstellar medium (Whittet et al., 1983  ###reference_b80###; Boogert et al., 2015  ###reference_b12###), the details of which are now being revealed by the James Webb Space Telescope (JWST; Yang et al., 2022  ###reference_b85###; McClure et al., 2023  ###reference_b47###; Rocha et al., 2024  ###reference_b64###).\nThe accretion timescale for CO molecules at a temperature of 10 K, expressed in years, can be estimated as  where  is the molecular H2 density (Bergin & Tafalla, 2007  ###reference_b8###). At the densities prevailing in prestellar cores, around  cm-3, this timescale is much shorter than typical core lifetimes of around  years (Könyves et al., 2015  ###reference_b39###). In the absence of any efficient mechanism returning frozen-out molecules back to the gas-phase, CO and other molecules should be absent from the gas phase, contrary to what is observed in these regions: within  years, for a density of  cm-3, the molecular abundance should drop by several dozen orders of magnitude, while observations show a much more moderate drop of a few orders of magnitude (Pagani et al., 2012  ###reference_b57###). Therefore, desorption mechanisms allowing the frozen-out molecules to return to the gas phase have to be considered (Leger, 1983  ###reference_b44###).\nAt typical prestellar core temperatures, around 10 K, the available thermal energy is insufficient to enable molecular desorption, but several non-thermal mechanisms have been invoked to account for the observed molecular abundances in the gas phase: UV photodesorption, cosmic-ray sputtering, desorption by cosmic-ray induced UV photons (secondary UV radiation), IR photodesorption, or reactive desorption, in which the exothermicity of grain surface reactions contributes to the release of the reaction’s products in the gas phase. In the last decades, experimental studies have endeavoured to characterise the efficiency of the various desorption processes. Photodesorption rates have been measured under broadband UV irradiation for molecules such as CO, N2, CO2, and H2O by Öberg et al. (2007  ###reference_b53###, 2009b  ###reference_b55###, 2009c  ###reference_b56###) or Muñoz Caro et al. (2010  ###reference_b50###). Further work using monochromatic synchrotron UV radiation provided insights into the mechanisms governing UV photodesorption (e.g. Fayolle et al., 2011  ###reference_b29###; Bertin et al., 2012  ###reference_b10###; Fayolle et al., 2013  ###reference_b30###). These experiments coupled with quadrupole mass spectrometry to detect ejected gas-phase species have revealed that some molecules can be fragmented upon UV irradiation so that the photodesorption yield of the intact molecules may represent only a minor component of the total photodesorbed fragments, as is the case for CH3OH (methanol), HCOOH (formic acid), CH3OCHO (methyl formate) (Bertin et al., 2016  ###reference_b11###, 2023  ###reference_b9###) and H2CO (formaldehyde) (Féraud et al., 2019  ###reference_b31###). As an illustration, the photodesorption yield measured by Bertin et al. (2016  ###reference_b11###) for intact CH3OH is two orders of magnitude smaller than previously derived from experiments using solely infrared spectroscopy ice measurements (Öberg et al., 2009a  ###reference_b54###), showing that it is therefore essential to monitor the products of the desorption process and not only the loss of the molecule in the solid state. Recent experiments of resonant infrared irradiation of CO and CH3OH ices suggest that IR photons could also induce desorption with a flux integrated efficiency similar to that of UV photons (Santos et al., 2023  ###reference_b66###, and references therein).\nChemical desorption, or reactive desorption, occurs when the excess energy of a grain surface reaction (typically involving two radicals) can be converted into kinetic energy perpendicular to the surface overcoming the binding energy of the product with the grain (Allen & Robinson, 1975  ###reference_b1###). However, the efficiency of this process is difficult to evaluate in situ. Recent experiments have shown that while this mechanism can be efficient in some cases, the nature of the substrate (whether composed of bare graphite or covered with water ice) and its porosity (Dulieu et al., 2013  ###reference_b26###), as well as the number of degrees of freedom of the reaction product plays a major role. In particular, Minissale et al. (2016  ###reference_b49###) did not observe chemical desorption of CH3OH formed from the reaction CH3O + H, and estimated that the efficiency of chemical desorption from water ice is at most a few percent. Therefore, in the dense interstellar medium, where the composition of ice mantles is dominated by water ice, chemical desorption is expected to have a low efficiency, for large molecules at least.\nCosmic rays are also believed to contribute to molecular desorption (e.g. Leger et al., 1985  ###reference_b45###; Willacy & Williams, 1993  ###reference_b83###; Hasegawa & Herbst, 1993  ###reference_b35###; Shen et al., 2004  ###reference_b71###) by sputtering ice species to the gas phase. The cosmic-ray induced desorption process consists of two main contributions: the ‘whole-grain’ heating and the ‘thermal spike’ sputtering (erosion) (Bringa & Johnson, 2004  ###reference_b14###). While many studies so far have relied on the formalism proposed by Hasegawa & Herbst (1993  ###reference_b35###) for whole-grain heating, cosmic-ray induced (thermal-spike) sputtering can be investigated experimentally by using swift heavy ions as cosmic-ray analogues. Studies of ice film irradiation by heavy ions carried out by Seperuelo Duarte et al. (2009  ###reference_b69###, 2010  ###reference_b70###) have determined sputtering yields for CO2 and CO ices by modelling the disappearance of the ice constituents from the solid phase. Of interest to account for the observed gas-phase abundances in the interstellar medium, however, is the amount of molecules that return to the solid phase intact per incident ion. Recent heavy-ion ice irradiation experiments coupled with a quadrupole mass spectrometer (QMS) to monitor the sputtered species in the gas phase (Dartois et al., 2019  ###reference_b20###) have measured this parameter, both for pure ices (e.g. CO2, CH3OH, CH3OOCH3) and for ice mixtures (CH3OH/CO2, CH3OH/H2O, CH3OOCH3/H2O). For the species in these studies, a large fraction of the molecules are desorbed intact, and the sputtering yield of a minor species in an ice mixture is close to that of the species making up the bulk of the ice (Dartois et al., 2019  ###reference_b20###).\nWhile the above-mentioned experiments provide us with essential quantitative data regarding the desorption processes, they have been included in few chemical models so far, and it is still unclear whether they can account for observed molecular abundances (Wakelam et al., 2021  ###reference_b77###). Moreover, a large body of experimental data is still missing, even regarding major species in the dense interstellar medium.\nFormaldehyde (H2CO) is a ubiquitous species in molecular clouds and prestellar cores (e.g. Dieter, 1973  ###reference_b24###; Sandqvist & Bernes, 1980  ###reference_b65###; Mundy et al., 1987  ###reference_b51###), with gas-phase column densities close to that of methanol, around  cm-2 in prestellar cores (Bacmann et al., 2003  ###reference_b5###; Bacmann & Faure, 2016  ###reference_b3###) and in protostellar envelopes (Parise et al., 2006  ###reference_b60###). In ice mantles, H2CO has only been tentatively detected towards protostellar envelopes and its abundance is estimated at around 5%, similar to CH3OH (Boogert et al., 2015  ###reference_b12###; Rocha et al., 2024  ###reference_b64###). Formaldehyde also represents an important intermediate step towards more complex molecules on grain surfaces (Chuang et al., 2016  ###reference_b17###), or towards complex organic molecule precursors like HCO in the gas phase (Bacmann & Faure, 2016  ###reference_b3###). In prestellar cores, it is believed to form chiefly via hydrogenation of CO on grain surfaces (Watanabe et al., 2004  ###reference_b78###; Minissale et al., 2016  ###reference_b49###), as an intermediate step to methanol formation. Gas phase formation mechanisms have also been proposed (Guzmán et al., 2011  ###reference_b33###; Ramal-Olmedo et al., 2021  ###reference_b62###), but distinguishing both formation mechanisms requires detailed knowledge of the physical processes (e.g. desorption), which is lacking.\nIn this paper we present a study of swift ion irradiation of pure H2CO  ices and determine the sputtering yield of the intact molecule. We calculate the sputtering rate over the cosmic-ray spectrum (from  eV/amu to  GeV/amu) and use it in a simple model to compare the derived H2CO gas-phase abundance with both H2CO observations in a prestellar source and the abundances predicted with other non-thermal desorption mechanisms.\nThe paper is organised as follows: In Sect. 2  ###reference_### we describe the irradiation experiments of thin H2CO films carried out at the Grand Accélérateur National d’Ions Lourds (GANIL, Caen, France) and in Sect. 3  ###reference_### the IRAM H2CO observations towards a prestellar core. In Sect. 4  ###reference_### we present the analysis of both the observational and the experimental data and determine the intact sputtering yield of the molecule. In Sect. 5  ###reference_### we discuss the astrophysical implications of our study and conclude in Sect. 6  ###reference_###."
        },
        {
            "section_id": "2",
            "parent_section_id": null,
            "section_name": "Experiments",
            "text": "Pure H2CO ice irradiation experiments were carried out at the GANIL ion accelerator on the IRRSUD beamline111https://www.ganil-spiral2.eu with the Irradiation de GLaces d’Intérêt AStrophysique (IGLIAS) setup (see Augé et al., 2018  ###reference_b2###, for a detailed description) between May 14 and 16, 2021. The vacuum chamber was cryocooled down to a temperature of about 10 K, and held at a pressure of  mbar. Infrared spectra were collected with a Bruker Vertex 70v Fourier transform infrared spectrometer (FTIR), operating with a HgCdTe-detector and a 1 cm-1 spectral resolution. The angle between the spectrometer beam and the sample surface was 12∘. Thin H2CO films with thicknesses of m were condensed on a ZnSe window at normal incidence with a needle placed at a distance of around 15 mm. The pressure during injection was typically  mbar. The deposition rate was adjusted to get a good optical quality, and the sample thickness was estimated using the band strengths of Bouilloud et al. (2015  ###reference_b13###) and the interference fringes from the infrared spectra. Gas-phase H2CO was produced from the thermal decomposition of paraformaldehyde (Sigma Aldrich, purity 95%), heated at 100∘C in a homemade oven maintained under secondary vacuum ( 10-7 mbar). The gaseous species sputtered in the chamber were detected with a MKS Microvision 2 QMS. The branching ratios of the species fragments were evaluated during their injection.\nIrradiations were conducted with a 86Kr18+ beam of 0.86 MeV/u (74 MeV) corresponding to an electronic stopping power of 2830 eV (1015 molecules cm-2)-1 for an H2CO ice of 0.81 g cm-3 (Bouilloud et al., 2015  ###reference_b13###), as computed with the SRIM-2013 code222http://www.srim.org. (Ziegler et al., 2010  ###reference_b87###). The flux was  ions cm-2 s-1, and the fluence reached at the end of the experiment was  ions cm-2. The corresponding doses are computed and compared to typical interstellar doses in Appendix A  ###reference_###. Infrared spectra monitoring the ice composition were taken every two minutes starting from the beginning of the irradiation. The QMS continously scanned masses from 0-80 u, with a scan duration of  s.\nAdditionally, a control experiment under the same conditions was carried out in which we irradiated a m CO2 (Air Liquide, purity ) ice film with the same beam, corresponding to an electronic stopping power of 3290 eV (1015 molecules cm-2)-1, also computed with SRIM-2013, for a CO2 density of 1.0 g cm3 (Satorre et al., 2008  ###reference_b67###). For this experiment, the flux varied between  and  ions cm-2 s-1 throughout the irradiation and the final fluence was 1013 ions cm-2.\nThe experimental data can be downloaded from https://zenodo.org/records/13383307."
        },
        {
            "section_id": "3",
            "parent_section_id": null,
            "section_name": "Observations",
            "text": "Observations of one prestellar core, L1689B, were carried out between 2013 and 2019 during several campaigns, at the IRAM 30 m telescope, located at Pico Veleta, Spain. L1689B is situated in the Rho Ophiuchi star-forming region, and is characterised by low central temperatures and high central densities (Steinacker et al., 2016  ###reference_b72###). It shows signs of gravitational contraction and appears dynamically evolved (Lee et al., 2001  ###reference_b42###, 2003  ###reference_b43###; Lee & Myers, 2011  ###reference_b41###) despite moderate molecular depletion and deuteration (Bacmann et al., 2003  ###reference_b5###). A wealth of oxygen-bearing molecules, including formaldehyde and more complex organics, have been detected in this source (Bacmann et al., 2003  ###reference_b5###, 2012  ###reference_b6###). The observed coordinates are RA:  Dec:, corresponding to the peak of the millimetre continuum emission in the source. Several frequency setups were used to target rare isotopes of formaldehyde lines at 2 mm and 1 mm with the Eight MIxers Receivers (EMIR) E1 and E2, respectively. We focused on H2CO  rotational transitions with upper energies typically lower than  K, as levels of higher energies are unlikely to be sufficiently populated at the low temperatures prevailing in the source (typically 10 K). Because the low-lying transitions of the main isotopologue are optically thick and self-absorbed towards the core centre (Bacmann et al., 2003  ###reference_b5###), we present here observations of the optically thinner isotopologues HCO and H2C18O, in both ortho and para nuclear-spin symmetries. The receivers were connected to the Fourier transform spectrometer (FTS) at a spectral resolution of  kHz over a bandwidth of 2 GHz, leading to velocity resolutions of  km s-1 at 2 mm and  km s-1 at 1 mm. The data were taken using the frequency switching procedure with a frequency throw of 7.5 MHz to reduce standing waves. Pointing and focus were typically checked every  hours on nearby quasars or planets, with additional focus checks carried out shortly after sunset or sunrise. Pointing was found to be accurate to . Calibrations were performed every 10 to 15 minutes, depending on atmospheric stability. The beam sizes vary from 18 at 134 GHz to 11 at 220 GHz. The beam efficiencies were taken following the Ruze formula , with  the wavelength, m the surface  of the 30 m antenna, and . The forward efficiencies were 93% and 91% at 2 mm and 1 mm, respectively. The spectra were converted from the antenna temperature scale  to the main beam temperature scale  using the values of the efficiencies given above.\nThe observational data were reduced with the Gildas/IRAM software.333https://www.iram.fr/IRAMFR/GILDAS The data reduction consisted in folding the spectra to recover the signal from the frequency switching procedure, except for the newer data for which folded spectra are delivered by the system. Then a low-order (typically 3) polynomial baseline was fitted to the spectra over line-less spectral regions and was subtracted before the spectra were co-added. The reduced spectra are presented in Appendix B  ###reference_###. Finally, the spectral lines were fitted with Gaussians. The spectroscopic parameters of the observed transitions and results of the Gaussian fits are presented in Table 1  ###reference_###. The error given in the integrated intensity includes the calibration uncertainty, which was taken to be  at 2 mm and  at 1 mm."
        },
        {
            "section_id": "4",
            "parent_section_id": null,
            "section_name": "Results",
            "text": ""
        },
        {
            "section_id": "4.1",
            "parent_section_id": "4",
            "section_name": "Experiments",
            "text": "The evolution of H2CO ice infrared (IR) spectra as a function of fluence is depicted in Fig. 1  ###reference_###. At fluence zero, the film is made of pure H2CO, and neither paraformaldehyde nor CO or CO2 can be seen in the spectra. As soon as irradiation starts, bands characteristic of CO2 and CO appear, as well as bands around 2920, 1230, 1100, and 920 cm-1, which we attribute to the formation of an H2CO polymer (polyoxymethylene, hereafter POM). Conversely, H2CO bands decrease with fluence. Apart from CO, CO2, and POM, the infrared analysis shows no evidence of the formation of any other chemical species during the irradiation of H2CO. The column densities of CO2, CO, and H2CO were derived using the band strengths given in Table 2  ###reference_### and the integrated absorbance of the bands at 2343 cm-1, 2139 cm-1, and 1725 cm-1, respectively. The POM column density was calculated using a combination mode at 1105 cm-1 and a band strength of  cm molecules-1 (Noble et al., 2012  ###reference_b52###). This band strength is not known with precision (Tadokoro et al., 1963  ###reference_b73###; Schutte et al., 1993  ###reference_b68###), and we assumed a factor of 2 uncertainty. An additional uncertainty arises from changes in the refractive index value across strong absorbance bands, resulting in some unphysical negative absorbances after baseline correction (see e.g. the C=0 stretch of H2CO). The derived column density evolution as a function of fluence, with uncertainty zones, is presented in Fig. 2  ###reference_###. As can be seen, the POM column density is not accurately determined, but it is consistent with a fast and efficient polymerisation of \\ceH2CO at very low fluence. Thus, at a fluence of  ions cm-1, the ice is mainly composed of POM.\n###figure_1### ###figure_2### In similar experiments on non-polymerisable ices such as \\ceCH3OH and \\ceCO2 (Dartois et al., 2019  ###reference_b20###; Seperuelo Duarte et al., 2009  ###reference_b69###), the column density evolution with fluence can be solved through a simple differential equation involving solely radiolysis and sputtering processes (see e.g. Eq. (3) in  Dartois et al., 2019  ###reference_b20###). Here, however, we were not able to solve such a differential equation, due to the additional polymerisation process of \\ceH2CO towards POM, whose exact nature is unknown.666In particular, the number of monomers is unknown and most probably the synthesised POM is a mixture of polymers of various chain sizes. In addition, while swift ion irradiation of H2CO is responsible for the formation of POM, it also destroys POM to CO and CO2 (see the decrease in POM column density beyond a fluence of  ions cm-2 in Fig. 2  ###reference_###). Therefore, in order to derive the sputtering yield, we resorted to another method based on the determination of the reduction in thin film thickness using the Fabry–Perot interference fringes observed in the infrared spectra (Dartois et al., 2020  ###reference_b22###, 2023  ###reference_b19###), combined with QMS analysis of the gas composition. We emphasise that in order to validate this method, it was first applied to measure the thickness evolution of an irradiated thin film of CO2, for which the usual fit of the column density evolution via a differential equation was also possible. As reported in Appendix C  ###reference_###, both methods were found to give consistent results, which are also in good agreement with the literature.\nIn the case of \\ceH2CO, as irradiation proceeds, the ice film becomes a mixture of mainly POM and H2CO for which the refractive index () is not available. Fitting the rigorous expression for the transmission () of a thin absorbing film on a thick transparent substrate is therefore not possible. Nevertheless, transmittance spectra follow a sinusoidal pattern, where the period is proportional to the thickness. Thus, we used the following simple expression to fit the transmittance spectra in the ranges of wavenumbers () free of molecular absorptions:\nHere  and  are free parameters,  is the refractive index taken as  (Bouilloud et al., 2015  ###reference_b13###), and  is ice thickness. The factor  corrects for the angle between the infrared beam and the sample. Fits obtained with this expression are shown in Fig. 3  ###reference_###. The ice film is composed of POM and H2CO, with a composition changing during irradiation. Therefore, evaluating the sample mass density  is challenging. Furthermore, even the mass density of a pure H2CO  ice film is unknown. Consequently, it is assumed to be constant at the value for liquid formaldehyde,  (Bouilloud et al., 2015  ###reference_b13###), with an assumed uncertainty of 20%. It was used to derive the surface density of the ice , as a function of fluence, as shown in Fig. 4  ###reference_###. The total mass sputtering yield can be directly estimated from the slope of the surface density evolution with fluence as  g ion-1. It should be noted that this total yield includes all sputtered species from the considered volume, both radiolysed species (C, O, H, H2, CO, and CO2) and intact \\ceH2CO fragments.\n###figure_3### ###figure_4### In order to determine the chemical composition of the sputtered mass volume, the various fragments ejected into the gas phase were measured with the QMS. The small residual or background signal observed before irradiation was subtracted from the recorded signal during the whole irradiation time, as reported in Fig. 5  ###reference_### (top panel). We note that there is no intact sputtered POM as no signal is observed at =31, a mass characteristic of POM fragmentation pattern (Butscher et al., 2019  ###reference_b15###; Duvernay et al., 2014  ###reference_b27###). The mass =30 can be used to follow H2CO molecules since no fragment at this mass is observed in the CO fragmentation pattern (Fig. 6  ###reference_###). Thus, the signals at m/z=30 and m/z=28 can be used to retrieve the total number of H2CO and CO species, respectively, by dividing each m/z signal by its relative contribution in the fragmentation pattern. The remaining signals at m/z=12 and m/z=16, after subtracting the contributions of CO and H2CO, indicate the abundances of C and O atoms, respectively. Once corrected for the total electron-impact ionisation cross-section  at 70 eV (energy of the QMS electron ionisation source), the relative fraction of each species  with fluence  is determined (Fig. 5  ###reference_###, bottom panel). QMS measurements at very low masses are not reliable, but the amount of hydrogen (H or H2) is supposed to be equal to the sum of the amounts of C, O, and CO. We note that CO2, a minor component of the ice (see Fig. 1  ###reference_###), was not detected in the gas phase by the QMS. As irradiation proceeds, the composition of the film changes (Fig. 2  ###reference_###) and this is also observed in the gas composition (Fig. 5  ###reference_###, bottom panel). The fraction of gaseous H2CO thus decreases significantly (by approximately 70 %) for initial fluences (up to 2 ions cm-2), which is consistent with the radiolysis and the rapid polymerisation of solid \\ceH2CO.\nIt then decreases more gradually, before a (noisy) slightly ascending plateau is reached beyond fluences of 3 ions cm-2. Conversely, the fractions of C and O increase rapidly (by approximately 70%), but also reach a plateau. Overall, the molecular fractions of these three chemical species in the gas vary by less than a factor of two. The larger molecular fractions of CO and H2 increase up to fluences of about 2 ions cm-2 before reaching a slightly descending plateau, with variations of less than 15%. We can extract the initial fraction of each species  in the gas phase  (Table 5  ###reference_###), and the subsequent evolution  was fitted by third-order polynomials.\n###figure_5### ###figure_6### By combining the total mass sputtering yield  with the fitted molecular fractions , we can derive the sputtering yield of each ejected species ,\nwhere  is the Avogadro constant,  is the molecular mass of species , and  represents the mass fraction of species  in the gas:\nThe derived sputtering yields for the various ejected species  are plotted as dashed lines in the bottom panel of Fig. 5  ###reference_### (right -axis). Similarly to the molecular fractions, the intact sputtering yields vary by less than a factor of 2 for C, O, and H2CO, and by less than 15% for CO and H2, as expected. The average intact sputtering yields  were computed over the full range of fluences and are listed in Table 5  ###reference_###. The average sputtering yield for intact \\ceH2CO is found to be  molecules ion-1.\nWe can now try to estimate the effective sputtering yield, . For non-polymerisable species,  is usually determined using the column density evolution with fluence measured from IR spectroscopy (Dartois et al., 2019  ###reference_b20###; Seperuelo Duarte et al., 2009  ###reference_b69###). For a pure ice ,  is defined as the semi-infinite thickness effective-sputtering yield for the ice under study. It includes both intact sputtered species  and radiolysed (daughter) sputtered species. Since radiolysis and sputtering occur simultaneously, IR spectroscopy captures the disappearance of H2CO, regardless of whether it is sputtered intact or radiolysed.  is simply related to  as\nwhere  is the intact fraction of sputtered H2CO.\nIn our experiment, the volume to be sputtered just before irradiation is composed of pristine \\ceH2CO ice. The impact of a swift heavy ion induces radiolysis along its track, affecting a fraction of this volume. Therefore, after irradiation has started, the sputtered volume is composed of intact \\ceH2CO, fresh products of radiolysis as well as primary radiolytic products that accumulate in the film (see Fig. 7  ###reference_###). Therefore, in order to determine the effective sputtering yield , the intact fraction () of sputtered H2CO during irradiation must be estimated using the initial fractions reported in Table 3  ###reference_###:\nIn practice, we derived an intact fraction of sputtered \\ceH2CO molecules =0.23, corresponding to an effective sputtering yield for the \\ceH2CO film of =(10.99.9)103 molecules ions-1.\n###figure_7### In their compendium of selected literature sputtering yields, Dartois et al. (2023  ###reference_b19###) show that the sputtering yield induced by swift heavy ions follows an empirical law that is directly proportional to the square of the electronic stopping power :\nHere, using a stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam, we obtain for a pure \\ceH2CO ice =(3.12.8)10-4 1030 eV-2 cm-4 molecule3.\nHowever, most studies only have access to the effective sputtering yield , which is therefore used for  in Eq. 6  ###reference_### (e.g. Dartois et al., 2023  ###reference_b19###). In this case, the effective prefactor value is =(1.4 1.3)10-3 1030 eV-2 cm-4 molecule3."
