diff --git "a/FOCAL-TESTING-NO-LABELS.jsonl" "b/FOCAL-TESTING-NO-LABELS.jsonl"
--- "a/FOCAL-TESTING-NO-LABELS.jsonl"
+++ "b/FOCAL-TESTING-NO-LABELS.jsonl"
@@ -1,3 +1,16 @@
+{"Identifier":"2022ApJ...940L..13A__Chen_et_al._2020_Instance_1","Paragraph":"Since 2018 the Parker Solar Probe (PSP) mission is collecting solar wind plasma and magnetic field data through the inner heliosphere, reaching the closest distance to the Sun ever reached by any previous mission (Fox et al. 2016; Kasper et al. 2021). Thanks to the PSP journey around the Sun (it has completed 11 orbits) a different picture has been drawn for the near-Sun solar wind with respect to the near-Earth one (Bale et al. 2019; Kasper et al. 2019; Chhiber et al. 2020; Malaspina et al. 2020; Bandyopadhyay et al. 2022; Zank et al. 2022). Different near-Sun phenomena have been frequently encountered, with the emergence of magnetic field flips, i.e., the so-called switchbacks (Dudok de Wit et al. 2020; Zank et al. 2020), kinetic-scale current sheets (Lotekar et al. 2022), and a scale-invariant population of current sheets between ion and electron inertial scales (Chhiber et al. 2021). Going away from the Sun (from 0.17 to 0.8 au), evidence of radial evolution of different properties of solar wind turbulence (Chen et al. 2020) as the spectral slope of the inertial range (from \u22123\/2 close to the Sun to \u22125\/3, at distances larger than 0.4 au), an increase of the outer scale of turbulence, a decrease of the Alfv\u00e9nic flux, and a decrease of the imbalance between outward (z\n+) and inward (z\n\u2212) propagating components (Chen et al. 2020) has been provided. Although the near-Sun solar wind shares different properties with the near-Earth one (Allen et al. 2020; Cuesta et al. 2022), significant differences have been also found in the variance of magnetic fluctuations (about 2 orders of magnitude) and in the compressive component of inertial range turbulence. In a similar way, Alberti et al. (2020) first reported a breakdown of the scaling properties of the energy transfer rate, likely related to the breaking of the phase-coherence of inertial range fluctuations. These findings, also highlighted by Telloni et al. (2021) and Alberti et al. (2022) analyzing a radial alignment between PSP and Solar Orbiter, and PSP and BepiColombo, respectively, have been interpreted as an increase in the efficiency of the nonlinear energy cascade mechanism when moving away from the Sun. More recently, by investigating the helical content of turbulence Alberti et al. (2022) highlighted a damping of magnetic helicity over the inertial range between 0.17 and 0.6 au suggesting that the solar wind develops into turbulence by a concurrent effect of large-scale convection of helicity and creation\/annihilation of helical wave structures. All these features shed new light onto the radial evolution of solar wind turbulence that urges to be considered in expanding models of the solar wind (Verdini et al. 2019; Grappin et al. 2021), and also to reproduce and investigate the role of proton heating and anisotropy of magnetic field fluctuations (Hellinger et al. 2015).","Citation Text":["Chen et al. 2020"],"Citation Start End":[[1067,1083]]}
+{"Identifier":"2022ApJ...940L..13A__Chen_et_al._2020_Instance_2","Paragraph":"Since 2018 the Parker Solar Probe (PSP) mission is collecting solar wind plasma and magnetic field data through the inner heliosphere, reaching the closest distance to the Sun ever reached by any previous mission (Fox et al. 2016; Kasper et al. 2021). Thanks to the PSP journey around the Sun (it has completed 11 orbits) a different picture has been drawn for the near-Sun solar wind with respect to the near-Earth one (Bale et al. 2019; Kasper et al. 2019; Chhiber et al. 2020; Malaspina et al. 2020; Bandyopadhyay et al. 2022; Zank et al. 2022). Different near-Sun phenomena have been frequently encountered, with the emergence of magnetic field flips, i.e., the so-called switchbacks (Dudok de Wit et al. 2020; Zank et al. 2020), kinetic-scale current sheets (Lotekar et al. 2022), and a scale-invariant population of current sheets between ion and electron inertial scales (Chhiber et al. 2021). Going away from the Sun (from 0.17 to 0.8 au), evidence of radial evolution of different properties of solar wind turbulence (Chen et al. 2020) as the spectral slope of the inertial range (from \u22123\/2 close to the Sun to \u22125\/3, at distances larger than 0.4 au), an increase of the outer scale of turbulence, a decrease of the Alfv\u00e9nic flux, and a decrease of the imbalance between outward (z\n+) and inward (z\n\u2212) propagating components (Chen et al. 2020) has been provided. Although the near-Sun solar wind shares different properties with the near-Earth one (Allen et al. 2020; Cuesta et al. 2022), significant differences have been also found in the variance of magnetic fluctuations (about 2 orders of magnitude) and in the compressive component of inertial range turbulence. In a similar way, Alberti et al. (2020) first reported a breakdown of the scaling properties of the energy transfer rate, likely related to the breaking of the phase-coherence of inertial range fluctuations. These findings, also highlighted by Telloni et al. (2021) and Alberti et al. (2022) analyzing a radial alignment between PSP and Solar Orbiter, and PSP and BepiColombo, respectively, have been interpreted as an increase in the efficiency of the nonlinear energy cascade mechanism when moving away from the Sun. More recently, by investigating the helical content of turbulence Alberti et al. (2022