        },
        {
            "section_id": "4.2",
            "parent_section_id": "4",
            "section_name": "H2CO abundance in L1689B",
            "text": "The H2CO column density in the L1689B prestellar core was determined using the RADEX radiative transfer code (van der Tak et al., 2007  ###reference_b76###) in the uniform sphere approximation. The collisional rate coefficients used in the computation are the H2COH2 coefficients from Wiesenfeld & Faure (2013  ###reference_b81###) adapted to the spectroscopy of H2C18O and HCO and were obtained from the Excitation of Molecules and Atoms for Astrophysics (EMAA) collisional rate database.888emaa.osug.fr Because there are no radiative or collisional mechanisms converting one form into the other, the ortho and para nuclear-spin isomers of each isotopologue were treated as two separate species. At thermal equilibrium, the ortho-to-para ratio of H2CO is  1.5 at 10 K, and reaches the statistical value of 3.0 at about 30 K.\nOnly collisions with para-H2 were considered as the ortho-H2 abundance represents at most  of the total H2 (Pagani et al., 2009  ###reference_b58###; Troscompt et al., 2009  ###reference_b75###; Dislaire et al., 2012  ###reference_b25###) and can be neglected in prestellar cores.\nUsing RADEX, we calculated grids of models for ranges of values in kinetic temperature, H2 density, and in the molecular column densities (ortho-HCO, para-HCO, ortho-H2C18O, or para-H2C18O). The grid points in temperature and H2 density were chosen to be the same for all species, which is based on the assumption that all of them are coexistent. The densities span a range between  cm-2 and  cm-2 and the temperatures between 3 K and 12 K. The column density of ortho-HCO  was varied between  cm-2 and  cm-2. The column density of para-HCO  was taken as  where  is the ortho-to-para ratio in the considered H2CO isotopologue (either in HCO or in H2C18O), and the free parameter  was varied between 1 and 6. For the column density of H2C18O, we assumed a ratio  such as the ortho-H2C18O column density  is  and the para-H2C18O column density  is , and varied this ratio between 7 and 10 (see e.g. Wilson, 1999  ###reference_b84###, for standard values of 13C/18O). The input linewidths for the calculations were taken to be 0.48 km s-1 for HCO and 0.38 km s-1 for H2C18O, but they have little influence on the results, because our fitting procedure relies on the velocity integrated intensities of the modelled lines compared to that of the observations.\nThe goodness of fit was estimated with a  defined as\nwhere  is the kinetic temperature; (H2) is the H2 density;  is the observed line integrated intensity;  is the error on the observed integrated intensity;  is the line integrated intensity calculated by RADEX; and the indices  refer to the transitions in ortho-HCO, para-HCO, ortho-H2C18O, and para-H2C18O, respectively.\nTypically, 10 to 15 points were chosen for each parameter. The grids were refined close to parameter values best reproducing the observations.\nThe best fitting parameters are given in Table 4  ###reference_###.\nBecause the ortho-to-para ratio is expected to be at most 3 for H2CO,101010A recent laboratory experiment has shown that the measured ortho-to-para ratio of \\ceH2CO molecules formed via UV photolysis of \\ceCH3OH ices is , with no correlation with ice temperature (Yocum et al., 2023  ###reference_b86###). we re-ran the model and kept the ortho-to-para ratio set to 3. In this case, the  value is slightly worse (5.5 instead of 4.3 for the best model), and the best fitting temperature is slightly lower (closer to 9 K). The other parameters (density, ortho-HCO column density, and 13C/18O ratio) remain unchanged. We also ran the fitting routine with the temperature and density values found for CH3OH by Bacmann & Faure (2016  ###reference_b3###) (i.e.  K and  cm-3), and again found results for the parameters very similar to the best fit:  cm-2.\nThe line integrated intensities from the best fit model are shown in Fig. 8  ###reference_### against the observed line integrated intensities. The model can account for the observations within the uncertainties.\n###figure_8### With the values in Table 4  ###reference_###, we obtain the following values for the molecular column densities:  cm-2,  cm-2,  cm-2, and  cm-2. Assuming a ratio  of 557 (Wilson, 1999  ###reference_b84###), we obtain a total (ortho  para) column density of  cm-2 for the main isotopologue H2CO.\nThe H2 column density at the same position as the H2CO observations was derived from the model of Steinacker et al. (2016  ###reference_b72###), by integrating the density profile along the line of sight and multiplying by two to account for the contribution of the far side of the core. The uncertainty was determined using the error bars from the fit including the interstellar radiation field (see Steinacker et al., 2016  ###reference_b72###, for details). We find a total H2 column density  cm-2, with a spread  cm-2. The corresponding relative abundance of \\ceH2CO with respect to total hydrogen ( is ."
        },
        {
            "section_id": "5",
            "parent_section_id": null,
            "section_name": "Astrophysical applications",
            "text": ""
        },
        {
            "section_id": "5.1",
            "parent_section_id": "5",
            "section_name": "Model",
            "text": "We investigate in this section whether non-thermal desorption from icy grains can explain the gas-phase abundance of \\ceH2CO derived in L1689B. A simple analytical model is employed: H2CO molecules from the gas phase can only accrete on the icy surface of dust grains, while H2CO molecules from the grain surface can only desorb via photodesorption (due to both external and internal cosmic-ray induced UV photons) and direct cosmic-ray induced sputtering.\nIn addition, a steady-state is assumed, with constant kinetic temperature, density, and total H2CO abundance (gas and ice) throughout the core. This total H2CO abundance is unknown in L1689B and taken as , which is the typical H2CO ice abundance in low-mass young stellar objects (LYSOS) (Boogert et al., 2015  ###reference_b12###), corresponding to about 6% with respect to H2O ice.111111This value is similar to the 4.1% recently measured by JWST towards the young-mass protostar NGC 1333 IRAS 2 (Rocha et al., 2024  ###reference_b64###). The kinetic temperature  is fixed at 10 K and the H2 density at  cm-3, as reported in Table 4  ###reference_### for the L1689B core.\nAt steady-state, the rates of accretion and desorption are equal and we can write:\nwhere  and  are the formaldehyde densities (in cm-3) in the gas and solid ice phase, respectively. The accretion rate (in s-1) can be written as\nwhere  is the average grain surface (in cm2),  the grain number density (cm-3),  the thermal velocity of H2CO molecules, and  the sticking coefficient taken as 1.0. The desorption rate (in s-1) can be written as (Flower et al., 2005  ###reference_b32###)\nwhere  is the sum of ice abundances such that  is the fractional abundance of \\ceH2CO in the ice. In the following, we note that . The quantity  is the total desorption rate (in molecules cm-2s-1) defined as\nwhere , , and  are the desorption rates due to external UV photodesorption, cosmic-ray induced UV phodesorption, and direct cosmic-ray sputtering, respectively. We note that cosmic-ray induced whole-grain heating can be neglected for a thick volatile mantle, as found at high density ( cm-3) (Bringa & Johnson, 2004  ###reference_b14###; Wakelam et al., 2021  ###reference_b77###)."
        },
        {
            "section_id": "5.2",
            "parent_section_id": "5",
            "section_name": "Desorption rates",
            "text": "The external UV photodesorption rate can be written as\nwhere  is the external interstellar far-UV radiation field (averaged between 6 and 13.6 eV) of  photons cm-2 s-1 (Habing, 1968  ###reference_b34###);  is the visual extinction;  is a measure of UV extinction relative to visual extinction, which is about 2 for interstellar grains (Roberge et al., 1991  ###reference_b63###); and  is the photodesorption yield of H2CO (in molecules photon-1). The last value was recently determined in the laboratory by Féraud et al. (2019  ###reference_b31###),\nwho were able to derive an intact H2CO photodesorption yield of  molecule/photon in various astrophysical environments, including interstellar clouds and prestellar cores (see their Table 1).\nIn the following we use an average experimental yield of  molecule/photon for the photodesorption of intact H2CO.\nThe cosmic-ray induced UV photodesorption rate can be written as\nwhere  is now the internal UV field induced by the cosmic-ray excitation of H2, which was taken as , where  is the rate of cosmic-ray ionisation of molecular hydrogen  in units of s-1 (see the definition of  below). This simple relation between  and  was deduced from Fig. 4 of Shen et al. (2004  ###reference_b71###), with  computed using Eqs. 16  ###reference_###-17  ###reference_### below.\nFinally, the direct cosmic-ray sputtering rate  is computed by summing and integrating the product of the sputtering yield  with the differential cosmic-ray flux :\nHere  is the kinetic energy per nucleon,  is the atomic number of the cosmic-ray nuclei, and  is the sputtering yield in H2CO/ion obtained by combining the experimental yield  for intact sputtering with the calculated electronic stopping power . It is multiplied by a factor of 2 to account for the entrance and exit points of the cosmic-rays through the grain. Assuming a quadratic dependence of  with the stopping power, as in Eq. 6  ###reference_###,\nthe intact sputtering yield of H2CO molecules can be described as\nwhere we combined  molecules ion-1 (see Table 3  ###reference_###) with the stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam.\nIn order to compute  for a range of kinetic energies (see below), the SRIM-2013 code was used to compute the electronic stopping powers  for an H2CO ice density of 0.81 g cm-3 and for the cosmic elements with the largest contributions, accounting for the  scaling of the sputtering yields (Dartois et al., 2023  ###reference_b19###). In practice, the 15 ions of H, He, C, O, Ne, Mg, Si, S, Ca, Ti, V, Cr, Mn, Fe, and Ni were included using the fractional abundances  of Kalvāns (2016  ###reference_b37###, their Table 1). It should be noted that iron, despite its low fractional abundance, gives the largest contribution (%) to the rate, as already found by Seperuelo Duarte et al. (2010  ###reference_b70###) for CO ice.\nFor the differential cosmic-ray flux  (in particles cm-2 s-1 sr-1 (MeV/amu)-1) we adopted the functional form proposed by Webber & Yushak (1983  ###reference_b79###)\nwhere  is a normalising constant and  a form parameter that varies between 0 and 940 MeV. This formulation corresponds to a primary spectrum since it neglects the energy-loss of cosmic rays through the dense interstellar gas. It allows, however, the full range\nof measured ionisation rates to be explored, from standard diffuse clouds (a few  s-1) to dense clouds (a few  s-1), by simply varying the parameter . In order to infer the relation between  and , the ionisation rate  was computed as in Faure et al. (2019  ###reference_b28###, their Appendix A):\nHere  is the cross-section for ionisation of H2 by proton impact,  is a correction factor accounting for the contribution of secondary electrons to ionisation, and where\nis the correction factor for heavy nuclei ionisation. Full details and references can be found in Appendix A of Faure et al. (2019  ###reference_b28###). In practice, the  parameter in Eq. (16  ###reference_###) was taken in the range 200900 MeV so that  was explored in the range  s-1. The integrals in Eqs. (14  ###reference_###) and (17  ###reference_###) were evaluated numerically from  eV/amu to  GeV/amu. The calibration plot between the intact sputtering rate of \\ceH2CO and the ionisation rate is displayed in Fig. 9  ###reference_### (black curve), where  is found to scale linearly with the ionisation rate. We note that although the low-energy content ( MeV) of the cosmic-ray spectrum is poorly constrained, the relation between  and  was found to be quite robust.\n###figure_9### It is now interesting to compare the sputtering rate of H2CO  with those of the main ice components of interstellar grains, that is H2O, CO, and CO2, where the latter two have a typical abundance of 20-30% with respect to H2O. Trace ice species such as NH3, CH4, H2CO, and CH3OH are expected to be embedded in H2O-rich, CO-rich, or CO2-rich layers. We assume that the intact sputtering yield of the trapped molecule is equal to the effective sputtering yield of the ice matrix. Simplistic but intuitive, this hypothesis is actually supported by irradiation experiments performed on methanol diluted in H2O and CO2 ice matrices, although the intact sputtering efficiency depends on the dilution factor121212Because \\ceH2CO easily polymerises, segregation effects could also play a role and reduce the intact sputtering efficiency.\n (see the detailed discussions in Dartois et al., 2019  ###reference_b20###, 2020  ###reference_b18###). We note that the effective sputtering yield of either water or CO2 was similarly employed to model the cosmic-ray induced sputtering of \\ceCH3OH in cold molecular cores (Wakelam et al., 2021  ###reference_b77###; Paulive et al., 2022  ###reference_b61###).\nThe above procedure was thus applied to pure CO, CO2, and H2O ices using the effective sputtering yield pre-factors reported in Table 1 of Dartois et al. (2023  ###reference_b19###) with ice densities (needed to compute ) of 0.88 g cm-3, 1.0 g cm-3, and 0.94 g cm-3, respectively (Luna et al., 2022  ###reference_b46###; Satorre et al., 2008  ###reference_b67###; Bouilloud et al., 2015  ###reference_b13###). The corresponding sputtering rates as functions of  are shown in Fig. 9  ###reference_###. As expected, our results for CO, CO2, and H2O are in very good agreement with those of Dartois et al. (2023  ###reference_b19###, see their Fig. 5). We can also observe that the intact sputtering rate of pure H2CO is a factor of 10-100 lower than the effective sputtering rates of H2O, CO, and CO2. For convenient use in astrochemical models, simple linear fits of the sputtering rates shown in Fig. 9  ###reference_### were performed over the range  s-1. These fits are reported in Table 5  ###reference_###."
        },
        {
            "section_id": "5.3",
            "parent_section_id": "5",
            "section_name": "\\ceH2CO gas-phase abundance",
            "text": "Because the total abundance of formaldehyde  is conserved, we have\nBy combining Eqs. (8  ###reference_###-10  ###reference_###) and (19  ###reference_###), we obtain\nSince in practice  and substituting , where  is the mass of H2CO, the H2CO gas-phase fractional abundance, , takes the simple form\nwhere  is the H2CO total fractional abundance, taken as  (see above). The total fractional abundance of ices, , is unknown in L1689B, but again we can assume typical ice abundances in LYSOS, as compiled by Boogert et al. (2015  ###reference_b12###, their Table 2). By including ‘securely’, ‘likely’, and ‘possibly’ identified species, we obtain . Finally, using the physical conditions derived from H2CO emission in L1689B (i.e.  K and  cm-3), we obtain numerically:\nIn order to reproduce the measured abundance in L1689B (), a total desorption rate  molecules cm2s-1 is required. We compare in Fig. 10  ###reference_### the observational abundance to our predictions from the above analytical model, assuming the cosmic-ray ionisation rate is  s-1 (i.e. ), which is the typical ionisation rate in molecular clouds, where  (see Fig. 19 in Indriolo & McCall, 2012  ###reference_b36###). Five different models are presented: desorption is either due to external and internal photons only (in orange) or to both photons and direct cosmic-ray sputtering, assuming H2CO ices are pure (in black) or embedded in H2O-rich (in blue), CO2-rich (in red), or CO-rich (in green) matrices. We can observe that photodesorption alone cannot explain the gas phase abundance of H2CO in L1689B and that direct cosmic-ray sputtering is much more efficient, except in the case of a pure H2CO ice. In particular, cosmic-ray sputtering of H2CO from CO-rich or CO2-rich ices can reproduce the gas phase abundance measured towards L1689B to within a factor of 3. Interestingly, this result is consistent with observational evidence that catastrophic CO freeze-out occurs at  and  cm-3, where CO hydrogenation may form a CH3OH-rich layer including H2CO and new CO2 molecules (Boogert et al., 2015  ###reference_b12###). It is also possible that part of the interstellar H2CO forms in the gas phase, for example via the barrierless reaction CH3 + O (see e.g. Terwisscha van Scheltinga et al., 2021  ###reference_b74###). Thus, while the present results emphasise the potential role of direct cosmic-ray sputtering of H2CO molecules from CO-rich or CO2-rich ices, the importance of gas-phase formation and destruction of \\ceH2CO will need to be explored in future works. Finally, we note that the \\ceH2CO gas-phase abundance in L1689B corresponds to about 0.02% of the total (gas and ice) \\ceH2CO abundance.\nIn summary, our simple model shows that the yields for experimentally determined direct cosmic-ray sputtering are large enough to release significant amounts of \\ceH2CO ice into the gas-phase, provided that \\ceH2CO is embedded in CO-rich or \\ceCO2-rich ice mantles and that \\ceH2CO molecules co-desorbwith the matrix (i.e. with the same yield). Obviously, further experiments with mixed ices (e.g. \\ceH2CO:CO), as well as more comprehensive (time-dependent and density-dependent) astrochemical models are needed to confirm these results.\n###figure_10###"
        },
        {
            "section_id": "6",
            "parent_section_id": null,
            "section_name": "Conclusions",
            "text": "We have studied the sputtering of pure formaldehyde ices under cosmic rays using swift-ion irradiation experiments of H2CO ice films at 10 K carried out at GANIL with the IGLIAS setup. Formaldehyde is found to quickly polymerise upon swift ion exposure. Other detected radiolysis products in the ice are CO and CO2. We determined the intact H2CO sputtering yield in the gas phase to be  molecule ion-1 for a stopping power of 2830 eV/1015 molecule cm-2. Assuming a quadratic dependence of the sputtering yield with stopping power, this corresponds to an intact sputtering prefactor   eV-2cm-4molecule3. The effective sputtering prefactor is   eV-2cm-4molecule3.\nWith these values we determined that the direct cosmic-ray sputtering rate for intact H2CO in pure ices can be expressed simply by  molecules cm-2 s-1, where  is the cosmic-ray ionisation rate in units of 10-17 s-1.\nUsing a simple steady-state chemical model including accretion of molecules from the gas phase onto the grains and their desorption by either UV photons (both external and secondary UV photons produced by cosmic-ray excitation of H2) or direct cosmic-ray impact, we find that photodesorption is not efficient enough to account for the gas-phase abundance of H2CO of  (with respect to H nuclei) measured in the prestellar core L1689B, nor is cosmic-ray induced sputtering of a pure H2CO ice. On the other hand, when H2CO is diluted in CO or in CO2 ices, our model can reproduce the H2CO gas-phase abundance, assuming that minor ice constituents like formaldehyde will be sputtered to the gas phase at the same effective rate as the ice mantle bulk. However, the cosmic-ray sputtering rate is insufficient if H2CO is embedded in a water ice mantle. Future experimental studies should be dedicated to investigating the polymerisation and sputtering of H2CO diluted in other ice matrices (e.g. H2O, CO, CO2). The competition between the cosmic-ray induced sputtering and the gas-phase chemistry of \\ceH2CO will also need to be explored."
        }
    ],
    "appendix": [
        {
            "section_id": "Appendix 1",
            "parent_section_id": null,
            "section_name": "Appendix A Comparison of the experimental and interstellar doses",
            "text": "In our experiments, the dose  ( where  is the fluence) lies between 0.0025 and 12 eV/molecule at the investigated experimental fluences ( ion cm-2). These values can be compared to the ”interstellar” dose received by a grain over 1 Myr (the typical age of a molecular cloud or prestellar core), which we estimate as  eV/molecule using the cosmic-ray flux given in Eq. 16  ###reference_###, with  MeV and  computed with the SRIM-2013 code. As a result, the most astrophysically relevant conditions in our experiment should be the early times of the measurements, when the fluence is lower than a few  ions cm-2. We note, however, that the experimental and calculated doses correspond to different kinds of ions, Kr and essentially H, He, C, O, and Fe, respectively. It is unclear whether the nature of ions has an effect on radiolysis. Thus, threshold effects have been reported for polymers that contain aromatic species, but not in the case of aliphatic polymers that are chemically more similar to ices (Balanzat et al. 1995  ###reference_b7###). To our knowledge, no similar studies have been published for ices, and firm conclusions about the relevance of experimental doses would require comparative radiolysis investigations with e.g. H, He and Fe ions."
        },
        {
            "section_id": "Appendix 2",
            "parent_section_id": null,
            "section_name": "Appendix B H2CO spectra",
            "text": "The spectra observed with the IRAM 30 m radiotelescope and used to determine the H2CO column density are presented in Fig. 11  ###reference_### for HCO and in Fig. 12  ###reference_### for H2C18O. In the figures,‘o’ and ‘p’ stand for ortho and para spin symmetry, respectively. The spectra were taken at coordinates RA = 16h34m48.3s, Dec = .\n###figure_11### ###figure_12###"
        },
        {
            "section_id": "Appendix 3",
            "parent_section_id": null,
            "section_name": "Appendix C Sputtering yield determination: The case of a thin CO2 ice film",
            "text": "High-energy heavy ions irradiation of \\ceCO2 ices has been thoroughly investigated (Seperuelo Duarte et al. 2009  ###reference_b69###; Mejía et al. 2015  ###reference_b48###; Dartois et al. 2021  ###reference_b21###). In this appendix, we compare sputtering yields estimated from the interference fringes analysis method (Method 1, as employed in this work for H2CO ice) to yields derived from the integration of IR bands (Method 2).\nThe procedure follows the steps explained in Section 4.1  ###reference_### for H2CO ice. The interference fringes observed in the IR spectra during irradiation are depicted in Fig. 13  ###reference_###. The adjustments were achieved using Eq. 1  ###reference_###. While a more rigorous equation including the optical indices could be applied in the case of \\ceCO2 (see Dartois et al. 2023  ###reference_b19###, for details), we opted for the simplified equation (Eq. 1  ###reference_###) in order to be consistent with the methodology employed in this study. The total mass sputtering yield ( g ion-1) was extracted from the linear fit of surface density as a function of fluence (Fig. 14  ###reference_###), using a density of CO2 of 1.0 g cm-3 (Bouilloud et al. 2015  ###reference_b13###). We note that in the case of CO2, there is no visible compaction phase, despite experimental conditions close to those of H2CO (similar film thicknesses, pressure and temperature, see Section 2  ###reference_###).\n###figure_13### ###figure_14### The CO2 fragmentation pattern was derived from the QMS signal during CO2 injection. It is composed of only four fragments at =44, =28, =16, and =12 (with intensity ratios of 0.748, 0.112, 0.07, and 0.07, respectively). Figure 15  ###reference_### shows the molecular fraction deduced from the QMS signal after (i) correction of the background, (ii) extracting the original CO2 signal intensity using the fragmentation pattern (), (iii) subtracting the CO2 fragments from other mass signals (e.g. ), and (iv) dividing by the total electron-impact ionisation cross sections ((CO2)=3.521, from the NIST database ).\nIn contrast to H2CO, no significant variation of the \\ceCO2 fraction is observed during the very early fluences; however, a similar smooth and continuous evolution is observed thereafter. Over the entire experiment, the molecular fraction of CO increases by , while that of \\ceCO2 decreases by . The sputtering yields were calculated using Eq. 3  ###reference_### after fitting the molecular fractions with a third-order polynomial, as in the case of \\ceH2CO. The fits are shown as dashed lines in the bottom panel of Fig. 15  ###reference_###. The average sputtering yields are provided in Table 5  ###reference_###.\n###figure_15### As in the case of \\ceH2CO, the intact fraction of sputtered CO2 was computed using the initial fractions  of species containing carbon atom (Table 6  ###reference_###) :\nWe obtain =0.250.02 from which the effective sputtering yield (see Eq. 4  ###reference_###) for a CO2 ice film was estimated as =(6.84.1)104 molecules ions-1. The corresponding effective prefactor derived from Eq. 6  ###reference_### is =(3.82.3)10-3 1030 eV-2 cm-4 molecule3, using a stopping power of 3290 eV/1015 molecules cm-2.\nFig. 16  ###reference_### illustrates the evolution of the CO2 infrared vibrational band at 2343 cm-1 with fluence. The integrated intensity of this band () was employed to derive the CO2 column density () with the first-order relation:\nwhere the band strength () is  cm molecules-1 (Bouilloud et al. 2015  ###reference_b13###). The derivative of the column density with respect to fluence was fitted using an equation involving both radiolysis and sputtering processes:\nwhere  is the destruction cross-section of CO2,  is the relative concentration of carbon dioxide molecules with respect to the total number of molecules in the ice film, and  is the semi-infinite sputtering depth. Similarly to the experiment of Mejía et al. (2015  ###reference_b48###) on CO2 ice irradiation, the fraction of CO2 in the ice remains significantly higher than that of CO at the observed fluences, and the value of  is set to 1. Adjusting the data with Eq. 25  ###reference_###, as shown in Fig. 17  ###reference_###, provides the following solution:  molecules ions-1,  cm2 ion-1, and  molecules cm-2. The derived effective sputtering yield corresponds to an effective prefator  = (6.5  0.8)  10-3 1030 eV-2 cm-4 molecule3, using again a stopping power of 3290 eV/1015 molecules cm-2.\n###figure_16### ###figure_17### Results from this work and previous studies are presented in Table 7  ###reference_###. The comparison with literature data is not straightforward due to various experimental conditions. For example, experiments have shown that the sputtering efficiency depends on the ice thickness: the effective sputtering yields  for CO and \\ceCO2 ices were indeed found to be constant for thick films (more than  100 monolayers) but to decrease significantly for thin ice films (Dartois et al. 2021  ###reference_b21###). We recall that  scales with the square of the heavy ion stopping power, while  should be roughly constant for a given target. We can observe in Table 7  ###reference_### that our  value derived from the integrated band method (Method 2) agrees with those of Seperuelo Duarte et al. (2009  ###reference_b69###) and Dartois et al. (2021  ###reference_b21###), who used the same method, to better than a factor of 2, and almost within error bars (whatever the thickness of the film). In addition, and more importantly, the interference fringes method (Method 1) gives an effective sputtering yield prefactor ( value) in very good agreement (i.e. within error bars) with the value we derived from Method 2.\nWe conclude that the interference fringes method, even using a simplified optical model, is a powerful alternative to the integrated bands method for the determination of sputtering yields. Furthermore, combined with QMS measurements, this method allows us to determine both effective and intact sputtering yields, this latter being challenging to estimate with other methods."
        }
    ],
    "tables": {
        "1": {
            "table_html": "<figure class=\"ltx_table\" id=\"S3.T1\">\n<figcaption class=\"ltx_caption\"><span class=\"ltx_tag ltx_tag_table\">Table 1: </span>Spectroscopic parameters of the observed lines.</figcaption>\n<div class=\"ltx_block\" id=\"S3.T1.40\">\n<table class=\"ltx_tabular ltx_guessed_headers ltx_align_middle\" id=\"S3.T1.39\">\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"S3.T1.6.6\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_tt\" id=\"S3.T1.6.6.7\">Transition<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex1\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_tag ltx_tag_note\"></span>Quantum numbers of the transition.</span></span></span>\n</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_tt\" id=\"S3.T1.6.6.8\">Frequency</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_tt\" id=\"S3.T1.1.1.1\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex2\"><sup class=\"ltx_note_mark\">b𝑏bitalic_b</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">b𝑏bitalic_b</sup><span class=\"ltx_tag ltx_tag_note\"></span>Einstein  coefficient.</span></span></span>\n</th>\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S3.T1.2.2.2\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex3\"><sup class=\"ltx_note_mark\">c𝑐citalic_c</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">c𝑐citalic_c</sup><span class=\"ltx_tag ltx_tag_note\"></span>Energy of the upper level.</span></span></span>\n</td>\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S3.T1.3.3.3\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex4\"><sup class=\"ltx_note_mark\">d𝑑ditalic_d</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">d𝑑ditalic_d</sup><span class=\"ltx_tag ltx_tag_note\"></span>Derived integrated intensity.</span></span></span>\n</td>\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S3.T1.4.4.4\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex5\"><sup class=\"ltx_note_mark\">e𝑒eitalic_e</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">e𝑒eitalic_e</sup><span class=\"ltx_tag ltx_tag_note\"></span>Rest velocity.</span></span></span>\n</td>\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S3.T1.5.5.5\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex6\"><sup class=\"ltx_note_mark\">f𝑓fitalic_f</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">f𝑓fitalic_f</sup><span class=\"ltx_tag ltx_tag_note\"></span>Full width at half maximum.</span></span></span>\n</td>\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S3.T1.6.6.6\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex7\"><sup class=\"ltx_note_mark\">g𝑔gitalic_g</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">g𝑔gitalic_g</sup><span class=\"ltx_tag ltx_tag_note\"></span>Peak temperature.</span></span></span>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.11.11\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.7.7.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.11.11.6\">MHz</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.8.8.2\">s<sup class=\"ltx_sup\" id=\"S3.T1.8.8.2.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S3.T1.8.8.2.1.1\">-1</span></sup>\n</th>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.11.11.7\">K</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.9.9.3\">K km s<sup class=\"ltx_sup\" id=\"S3.T1.9.9.3.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S3.T1.9.9.3.1.1\">-1</span></sup>\n</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.10.10.4\">km s<sup class=\"ltx_sup\" id=\"S3.T1.10.10.4.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S3.T1.10.10.4.1.1\">-1</span></sup>\n</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.11.11.5\">km s<sup class=\"ltx_sup\" id=\"S3.T1.11.11.5.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S3.T1.11.11.5.1.1\">-1</span></sup>\n</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.11.11.8\">K</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.13.13\">\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_t\" colspan=\"8\" id=\"S3.T1.13.13.2\">orthoHCO</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.15.15\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S3.T1.14.14.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S3.T1.15.15.3\">137449.9503</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S3.T1.15.15.2\"></th>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.15.15.4\">21.7</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.15.15.5\">0.331 (1)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.15.15.6\">3.64 (0)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.15.15.7\">0.48 (0)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.15.15.8\">0.65</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.17.17\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.16.16.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.17.17.3\">146635.6717</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.17.17.2\"></th>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.17.17.4\">22.4</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.17.17.5\">0.222 (1)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.17.17.6\">3.61 (0)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.17.17.7\">0.47 (0)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.17.17.8\">0.44</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.19.19\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.18.18.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.19.19.3\">206131.6260</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.19.19.2\"></th>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.19.19.4\">31.6</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.19.19.5\">0.166 (11)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.19.19.6\">3.46 (1)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.19.19.7\">0.41 (3)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.19.19.8\">0.38</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.21.21\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.20.20.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.21.21.3\">219908.5250</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.21.21.2\"></th>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.21.21.4\">32.9</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.21.21.5\">0.095 (16)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.21.21.6\">3.61 (5)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.21.21.7\">0.62 (13)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.21.21.8\">0.14</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.23.23\">\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_t\" colspan=\"8\" id=\"S3.T1.23.23.2\">paraHCO</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.25.25\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S3.T1.24.24.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S3.T1.25.25.3\">141983.7404</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S3.T1.25.25.2\"></th>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.25.25.4\">10.2</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.25.25.5\">0.169 (2)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.25.25.6\">3.44 (0)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.25.25.7\">0.44 (1)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.25.25.8\">0.36</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.27.27\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.26.26.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.27.27.3\">212811.1840</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.27.27.2\"></th>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.27.27.4\">20.4</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.27.27.5\">0.041 (3)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.27.27.6\">3.49 (1)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.27.27.7\">0.27 (2)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.27.27.8\">0.14</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.30.30\">\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_t\" colspan=\"8\" id=\"S3.T1.30.30.3\">orthoH<sub class=\"ltx_sub\" id=\"S3.T1.30.30.3.1\">2</sub>C<sup class=\"ltx_sup\" id=\"S3.T1.30.30.3.2\"><span class=\"ltx_text ltx_font_italic\" id=\"S3.T1.30.30.3.2.1\">18</span></sup>O</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.32.32\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S3.T1.31.31.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S3.T1.32.32.3\">134435.9203</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S3.T1.32.32.2\"></th>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.32.32.4\">21.5</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.32.32.5\">0.039 (3)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.32.32.6\">3.49 (2)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.32.32.7\">0.39 (4)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_t\" id=\"S3.T1.32.32.8\">0.09</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.34.34\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.33.33.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.34.34.3\">143213.0680</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S3.T1.34.34.2\"></th>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.34.34.4\">22.2</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.34.34.5\">0.020 (0)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.34.34.6\">3.57 (0)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.34.34.7\">0.43 (1)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S3.T1.34.34.8\">0.04</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.37.37\">\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_t\" colspan=\"8\" id=\"S3.T1.37.37.3\">paraH<sub class=\"ltx_sub\" id=\"S3.T1.37.37.3.1\">2</sub>C<sup class=\"ltx_sup\" id=\"S3.T1.37.37.3.2\"><span class=\"ltx_text ltx_font_italic\" id=\"S3.T1.37.37.3.2.1\">18</span></sup>O</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S3.T1.39.39\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_b ltx_border_t\" id=\"S3.T1.38.38.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_b ltx_border_t\" id=\"S3.T1.39.39.3\">138770.861</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_b ltx_border_t\" id=\"S3.T1.39.39.2\"></th>\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S3.T1.39.39.4\">10.0</td>\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S3.T1.39.39.5\">0.021 (2)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S3.T1.39.39.6\">3.63 (2)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S3.T1.39.39.7\">0.40 (5)</td>\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S3.T1.39.39.8\">0.05</td>\n</tr>\n</tbody>\n</table>\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnote4\"><sup class=\"ltx_note_mark\">4</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">4</sup><span class=\"ltx_tag ltx_tag_note\">4</span>\n</span></span></span>\n</div>\n</figure>",
            "capture": "Table 1: Spectroscopic parameters of the observed lines."
        },
        "2": {
            "table_html": "<figure class=\"ltx_table\" id=\"S4.T2\">\n<figcaption class=\"ltx_caption\"><span class=\"ltx_tag ltx_tag_table\">Table 2: </span>\nPeak position, assignments, and band strengths (at 25 K).</figcaption>\n<div class=\"ltx_block\" id=\"S4.T2.41\">\n<table class=\"ltx_tabular ltx_guessed_headers ltx_align_middle\" id=\"S4.T2.40\">\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"S4.T2.1.1\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_tt\" id=\"S4.T2.1.1.2\">Label</th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_tt\" id=\"S4.T2.1.1.3\">mode</th>\n<td class=\"ltx_td ltx_align_center ltx_border_tt\" id=\"S4.T2.1.1.4\">Position</td>\n<td class=\"ltx_td ltx_align_center ltx_border_tt\" id=\"S4.T2.1.1.1\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.3.3\">\n<th class=\"ltx_td ltx_th ltx_th_row\" id=\"S4.T2.3.3.3\"></th>\n<th class=\"ltx_td ltx_th ltx_th_row\" id=\"S4.T2.3.3.4\"></th>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.2.2.1\">cm<sup class=\"ltx_sup\" id=\"S4.T2.2.2.1.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.2.2.1.1.1\">-1</span></sup>\n</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.3.3.2\">cm molecules<sup class=\"ltx_sup\" id=\"S4.T2.3.3.2.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.3.3.2.1.1\">-1</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.4.4\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" colspan=\"4\" id=\"S4.T2.4.4.1\">H<sub class=\"ltx_sub\" id=\"S4.T2.4.4.1.1\">2</sub>CO <span class=\"ltx_note ltx_role_footnote\" id=\"footnotex15\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_tag ltx_tag_note\"></span> <cite class=\"ltx_cite ltx_citemacro_citet\">Bouilloud et al. (<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2409.01700v2#bib.bib13\" title=\"\">2015</a>)</cite>.</span></span></span>\n</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.7.7\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S4.T2.5.5.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S4.T2.7.7.4\">comb.</th>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T2.7.7.5\">2997</td>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T2.7.7.3\">3.2  10<sup class=\"ltx_sup\" id=\"S4.T2.7.7.3.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.7.7.3.1.1\">-18</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.11.11\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.8.8.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.9.9.2\">CH<sub class=\"ltx_sub\" id=\"S4.T2.9.9.2.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.9.9.2.1.1\">2</span></sub> a-str.</th>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.11.11.5\">2891</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.11.11.4\">4.7  10<sup class=\"ltx_sup\" id=\"S4.T2.11.11.4.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.11.11.4.1.1\">-18</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.15.15\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.12.12.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.13.13.2\">CH<sub class=\"ltx_sub\" id=\"S4.T2.13.13.2.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.13.13.2.1.1\">2</span></sub> s-str.</th>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.15.15.5\">2829</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.15.15.4\">1.3  10<sup class=\"ltx_sup\" id=\"S4.T2.15.15.4.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.15.15.4.1.1\">-17</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.18.18\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.16.16.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.18.18.4\">C=O str.</th>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.18.18.5\">1725</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.18.18.3\">1.6  10<sup class=\"ltx_sup\" id=\"S4.T2.18.18.3.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.18.18.3.1.1\">-17</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.22.22\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.19.19.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.20.20.2\">CH<sub class=\"ltx_sub\" id=\"S4.T2.20.20.2.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.20.20.2.1.1\">2</span></sub> scis.</th>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.22.22.5\">1500</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.22.22.4\">5.1  10<sup class=\"ltx_sup\" id=\"S4.T2.22.22.4.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.22.22.4.1.1\">-18</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.26.26\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.23.23.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.24.24.2\">CH<sub class=\"ltx_sub\" id=\"S4.T2.24.24.2.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.24.24.2.1.1\">2</span></sub> rock.</th>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.26.26.5\">1247</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.26.26.4\">1.5  10<sup class=\"ltx_sup\" id=\"S4.T2.26.26.4.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.26.26.4.1.1\">-18</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.30.30\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.27.27.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.28.28.2\">CH<sub class=\"ltx_sub\" id=\"S4.T2.28.28.2.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.28.28.2.1.1\">2</span></sub> wag.</th>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.30.30.5\">1178</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.30.30.4\">7.2  10<sup class=\"ltx_sup\" id=\"S4.T2.30.30.4.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.30.30.4.1.1\">-19</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.31.31\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" colspan=\"4\" id=\"S4.T2.31.31.1\">CO<sub class=\"ltx_sub\" id=\"S4.T2.31.31.1.1\">2</sub> <span class=\"ltx_note ltx_role_footnote\" id=\"footnotex16\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_tag ltx_tag_note\"></span> <cite class=\"ltx_cite ltx_citemacro_citet\">Bouilloud et al. (<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2409.01700v2#bib.bib13\" title=\"\">2015</a>)</cite>.</span></span></span>\n</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.34.34\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S4.T2.32.32.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S4.T2.34.34.4\">a-str.</th>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T2.34.34.5\">2343</td>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T2.34.34.3\">7.6  10<sup class=\"ltx_sup\" id=\"S4.T2.34.34.3.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.34.34.3.1.1\">-17</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.40.41.1\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" colspan=\"4\" id=\"S4.T2.40.41.1.1\">CO <span class=\"ltx_note ltx_role_footnote\" id=\"footnotex17\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_tag ltx_tag_note\"></span> <cite class=\"ltx_cite ltx_citemacro_citet\">Bouilloud et al. (<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2409.01700v2#bib.bib13\" title=\"\">2015</a>)</cite>.</span></span></span>\n</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.37.37\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S4.T2.35.35.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S4.T2.37.37.4\">str.</th>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T2.37.37.5\">2139</td>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T2.37.37.3\">1.12  10<sup class=\"ltx_sup\" id=\"S4.T2.37.37.3.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.37.37.3.1.1\">-17</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.40.42.2\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" colspan=\"4\" id=\"S4.T2.40.42.2.1\">POM <span class=\"ltx_note ltx_role_footnote\" id=\"footnotex18\"><sup class=\"ltx_note_mark\">b𝑏bitalic_b</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">b𝑏bitalic_b</sup><span class=\"ltx_tag ltx_tag_note\"></span><cite class=\"ltx_cite ltx_citemacro_citet\">Schutte et al. (<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2409.01700v2#bib.bib68\" title=\"\">1993</a>)</cite>.</span></span></span>\n</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.38.38\">\n<th class=\"ltx_td ltx_th ltx_th_row ltx_border_t\" id=\"S4.T2.38.38.2\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S4.T2.38.38.1\">CH<sub class=\"ltx_sub\" id=\"S4.T2.38.38.1.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.38.38.1.1.1\">2</span></sub> s-str.</th>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T2.38.38.3\">2924</td>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T2.38.38.4\">-</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.40.43.3\">\n<th class=\"ltx_td ltx_th ltx_th_row\" id=\"S4.T2.40.43.3.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.40.43.3.2\">comb.</th>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.40.43.3.3\">1235</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.40.43.3.4\">-</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.40.40\">\n<th class=\"ltx_td ltx_th ltx_th_row\" id=\"S4.T2.40.40.3\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S4.T2.40.40.4\">comb.</th>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.40.40.5\">1105</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T2.40.40.2\">1.9  10<sup class=\"ltx_sup\" id=\"S4.T2.40.40.2.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T2.40.40.2.1.1\">-18</span></sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T2.40.44.4\">\n<th class=\"ltx_td ltx_th ltx_th_row ltx_border_b\" id=\"S4.T2.40.44.4.1\"></th>\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_b\" id=\"S4.T2.40.44.4.2\">comb.</th>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"S4.T2.40.44.4.3\">907-942</td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"S4.T2.40.44.4.4\">-</td>\n</tr>\n</tbody>\n</table>\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnote5\"><sup class=\"ltx_note_mark\">5</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">5</sup><span class=\"ltx_tag ltx_tag_note\">5</span>\n</span></span></span>\n</div>\n</figure>",
            "capture": "Table 2: \nPeak position, assignments, and band strengths (at 25 K)."
        },
        "3": {
            "table_html": "<figure class=\"ltx_table\" id=\"S4.T3\">\n<figcaption class=\"ltx_caption\"><span class=\"ltx_tag ltx_tag_table\">Table 3: </span> Total electron-impact ionisation cross-sections ; initial fractions  and averaged sputtering yield .</figcaption>\n<div class=\"ltx_block\" id=\"S4.T3.29\">\n<table class=\"ltx_tabular ltx_guessed_headers ltx_align_middle\" id=\"S4.T3.28\">\n<thead class=\"ltx_thead\">\n<tr class=\"ltx_tr\" id=\"S4.T3.9.3\">\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"S4.T3.9.3.4\">Species (X)</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"S4.T3.7.1.1\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex21\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_tag ltx_tag_note\"></span>From the NIST database (https://webbook.nist.gov/chemistry/), except  and  from <cite class=\"ltx_cite ltx_citemacro_cite\">Kim &amp; Desclaux (<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2409.01700v2#bib.bib38\" title=\"\">2002</a>)</cite>.</span></span></span>\n</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"S4.T3.8.2.2\"></th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"S4.T3.9.3.3\"></th>\n</tr>\n</thead>\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"S4.T3.11.5\">\n<td class=\"ltx_td\" id=\"S4.T3.11.5.3\"></td>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column\" id=\"S4.T3.10.4.1\"></th>\n<th class=\"ltx_td ltx_th ltx_th_column\" id=\"S4.T3.11.5.4\"></th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column\" id=\"S4.T3.11.5.2\">molecules ion<sup class=\"ltx_sup\" id=\"S4.T3.11.5.2.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T3.11.5.2.1.1\">-1</span></sup>\n</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T3.15.9\">\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T3.12.6.1\">H<sub class=\"ltx_sub\" id=\"S4.T3.12.6.1.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T3.12.6.1.1.1\">2</span></sub>\n</td>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T3.15.9.5\">1.021</td>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T3.15.9.6\">0.43</td>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S4.T3.15.9.4\">(3.41.0)10<sup class=\"ltx_sup\" id=\"S4.T3.15.9.4.1\">4</sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T3.18.12\">\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.18.12.4\">CO</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.18.12.5\">2.516</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.18.12.6\">0.39</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.18.12.3\">(2.90.8)10<sup class=\"ltx_sup\" id=\"S4.T3.18.12.3.1\">4</sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T3.21.15\">\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.21.15.4\">C</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.21.15.5\">2.317</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.21.15.6\">0.04</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.21.15.3\">(4.54.1)10<sup class=\"ltx_sup\" id=\"S4.T3.21.15.3.1\">3</sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T3.24.18\">\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.24.18.4\">O</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.24.18.5\">1.363</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.24.18.6\">0.01</td>\n<td class=\"ltx_td ltx_align_center\" id=\"S4.T3.24.18.3\">(4.33.9)10<sup class=\"ltx_sup\" id=\"S4.T3.24.18.3.1\">3</sup>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T3.28.22\">\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"S4.T3.25.19.1\">H<sub class=\"ltx_sub\" id=\"S4.T3.25.19.1.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T3.25.19.1.1.1\">2</span></sub>CO</td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"S4.T3.28.22.5\">4.140</td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"S4.T3.28.22.6\">0.13</td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"S4.T3.28.22.4\">(2.52.3)10<sup class=\"ltx_sup\" id=\"S4.T3.28.22.4.1\">3</sup>\n</td>\n</tr>\n</tbody>\n</table>\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnote7\"><sup class=\"ltx_note_mark\">7</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">7</sup><span class=\"ltx_tag ltx_tag_note\">7</span>\n</span></span></span>\n</div>\n</figure>",
            "capture": "Table 3:  Total electron-impact ionisation cross-sections ; initial fractions  and averaged sputtering yield ."
        },
        "4": {
            "table_html": "<figure class=\"ltx_table\" id=\"S4.T4\">\n<figcaption class=\"ltx_caption\"><span class=\"ltx_tag ltx_tag_table\">Table 4: </span>\nNon-LTE model parameters best fitting the observed spectra.</figcaption>\n<div class=\"ltx_block\" id=\"S4.T4.11\">\n<table class=\"ltx_tabular ltx_align_middle\" id=\"S4.T4.10\">\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"S4.T4.6.6\">\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S4.T4.1.1.1\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex23\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_tag ltx_tag_note\"></span>Temperature.</span></span></span>\n</td>\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S4.T4.2.2.2\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex24\"><sup class=\"ltx_note_mark\">b𝑏bitalic_b</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">b𝑏bitalic_b</sup><span class=\"ltx_tag ltx_tag_note\"></span>H<sub class=\"ltx_sub\" id=\"footnotex24.5\">2</sub> density.</span></span></span>\n</td>\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S4.T4.3.3.3\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex25\"><sup class=\"ltx_note_mark\">c𝑐citalic_c</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">c𝑐citalic_c</sup><span class=\"ltx_tag ltx_tag_note\"></span>ortho-HCO column density.</span></span></span>\n</td>\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S4.T4.4.4.4\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex26\"><sup class=\"ltx_note_mark\">d𝑑ditalic_d</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">d𝑑ditalic_d</sup><span class=\"ltx_tag ltx_tag_note\"></span>ortho-to-para ratio for H<sub class=\"ltx_sub\" id=\"footnotex26.5\">2</sub>CO isotopologues.</span></span></span>\n</td>\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S4.T4.5.5.5\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex27\"><sup class=\"ltx_note_mark\">e𝑒eitalic_e</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">e𝑒eitalic_e</sup><span class=\"ltx_tag ltx_tag_note\"></span><sup class=\"ltx_sup\" id=\"footnotex27.5\"><span class=\"ltx_text ltx_font_italic\" id=\"footnotex27.5.1\">13</span></sup>C/<sup class=\"ltx_sup\" id=\"footnotex27.6\"><span class=\"ltx_text ltx_font_italic\" id=\"footnotex27.6.1\">18</span></sup>O ratio.</span></span></span>\n</td>\n<td class=\"ltx_td ltx_align_left ltx_border_tt\" id=\"S4.T4.6.6.6\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T4.8.8\">\n<td class=\"ltx_td ltx_align_left\" id=\"S4.T4.8.8.3\">(K)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S4.T4.7.7.1\">(cm<sup class=\"ltx_sup\" id=\"S4.T4.7.7.1.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T4.7.7.1.1.1\">-3</span></sup>)</td>\n<td class=\"ltx_td ltx_align_left\" id=\"S4.T4.8.8.2\">(cm<sup class=\"ltx_sup\" id=\"S4.T4.8.8.2.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S4.T4.8.8.2.1.1\">-2</span></sup>)</td>\n<td class=\"ltx_td\" id=\"S4.T4.8.8.4\"></td>\n<td class=\"ltx_td\" id=\"S4.T4.8.8.5\"></td>\n<td class=\"ltx_td\" id=\"S4.T4.8.8.6\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S4.T4.10.10\">\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S4.T4.10.10.3\">10</td>\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S4.T4.9.9.1\"></td>\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S4.T4.10.10.2\"></td>\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S4.T4.10.10.4\">3.6</td>\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S4.T4.10.10.5\">9.1</td>\n<td class=\"ltx_td ltx_align_left ltx_border_b ltx_border_t\" id=\"S4.T4.10.10.6\">4.3</td>\n</tr>\n</tbody>\n</table>\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnote9\"><sup class=\"ltx_note_mark\">9</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">9</sup><span class=\"ltx_tag ltx_tag_note\">9</span>\n</span></span></span>\n</div>\n</figure>",
            "capture": "Table 4: \nNon-LTE model parameters best fitting the observed spectra."
        },
        "5": {
            "table_html": "<figure class=\"ltx_table\" id=\"S5.T5\">\n<figcaption class=\"ltx_caption\"><span class=\"ltx_tag ltx_tag_table\">Table 5: </span>\nFits of direct cosmic-ray sputtering rates  of pure H<sub class=\"ltx_sub\" id=\"S5.T5.22.1\">2</sub>CO, H<sub class=\"ltx_sub\" id=\"S5.T5.23.2\">2</sub>O, CO<sub class=\"ltx_sub\" id=\"S5.T5.24.3\">2</sub>, and CO ices, as plotted in Fig. <a class=\"ltx_ref\" href=\"https://arxiv.org/html/2409.01700v2#S5.F9\" title=\"Figure 9 ‣ 5.2 Desorption rates ‣ 5 Astrophysical applications ‣ Cosmic-ray induced sputtering of interstellar formaldehyde ices\"><span class=\"ltx_text ltx_ref_tag\">9</span></a>. See text for details. </figcaption>\n<div class=\"ltx_block\" id=\"S5.T5.25\">\n<table class=\"ltx_tabular ltx_guessed_headers ltx_align_middle\" id=\"S5.T5.18\">\n<thead class=\"ltx_thead\">\n<tr class=\"ltx_tr\" id=\"S5.T5.11.3\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_tt\" id=\"S5.T5.11.3.4\">ice</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"S5.T5.11.3.3\">\n (molecules cm<sup class=\"ltx_sup\" id=\"S5.T5.11.3.3.1\"><span class=\"ltx_text ltx_font_italic\" id=\"S5.T5.11.3.3.1.1\">-2</span></sup>s<sup class=\"ltx_sup\" id=\"S5.T5.11.3.3.2\"><span class=\"ltx_text ltx_font_italic\" id=\"S5.T5.11.3.3.2.1\">-1</span></sup>)</th>\n</tr>\n</thead>\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"S5.T5.13.5\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t\" id=\"S5.T5.12.4.1\">H<sub class=\"ltx_sub\" id=\"S5.T5.12.4.1.1\">2</sub>CO</th>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"S5.T5.13.5.2\">0.15 <span class=\"ltx_note ltx_role_footnote\" id=\"footnotex33\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_tag ltx_tag_note\"></span> is the rate of cosmic-ray ionisation of molecular hydrogen in units of s<sup class=\"ltx_sup\" id=\"footnotex33.5\"><span class=\"ltx_text ltx_font_italic\" id=\"footnotex33.5.1\">-1</span></sup>. </span></span></span>\n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.15.7\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S5.T5.14.6.1\">H<sub class=\"ltx_sub\" id=\"S5.T5.14.6.1.1\">2</sub>O</th>\n<td class=\"ltx_td ltx_align_center\" id=\"S5.T5.15.7.2\">1.2 \n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.17.9\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row\" id=\"S5.T5.16.8.1\">CO<sub class=\"ltx_sub\" id=\"S5.T5.16.8.1.1\">2</sub>\n</th>\n<td class=\"ltx_td ltx_align_center\" id=\"S5.T5.17.9.2\">6.1 \n</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.18.10\">\n<th class=\"ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_b\" id=\"S5.T5.18.10.2\">CO</th>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"S5.T5.18.10.1\">13 \n</td>\n</tr>\n</tbody>\n</table>\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnote13\"><sup class=\"ltx_note_mark\">13</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">13</sup><span class=\"ltx_tag ltx_tag_note\">13</span>\n</span></span></span>\n</div>\n</figure>",
            "capture": "Table 5: \nFits of direct cosmic-ray sputtering rates  of pure H2CO, H2O, CO2, and CO ices, as plotted in Fig. 9. See text for details. "
        },
        "6": {
            "table_html": "<figure class=\"ltx_table\" id=\"A3.T6\">\n<figcaption class=\"ltx_caption\"><span class=\"ltx_tag ltx_tag_table\">Table 6: </span> Initial gas phase species fractions  and average sputtering yield  for each species .</figcaption>\n<table class=\"ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle\" id=\"A3.T6.16\">\n<thead class=\"ltx_thead\">\n<tr class=\"ltx_tr\" id=\"A3.T6.8.2\">\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"A3.T6.8.2.3\">Species</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"A3.T6.7.1.1\"></th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"A3.T6.8.2.2\"></th>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T6.9.3\">\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column\" id=\"A3.T6.9.3.2\">(X)</th>\n<th class=\"ltx_td ltx_th ltx_th_column\" id=\"A3.T6.9.3.3\"></th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column\" id=\"A3.T6.9.3.1\">molecules ion<sup class=\"ltx_sup\" id=\"A3.T6.9.3.1.1\"><span class=\"ltx_text ltx_font_italic\" id=\"A3.T6.9.3.1.1.1\">-1</span></sup>\n</th>\n</tr>\n</thead>\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"A3.T6.10.4\">\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"A3.T6.10.4.2\">CO</td>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"A3.T6.10.4.3\">0.55</td>\n<td class=\"ltx_td ltx_align_center ltx_border_t\" id=\"A3.T6.10.4.1\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T6.12.6\">\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T6.11.5.1\">CO<sub class=\"ltx_sub\" id=\"A3.T6.11.5.1.1\"><span class=\"ltx_text ltx_font_italic\" id=\"A3.T6.11.5.1.1.1\">2</span></sub>\n</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T6.12.6.3\">0.21</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T6.12.6.2\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T6.13.7\">\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T6.13.7.2\">O</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T6.13.7.3\">0.14</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T6.13.7.1\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T6.14.8\">\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T6.14.8.2\">C</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T6.14.8.3\">0.07</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T6.14.8.1\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T6.16.10\">\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"A3.T6.15.9.1\">O<sub class=\"ltx_sub\" id=\"A3.T6.15.9.1.1\"><span class=\"ltx_text ltx_font_italic\" id=\"A3.T6.15.9.1.1.1\">2</span></sub>\n</td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"A3.T6.16.10.3\">0.04</td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"A3.T6.16.10.2\"></td>\n</tr>\n</tbody>\n</table>\n</figure>",
            "capture": "Table 6:  Initial gas phase species fractions  and average sputtering yield  for each species ."
        },
        "7": {
            "table_html": "<figure class=\"ltx_table\" id=\"A3.T7\">\n<figcaption class=\"ltx_caption\"><span class=\"ltx_tag ltx_tag_table\">Table 7: </span> Comparison of results for swift heavy ion irradiation of pure CO<sub class=\"ltx_sub\" id=\"A3.T7.28.1\">2</sub> ice films.</figcaption><div class=\"ltx_flex_figure\">\n<div class=\"ltx_flex_cell ltx_flex_size_1\">\n<table class=\"ltx_tabular ltx_centering ltx_figure_panel ltx_guessed_headers ltx_align_middle\" id=\"A3.T7.26\">\n<thead class=\"ltx_thead\">\n<tr class=\"ltx_tr\" id=\"A3.T7.10.8\">\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"A3.T7.10.8.9\">Method</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"A3.T7.10.8.10\">Reference</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"A3.T7.3.1.1\">\n<span class=\"ltx_note ltx_role_footnote\" id=\"footnotex35\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">a𝑎aitalic_a</sup><span class=\"ltx_tag ltx_tag_note\"></span>Initial thickness of the film, before irradiation.</span></span></span>\n</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"A3.T7.4.2.2\"></th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"A3.T7.7.5.5\">\n ( 10<sup class=\"ltx_sup\" id=\"A3.T7.7.5.5.1\"><span class=\"ltx_text ltx_font_italic\" id=\"A3.T7.7.5.5.1.1\">3</span></sup>)</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_tt\" id=\"A3.T7.10.8.8\">\n (10<sup class=\"ltx_sup\" id=\"A3.T7.10.8.8.1\"><span class=\"ltx_text ltx_font_italic\" id=\"A3.T7.10.8.8.1.1\">-3</span></sup>)</th>\n</tr>\n</thead>\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"A3.T7.14.12\">\n<td class=\"ltx_td\" id=\"A3.T7.14.12.5\"></td>\n<th class=\"ltx_td ltx_th ltx_th_column\" id=\"A3.T7.14.12.6\"></th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column\" id=\"A3.T7.11.9.1\">(m)</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column\" id=\"A3.T7.13.11.3\">(eV/10<sup class=\"ltx_sup\" id=\"A3.T7.13.11.3.1\"><span class=\"ltx_text ltx_font_italic\" id=\"A3.T7.13.11.3.1.1\">15</span></sup> molecules cm<sup class=\"ltx_sup\" id=\"A3.T7.13.11.3.2\"><span class=\"ltx_text ltx_font_italic\" id=\"A3.T7.13.11.3.2.1\">-2</span></sup>)</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column\" id=\"A3.T7.14.12.4\">(molecule ions<sup class=\"ltx_sup\" id=\"A3.T7.14.12.4.1\"><span class=\"ltx_text ltx_font_italic\" id=\"A3.T7.14.12.4.1.1\">-1</span></sup>)</th>\n<td class=\"ltx_td\" id=\"A3.T7.14.12.7\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T7.16.14\">\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.16.14.3\">Interference fringes</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.16.14.4\">This work</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.16.14.5\">0.81</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.16.14.6\">3290</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.15.13.1\">68  41</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.16.14.2\">6.3 3.4</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T7.18.16\">\n<td class=\"ltx_td ltx_border_t\" id=\"A3.T7.18.16.3\"></td>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.18.16.4\">This work</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.18.16.5\">0.81</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.18.16.6\">3290</th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.17.15.1\"></th>\n<th class=\"ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t\" id=\"A3.T7.18.16.2\"></th>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T7.20.18\">\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.20.18.3\">Column density</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.20.18.4\"><cite class=\"ltx_cite ltx_citemacro_cite\">Seperuelo Duarte et al. (<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2409.01700v2#bib.bib69\" title=\"\">2009</a>)</cite></td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.20.18.5\">1.08</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.20.18.6\">2601.9</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.19.17.1\"></td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.20.18.2\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T7.22.20\">\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.22.20.3\">from band</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.22.20.4\"><cite class=\"ltx_cite ltx_citemacro_cite\">Dartois et al. (<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2409.01700v2#bib.bib21\" title=\"\">2021</a>)</cite></td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.22.20.5\">0.51</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.22.20.6\">2487.8</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.21.19.1\"></td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.22.20.2\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T7.24.22\">\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.24.22.3\">integration</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.24.22.4\"><cite class=\"ltx_cite ltx_citemacro_cite\">Dartois et al. (<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2409.01700v2#bib.bib21\" title=\"\">2021</a>)</cite></td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.24.22.5\">1.67</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.24.22.6\">2487.8</td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.23.21.1\"></td>\n<td class=\"ltx_td ltx_align_center\" id=\"A3.T7.24.22.2\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"A3.T7.26.24\">\n<td class=\"ltx_td ltx_border_b\" id=\"A3.T7.26.24.3\"></td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"A3.T7.26.24.4\"><cite class=\"ltx_cite ltx_citemacro_cite\">Dartois et al. (<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2409.01700v2#bib.bib21\" title=\"\">2021</a>)</cite></td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"A3.T7.26.24.5\">0.80</td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"A3.T7.26.24.6\">1919.1</td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"A3.T7.25.23.1\"></td>\n<td class=\"ltx_td ltx_align_center ltx_border_b\" id=\"A3.T7.26.24.2\"></td>\n</tr>\n</tbody>\n</table>\n</div>\n<div class=\"ltx_flex_break\"></div>\n<div class=\"ltx_flex_cell ltx_flex_size_1\"><span class=\"ltx_note ltx_centering ltx_figure_panel ltx_role_footnote\" id=\"footnote14\"><sup class=\"ltx_note_mark\">14</sup><span class=\"ltx_note_outer\"><span class=\"ltx_note_content\"><sup class=\"ltx_note_mark\">14</sup><span class=\"ltx_tag ltx_tag_note\">14</span>\n</span></span></span></div>\n</div>\n</figure>",
            "capture": "Table 7:  Comparison of results for swift heavy ion irradiation of pure CO2 ice films."
        }
    },
    "image_paths": {
        "1": {
            "figure_path": "2409.01700v2_figure_1.png",
            "caption": "Figure 1: IR spectra of irradiated H2CO ice. Left panel: Full range spectra, corrected for baseline, with assigned spectral peaks (see Table 2). Right panel: Focus on the evolution of the four bands used to derive column density of CO2, CO, H2CO, and POM in the ice.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/IRspectra_Tot.png"
        },
        "2": {
            "figure_path": "2409.01700v2_figure_2.png",
            "caption": "Figure 2: Column density evolution of CO2, CO, H2CO, and POM ices as a function of fluence. In the case of POM, a factor of 2 uncertainty was assumed for the band strength of the combination mode at 1105 cm-1 (see text), as depicted by the shaded green zone. In the case of H2CO, the band strength of the stretching mode at 1725 cm-1 was also evaluated by Schutte et al. (1993) as 9.6×\\times×10-18 cm molecules-1 at 10 K, which corresponds to the highest column density value of the shaded red zone. Otherwise, an uncertainty of 20% was assumed for the band strengths.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/CD_IR_vs_fluence_V2.png"
        },
        "3": {
            "figure_path": "2409.01700v2_figure_3.png",
            "caption": "Figure 3: Infrared transmittance spectra of a H2CO ice film evolution as a\nfunction of fluence. Solid lines: Experimental data. Dashed lines: Model spectra fitted to the\ndata. See text for details.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/Transmittance_baselineFit.png"
        },
        "4": {
            "figure_path": "2409.01700v2_figure_4.png",
            "caption": "Figure 4: Evolution of the surface density as a function of fluence deduced from interference fringes. The fit was performed for fluences greater than 6×1011absentsuperscript1011\\times 10^{11}× 10 start_POSTSUPERSCRIPT 11 end_POSTSUPERSCRIPT ions cm-2 since the very beginning of the irradiation corresponds to ice compaction (e.g. Palumbo, 2006; Dartois et al., 2013).",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/MassPerArea_vs_Fluence.png"
        },
        "5": {
            "figure_path": "2409.01700v2_figure_5.png",
            "caption": "Figure 5: QMS signals as a function of fluence. Top panel: Background corrected signals. Bottom panel: Molecular fractions in the gas (solid lines, left y𝑦yitalic_y-axis) derived from the fragmentation patterns and ionisation cross sections, and sputtering yield of each species (dashed lines, right y𝑦yitalic_y-axis). See text for details.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/QMS.png"
        },
        "6": {
            "figure_path": "2409.01700v2_figure_6.png",
            "caption": "Figure 6: Mass fragmentation pattern monitored during species injection (for ice sample deposition) for H2CO (top panel) and CO (unpublished data) (bottom panel).",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/Fragmentation_pattern.png"
        },
        "7": {
            "figure_path": "2409.01700v2_figure_7.png",
            "caption": "Figure 7: Schematic timeline of events during the first impact of a swift heavy ion (SHI) on an ice sample, within the thermal spike model. Chemistry and sputtering occur almost simultaneously within 10-9 seconds of the ion’s passage (Lang et al., 2020). The length dssubscript𝑑𝑠d_{s}italic_d start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT corresponds to the sputtering depth probed by an individual ion incident, which is inferior to d0subscript𝑑0d_{0}italic_d start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, the initial ice film thickness; rrsubscript𝑟𝑟r_{r}italic_r start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT corresponds to the radiolysis destruction radius, which is at most equal to the sputtering cylinder radius rssubscript𝑟𝑠r_{s}italic_r start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT (Dartois et al., 2021). Considering the timescales involved, infrared spectroscopy cannot observe the radiolysis effects within the sputtered volume during the passage of an ion.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/Dessin_Film_evolution.png"
        },
        "8": {
            "figure_path": "2409.01700v2_figure_8.png",
            "caption": "Figure 8: Comparison between the observed integrated intensities (blue dots) and the integrated intensities derived from the non-LTE model (red diamonds), for each of the observed lines, labelled by their rest frequencies. In the figure, ‘o’ stands for ortho and ‘p’ stands for para.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/bestmodel_6.png"
        },
        "9": {
            "figure_path": "2409.01700v2_figure_9.png",
            "caption": "Figure 9: Intact sputtering rate of pure \\ceH2CO and effective sputtering rates of the pure ices \\ceCO, \\ceCO2, and \\ceH2O as a function of the ζ𝜁\\zetaitalic_ζ cosmic-ray ionisation rate. Effective sputtering yield pre-factors are taken from Dartois et al. (2023).",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/calib_all.png"
        },
        "10": {
            "figure_path": "2409.01700v2_figure_10.png",
            "caption": "Figure 10: \\ceH2CO gas phase abundance with respect to H nuclei as a function of visual extinction. The observational value derived in this study for the prestellar core L1689B (blue hatched zone) is compared to five different models for \\ceH2CO sputtering: pure \\ceH2CO ice and \\ceH2CO ideally diluted in \\ceH2O, \\ceCO2, and CO matrices. See text for details.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/h2co.png"
        },
        "11": {
            "figure_path": "2409.01700v2_figure_11.png",
            "caption": "Figure 11: Observed H132superscriptsubscriptabsent213{}_{2}^{13}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT start_POSTSUPERSCRIPT 13 end_POSTSUPERSCRIPTCO spectra. The vertical dotted line shows the source velocity (v=3.5𝑣3.5v=3.5italic_v = 3.5 km s-1). The spin symmetry is indicated in the upper left corner of each plot, with ‘o’ standing for ortho and ‘p’ standing for para.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/h213co_fig.png"
        },
        "12": {
            "figure_path": "2409.01700v2_figure_12.png",
            "caption": "Figure 12: Observed H2C18O spectra. The vertical dotted line shows the source velocity (v=3.5𝑣3.5v=3.5italic_v = 3.5 km s-1).The spin symmetry is indicated in the upper left corner of each plot, with ‘o’ standing for ortho and ‘p’ standing for para.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/h2c18o_fig.png"
        },
        "13": {
            "figure_path": "2409.01700v2_figure_13.png",
            "caption": "Figure 13: Infrared transmittance spectra of a CO2 ice film evolution upon 74 MeV 86Kr18+ swift heavy ion irradiation. Solid lines: Experimental data. Dashed lines: Model spectra fitted to the data, without considering the absorption bands. The QMS signal ends around a fluence of 4.1012superscript4.10124.10^{12}4.10 start_POSTSUPERSCRIPT 12 end_POSTSUPERSCRIPT ion cm-2, before the end of the irradiation as the instrument stopped prematurely.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/CO2_IR_interference_FIT.png"
        },
        "14": {
            "figure_path": "2409.01700v2_figure_14.png",
            "caption": "Figure 14: Evolution of the bulk mass per area as a function of fluence deduced from interference fringes for a CO2 ice film.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/CO2_Mass_per_area_vs_F.png"
        },
        "15": {
            "figure_path": "2409.01700v2_figure_15.png",
            "caption": "Figure 15: QMS signals as a function of fluence. Top panel: Background corrected signals. Bottom panel: Molecular fractions in the gas (solid lines, left y𝑦yitalic_y-axis) derived from the fragmentation patterns and ionisation cross sections, and sputtering yield of each species (dashed lines, right y𝑦yitalic_y-axis). See text for details.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/CO2_QMS_Tot.png"
        },
        "16": {
            "figure_path": "2409.01700v2_figure_16.png",
            "caption": "Figure 16: Evolution of the background-corrected IR spectrum centered on the ν3subscript𝜈3\\nu_{3}italic_ν start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT stretching mode of \\ceCO2 upon 74 MeV 86Kr18+ swift ion irradiation",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/CO2_IR_spectra_evolution.png"
        },
        "17": {
            "figure_path": "2409.01700v2_figure_17.png",
            "caption": "Figure 17: Column density derivative with respect to fluence. The solid and dashed lines are fits with or without including the sputtering depth Ndsubscript𝑁𝑑N_{d}italic_N start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT in Eq. 25, respectively.",
            "url": "http://arxiv.org/html/2409.01700v2/extracted/5842210/CO2_mdNdF_vs_N.png"
        }
    },
    "validation": true,
    "references": [],
    "url": "http://arxiv.org/html/2409.01700v2",
    "Chart": [
        "1",
        "2",
        "3",
        "4",
        "5",
        "6",
        "8",
        "9",
        "10",
        "11",
        "12",
        "13",
        "14",
        "15",
        "16",
        "17"
    ],
    "extract_figure_info": {
        "1": {
            "4.1": [
                "The evolution of H2CO ice infrared (IR) spectra as a function of fluence is depicted in Figure 1 .",
                "At fluence zero, the film is made of pure H2CO, and neither paraformaldehyde nor CO or CO2 can be seen in the spectra.",
                "As soon as irradiation starts, bands characteristic of CO2 and CO appear, as well as bands around 2920, 1230, 1100, and 920 cm-1, which we attribute to the formation of an H2CO polymer (polyoxymethylene, hereafter POM).",
                "Conversely, H2CO bands decrease with fluence.",
                "Apart from CO, CO2, and POM, the infrared analysis shows no evidence of the formation of any other chemical species during the irradiation of H2CO.",
                "The column densities of CO2, CO, and H2CO were derived using the band strengths given in Table 2 and the integrated absorbance of the bands at 2343 cm-1, 2139 cm-1, and 1725 cm-1, respectively.",
                "The POM column density was calculated using a combination mode at 1105 cm-1 and a band strength of cm molecules-1 (Noble et al., 2012 ).",
                "This band strength is not known with precision (Tadokoro et al., 1963 ; Schutte et al., 1993 ), and we assumed a factor of 2 uncertainty.",
                "An additional uncertainty arises from changes in the refractive index value across strong absorbance bands, resulting in some unphysical negative absorbances after baseline correction (see e.g.",
                "the C=0 stretch of H2CO).",
                "The derived column density evolution as a function of fluence, with uncertainty zones, is presented in Figure 2 .",
                "As can be seen, the POM column density is not accurately determined, but it is consistent with a fast and efficient polymerisation of \\ceH2CO at very low fluence.",
                "Thus, at a fluence of ions cm-1, the ice is mainly composed of POM.",
                "In similar experiments on non-polymerisable ices such as \\ceCH3OH and \\ceCO2 (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ), the column density evolution with fluence can be solved through a simple differential equation involving solely radiolysis and sputtering processes (see e.g.",
                "(3) in Dartois et al., 2019 ).",
                "Here, however, we were not able to solve such a differential equation, due to the additional polymerisation process of \\ceH2CO towards POM, whose exact nature is unknown.666In particular, the number of monomers is unknown and most probably the synthesised POM is a mixture of polymers of various chain sizes.",
                "In addition, while swift ion irradiation of H2CO is responsible for the formation of POM, it also destroys POM to CO and CO2 (see the decrease in POM column density beyond a fluence of ions cm-2 in Figure 2 ).",
                "Therefore, in order to derive the sputtering yield, we resorted to another method based on the determination of the reduction in thin film thickness using the Fabry–Perot interference fringes observed in the infrared spectra (Dartois et al., 2020 , 2023 ), combined with QMS analysis of the gas composition.",
                "We emphasise that in order to validate this method, it was first applied to measure the thickness evolution of an irradiated thin film of CO2, for which the usual fit of the column density evolution via a differential equation was also possible.",
                "As reported in Appendix C , both methods were found to give consistent results, which are also in good agreement with the literature.",
                "In the case of \\ceH2CO, as irradiation proceeds, the ice film becomes a mixture of mainly POM and H2CO for which the refractive index () is not available.",
                "Fitting the rigorous expression for the transmission () of a thin absorbing film on a thick transparent substrate is therefore not possible.",
                "Nevertheless, transmittance spectra follow a sinusoidal pattern, where the period is proportional to the thickness.",
                "Thus, we used the following simple expression to fit the transmittance spectra in the ranges of wavenumbers () free of molecular absorptions: Here and are free parameters, is the refractive index taken as (Bouilloud et al., 2015 ), and is ice thickness.",
                "The factor corrects for the angle between the infrared beam and the sample.",
                "Fits obtained with this expression are shown in Figure 3 .",
                "The ice film is composed of POM and H2CO, with a composition changing during irradiation.",
                "Therefore, evaluating the sample mass density is challenging.",
                "Furthermore, even the mass density of a pure H2CO ice film is unknown.",
                "Consequently, it is assumed to be constant at the value for liquid formaldehyde, (Bouilloud et al., 2015 ), with an assumed uncertainty of 20%.",
                "It was used to derive the surface density of the ice , as a function of fluence, as shown in Figure 4 .",
                "The total mass sputtering yield can be directly estimated from the slope of the surface density evolution with fluence as g ion-1.",
                "It should be noted that this total yield includes all sputtered species from the considered volume, both radiolysed species (C, O, H, H2, CO, and CO2) and intact \\ceH2CO fragments.",
                "In order to determine the chemical composition of the sputtered mass volume, the various fragments ejected into the gas phase were measured with the QMS.",
                "The small residual or background signal observed before irradiation was subtracted from the recorded signal during the whole irradiation time, as reported in Figure 5 (top panel).",
                "We note that there is no intact sputtered POM as no signal is observed at =31, a mass characteristic of POM fragmentation pattern (Butscher et al., 2019 ; Duvernay et al., 2014 ).",
                "The mass =30 can be used to follow H2CO molecules since no fragment at this mass is observed in the CO fragmentation pattern (Figure 6 ).",
                "Thus, the signals at m/z=30 and m/z=28 can be used to retrieve the total number of H2CO and CO species, respectively, by dividing each m/z signal by its relative contribution in the fragmentation pattern.",
                "The remaining signals at m/z=12 and m/z=16, after subtracting the contributions of CO and H2CO, indicate the abundances of C and O atoms, respectively.",
                "Once corrected for the total electron-impact ionisation cross-section at 70 eV (energy of the QMS electron ionisation source), the relative fraction of each species with fluence is determined (Figure 5 , bottom panel).",
                "QMS measurements at very low masses are not reliable, but the amount of hydrogen (H or H2) is supposed to be equal to the sum of the amounts of C, O, and CO. We note that CO2, a minor component of the ice (see Figure 1 ), was not detected in the gas phase by the QMS.",
                "As irradiation proceeds, the composition of the film changes (Figure 2 ) and this is also observed in the gas composition (Figure 5 , bottom panel).",
                "The fraction of gaseous H2CO thus decreases significantly (by approximately 70 %) for initial fluences (up to 2 ions cm-2), which is consistent with the radiolysis and the rapid polymerisation of solid \\ceH2CO.",
                "It then decreases more gradually, before a (noisy) slightly ascending plateau is reached beyond fluences of 3 ions cm-2.",
                "Conversely, the fractions of C and O increase rapidly (by approximately 70%), but also reach a plateau.",
                "Overall, the molecular fractions of these three chemical species in the gas vary by less than a factor of two.",
                "The larger molecular fractions of CO and H2 increase up to fluences of about 2 ions cm-2 before reaching a slightly descending plateau, with variations of less than 15%.",
                "We can extract the initial fraction of each species in the gas phase (Table 5 ), and the subsequent evolution was fitted by third-order polynomials.",
                "By combining the total mass sputtering yield with the fitted molecular fractions , we can derive the sputtering yield of each ejected species , where is the Avogadro constant, is the molecular mass of species , and represents the mass fraction of species in the gas: The derived sputtering yields for the various ejected species are plotted as dashed lines in the bottom panel of Figure 5 (right -axis).",
                "Similarly to the molecular fractions, the intact sputtering yields vary by less than a factor of 2 for C, O, and H2CO, and by less than 15% for CO and H2, as expected.",
                "The average intact sputtering yields were computed over the full range of fluences and are listed in Table 5 .",
                "The average sputtering yield for intact \\ceH2CO is found to be molecules ion-1.",
                "We can now try to estimate the effective sputtering yield, .",
                "For non-polymerisable species, is usually determined using the column density evolution with fluence measured from IR spectroscopy (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ).",
                "For a pure ice , is defined as the semi-infinite thickness effective-sputtering yield for the ice under study.",
                "It includes both intact sputtered species and radiolysed (daughter) sputtered species.",
                "Since radiolysis and sputtering occur simultaneously, IR spectroscopy captures the disappearance of H2CO, regardless of whether it is sputtered intact or radiolysed.",
                "is simply related to as where is the intact fraction of sputtered H2CO.",
                "In our experiment, the volume to be sputtered just before irradiation is composed of pristine \\ceH2CO ice.",
                "The impact of a swift heavy ion induces radiolysis along its track, affecting a fraction of this volume.",
                "Therefore, after irradiation has started, the sputtered volume is composed of intact \\ceH2CO, fresh products of radiolysis as well as primary radiolytic products that accumulate in the film (see Figure 7 ).",
                "Therefore, in order to determine the effective sputtering yield , the intact fraction () of sputtered H2CO during irradiation must be estimated using the initial fractions reported in Table 3 : In practice, we derived an intact fraction of sputtered \\ceH2CO molecules =0.23, corresponding to an effective sputtering yield for the \\ceH2CO film of =(10.99.9)103 molecules ions-1.",
                "In their compendium of selected literature sputtering yields, Dartois et al.",
                "(2023 ) show that the sputtering yield induced by swift heavy ions follows an empirical law that is directly proportional to the square of the electronic stopping power : Here, using a stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam, we obtain for a pure \\ceH2CO ice =(3.12.8)10-4 1030 eV-2 cm-4 molecule3.",
                "However, most studies only have access to the effective sputtering yield , which is therefore used for in Eq.",
                "6 (e.g.",
                "Dartois et al., 2023 ).",
                "In this case, the effective prefactor value is =(1.4 1.3)10-3 1030 eV-2 cm-4 molecule3."
            ]
        },
        "2": {
            "4.1": [
                "The evolution of H2CO ice infrared (IR) spectra as a function of fluence is depicted in Figure 1 .",
                "At fluence zero, the film is made of pure H2CO, and neither paraformaldehyde nor CO or CO2 can be seen in the spectra.",
                "As soon as irradiation starts, bands characteristic of CO2 and CO appear, as well as bands around 2920, 1230, 1100, and 920 cm-1, which we attribute to the formation of an H2CO polymer (polyoxymethylene, hereafter POM).",
                "Conversely, H2CO bands decrease with fluence.",
                "Apart from CO, CO2, and POM, the infrared analysis shows no evidence of the formation of any other chemical species during the irradiation of H2CO.",
                "The column densities of CO2, CO, and H2CO were derived using the band strengths given in Table 2 and the integrated absorbance of the bands at 2343 cm-1, 2139 cm-1, and 1725 cm-1, respectively.",
                "The POM column density was calculated using a combination mode at 1105 cm-1 and a band strength of cm molecules-1 (Noble et al., 2012 ).",
                "This band strength is not known with precision (Tadokoro et al., 1963 ; Schutte et al., 1993 ), and we assumed a factor of 2 uncertainty.",
                "An additional uncertainty arises from changes in the refractive index value across strong absorbance bands, resulting in some unphysical negative absorbances after baseline correction (see e.g.",
                "the C=0 stretch of H2CO).",
                "The derived column density evolution as a function of fluence, with uncertainty zones, is presented in Figure 2 .",
                "As can be seen, the POM column density is not accurately determined, but it is consistent with a fast and efficient polymerisation of \\ceH2CO at very low fluence.",
                "Thus, at a fluence of ions cm-1, the ice is mainly composed of POM.",
                "In similar experiments on non-polymerisable ices such as \\ceCH3OH and \\ceCO2 (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ), the column density evolution with fluence can be solved through a simple differential equation involving solely radiolysis and sputtering processes (see e.g.",
                "(3) in Dartois et al., 2019 ).",
                "Here, however, we were not able to solve such a differential equation, due to the additional polymerisation process of \\ceH2CO towards POM, whose exact nature is unknown.666In particular, the number of monomers is unknown and most probably the synthesised POM is a mixture of polymers of various chain sizes.",
                "In addition, while swift ion irradiation of H2CO is responsible for the formation of POM, it also destroys POM to CO and CO2 (see the decrease in POM column density beyond a fluence of ions cm-2 in Figure 2 ).",
                "Therefore, in order to derive the sputtering yield, we resorted to another method based on the determination of the reduction in thin film thickness using the Fabry–Perot interference fringes observed in the infrared spectra (Dartois et al., 2020 , 2023 ), combined with QMS analysis of the gas composition.",
                "We emphasise that in order to validate this method, it was first applied to measure the thickness evolution of an irradiated thin film of CO2, for which the usual fit of the column density evolution via a differential equation was also possible.",
                "As reported in Appendix C , both methods were found to give consistent results, which are also in good agreement with the literature.",
                "In the case of \\ceH2CO, as irradiation proceeds, the ice film becomes a mixture of mainly POM and H2CO for which the refractive index () is not available.",
                "Fitting the rigorous expression for the transmission () of a thin absorbing film on a thick transparent substrate is therefore not possible.",
                "Nevertheless, transmittance spectra follow a sinusoidal pattern, where the period is proportional to the thickness.",
                "Thus, we used the following simple expression to fit the transmittance spectra in the ranges of wavenumbers () free of molecular absorptions: Here and are free parameters, is the refractive index taken as (Bouilloud et al., 2015 ), and is ice thickness.",
                "The factor corrects for the angle between the infrared beam and the sample.",
                "Fits obtained with this expression are shown in Figure 3 .",
                "The ice film is composed of POM and H2CO, with a composition changing during irradiation.",
                "Therefore, evaluating the sample mass density is challenging.",
                "Furthermore, even the mass density of a pure H2CO ice film is unknown.",
                "Consequently, it is assumed to be constant at the value for liquid formaldehyde, (Bouilloud et al., 2015 ), with an assumed uncertainty of 20%.",
                "It was used to derive the surface density of the ice , as a function of fluence, as shown in Figure 4 .",
                "The total mass sputtering yield can be directly estimated from the slope of the surface density evolution with fluence as g ion-1.",
                "It should be noted that this total yield includes all sputtered species from the considered volume, both radiolysed species (C, O, H, H2, CO, and CO2) and intact \\ceH2CO fragments.",
                "In order to determine the chemical composition of the sputtered mass volume, the various fragments ejected into the gas phase were measured with the QMS.",
                "The small residual or background signal observed before irradiation was subtracted from the recorded signal during the whole irradiation time, as reported in Figure 5 (top panel).",
                "We note that there is no intact sputtered POM as no signal is observed at =31, a mass characteristic of POM fragmentation pattern (Butscher et al., 2019 ; Duvernay et al., 2014 ).",
                "The mass =30 can be used to follow H2CO molecules since no fragment at this mass is observed in the CO fragmentation pattern (Figure 6 ).",
                "Thus, the signals at m/z=30 and m/z=28 can be used to retrieve the total number of H2CO and CO species, respectively, by dividing each m/z signal by its relative contribution in the fragmentation pattern.",
                "The remaining signals at m/z=12 and m/z=16, after subtracting the contributions of CO and H2CO, indicate the abundances of C and O atoms, respectively.",
                "Once corrected for the total electron-impact ionisation cross-section at 70 eV (energy of the QMS electron ionisation source), the relative fraction of each species with fluence is determined (Figure 5 , bottom panel).",
                "QMS measurements at very low masses are not reliable, but the amount of hydrogen (H or H2) is supposed to be equal to the sum of the amounts of C, O, and CO. We note that CO2, a minor component of the ice (see Figure 1 ), was not detected in the gas phase by the QMS.",
                "As irradiation proceeds, the composition of the film changes (Figure 2 ) and this is also observed in the gas composition (Figure 5 , bottom panel).",
                "The fraction of gaseous H2CO thus decreases significantly (by approximately 70 %) for initial fluences (up to 2 ions cm-2), which is consistent with the radiolysis and the rapid polymerisation of solid \\ceH2CO.",
                "It then decreases more gradually, before a (noisy) slightly ascending plateau is reached beyond fluences of 3 ions cm-2.",
                "Conversely, the fractions of C and O increase rapidly (by approximately 70%), but also reach a plateau.",
                "Overall, the molecular fractions of these three chemical species in the gas vary by less than a factor of two.",
                "The larger molecular fractions of CO and H2 increase up to fluences of about 2 ions cm-2 before reaching a slightly descending plateau, with variations of less than 15%.",
                "We can extract the initial fraction of each species in the gas phase (Table 5 ), and the subsequent evolution was fitted by third-order polynomials.",
                "By combining the total mass sputtering yield with the fitted molecular fractions , we can derive the sputtering yield of each ejected species , where is the Avogadro constant, is the molecular mass of species , and represents the mass fraction of species in the gas: The derived sputtering yields for the various ejected species are plotted as dashed lines in the bottom panel of Figure 5 (right -axis).",
                "Similarly to the molecular fractions, the intact sputtering yields vary by less than a factor of 2 for C, O, and H2CO, and by less than 15% for CO and H2, as expected.",
                "The average intact sputtering yields were computed over the full range of fluences and are listed in Table 5 .",
                "The average sputtering yield for intact \\ceH2CO is found to be molecules ion-1.",
                "We can now try to estimate the effective sputtering yield, .",
                "For non-polymerisable species, is usually determined using the column density evolution with fluence measured from IR spectroscopy (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ).",
                "For a pure ice , is defined as the semi-infinite thickness effective-sputtering yield for the ice under study.",
                "It includes both intact sputtered species and radiolysed (daughter) sputtered species.",
                "Since radiolysis and sputtering occur simultaneously, IR spectroscopy captures the disappearance of H2CO, regardless of whether it is sputtered intact or radiolysed.",
                "is simply related to as where is the intact fraction of sputtered H2CO.",
                "In our experiment, the volume to be sputtered just before irradiation is composed of pristine \\ceH2CO ice.",
                "The impact of a swift heavy ion induces radiolysis along its track, affecting a fraction of this volume.",
                "Therefore, after irradiation has started, the sputtered volume is composed of intact \\ceH2CO, fresh products of radiolysis as well as primary radiolytic products that accumulate in the film (see Figure 7 ).",
                "Therefore, in order to determine the effective sputtering yield , the intact fraction () of sputtered H2CO during irradiation must be estimated using the initial fractions reported in Table 3 : In practice, we derived an intact fraction of sputtered \\ceH2CO molecules =0.23, corresponding to an effective sputtering yield for the \\ceH2CO film of =(10.99.9)103 molecules ions-1.",
                "In their compendium of selected literature sputtering yields, Dartois et al.",
                "(2023 ) show that the sputtering yield induced by swift heavy ions follows an empirical law that is directly proportional to the square of the electronic stopping power : Here, using a stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam, we obtain for a pure \\ceH2CO ice =(3.12.8)10-4 1030 eV-2 cm-4 molecule3.",
                "However, most studies only have access to the effective sputtering yield , which is therefore used for in Eq.",
                "6 (e.g.",
                "Dartois et al., 2023 ).",
                "In this case, the effective prefactor value is =(1.4 1.3)10-3 1030 eV-2 cm-4 molecule3."
            ]
        },
        "3": {
            "4.1": [
                "The evolution of H2CO ice infrared (IR) spectra as a function of fluence is depicted in Figure 1 .",
                "At fluence zero, the film is made of pure H2CO, and neither paraformaldehyde nor CO or CO2 can be seen in the spectra.",
                "As soon as irradiation starts, bands characteristic of CO2 and CO appear, as well as bands around 2920, 1230, 1100, and 920 cm-1, which we attribute to the formation of an H2CO polymer (polyoxymethylene, hereafter POM).",
                "Conversely, H2CO bands decrease with fluence.",
                "Apart from CO, CO2, and POM, the infrared analysis shows no evidence of the formation of any other chemical species during the irradiation of H2CO.",
                "The column densities of CO2, CO, and H2CO were derived using the band strengths given in Table 2 and the integrated absorbance of the bands at 2343 cm-1, 2139 cm-1, and 1725 cm-1, respectively.",
                "The POM column density was calculated using a combination mode at 1105 cm-1 and a band strength of cm molecules-1 (Noble et al., 2012 ).",
                "This band strength is not known with precision (Tadokoro et al., 1963 ; Schutte et al., 1993 ), and we assumed a factor of 2 uncertainty.",
                "An additional uncertainty arises from changes in the refractive index value across strong absorbance bands, resulting in some unphysical negative absorbances after baseline correction (see e.g.",
                "the C=0 stretch of H2CO).",
                "The derived column density evolution as a function of fluence, with uncertainty zones, is presented in Figure 2 .",
                "As can be seen, the POM column density is not accurately determined, but it is consistent with a fast and efficient polymerisation of \\ceH2CO at very low fluence.",
                "Thus, at a fluence of ions cm-1, the ice is mainly composed of POM.",
                "In similar experiments on non-polymerisable ices such as \\ceCH3OH and \\ceCO2 (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ), the column density evolution with fluence can be solved through a simple differential equation involving solely radiolysis and sputtering processes (see e.g.",
                "(3) in Dartois et al., 2019 ).",
                "Here, however, we were not able to solve such a differential equation, due to the additional polymerisation process of \\ceH2CO towards POM, whose exact nature is unknown.666In particular, the number of monomers is unknown and most probably the synthesised POM is a mixture of polymers of various chain sizes.",
                "In addition, while swift ion irradiation of H2CO is responsible for the formation of POM, it also destroys POM to CO and CO2 (see the decrease in POM column density beyond a fluence of ions cm-2 in Figure 2 ).",
                "Therefore, in order to derive the sputtering yield, we resorted to another method based on the determination of the reduction in thin film thickness using the Fabry–Perot interference fringes observed in the infrared spectra (Dartois et al., 2020 , 2023 ), combined with QMS analysis of the gas composition.",
                "We emphasise that in order to validate this method, it was first applied to measure the thickness evolution of an irradiated thin film of CO2, for which the usual fit of the column density evolution via a differential equation was also possible.",
                "As reported in Appendix C , both methods were found to give consistent results, which are also in good agreement with the literature.",
                "In the case of \\ceH2CO, as irradiation proceeds, the ice film becomes a mixture of mainly POM and H2CO for which the refractive index () is not available.",
                "Fitting the rigorous expression for the transmission () of a thin absorbing film on a thick transparent substrate is therefore not possible.",
                "Nevertheless, transmittance spectra follow a sinusoidal pattern, where the period is proportional to the thickness.",
                "Thus, we used the following simple expression to fit the transmittance spectra in the ranges of wavenumbers () free of molecular absorptions: Here and are free parameters, is the refractive index taken as (Bouilloud et al., 2015 ), and is ice thickness.",
                "The factor corrects for the angle between the infrared beam and the sample.",
                "Fits obtained with this expression are shown in Figure 3 .",
                "The ice film is composed of POM and H2CO, with a composition changing during irradiation.",
                "Therefore, evaluating the sample mass density is challenging.",
                "Furthermore, even the mass density of a pure H2CO ice film is unknown.",
                "Consequently, it is assumed to be constant at the value for liquid formaldehyde, (Bouilloud et al., 2015 ), with an assumed uncertainty of 20%.",
                "It was used to derive the surface density of the ice , as a function of fluence, as shown in Figure 4 .",
                "The total mass sputtering yield can be directly estimated from the slope of the surface density evolution with fluence as g ion-1.",
                "It should be noted that this total yield includes all sputtered species from the considered volume, both radiolysed species (C, O, H, H2, CO, and CO2) and intact \\ceH2CO fragments.",
                "In order to determine the chemical composition of the sputtered mass volume, the various fragments ejected into the gas phase were measured with the QMS.",
                "The small residual or background signal observed before irradiation was subtracted from the recorded signal during the whole irradiation time, as reported in Figure 5 (top panel).",
                "We note that there is no intact sputtered POM as no signal is observed at =31, a mass characteristic of POM fragmentation pattern (Butscher et al., 2019 ; Duvernay et al., 2014 ).",
                "The mass =30 can be used to follow H2CO molecules since no fragment at this mass is observed in the CO fragmentation pattern (Figure 6 ).",
                "Thus, the signals at m/z=30 and m/z=28 can be used to retrieve the total number of H2CO and CO species, respectively, by dividing each m/z signal by its relative contribution in the fragmentation pattern.",
                "The remaining signals at m/z=12 and m/z=16, after subtracting the contributions of CO and H2CO, indicate the abundances of C and O atoms, respectively.",
                "Once corrected for the total electron-impact ionisation cross-section at 70 eV (energy of the QMS electron ionisation source), the relative fraction of each species with fluence is determined (Figure 5 , bottom panel).",
                "QMS measurements at very low masses are not reliable, but the amount of hydrogen (H or H2) is supposed to be equal to the sum of the amounts of C, O, and CO. We note that CO2, a minor component of the ice (see Figure 1 ), was not detected in the gas phase by the QMS.",
                "As irradiation proceeds, the composition of the film changes (Figure 2 ) and this is also observed in the gas composition (Figure 5 , bottom panel).",
                "The fraction of gaseous H2CO thus decreases significantly (by approximately 70 %) for initial fluences (up to 2 ions cm-2), which is consistent with the radiolysis and the rapid polymerisation of solid \\ceH2CO.",
                "It then decreases more gradually, before a (noisy) slightly ascending plateau is reached beyond fluences of 3 ions cm-2.",
                "Conversely, the fractions of C and O increase rapidly (by approximately 70%), but also reach a plateau.",
                "Overall, the molecular fractions of these three chemical species in the gas vary by less than a factor of two.",
                "The larger molecular fractions of CO and H2 increase up to fluences of about 2 ions cm-2 before reaching a slightly descending plateau, with variations of less than 15%.",
                "We can extract the initial fraction of each species in the gas phase (Table 5 ), and the subsequent evolution was fitted by third-order polynomials.",
                "By combining the total mass sputtering yield with the fitted molecular fractions , we can derive the sputtering yield of each ejected species , where is the Avogadro constant, is the molecular mass of species , and represents the mass fraction of species in the gas: The derived sputtering yields for the various ejected species are plotted as dashed lines in the bottom panel of Figure 5 (right -axis).",
                "Similarly to the molecular fractions, the intact sputtering yields vary by less than a factor of 2 for C, O, and H2CO, and by less than 15% for CO and H2, as expected.",
                "The average intact sputtering yields were computed over the full range of fluences and are listed in Table 5 .",
                "The average sputtering yield for intact \\ceH2CO is found to be molecules ion-1.",
                "We can now try to estimate the effective sputtering yield, .",
                "For non-polymerisable species, is usually determined using the column density evolution with fluence measured from IR spectroscopy (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ).",
                "For a pure ice , is defined as the semi-infinite thickness effective-sputtering yield for the ice under study.",
                "It includes both intact sputtered species and radiolysed (daughter) sputtered species.",
                "Since radiolysis and sputtering occur simultaneously, IR spectroscopy captures the disappearance of H2CO, regardless of whether it is sputtered intact or radiolysed.",
                "is simply related to as where is the intact fraction of sputtered H2CO.",
                "In our experiment, the volume to be sputtered just before irradiation is composed of pristine \\ceH2CO ice.",
                "The impact of a swift heavy ion induces radiolysis along its track, affecting a fraction of this volume.",
                "Therefore, after irradiation has started, the sputtered volume is composed of intact \\ceH2CO, fresh products of radiolysis as well as primary radiolytic products that accumulate in the film (see Figure 7 ).",
                "Therefore, in order to determine the effective sputtering yield , the intact fraction () of sputtered H2CO during irradiation must be estimated using the initial fractions reported in Table 3 : In practice, we derived an intact fraction of sputtered \\ceH2CO molecules =0.23, corresponding to an effective sputtering yield for the \\ceH2CO film of =(10.99.9)103 molecules ions-1.",
                "In their compendium of selected literature sputtering yields, Dartois et al.",
                "(2023 ) show that the sputtering yield induced by swift heavy ions follows an empirical law that is directly proportional to the square of the electronic stopping power : Here, using a stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam, we obtain for a pure \\ceH2CO ice =(3.12.8)10-4 1030 eV-2 cm-4 molecule3.",
                "However, most studies only have access to the effective sputtering yield , which is therefore used for in Eq.",
                "6 (e.g.",
                "Dartois et al., 2023 ).",
                "In this case, the effective prefactor value is =(1.4 1.3)10-3 1030 eV-2 cm-4 molecule3."
            ]
        },
        "4": {},
        "5": {
            "4.1": [
                "The evolution of H2CO ice infrared (IR) spectra as a function of fluence is depicted in Figure 1 .",
                "At fluence zero, the film is made of pure H2CO, and neither paraformaldehyde nor CO or CO2 can be seen in the spectra.",
                "As soon as irradiation starts, bands characteristic of CO2 and CO appear, as well as bands around 2920, 1230, 1100, and 920 cm-1, which we attribute to the formation of an H2CO polymer (polyoxymethylene, hereafter POM).",
                "Conversely, H2CO bands decrease with fluence.",
                "Apart from CO, CO2, and POM, the infrared analysis shows no evidence of the formation of any other chemical species during the irradiation of H2CO.",
                "The column densities of CO2, CO, and H2CO were derived using the band strengths given in Table 2 and the integrated absorbance of the bands at 2343 cm-1, 2139 cm-1, and 1725 cm-1, respectively.",
                "The POM column density was calculated using a combination mode at 1105 cm-1 and a band strength of cm molecules-1 (Noble et al., 2012 ).",
                "This band strength is not known with precision (Tadokoro et al., 1963 ; Schutte et al., 1993 ), and we assumed a factor of 2 uncertainty.",
                "An additional uncertainty arises from changes in the refractive index value across strong absorbance bands, resulting in some unphysical negative absorbances after baseline correction (see e.g.",
                "the C=0 stretch of H2CO).",
                "The derived column density evolution as a function of fluence, with uncertainty zones, is presented in Figure 2 .",
                "As can be seen, the POM column density is not accurately determined, but it is consistent with a fast and efficient polymerisation of \\ceH2CO at very low fluence.",
                "Thus, at a fluence of ions cm-1, the ice is mainly composed of POM.",
                "In similar experiments on non-polymerisable ices such as \\ceCH3OH and \\ceCO2 (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ), the column density evolution with fluence can be solved through a simple differential equation involving solely radiolysis and sputtering processes (see e.g.",
                "(3) in Dartois et al., 2019 ).",
                "Here, however, we were not able to solve such a differential equation, due to the additional polymerisation process of \\ceH2CO towards POM, whose exact nature is unknown.666In particular, the number of monomers is unknown and most probably the synthesised POM is a mixture of polymers of various chain sizes.",
                "In addition, while swift ion irradiation of H2CO is responsible for the formation of POM, it also destroys POM to CO and CO2 (see the decrease in POM column density beyond a fluence of ions cm-2 in Figure 2 ).",
                "Therefore, in order to derive the sputtering yield, we resorted to another method based on the determination of the reduction in thin film thickness using the Fabry–Perot interference fringes observed in the infrared spectra (Dartois et al., 2020 , 2023 ), combined with QMS analysis of the gas composition.",
                "We emphasise that in order to validate this method, it was first applied to measure the thickness evolution of an irradiated thin film of CO2, for which the usual fit of the column density evolution via a differential equation was also possible.",
                "As reported in Appendix C , both methods were found to give consistent results, which are also in good agreement with the literature.",
                "In the case of \\ceH2CO, as irradiation proceeds, the ice film becomes a mixture of mainly POM and H2CO for which the refractive index () is not available.",
                "Fitting the rigorous expression for the transmission () of a thin absorbing film on a thick transparent substrate is therefore not possible.",
                "Nevertheless, transmittance spectra follow a sinusoidal pattern, where the period is proportional to the thickness.",
                "Thus, we used the following simple expression to fit the transmittance spectra in the ranges of wavenumbers () free of molecular absorptions: Here and are free parameters, is the refractive index taken as (Bouilloud et al., 2015 ), and is ice thickness.",
                "The factor corrects for the angle between the infrared beam and the sample.",
                "Fits obtained with this expression are shown in Figure 3 .",
                "The ice film is composed of POM and H2CO, with a composition changing during irradiation.",
                "Therefore, evaluating the sample mass density is challenging.",
                "Furthermore, even the mass density of a pure H2CO ice film is unknown.",
                "Consequently, it is assumed to be constant at the value for liquid formaldehyde, (Bouilloud et al., 2015 ), with an assumed uncertainty of 20%.",
                "It was used to derive the surface density of the ice , as a function of fluence, as shown in Figure 4 .",
                "The total mass sputtering yield can be directly estimated from the slope of the surface density evolution with fluence as g ion-1.",
                "It should be noted that this total yield includes all sputtered species from the considered volume, both radiolysed species (C, O, H, H2, CO, and CO2) and intact \\ceH2CO fragments.",
                "In order to determine the chemical composition of the sputtered mass volume, the various fragments ejected into the gas phase were measured with the QMS.",
                "The small residual or background signal observed before irradiation was subtracted from the recorded signal during the whole irradiation time, as reported in Figure 5 (top panel).",
                "We note that there is no intact sputtered POM as no signal is observed at =31, a mass characteristic of POM fragmentation pattern (Butscher et al., 2019 ; Duvernay et al., 2014 ).",
                "The mass =30 can be used to follow H2CO molecules since no fragment at this mass is observed in the CO fragmentation pattern (Figure 6 ).",
                "Thus, the signals at m/z=30 and m/z=28 can be used to retrieve the total number of H2CO and CO species, respectively, by dividing each m/z signal by its relative contribution in the fragmentation pattern.",
                "The remaining signals at m/z=12 and m/z=16, after subtracting the contributions of CO and H2CO, indicate the abundances of C and O atoms, respectively.",
                "Once corrected for the total electron-impact ionisation cross-section at 70 eV (energy of the QMS electron ionisation source), the relative fraction of each species with fluence is determined (Figure 5 , bottom panel).",
                "QMS measurements at very low masses are not reliable, but the amount of hydrogen (H or H2) is supposed to be equal to the sum of the amounts of C, O, and CO. We note that CO2, a minor component of the ice (see Figure 1 ), was not detected in the gas phase by the QMS.",
                "As irradiation proceeds, the composition of the film changes (Figure 2 ) and this is also observed in the gas composition (Figure 5 , bottom panel).",
                "The fraction of gaseous H2CO thus decreases significantly (by approximately 70 %) for initial fluences (up to 2 ions cm-2), which is consistent with the radiolysis and the rapid polymerisation of solid \\ceH2CO.",
                "It then decreases more gradually, before a (noisy) slightly ascending plateau is reached beyond fluences of 3 ions cm-2.",
                "Conversely, the fractions of C and O increase rapidly (by approximately 70%), but also reach a plateau.",
                "Overall, the molecular fractions of these three chemical species in the gas vary by less than a factor of two.",
                "The larger molecular fractions of CO and H2 increase up to fluences of about 2 ions cm-2 before reaching a slightly descending plateau, with variations of less than 15%.",
                "We can extract the initial fraction of each species in the gas phase (Table 5 ), and the subsequent evolution was fitted by third-order polynomials.",
                "By combining the total mass sputtering yield with the fitted molecular fractions , we can derive the sputtering yield of each ejected species , where is the Avogadro constant, is the molecular mass of species , and represents the mass fraction of species in the gas: The derived sputtering yields for the various ejected species are plotted as dashed lines in the bottom panel of Figure 5 (right -axis).",
                "Similarly to the molecular fractions, the intact sputtering yields vary by less than a factor of 2 for C, O, and H2CO, and by less than 15% for CO and H2, as expected.",
                "The average intact sputtering yields were computed over the full range of fluences and are listed in Table 5 .",
                "The average sputtering yield for intact \\ceH2CO is found to be molecules ion-1.",
                "We can now try to estimate the effective sputtering yield, .",
                "For non-polymerisable species, is usually determined using the column density evolution with fluence measured from IR spectroscopy (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ).",
                "For a pure ice , is defined as the semi-infinite thickness effective-sputtering yield for the ice under study.",
                "It includes both intact sputtered species and radiolysed (daughter) sputtered species.",
                "Since radiolysis and sputtering occur simultaneously, IR spectroscopy captures the disappearance of H2CO, regardless of whether it is sputtered intact or radiolysed.",
                "is simply related to as where is the intact fraction of sputtered H2CO.",
                "In our experiment, the volume to be sputtered just before irradiation is composed of pristine \\ceH2CO ice.",
                "The impact of a swift heavy ion induces radiolysis along its track, affecting a fraction of this volume.",
                "Therefore, after irradiation has started, the sputtered volume is composed of intact \\ceH2CO, fresh products of radiolysis as well as primary radiolytic products that accumulate in the film (see Figure 7 ).",
                "Therefore, in order to determine the effective sputtering yield , the intact fraction () of sputtered H2CO during irradiation must be estimated using the initial fractions reported in Table 3 : In practice, we derived an intact fraction of sputtered \\ceH2CO molecules =0.23, corresponding to an effective sputtering yield for the \\ceH2CO film of =(10.99.9)103 molecules ions-1.",
                "In their compendium of selected literature sputtering yields, Dartois et al.",
                "(2023 ) show that the sputtering yield induced by swift heavy ions follows an empirical law that is directly proportional to the square of the electronic stopping power : Here, using a stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam, we obtain for a pure \\ceH2CO ice =(3.12.8)10-4 1030 eV-2 cm-4 molecule3.",
                "However, most studies only have access to the effective sputtering yield , which is therefore used for in Eq.",
                "6 (e.g.",
                "Dartois et al., 2023 ).",
                "In this case, the effective prefactor value is =(1.4 1.3)10-3 1030 eV-2 cm-4 molecule3."
            ]
        },
        "6": {
            "4.1": [
                "The evolution of H2CO ice infrared (IR) spectra as a function of fluence is depicted in Figure 1 .",
                "At fluence zero, the film is made of pure H2CO, and neither paraformaldehyde nor CO or CO2 can be seen in the spectra.",
                "As soon as irradiation starts, bands characteristic of CO2 and CO appear, as well as bands around 2920, 1230, 1100, and 920 cm-1, which we attribute to the formation of an H2CO polymer (polyoxymethylene, hereafter POM).",
                "Conversely, H2CO bands decrease with fluence.",
                "Apart from CO, CO2, and POM, the infrared analysis shows no evidence of the formation of any other chemical species during the irradiation of H2CO.",
                "The column densities of CO2, CO, and H2CO were derived using the band strengths given in Table 2 and the integrated absorbance of the bands at 2343 cm-1, 2139 cm-1, and 1725 cm-1, respectively.",
                "The POM column density was calculated using a combination mode at 1105 cm-1 and a band strength of cm molecules-1 (Noble et al., 2012 ).",
                "This band strength is not known with precision (Tadokoro et al., 1963 ; Schutte et al., 1993 ), and we assumed a factor of 2 uncertainty.",
                "An additional uncertainty arises from changes in the refractive index value across strong absorbance bands, resulting in some unphysical negative absorbances after baseline correction (see e.g.",
                "the C=0 stretch of H2CO).",
                "The derived column density evolution as a function of fluence, with uncertainty zones, is presented in Figure 2 .",
                "As can be seen, the POM column density is not accurately determined, but it is consistent with a fast and efficient polymerisation of \\ceH2CO at very low fluence.",
                "Thus, at a fluence of ions cm-1, the ice is mainly composed of POM.",
                "In similar experiments on non-polymerisable ices such as \\ceCH3OH and \\ceCO2 (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ), the column density evolution with fluence can be solved through a simple differential equation involving solely radiolysis and sputtering processes (see e.g.",
                "(3) in Dartois et al., 2019 ).",
                "Here, however, we were not able to solve such a differential equation, due to the additional polymerisation process of \\ceH2CO towards POM, whose exact nature is unknown.666In particular, the number of monomers is unknown and most probably the synthesised POM is a mixture of polymers of various chain sizes.",
                "In addition, while swift ion irradiation of H2CO is responsible for the formation of POM, it also destroys POM to CO and CO2 (see the decrease in POM column density beyond a fluence of ions cm-2 in Figure 2 ).",
                "Therefore, in order to derive the sputtering yield, we resorted to another method based on the determination of the reduction in thin film thickness using the Fabry–Perot interference fringes observed in the infrared spectra (Dartois et al., 2020 , 2023 ), combined with QMS analysis of the gas composition.",
                "We emphasise that in order to validate this method, it was first applied to measure the thickness evolution of an irradiated thin film of CO2, for which the usual fit of the column density evolution via a differential equation was also possible.",
                "As reported in Appendix C , both methods were found to give consistent results, which are also in good agreement with the literature.",
                "In the case of \\ceH2CO, as irradiation proceeds, the ice film becomes a mixture of mainly POM and H2CO for which the refractive index () is not available.",
                "Fitting the rigorous expression for the transmission () of a thin absorbing film on a thick transparent substrate is therefore not possible.",
                "Nevertheless, transmittance spectra follow a sinusoidal pattern, where the period is proportional to the thickness.",
                "Thus, we used the following simple expression to fit the transmittance spectra in the ranges of wavenumbers () free of molecular absorptions: Here and are free parameters, is the refractive index taken as (Bouilloud et al., 2015 ), and is ice thickness.",
                "The factor corrects for the angle between the infrared beam and the sample.",
                "Fits obtained with this expression are shown in Figure 3 .",
                "The ice film is composed of POM and H2CO, with a composition changing during irradiation.",
                "Therefore, evaluating the sample mass density is challenging.",
                "Furthermore, even the mass density of a pure H2CO ice film is unknown.",
                "Consequently, it is assumed to be constant at the value for liquid formaldehyde, (Bouilloud et al., 2015 ), with an assumed uncertainty of 20%.",
                "It was used to derive the surface density of the ice , as a function of fluence, as shown in Figure 4 .",
                "The total mass sputtering yield can be directly estimated from the slope of the surface density evolution with fluence as g ion-1.",
                "It should be noted that this total yield includes all sputtered species from the considered volume, both radiolysed species (C, O, H, H2, CO, and CO2) and intact \\ceH2CO fragments.",
                "In order to determine the chemical composition of the sputtered mass volume, the various fragments ejected into the gas phase were measured with the QMS.",
                "The small residual or background signal observed before irradiation was subtracted from the recorded signal during the whole irradiation time, as reported in Figure 5 (top panel).",
                "We note that there is no intact sputtered POM as no signal is observed at =31, a mass characteristic of POM fragmentation pattern (Butscher et al., 2019 ; Duvernay et al., 2014 ).",
                "The mass =30 can be used to follow H2CO molecules since no fragment at this mass is observed in the CO fragmentation pattern (Figure 6 ).",
                "Thus, the signals at m/z=30 and m/z=28 can be used to retrieve the total number of H2CO and CO species, respectively, by dividing each m/z signal by its relative contribution in the fragmentation pattern.",
                "The remaining signals at m/z=12 and m/z=16, after subtracting the contributions of CO and H2CO, indicate the abundances of C and O atoms, respectively.",
                "Once corrected for the total electron-impact ionisation cross-section at 70 eV (energy of the QMS electron ionisation source), the relative fraction of each species with fluence is determined (Figure 5 , bottom panel).",
                "QMS measurements at very low masses are not reliable, but the amount of hydrogen (H or H2) is supposed to be equal to the sum of the amounts of C, O, and CO. We note that CO2, a minor component of the ice (see Figure 1 ), was not detected in the gas phase by the QMS.",
                "As irradiation proceeds, the composition of the film changes (Figure 2 ) and this is also observed in the gas composition (Figure 5 , bottom panel).",
                "The fraction of gaseous H2CO thus decreases significantly (by approximately 70 %) for initial fluences (up to 2 ions cm-2), which is consistent with the radiolysis and the rapid polymerisation of solid \\ceH2CO.",
                "It then decreases more gradually, before a (noisy) slightly ascending plateau is reached beyond fluences of 3 ions cm-2.",
                "Conversely, the fractions of C and O increase rapidly (by approximately 70%), but also reach a plateau.",
                "Overall, the molecular fractions of these three chemical species in the gas vary by less than a factor of two.",
                "The larger molecular fractions of CO and H2 increase up to fluences of about 2 ions cm-2 before reaching a slightly descending plateau, with variations of less than 15%.",
                "We can extract the initial fraction of each species in the gas phase (Table 5 ), and the subsequent evolution was fitted by third-order polynomials.",
                "By combining the total mass sputtering yield with the fitted molecular fractions , we can derive the sputtering yield of each ejected species , where is the Avogadro constant, is the molecular mass of species , and represents the mass fraction of species in the gas: The derived sputtering yields for the various ejected species are plotted as dashed lines in the bottom panel of Figure 5 (right -axis).",
                "Similarly to the molecular fractions, the intact sputtering yields vary by less than a factor of 2 for C, O, and H2CO, and by less than 15% for CO and H2, as expected.",
                "The average intact sputtering yields were computed over the full range of fluences and are listed in Table 5 .",
                "The average sputtering yield for intact \\ceH2CO is found to be molecules ion-1.",
                "We can now try to estimate the effective sputtering yield, .",
                "For non-polymerisable species, is usually determined using the column density evolution with fluence measured from IR spectroscopy (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ).",
                "For a pure ice , is defined as the semi-infinite thickness effective-sputtering yield for the ice under study.",
                "It includes both intact sputtered species and radiolysed (daughter) sputtered species.",
                "Since radiolysis and sputtering occur simultaneously, IR spectroscopy captures the disappearance of H2CO, regardless of whether it is sputtered intact or radiolysed.",
                "is simply related to as where is the intact fraction of sputtered H2CO.",
                "In our experiment, the volume to be sputtered just before irradiation is composed of pristine \\ceH2CO ice.",
                "The impact of a swift heavy ion induces radiolysis along its track, affecting a fraction of this volume.",
                "Therefore, after irradiation has started, the sputtered volume is composed of intact \\ceH2CO, fresh products of radiolysis as well as primary radiolytic products that accumulate in the film (see Figure 7 ).",
                "Therefore, in order to determine the effective sputtering yield , the intact fraction () of sputtered H2CO during irradiation must be estimated using the initial fractions reported in Table 3 : In practice, we derived an intact fraction of sputtered \\ceH2CO molecules =0.23, corresponding to an effective sputtering yield for the \\ceH2CO film of =(10.99.9)103 molecules ions-1.",
                "In their compendium of selected literature sputtering yields, Dartois et al.",
                "(2023 ) show that the sputtering yield induced by swift heavy ions follows an empirical law that is directly proportional to the square of the electronic stopping power : Here, using a stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam, we obtain for a pure \\ceH2CO ice =(3.12.8)10-4 1030 eV-2 cm-4 molecule3.",
                "However, most studies only have access to the effective sputtering yield , which is therefore used for in Eq.",
                "6 (e.g.",
                "Dartois et al., 2023 ).",
                "In this case, the effective prefactor value is =(1.4 1.3)10-3 1030 eV-2 cm-4 molecule3."
            ]
        },
        "7": {
            "4.1": [
                "The evolution of H2CO ice infrared (IR) spectra as a function of fluence is depicted in Figure 1 .",
                "At fluence zero, the film is made of pure H2CO, and neither paraformaldehyde nor CO or CO2 can be seen in the spectra.",
                "As soon as irradiation starts, bands characteristic of CO2 and CO appear, as well as bands around 2920, 1230, 1100, and 920 cm-1, which we attribute to the formation of an H2CO polymer (polyoxymethylene, hereafter POM).",
                "Conversely, H2CO bands decrease with fluence.",
                "Apart from CO, CO2, and POM, the infrared analysis shows no evidence of the formation of any other chemical species during the irradiation of H2CO.",
                "The column densities of CO2, CO, and H2CO were derived using the band strengths given in Table 2 and the integrated absorbance of the bands at 2343 cm-1, 2139 cm-1, and 1725 cm-1, respectively.",
                "The POM column density was calculated using a combination mode at 1105 cm-1 and a band strength of cm molecules-1 (Noble et al., 2012 ).",
                "This band strength is not known with precision (Tadokoro et al., 1963 ; Schutte et al., 1993 ), and we assumed a factor of 2 uncertainty.",
                "An additional uncertainty arises from changes in the refractive index value across strong absorbance bands, resulting in some unphysical negative absorbances after baseline correction (see e.g.",
                "the C=0 stretch of H2CO).",
                "The derived column density evolution as a function of fluence, with uncertainty zones, is presented in Figure 2 .",
                "As can be seen, the POM column density is not accurately determined, but it is consistent with a fast and efficient polymerisation of \\ceH2CO at very low fluence.",
                "Thus, at a fluence of ions cm-1, the ice is mainly composed of POM.",
                "In similar experiments on non-polymerisable ices such as \\ceCH3OH and \\ceCO2 (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ), the column density evolution with fluence can be solved through a simple differential equation involving solely radiolysis and sputtering processes (see e.g.",
                "(3) in Dartois et al., 2019 ).",
                "Here, however, we were not able to solve such a differential equation, due to the additional polymerisation process of \\ceH2CO towards POM, whose exact nature is unknown.666In particular, the number of monomers is unknown and most probably the synthesised POM is a mixture of polymers of various chain sizes.",
                "In addition, while swift ion irradiation of H2CO is responsible for the formation of POM, it also destroys POM to CO and CO2 (see the decrease in POM column density beyond a fluence of ions cm-2 in Figure 2 ).",
                "Therefore, in order to derive the sputtering yield, we resorted to another method based on the determination of the reduction in thin film thickness using the Fabry–Perot interference fringes observed in the infrared spectra (Dartois et al., 2020 , 2023 ), combined with QMS analysis of the gas composition.",
                "We emphasise that in order to validate this method, it was first applied to measure the thickness evolution of an irradiated thin film of CO2, for which the usual fit of the column density evolution via a differential equation was also possible.",
                "As reported in Appendix C , both methods were found to give consistent results, which are also in good agreement with the literature.",
                "In the case of \\ceH2CO, as irradiation proceeds, the ice film becomes a mixture of mainly POM and H2CO for which the refractive index () is not available.",
                "Fitting the rigorous expression for the transmission () of a thin absorbing film on a thick transparent substrate is therefore not possible.",
                "Nevertheless, transmittance spectra follow a sinusoidal pattern, where the period is proportional to the thickness.",
                "Thus, we used the following simple expression to fit the transmittance spectra in the ranges of wavenumbers () free of molecular absorptions: Here and are free parameters, is the refractive index taken as (Bouilloud et al., 2015 ), and is ice thickness.",
                "The factor corrects for the angle between the infrared beam and the sample.",
                "Fits obtained with this expression are shown in Figure 3 .",
                "The ice film is composed of POM and H2CO, with a composition changing during irradiation.",
                "Therefore, evaluating the sample mass density is challenging.",
                "Furthermore, even the mass density of a pure H2CO ice film is unknown.",
                "Consequently, it is assumed to be constant at the value for liquid formaldehyde, (Bouilloud et al., 2015 ), with an assumed uncertainty of 20%.",
                "It was used to derive the surface density of the ice , as a function of fluence, as shown in Figure 4 .",
                "The total mass sputtering yield can be directly estimated from the slope of the surface density evolution with fluence as g ion-1.",
                "It should be noted that this total yield includes all sputtered species from the considered volume, both radiolysed species (C, O, H, H2, CO, and CO2) and intact \\ceH2CO fragments.",
                "In order to determine the chemical composition of the sputtered mass volume, the various fragments ejected into the gas phase were measured with the QMS.",
                "The small residual or background signal observed before irradiation was subtracted from the recorded signal during the whole irradiation time, as reported in Figure 5 (top panel).",
                "We note that there is no intact sputtered POM as no signal is observed at =31, a mass characteristic of POM fragmentation pattern (Butscher et al., 2019 ; Duvernay et al., 2014 ).",
                "The mass =30 can be used to follow H2CO molecules since no fragment at this mass is observed in the CO fragmentation pattern (Figure 6 ).",
                "Thus, the signals at m/z=30 and m/z=28 can be used to retrieve the total number of H2CO and CO species, respectively, by dividing each m/z signal by its relative contribution in the fragmentation pattern.",
                "The remaining signals at m/z=12 and m/z=16, after subtracting the contributions of CO and H2CO, indicate the abundances of C and O atoms, respectively.",
                "Once corrected for the total electron-impact ionisation cross-section at 70 eV (energy of the QMS electron ionisation source), the relative fraction of each species with fluence is determined (Figure 5 , bottom panel).",
                "QMS measurements at very low masses are not reliable, but the amount of hydrogen (H or H2) is supposed to be equal to the sum of the amounts of C, O, and CO. We note that CO2, a minor component of the ice (see Figure 1 ), was not detected in the gas phase by the QMS.",
                "As irradiation proceeds, the composition of the film changes (Figure 2 ) and this is also observed in the gas composition (Figure 5 , bottom panel).",
                "The fraction of gaseous H2CO thus decreases significantly (by approximately 70 %) for initial fluences (up to 2 ions cm-2), which is consistent with the radiolysis and the rapid polymerisation of solid \\ceH2CO.",
                "It then decreases more gradually, before a (noisy) slightly ascending plateau is reached beyond fluences of 3 ions cm-2.",
                "Conversely, the fractions of C and O increase rapidly (by approximately 70%), but also reach a plateau.",
                "Overall, the molecular fractions of these three chemical species in the gas vary by less than a factor of two.",
                "The larger molecular fractions of CO and H2 increase up to fluences of about 2 ions cm-2 before reaching a slightly descending plateau, with variations of less than 15%.",
                "We can extract the initial fraction of each species in the gas phase (Table 5 ), and the subsequent evolution was fitted by third-order polynomials.",
                "By combining the total mass sputtering yield with the fitted molecular fractions , we can derive the sputtering yield of each ejected species , where is the Avogadro constant, is the molecular mass of species , and represents the mass fraction of species in the gas: The derived sputtering yields for the various ejected species are plotted as dashed lines in the bottom panel of Figure 5 (right -axis).",
                "Similarly to the molecular fractions, the intact sputtering yields vary by less than a factor of 2 for C, O, and H2CO, and by less than 15% for CO and H2, as expected.",
                "The average intact sputtering yields were computed over the full range of fluences and are listed in Table 5 .",
                "The average sputtering yield for intact \\ceH2CO is found to be molecules ion-1.",
                "We can now try to estimate the effective sputtering yield, .",
                "For non-polymerisable species, is usually determined using the column density evolution with fluence measured from IR spectroscopy (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ).",
                "For a pure ice , is defined as the semi-infinite thickness effective-sputtering yield for the ice under study.",
                "It includes both intact sputtered species and radiolysed (daughter) sputtered species.",
                "Since radiolysis and sputtering occur simultaneously, IR spectroscopy captures the disappearance of H2CO, regardless of whether it is sputtered intact or radiolysed.",
                "is simply related to as where is the intact fraction of sputtered H2CO.",
                "In our experiment, the volume to be sputtered just before irradiation is composed of pristine \\ceH2CO ice.",
                "The impact of a swift heavy ion induces radiolysis along its track, affecting a fraction of this volume.",
                "Therefore, after irradiation has started, the sputtered volume is composed of intact \\ceH2CO, fresh products of radiolysis as well as primary radiolytic products that accumulate in the film (see Figure 7 ).",
                "Therefore, in order to determine the effective sputtering yield , the intact fraction () of sputtered H2CO during irradiation must be estimated using the initial fractions reported in Table 3 : In practice, we derived an intact fraction of sputtered \\ceH2CO molecules =0.23, corresponding to an effective sputtering yield for the \\ceH2CO film of =(10.99.9)103 molecules ions-1.",
                "In their compendium of selected literature sputtering yields, Dartois et al.",
                "(2023 ) show that the sputtering yield induced by swift heavy ions follows an empirical law that is directly proportional to the square of the electronic stopping power : Here, using a stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam, we obtain for a pure \\ceH2CO ice =(3.12.8)10-4 1030 eV-2 cm-4 molecule3.",
                "However, most studies only have access to the effective sputtering yield , which is therefore used for in Eq.",
                "6 (e.g.",
                "Dartois et al., 2023 ).",
                "In this case, the effective prefactor value is =(1.4 1.3)10-3 1030 eV-2 cm-4 molecule3."
            ]
        },
        "8": {},
        "9": {
            "5.2": [
                "The external UV photodesorption rate can be written as where is the external interstellar far-UV radiation field (averaged between 6 and 13.6 eV) of photons cm-2 s-1 (Habing, 1968 ); is the visual extinction; is a measure of UV extinction relative to visual extinction, which is about 2 for interstellar grains (Roberge et al., 1991 ); and is the photodesorption yield of H2CO (in molecules photon-1).",
                "The last value was recently determined in the laboratory by Féraud et al.",
                "(2019 ), who were able to derive an intact H2CO photodesorption yield of molecule/photon in various astrophysical environments, including interstellar clouds and prestellar cores (see their Table 1).",
                "In the following we use an average experimental yield of molecule/photon for the photodesorption of intact H2CO.",
                "The cosmic-ray induced UV photodesorption rate can be written as where is now the internal UV field induced by the cosmic-ray excitation of H2, which was taken as , where is the rate of cosmic-ray ionisation of molecular hydrogen in units of s-1 (see the definition of below).",
                "This simple relation between and was deduced from Figure 4 of Shen et al.",
                "(2004 ), with computed using Eqs.",
                "16 -17 below.",
                "Finally, the direct cosmic-ray sputtering rate is computed by summing and integrating the product of the sputtering yield with the differential cosmic-ray flux : Here is the kinetic energy per nucleon, is the atomic number of the cosmic-ray nuclei, and is the sputtering yield in H2CO/ion obtained by combining the experimental yield for intact sputtering with the calculated electronic stopping power .",
                "It is multiplied by a factor of 2 to account for the entrance and exit points of the cosmic-rays through the grain.",
                "Assuming a quadratic dependence of with the stopping power, as in Eq.",
                "6 , the intact sputtering yield of H2CO molecules can be described as where we combined molecules ion-1 (see Table 3 ) with the stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam.",
                "In order to compute for a range of kinetic energies (see below), the SRIM-2013 code was used to compute the electronic stopping powers for an H2CO ice density of 0.81 g cm-3 and for the cosmic elements with the largest contributions, accounting for the scaling of the sputtering yields (Dartois et al., 2023 ).",
                "In practice, the 15 ions of H, He, C, O, Ne, Mg, Si, S, Ca, Ti, V, Cr, Mn, Fe, and Ni were included using the fractional abundances of Kalvāns (2016 , their Table 1).",
                "It should be noted that iron, despite its low fractional abundance, gives the largest contribution (%) to the rate, as already found by Seperuelo Duarte et al.",
                "(2010 ) for CO ice.",
                "For the differential cosmic-ray flux (in particles cm-2 s-1 sr-1 (MeV/amu)-1) we adopted the functional form proposed by Webber & Yushak (1983 ) where is a normalising constant and a form parameter that varies between 0 and 940 MeV.",
                "This formulation corresponds to a primary spectrum since it neglects the energy-loss of cosmic rays through the dense interstellar gas.",
                "It allows, however, the full range of measured ionisation rates to be explored, from standard diffuse clouds (a few s-1) to dense clouds (a few s-1), by simply varying the parameter .",
                "In order to infer the relation between and , the ionisation rate was computed as in Faure et al.",
                "(2019 , their Appendix A): Here is the cross-section for ionisation of H2 by proton impact, is a correction factor accounting for the contribution of secondary electrons to ionisation, and where is the correction factor for heavy nuclei ionisation.",
                "Full details and references can be found in Appendix A of Faure et al.",
                "(2019 ).",
                "In practice, the parameter in Eq.",
                "(16 ) was taken in the range 200900 MeV so that was explored in the range s-1.",
                "The integrals in Eqs.",
                "(14 ) and (17 ) were evaluated numerically from eV/amu to GeV/amu.",
                "The calibration plot between the intact sputtering rate of \\ceH2CO and the ionisation rate is displayed in Figure 9 (black curve), where is found to scale linearly with the ionisation rate.",
                "We note that although the low-energy content ( MeV) of the cosmic-ray spectrum is poorly constrained, the relation between and was found to be quite robust.",
                "It is now interesting to compare the sputtering rate of H2CO with those of the main ice components of interstellar grains, that is H2O, CO, and CO2, where the latter two have a typical abundance of 20-30% with respect to H2O.",
                "Trace ice species such as NH3, CH4, H2CO, and CH3OH are expected to be embedded in H2O-rich, CO-rich, or CO2-rich layers.",
                "We assume that the intact sputtering yield of the trapped molecule is equal to the effective sputtering yield of the ice matrix.",
                "Simplistic but intuitive, this hypothesis is actually supported by irradiation experiments performed on methanol diluted in H2O and CO2 ice matrices, although the intact sputtering efficiency depends on the dilution factor121212Because \\ceH2CO easily polymerises, segregation effects could also play a role and reduce the intact sputtering efficiency.",
                "(see the detailed discussions in Dartois et al., 2019 , 2020 ).",
                "We note that the effective sputtering yield of either water or CO2 was similarly employed to model the cosmic-ray induced sputtering of \\ceCH3OH in cold molecular cores (Wakelam et al., 2021 ; Paulive et al., 2022 ).",
                "The above procedure was thus applied to pure CO, CO2, and H2O ices using the effective sputtering yield pre-factors reported in Table 1 of Dartois et al.",
                "(2023 ) with ice densities (needed to compute ) of 0.88 g cm-3, 1.0 g cm-3, and 0.94 g cm-3, respectively (Luna et al., 2022 ; Satorre et al., 2008 ; Bouilloud et al., 2015 ).",
                "The corresponding sputtering rates as functions of are shown in Figure 9 .",
                "As expected, our results for CO, CO2, and H2O are in very good agreement with those of Dartois et al.",
                "(2023 , see their Figure 5).",
                "We can also observe that the intact sputtering rate of pure H2CO is a factor of 10-100 lower than the effective sputtering rates of H2O, CO, and CO2.",
                "For convenient use in astrochemical models, simple linear fits of the sputtering rates shown in Figure 9 were performed over the range s-1.",
                "These fits are reported in Table 5 ."
            ]
        },
        "10": {
            "5.3": [
                "Because the total abundance of formaldehyde is conserved, we have By combining Eqs.",
                "(8 -10 ) and (19 ), we obtain Since in practice and substituting , where is the mass of H2CO, the H2CO gas-phase fractional abundance, , takes the simple form where is the H2CO total fractional abundance, taken as (see above).",
                "The total fractional abundance of ices, , is unknown in L1689B, but again we can assume typical ice abundances in LYSOS, as compiled by Boogert et al.",
                "(2015 , their Table 2).",
                "By including ‘securely’, ‘likely’, and ‘possibly’ identified species, we obtain .",
                "Finally, using the physical conditions derived from H2CO emission in L1689B (i.e.",
                "K and cm-3), we obtain numerically: In order to reproduce the measured abundance in L1689B (), a total desorption rate molecules cm2s-1 is required.",
                "We compare in Figure 10 the observational abundance to our predictions from the above analytical model, assuming the cosmic-ray ionisation rate is s-1 (i.e.",
                "), which is the typical ionisation rate in molecular clouds, where (see Figure 19 in Indriolo & McCall, 2012 ).",
                "Five different models are presented: desorption is either due to external and internal photons only (in orange) or to both photons and direct cosmic-ray sputtering, assuming H2CO ices are pure (in black) or embedded in H2O-rich (in blue), CO2-rich (in red), or CO-rich (in green) matrices.",
                "We can observe that photodesorption alone cannot explain the gas phase abundance of H2CO in L1689B and that direct cosmic-ray sputtering is much more efficient, except in the case of a pure H2CO ice.",
                "In particular, cosmic-ray sputtering of H2CO from CO-rich or CO2-rich ices can reproduce the gas phase abundance measured towards L1689B to within a factor of 3.",
                "Interestingly, this result is consistent with observational evidence that catastrophic CO freeze-out occurs at and cm-3, where CO hydrogenation may form a CH3OH-rich layer including H2CO and new CO2 molecules (Boogert et al., 2015 ).",
                "It is also possible that part of the interstellar H2CO forms in the gas phase, for example via the barrierless reaction CH3 + O (see e.g.",
                "Terwisscha van Scheltinga et al., 2021 ).",
                "Thus, while the present results emphasise the potential role of direct cosmic-ray sputtering of H2CO molecules from CO-rich or CO2-rich ices, the importance of gas-phase formation and destruction of \\ceH2CO will need to be explored in future works.",
                "Finally, we note that the \\ceH2CO gas-phase abundance in L1689B corresponds to about 0.02% of the total (gas and ice) \\ceH2CO abundance.",
                "In summary, our simple model shows that the yields for experimentally determined direct cosmic-ray sputtering are large enough to release significant amounts of \\ceH2CO ice into the gas-phase, provided that \\ceH2CO is embedded in CO-rich or \\ceCO2-rich ice mantles and that \\ceH2CO molecules co-desorbwith the matrix (i.e.",
                "with the same yield).",
                "Obviously, further experiments with mixed ices (e.g.",
                "\\ceH2CO:CO), as well as more comprehensive (time-dependent and density-dependent) astrochemical models are needed to confirm these results."
            ]
        },
        "11": {},
        "12": {},
        "13": {},
        "14": {},
        "15": {},
        "16": {},
        "17": {}
    },
    "extract_table_info": {
        "1": {
            "5.2": [
                "The external UV photodesorption rate can be written as where is the external interstellar far-UV radiation field (averaged between 6 and 13.6 eV) of photons cm-2 s-1 (Habing, 1968 ); is the visual extinction; is a measure of UV extinction relative to visual extinction, which is about 2 for interstellar grains (Roberge et al., 1991 ); and is the photodesorption yield of H2CO (in molecules photon-1).",
                "The last value was recently determined in the laboratory by Féraud et al.",
                "(2019 ), who were able to derive an intact H2CO photodesorption yield of molecule/photon in various astrophysical environments, including interstellar clouds and prestellar cores (see their Table 1).",
                "In the following we use an average experimental yield of molecule/photon for the photodesorption of intact H2CO.",
                "The cosmic-ray induced UV photodesorption rate can be written as where is now the internal UV field induced by the cosmic-ray excitation of H2, which was taken as , where is the rate of cosmic-ray ionisation of molecular hydrogen in units of s-1 (see the definition of below).",
                "This simple relation between and was deduced from Figure 4 of Shen et al.",
                "(2004 ), with computed using Eqs.",
                "16 -17 below.",
                "Finally, the direct cosmic-ray sputtering rate is computed by summing and integrating the product of the sputtering yield with the differential cosmic-ray flux : Here is the kinetic energy per nucleon, is the atomic number of the cosmic-ray nuclei, and is the sputtering yield in H2CO/ion obtained by combining the experimental yield for intact sputtering with the calculated electronic stopping power .",
                "It is multiplied by a factor of 2 to account for the entrance and exit points of the cosmic-rays through the grain.",
                "Assuming a quadratic dependence of with the stopping power, as in Eq.",
                "6 , the intact sputtering yield of H2CO molecules can be described as where we combined molecules ion-1 (see Table 3 ) with the stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam.",
                "In order to compute for a range of kinetic energies (see below), the SRIM-2013 code was used to compute the electronic stopping powers for an H2CO ice density of 0.81 g cm-3 and for the cosmic elements with the largest contributions, accounting for the scaling of the sputtering yields (Dartois et al., 2023 ).",
                "In practice, the 15 ions of H, He, C, O, Ne, Mg, Si, S, Ca, Ti, V, Cr, Mn, Fe, and Ni were included using the fractional abundances of Kalvāns (2016 , their Table 1).",
                "It should be noted that iron, despite its low fractional abundance, gives the largest contribution (%) to the rate, as already found by Seperuelo Duarte et al.",
                "(2010 ) for CO ice.",
                "For the differential cosmic-ray flux (in particles cm-2 s-1 sr-1 (MeV/amu)-1) we adopted the functional form proposed by Webber & Yushak (1983 ) where is a normalising constant and a form parameter that varies between 0 and 940 MeV.",
                "This formulation corresponds to a primary spectrum since it neglects the energy-loss of cosmic rays through the dense interstellar gas.",
                "It allows, however, the full range of measured ionisation rates to be explored, from standard diffuse clouds (a few s-1) to dense clouds (a few s-1), by simply varying the parameter .",
                "In order to infer the relation between and , the ionisation rate was computed as in Faure et al.",
                "(2019 , their Appendix A): Here is the cross-section for ionisation of H2 by proton impact, is a correction factor accounting for the contribution of secondary electrons to ionisation, and where is the correction factor for heavy nuclei ionisation.",
                "Full details and references can be found in Appendix A of Faure et al.",
                "(2019 ).",
                "In practice, the parameter in Eq.",
                "(16 ) was taken in the range 200900 MeV so that was explored in the range s-1.",
                "The integrals in Eqs.",
                "(14 ) and (17 ) were evaluated numerically from eV/amu to GeV/amu.",
                "The calibration plot between the intact sputtering rate of \\ceH2CO and the ionisation rate is displayed in Figure 9 (black curve), where is found to scale linearly with the ionisation rate.",
                "We note that although the low-energy content ( MeV) of the cosmic-ray spectrum is poorly constrained, the relation between and was found to be quite robust.",
                "It is now interesting to compare the sputtering rate of H2CO with those of the main ice components of interstellar grains, that is H2O, CO, and CO2, where the latter two have a typical abundance of 20-30% with respect to H2O.",
                "Trace ice species such as NH3, CH4, H2CO, and CH3OH are expected to be embedded in H2O-rich, CO-rich, or CO2-rich layers.",
                "We assume that the intact sputtering yield of the trapped molecule is equal to the effective sputtering yield of the ice matrix.",
                "Simplistic but intuitive, this hypothesis is actually supported by irradiation experiments performed on methanol diluted in H2O and CO2 ice matrices, although the intact sputtering efficiency depends on the dilution factor121212Because \\ceH2CO easily polymerises, segregation effects could also play a role and reduce the intact sputtering efficiency.",
                "(see the detailed discussions in Dartois et al., 2019 , 2020 ).",
                "We note that the effective sputtering yield of either water or CO2 was similarly employed to model the cosmic-ray induced sputtering of \\ceCH3OH in cold molecular cores (Wakelam et al., 2021 ; Paulive et al., 2022 ).",
                "The above procedure was thus applied to pure CO, CO2, and H2O ices using the effective sputtering yield pre-factors reported in Table 1 of Dartois et al.",
                "(2023 ) with ice densities (needed to compute ) of 0.88 g cm-3, 1.0 g cm-3, and 0.94 g cm-3, respectively (Luna et al., 2022 ; Satorre et al., 2008 ; Bouilloud et al., 2015 ).",
                "The corresponding sputtering rates as functions of are shown in Figure 9 .",
                "As expected, our results for CO, CO2, and H2O are in very good agreement with those of Dartois et al.",
                "(2023 , see their Figure 5).",
                "We can also observe that the intact sputtering rate of pure H2CO is a factor of 10-100 lower than the effective sputtering rates of H2O, CO, and CO2.",
                "For convenient use in astrochemical models, simple linear fits of the sputtering rates shown in Figure 9 were performed over the range s-1.",
                "These fits are reported in Table 5 ."
            ]
        },
        "2": {
            "5.3": [
                "Because the total abundance of formaldehyde is conserved, we have By combining Eqs.",
                "(8 -10 ) and (19 ), we obtain Since in practice and substituting , where is the mass of H2CO, the H2CO gas-phase fractional abundance, , takes the simple form where is the H2CO total fractional abundance, taken as (see above).",
                "The total fractional abundance of ices, , is unknown in L1689B, but again we can assume typical ice abundances in LYSOS, as compiled by Boogert et al.",
                "(2015 , their Table 2).",
                "By including ‘securely’, ‘likely’, and ‘possibly’ identified species, we obtain .",
                "Finally, using the physical conditions derived from H2CO emission in L1689B (i.e.",
                "K and cm-3), we obtain numerically: In order to reproduce the measured abundance in L1689B (), a total desorption rate molecules cm2s-1 is required.",
                "We compare in Figure 10 the observational abundance to our predictions from the above analytical model, assuming the cosmic-ray ionisation rate is s-1 (i.e.",
                "), which is the typical ionisation rate in molecular clouds, where (see Figure 19 in Indriolo & McCall, 2012 ).",
                "Five different models are presented: desorption is either due to external and internal photons only (in orange) or to both photons and direct cosmic-ray sputtering, assuming H2CO ices are pure (in black) or embedded in H2O-rich (in blue), CO2-rich (in red), or CO-rich (in green) matrices.",
                "We can observe that photodesorption alone cannot explain the gas phase abundance of H2CO in L1689B and that direct cosmic-ray sputtering is much more efficient, except in the case of a pure H2CO ice.",
                "In particular, cosmic-ray sputtering of H2CO from CO-rich or CO2-rich ices can reproduce the gas phase abundance measured towards L1689B to within a factor of 3.",
                "Interestingly, this result is consistent with observational evidence that catastrophic CO freeze-out occurs at and cm-3, where CO hydrogenation may form a CH3OH-rich layer including H2CO and new CO2 molecules (Boogert et al., 2015 ).",
                "It is also possible that part of the interstellar H2CO forms in the gas phase, for example via the barrierless reaction CH3 + O (see e.g.",
                "Terwisscha van Scheltinga et al., 2021 ).",
                "Thus, while the present results emphasise the potential role of direct cosmic-ray sputtering of H2CO molecules from CO-rich or CO2-rich ices, the importance of gas-phase formation and destruction of \\ceH2CO will need to be explored in future works.",
                "Finally, we note that the \\ceH2CO gas-phase abundance in L1689B corresponds to about 0.02% of the total (gas and ice) \\ceH2CO abundance.",
                "In summary, our simple model shows that the yields for experimentally determined direct cosmic-ray sputtering are large enough to release significant amounts of \\ceH2CO ice into the gas-phase, provided that \\ceH2CO is embedded in CO-rich or \\ceCO2-rich ice mantles and that \\ceH2CO molecules co-desorbwith the matrix (i.e.",
                "with the same yield).",
                "Obviously, further experiments with mixed ices (e.g.",
                "\\ceH2CO:CO), as well as more comprehensive (time-dependent and density-dependent) astrochemical models are needed to confirm these results."
            ]
        },
        "3": {
            "4.1": [
                "The evolution of H2CO ice infrared (IR) spectra as a function of fluence is depicted in Figure 1 .",
                "At fluence zero, the film is made of pure H2CO, and neither paraformaldehyde nor CO or CO2 can be seen in the spectra.",
                "As soon as irradiation starts, bands characteristic of CO2 and CO appear, as well as bands around 2920, 1230, 1100, and 920 cm-1, which we attribute to the formation of an H2CO polymer (polyoxymethylene, hereafter POM).",
                "Conversely, H2CO bands decrease with fluence.",
                "Apart from CO, CO2, and POM, the infrared analysis shows no evidence of the formation of any other chemical species during the irradiation of H2CO.",
                "The column densities of CO2, CO, and H2CO were derived using the band strengths given in Table 2 and the integrated absorbance of the bands at 2343 cm-1, 2139 cm-1, and 1725 cm-1, respectively.",
                "The POM column density was calculated using a combination mode at 1105 cm-1 and a band strength of cm molecules-1 (Noble et al., 2012 ).",
                "This band strength is not known with precision (Tadokoro et al., 1963 ; Schutte et al., 1993 ), and we assumed a factor of 2 uncertainty.",
                "An additional uncertainty arises from changes in the refractive index value across strong absorbance bands, resulting in some unphysical negative absorbances after baseline correction (see e.g.",
                "the C=0 stretch of H2CO).",
                "The derived column density evolution as a function of fluence, with uncertainty zones, is presented in Figure 2 .",
                "As can be seen, the POM column density is not accurately determined, but it is consistent with a fast and efficient polymerisation of \\ceH2CO at very low fluence.",
                "Thus, at a fluence of ions cm-1, the ice is mainly composed of POM.",
                "In similar experiments on non-polymerisable ices such as \\ceCH3OH and \\ceCO2 (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ), the column density evolution with fluence can be solved through a simple differential equation involving solely radiolysis and sputtering processes (see e.g.",
                "(3) in Dartois et al., 2019 ).",
                "Here, however, we were not able to solve such a differential equation, due to the additional polymerisation process of \\ceH2CO towards POM, whose exact nature is unknown.666In particular, the number of monomers is unknown and most probably the synthesised POM is a mixture of polymers of various chain sizes.",
                "In addition, while swift ion irradiation of H2CO is responsible for the formation of POM, it also destroys POM to CO and CO2 (see the decrease in POM column density beyond a fluence of ions cm-2 in Figure 2 ).",
                "Therefore, in order to derive the sputtering yield, we resorted to another method based on the determination of the reduction in thin film thickness using the Fabry–Perot interference fringes observed in the infrared spectra (Dartois et al., 2020 , 2023 ), combined with QMS analysis of the gas composition.",
                "We emphasise that in order to validate this method, it was first applied to measure the thickness evolution of an irradiated thin film of CO2, for which the usual fit of the column density evolution via a differential equation was also possible.",
                "As reported in Appendix C , both methods were found to give consistent results, which are also in good agreement with the literature.",
                "In the case of \\ceH2CO, as irradiation proceeds, the ice film becomes a mixture of mainly POM and H2CO for which the refractive index () is not available.",
                "Fitting the rigorous expression for the transmission () of a thin absorbing film on a thick transparent substrate is therefore not possible.",
                "Nevertheless, transmittance spectra follow a sinusoidal pattern, where the period is proportional to the thickness.",
                "Thus, we used the following simple expression to fit the transmittance spectra in the ranges of wavenumbers () free of molecular absorptions: Here and are free parameters, is the refractive index taken as (Bouilloud et al., 2015 ), and is ice thickness.",
                "The factor corrects for the angle between the infrared beam and the sample.",
                "Fits obtained with this expression are shown in Figure 3 .",
                "The ice film is composed of POM and H2CO, with a composition changing during irradiation.",
                "Therefore, evaluating the sample mass density is challenging.",
                "Furthermore, even the mass density of a pure H2CO ice film is unknown.",
                "Consequently, it is assumed to be constant at the value for liquid formaldehyde, (Bouilloud et al., 2015 ), with an assumed uncertainty of 20%.",
                "It was used to derive the surface density of the ice , as a function of fluence, as shown in Figure 4 .",
                "The total mass sputtering yield can be directly estimated from the slope of the surface density evolution with fluence as g ion-1.",
                "It should be noted that this total yield includes all sputtered species from the considered volume, both radiolysed species (C, O, H, H2, CO, and CO2) and intact \\ceH2CO fragments.",
                "In order to determine the chemical composition of the sputtered mass volume, the various fragments ejected into the gas phase were measured with the QMS.",
                "The small residual or background signal observed before irradiation was subtracted from the recorded signal during the whole irradiation time, as reported in Figure 5 (top panel).",
                "We note that there is no intact sputtered POM as no signal is observed at =31, a mass characteristic of POM fragmentation pattern (Butscher et al., 2019 ; Duvernay et al., 2014 ).",
                "The mass =30 can be used to follow H2CO molecules since no fragment at this mass is observed in the CO fragmentation pattern (Figure 6 ).",
                "Thus, the signals at m/z=30 and m/z=28 can be used to retrieve the total number of H2CO and CO species, respectively, by dividing each m/z signal by its relative contribution in the fragmentation pattern.",
                "The remaining signals at m/z=12 and m/z=16, after subtracting the contributions of CO and H2CO, indicate the abundances of C and O atoms, respectively.",
                "Once corrected for the total electron-impact ionisation cross-section at 70 eV (energy of the QMS electron ionisation source), the relative fraction of each species with fluence is determined (Figure 5 , bottom panel).",
                "QMS measurements at very low masses are not reliable, but the amount of hydrogen (H or H2) is supposed to be equal to the sum of the amounts of C, O, and CO. We note that CO2, a minor component of the ice (see Figure 1 ), was not detected in the gas phase by the QMS.",
                "As irradiation proceeds, the composition of the film changes (Figure 2 ) and this is also observed in the gas composition (Figure 5 , bottom panel).",
                "The fraction of gaseous H2CO thus decreases significantly (by approximately 70 %) for initial fluences (up to 2 ions cm-2), which is consistent with the radiolysis and the rapid polymerisation of solid \\ceH2CO.",
                "It then decreases more gradually, before a (noisy) slightly ascending plateau is reached beyond fluences of 3 ions cm-2.",
                "Conversely, the fractions of C and O increase rapidly (by approximately 70%), but also reach a plateau.",
                "Overall, the molecular fractions of these three chemical species in the gas vary by less than a factor of two.",
                "The larger molecular fractions of CO and H2 increase up to fluences of about 2 ions cm-2 before reaching a slightly descending plateau, with variations of less than 15%.",
                "We can extract the initial fraction of each species in the gas phase (Table 5 ), and the subsequent evolution was fitted by third-order polynomials.",
                "By combining the total mass sputtering yield with the fitted molecular fractions , we can derive the sputtering yield of each ejected species , where is the Avogadro constant, is the molecular mass of species , and represents the mass fraction of species in the gas: The derived sputtering yields for the various ejected species are plotted as dashed lines in the bottom panel of Figure 5 (right -axis).",
                "Similarly to the molecular fractions, the intact sputtering yields vary by less than a factor of 2 for C, O, and H2CO, and by less than 15% for CO and H2, as expected.",
                "The average intact sputtering yields were computed over the full range of fluences and are listed in Table 5 .",
                "The average sputtering yield for intact \\ceH2CO is found to be molecules ion-1.",
                "We can now try to estimate the effective sputtering yield, .",
                "For non-polymerisable species, is usually determined using the column density evolution with fluence measured from IR spectroscopy (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ).",
                "For a pure ice , is defined as the semi-infinite thickness effective-sputtering yield for the ice under study.",
                "It includes both intact sputtered species and radiolysed (daughter) sputtered species.",
                "Since radiolysis and sputtering occur simultaneously, IR spectroscopy captures the disappearance of H2CO, regardless of whether it is sputtered intact or radiolysed.",
                "is simply related to as where is the intact fraction of sputtered H2CO.",
                "In our experiment, the volume to be sputtered just before irradiation is composed of pristine \\ceH2CO ice.",
                "The impact of a swift heavy ion induces radiolysis along its track, affecting a fraction of this volume.",
                "Therefore, after irradiation has started, the sputtered volume is composed of intact \\ceH2CO, fresh products of radiolysis as well as primary radiolytic products that accumulate in the film (see Figure 7 ).",
                "Therefore, in order to determine the effective sputtering yield , the intact fraction () of sputtered H2CO during irradiation must be estimated using the initial fractions reported in Table 3 : In practice, we derived an intact fraction of sputtered \\ceH2CO molecules =0.23, corresponding to an effective sputtering yield for the \\ceH2CO film of =(10.99.9)103 molecules ions-1.",
                "In their compendium of selected literature sputtering yields, Dartois et al.",
                "(2023 ) show that the sputtering yield induced by swift heavy ions follows an empirical law that is directly proportional to the square of the electronic stopping power : Here, using a stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam, we obtain for a pure \\ceH2CO ice =(3.12.8)10-4 1030 eV-2 cm-4 molecule3.",
                "However, most studies only have access to the effective sputtering yield , which is therefore used for in Eq.",
                "6 (e.g.",
                "Dartois et al., 2023 ).",
                "In this case, the effective prefactor value is =(1.4 1.3)10-3 1030 eV-2 cm-4 molecule3."
            ],
            "5.2": [
                "The external UV photodesorption rate can be written as where is the external interstellar far-UV radiation field (averaged between 6 and 13.6 eV) of photons cm-2 s-1 (Habing, 1968 ); is the visual extinction; is a measure of UV extinction relative to visual extinction, which is about 2 for interstellar grains (Roberge et al., 1991 ); and is the photodesorption yield of H2CO (in molecules photon-1).",
                "The last value was recently determined in the laboratory by Féraud et al.",
                "(2019 ), who were able to derive an intact H2CO photodesorption yield of molecule/photon in various astrophysical environments, including interstellar clouds and prestellar cores (see their Table 1).",
                "In the following we use an average experimental yield of molecule/photon for the photodesorption of intact H2CO.",
                "The cosmic-ray induced UV photodesorption rate can be written as where is now the internal UV field induced by the cosmic-ray excitation of H2, which was taken as , where is the rate of cosmic-ray ionisation of molecular hydrogen in units of s-1 (see the definition of below).",
                "This simple relation between and was deduced from Figure 4 of Shen et al.",
                "(2004 ), with computed using Eqs.",
                "16 -17 below.",
                "Finally, the direct cosmic-ray sputtering rate is computed by summing and integrating the product of the sputtering yield with the differential cosmic-ray flux : Here is the kinetic energy per nucleon, is the atomic number of the cosmic-ray nuclei, and is the sputtering yield in H2CO/ion obtained by combining the experimental yield for intact sputtering with the calculated electronic stopping power .",
                "It is multiplied by a factor of 2 to account for the entrance and exit points of the cosmic-rays through the grain.",
                "Assuming a quadratic dependence of with the stopping power, as in Eq.",
                "6 , the intact sputtering yield of H2CO molecules can be described as where we combined molecules ion-1 (see Table 3 ) with the stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam.",
                "In order to compute for a range of kinetic energies (see below), the SRIM-2013 code was used to compute the electronic stopping powers for an H2CO ice density of 0.81 g cm-3 and for the cosmic elements with the largest contributions, accounting for the scaling of the sputtering yields (Dartois et al., 2023 ).",
                "In practice, the 15 ions of H, He, C, O, Ne, Mg, Si, S, Ca, Ti, V, Cr, Mn, Fe, and Ni were included using the fractional abundances of Kalvāns (2016 , their Table 1).",
                "It should be noted that iron, despite its low fractional abundance, gives the largest contribution (%) to the rate, as already found by Seperuelo Duarte et al.",
                "(2010 ) for CO ice.",
                "For the differential cosmic-ray flux (in particles cm-2 s-1 sr-1 (MeV/amu)-1) we adopted the functional form proposed by Webber & Yushak (1983 ) where is a normalising constant and a form parameter that varies between 0 and 940 MeV.",
                "This formulation corresponds to a primary spectrum since it neglects the energy-loss of cosmic rays through the dense interstellar gas.",
                "It allows, however, the full range of measured ionisation rates to be explored, from standard diffuse clouds (a few s-1) to dense clouds (a few s-1), by simply varying the parameter .",
                "In order to infer the relation between and , the ionisation rate was computed as in Faure et al.",
                "(2019 , their Appendix A): Here is the cross-section for ionisation of H2 by proton impact, is a correction factor accounting for the contribution of secondary electrons to ionisation, and where is the correction factor for heavy nuclei ionisation.",
                "Full details and references can be found in Appendix A of Faure et al.",
                "(2019 ).",
                "In practice, the parameter in Eq.",
                "(16 ) was taken in the range 200900 MeV so that was explored in the range s-1.",
                "The integrals in Eqs.",
                "(14 ) and (17 ) were evaluated numerically from eV/amu to GeV/amu.",
                "The calibration plot between the intact sputtering rate of \\ceH2CO and the ionisation rate is displayed in Figure 9 (black curve), where is found to scale linearly with the ionisation rate.",
                "We note that although the low-energy content ( MeV) of the cosmic-ray spectrum is poorly constrained, the relation between and was found to be quite robust.",
                "It is now interesting to compare the sputtering rate of H2CO with those of the main ice components of interstellar grains, that is H2O, CO, and CO2, where the latter two have a typical abundance of 20-30% with respect to H2O.",
                "Trace ice species such as NH3, CH4, H2CO, and CH3OH are expected to be embedded in H2O-rich, CO-rich, or CO2-rich layers.",
                "We assume that the intact sputtering yield of the trapped molecule is equal to the effective sputtering yield of the ice matrix.",
                "Simplistic but intuitive, this hypothesis is actually supported by irradiation experiments performed on methanol diluted in H2O and CO2 ice matrices, although the intact sputtering efficiency depends on the dilution factor121212Because \\ceH2CO easily polymerises, segregation effects could also play a role and reduce the intact sputtering efficiency.",
                "(see the detailed discussions in Dartois et al., 2019 , 2020 ).",
                "We note that the effective sputtering yield of either water or CO2 was similarly employed to model the cosmic-ray induced sputtering of \\ceCH3OH in cold molecular cores (Wakelam et al., 2021 ; Paulive et al., 2022 ).",
                "The above procedure was thus applied to pure CO, CO2, and H2O ices using the effective sputtering yield pre-factors reported in Table 1 of Dartois et al.",
                "(2023 ) with ice densities (needed to compute ) of 0.88 g cm-3, 1.0 g cm-3, and 0.94 g cm-3, respectively (Luna et al., 2022 ; Satorre et al., 2008 ; Bouilloud et al., 2015 ).",
                "The corresponding sputtering rates as functions of are shown in Figure 9 .",
                "As expected, our results for CO, CO2, and H2O are in very good agreement with those of Dartois et al.",
                "(2023 , see their Figure 5).",
                "We can also observe that the intact sputtering rate of pure H2CO is a factor of 10-100 lower than the effective sputtering rates of H2O, CO, and CO2.",
                "For convenient use in astrochemical models, simple linear fits of the sputtering rates shown in Figure 9 were performed over the range s-1.",
                "These fits are reported in Table 5 ."
            ]
        },
        "4": {},
        "5": {
            "4.1": [
                "The evolution of H2CO ice infrared (IR) spectra as a function of fluence is depicted in Figure 1 .",
                "At fluence zero, the film is made of pure H2CO, and neither paraformaldehyde nor CO or CO2 can be seen in the spectra.",
                "As soon as irradiation starts, bands characteristic of CO2 and CO appear, as well as bands around 2920, 1230, 1100, and 920 cm-1, which we attribute to the formation of an H2CO polymer (polyoxymethylene, hereafter POM).",
                "Conversely, H2CO bands decrease with fluence.",
                "Apart from CO, CO2, and POM, the infrared analysis shows no evidence of the formation of any other chemical species during the irradiation of H2CO.",
                "The column densities of CO2, CO, and H2CO were derived using the band strengths given in Table 2 and the integrated absorbance of the bands at 2343 cm-1, 2139 cm-1, and 1725 cm-1, respectively.",
                "The POM column density was calculated using a combination mode at 1105 cm-1 and a band strength of cm molecules-1 (Noble et al., 2012 ).",
                "This band strength is not known with precision (Tadokoro et al., 1963 ; Schutte et al., 1993 ), and we assumed a factor of 2 uncertainty.",
                "An additional uncertainty arises from changes in the refractive index value across strong absorbance bands, resulting in some unphysical negative absorbances after baseline correction (see e.g.",
                "the C=0 stretch of H2CO).",
                "The derived column density evolution as a function of fluence, with uncertainty zones, is presented in Figure 2 .",
                "As can be seen, the POM column density is not accurately determined, but it is consistent with a fast and efficient polymerisation of \\ceH2CO at very low fluence.",
                "Thus, at a fluence of ions cm-1, the ice is mainly composed of POM.",
                "In similar experiments on non-polymerisable ices such as \\ceCH3OH and \\ceCO2 (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ), the column density evolution with fluence can be solved through a simple differential equation involving solely radiolysis and sputtering processes (see e.g.",
                "(3) in Dartois et al., 2019 ).",
                "Here, however, we were not able to solve such a differential equation, due to the additional polymerisation process of \\ceH2CO towards POM, whose exact nature is unknown.666In particular, the number of monomers is unknown and most probably the synthesised POM is a mixture of polymers of various chain sizes.",
                "In addition, while swift ion irradiation of H2CO is responsible for the formation of POM, it also destroys POM to CO and CO2 (see the decrease in POM column density beyond a fluence of ions cm-2 in Figure 2 ).",
                "Therefore, in order to derive the sputtering yield, we resorted to another method based on the determination of the reduction in thin film thickness using the Fabry–Perot interference fringes observed in the infrared spectra (Dartois et al., 2020 , 2023 ), combined with QMS analysis of the gas composition.",
                "We emphasise that in order to validate this method, it was first applied to measure the thickness evolution of an irradiated thin film of CO2, for which the usual fit of the column density evolution via a differential equation was also possible.",
                "As reported in Appendix C , both methods were found to give consistent results, which are also in good agreement with the literature.",
                "In the case of \\ceH2CO, as irradiation proceeds, the ice film becomes a mixture of mainly POM and H2CO for which the refractive index () is not available.",
                "Fitting the rigorous expression for the transmission () of a thin absorbing film on a thick transparent substrate is therefore not possible.",
                "Nevertheless, transmittance spectra follow a sinusoidal pattern, where the period is proportional to the thickness.",
                "Thus, we used the following simple expression to fit the transmittance spectra in the ranges of wavenumbers () free of molecular absorptions: Here and are free parameters, is the refractive index taken as (Bouilloud et al., 2015 ), and is ice thickness.",
                "The factor corrects for the angle between the infrared beam and the sample.",
                "Fits obtained with this expression are shown in Figure 3 .",
                "The ice film is composed of POM and H2CO, with a composition changing during irradiation.",
                "Therefore, evaluating the sample mass density is challenging.",
                "Furthermore, even the mass density of a pure H2CO ice film is unknown.",
                "Consequently, it is assumed to be constant at the value for liquid formaldehyde, (Bouilloud et al., 2015 ), with an assumed uncertainty of 20%.",
                "It was used to derive the surface density of the ice , as a function of fluence, as shown in Figure 4 .",
                "The total mass sputtering yield can be directly estimated from the slope of the surface density evolution with fluence as g ion-1.",
                "It should be noted that this total yield includes all sputtered species from the considered volume, both radiolysed species (C, O, H, H2, CO, and CO2) and intact \\ceH2CO fragments.",
                "In order to determine the chemical composition of the sputtered mass volume, the various fragments ejected into the gas phase were measured with the QMS.",
                "The small residual or background signal observed before irradiation was subtracted from the recorded signal during the whole irradiation time, as reported in Figure 5 (top panel).",
                "We note that there is no intact sputtered POM as no signal is observed at =31, a mass characteristic of POM fragmentation pattern (Butscher et al., 2019 ; Duvernay et al., 2014 ).",
                "The mass =30 can be used to follow H2CO molecules since no fragment at this mass is observed in the CO fragmentation pattern (Figure 6 ).",
                "Thus, the signals at m/z=30 and m/z=28 can be used to retrieve the total number of H2CO and CO species, respectively, by dividing each m/z signal by its relative contribution in the fragmentation pattern.",
                "The remaining signals at m/z=12 and m/z=16, after subtracting the contributions of CO and H2CO, indicate the abundances of C and O atoms, respectively.",
                "Once corrected for the total electron-impact ionisation cross-section at 70 eV (energy of the QMS electron ionisation source), the relative fraction of each species with fluence is determined (Figure 5 , bottom panel).",
                "QMS measurements at very low masses are not reliable, but the amount of hydrogen (H or H2) is supposed to be equal to the sum of the amounts of C, O, and CO. We note that CO2, a minor component of the ice (see Figure 1 ), was not detected in the gas phase by the QMS.",
                "As irradiation proceeds, the composition of the film changes (Figure 2 ) and this is also observed in the gas composition (Figure 5 , bottom panel).",
                "The fraction of gaseous H2CO thus decreases significantly (by approximately 70 %) for initial fluences (up to 2 ions cm-2), which is consistent with the radiolysis and the rapid polymerisation of solid \\ceH2CO.",
                "It then decreases more gradually, before a (noisy) slightly ascending plateau is reached beyond fluences of 3 ions cm-2.",
                "Conversely, the fractions of C and O increase rapidly (by approximately 70%), but also reach a plateau.",
                "Overall, the molecular fractions of these three chemical species in the gas vary by less than a factor of two.",
                "The larger molecular fractions of CO and H2 increase up to fluences of about 2 ions cm-2 before reaching a slightly descending plateau, with variations of less than 15%.",
                "We can extract the initial fraction of each species in the gas phase (Table 5 ), and the subsequent evolution was fitted by third-order polynomials.",
                "By combining the total mass sputtering yield with the fitted molecular fractions , we can derive the sputtering yield of each ejected species , where is the Avogadro constant, is the molecular mass of species , and represents the mass fraction of species in the gas: The derived sputtering yields for the various ejected species are plotted as dashed lines in the bottom panel of Figure 5 (right -axis).",
                "Similarly to the molecular fractions, the intact sputtering yields vary by less than a factor of 2 for C, O, and H2CO, and by less than 15% for CO and H2, as expected.",
                "The average intact sputtering yields were computed over the full range of fluences and are listed in Table 5 .",
                "The average sputtering yield for intact \\ceH2CO is found to be molecules ion-1.",
                "We can now try to estimate the effective sputtering yield, .",
                "For non-polymerisable species, is usually determined using the column density evolution with fluence measured from IR spectroscopy (Dartois et al., 2019 ; Seperuelo Duarte et al., 2009 ).",
                "For a pure ice , is defined as the semi-infinite thickness effective-sputtering yield for the ice under study.",
                "It includes both intact sputtered species and radiolysed (daughter) sputtered species.",
                "Since radiolysis and sputtering occur simultaneously, IR spectroscopy captures the disappearance of H2CO, regardless of whether it is sputtered intact or radiolysed.",
                "is simply related to as where is the intact fraction of sputtered H2CO.",
                "In our experiment, the volume to be sputtered just before irradiation is composed of pristine \\ceH2CO ice.",
                "The impact of a swift heavy ion induces radiolysis along its track, affecting a fraction of this volume.",
                "Therefore, after irradiation has started, the sputtered volume is composed of intact \\ceH2CO, fresh products of radiolysis as well as primary radiolytic products that accumulate in the film (see Figure 7 ).",
                "Therefore, in order to determine the effective sputtering yield , the intact fraction () of sputtered H2CO during irradiation must be estimated using the initial fractions reported in Table 3 : In practice, we derived an intact fraction of sputtered \\ceH2CO molecules =0.23, corresponding to an effective sputtering yield for the \\ceH2CO film of =(10.99.9)103 molecules ions-1.",
                "In their compendium of selected literature sputtering yields, Dartois et al.",
                "(2023 ) show that the sputtering yield induced by swift heavy ions follows an empirical law that is directly proportional to the square of the electronic stopping power : Here, using a stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam, we obtain for a pure \\ceH2CO ice =(3.12.8)10-4 1030 eV-2 cm-4 molecule3.",
                "However, most studies only have access to the effective sputtering yield , which is therefore used for in Eq.",
                "6 (e.g.",
                "Dartois et al., 2023 ).",
                "In this case, the effective prefactor value is =(1.4 1.3)10-3 1030 eV-2 cm-4 molecule3."
            ],
            "5.2": [
                "The external UV photodesorption rate can be written as where is the external interstellar far-UV radiation field (averaged between 6 and 13.6 eV) of photons cm-2 s-1 (Habing, 1968 ); is the visual extinction; is a measure of UV extinction relative to visual extinction, which is about 2 for interstellar grains (Roberge et al., 1991 ); and is the photodesorption yield of H2CO (in molecules photon-1).",
                "The last value was recently determined in the laboratory by Féraud et al.",
                "(2019 ), who were able to derive an intact H2CO photodesorption yield of molecule/photon in various astrophysical environments, including interstellar clouds and prestellar cores (see their Table 1).",
                "In the following we use an average experimental yield of molecule/photon for the photodesorption of intact H2CO.",
                "The cosmic-ray induced UV photodesorption rate can be written as where is now the internal UV field induced by the cosmic-ray excitation of H2, which was taken as , where is the rate of cosmic-ray ionisation of molecular hydrogen in units of s-1 (see the definition of below).",
                "This simple relation between and was deduced from Figure 4 of Shen et al.",
                "(2004 ), with computed using Eqs.",
                "16 -17 below.",
                "Finally, the direct cosmic-ray sputtering rate is computed by summing and integrating the product of the sputtering yield with the differential cosmic-ray flux : Here is the kinetic energy per nucleon, is the atomic number of the cosmic-ray nuclei, and is the sputtering yield in H2CO/ion obtained by combining the experimental yield for intact sputtering with the calculated electronic stopping power .",
                "It is multiplied by a factor of 2 to account for the entrance and exit points of the cosmic-rays through the grain.",
                "Assuming a quadratic dependence of with the stopping power, as in Eq.",
                "6 , the intact sputtering yield of H2CO molecules can be described as where we combined molecules ion-1 (see Table 3 ) with the stopping power of 2830 eV (1015 molecules cm-2)-1 for the 86Kr18+ beam.",
                "In order to compute for a range of kinetic energies (see below), the SRIM-2013 code was used to compute the electronic stopping powers for an H2CO ice density of 0.81 g cm-3 and for the cosmic elements with the largest contributions, accounting for the scaling of the sputtering yields (Dartois et al., 2023 ).",
                "In practice, the 15 ions of H, He, C, O, Ne, Mg, Si, S, Ca, Ti, V, Cr, Mn, Fe, and Ni were included using the fractional abundances of Kalvāns (2016 , their Table 1).",
                "It should be noted that iron, despite its low fractional abundance, gives the largest contribution (%) to the rate, as already found by Seperuelo Duarte et al.",
                "(2010 ) for CO ice.",
                "For the differential cosmic-ray flux (in particles cm-2 s-1 sr-1 (MeV/amu)-1) we adopted the functional form proposed by Webber & Yushak (1983 ) where is a normalising constant and a form parameter that varies between 0 and 940 MeV.",
                "This formulation corresponds to a primary spectrum since it neglects the energy-loss of cosmic rays through the dense interstellar gas.",
                "It allows, however, the full range of measured ionisation rates to be explored, from standard diffuse clouds (a few s-1) to dense clouds (a few s-1), by simply varying the parameter .",
                "In order to infer the relation between and , the ionisation rate was computed as in Faure et al.",
                "(2019 , their Appendix A): Here is the cross-section for ionisation of H2 by proton impact, is a correction factor accounting for the contribution of secondary electrons to ionisation, and where is the correction factor for heavy nuclei ionisation.",
                "Full details and references can be found in Appendix A of Faure et al.",
                "(2019 ).",
                "In practice, the parameter in Eq.",
                "(16 ) was taken in the range 200900 MeV so that was explored in the range s-1.",
                "The integrals in Eqs.",
                "(14 ) and (17 ) were evaluated numerically from eV/amu to GeV/amu.",
                "The calibration plot between the intact sputtering rate of \\ceH2CO and the ionisation rate is displayed in Figure 9 (black curve), where is found to scale linearly with the ionisation rate.",
                "We note that although the low-energy content ( MeV) of the cosmic-ray spectrum is poorly constrained, the relation between and was found to be quite robust.",
                "It is now interesting to compare the sputtering rate of H2CO with those of the main ice components of interstellar grains, that is H2O, CO, and CO2, where the latter two have a typical abundance of 20-30% with respect to H2O.",
                "Trace ice species such as NH3, CH4, H2CO, and CH3OH are expected to be embedded in H2O-rich, CO-rich, or CO2-rich layers.",
                "We assume that the intact sputtering yield of the trapped molecule is equal to the effective sputtering yield of the ice matrix.",
                "Simplistic but intuitive, this hypothesis is actually supported by irradiation experiments performed on methanol diluted in H2O and CO2 ice matrices, although the intact sputtering efficiency depends on the dilution factor121212Because \\ceH2CO easily polymerises, segregation effects could also play a role and reduce the intact sputtering efficiency.",
                "(see the detailed discussions in Dartois et al., 2019 , 2020 ).",
                "We note that the effective sputtering yield of either water or CO2 was similarly employed to model the cosmic-ray induced sputtering of \\ceCH3OH in cold molecular cores (Wakelam et al., 2021 ; Paulive et al., 2022 ).",
                "The above procedure was thus applied to pure CO, CO2, and H2O ices using the effective sputtering yield pre-factors reported in Table 1 of Dartois et al.",
                "(2023 ) with ice densities (needed to compute ) of 0.88 g cm-3, 1.0 g cm-3, and 0.94 g cm-3, respectively (Luna et al., 2022 ; Satorre et al., 2008 ; Bouilloud et al., 2015 ).",
                "The corresponding sputtering rates as functions of are shown in Figure 9 .",
                "As expected, our results for CO, CO2, and H2O are in very good agreement with those of Dartois et al.",
                "(2023 , see their Figure 5).",
                "We can also observe that the intact sputtering rate of pure H2CO is a factor of 10-100 lower than the effective sputtering rates of H2O, CO, and CO2.",
                "For convenient use in astrochemical models, simple linear fits of the sputtering rates shown in Figure 9 were performed over the range s-1.",
                "These fits are reported in Table 5 ."
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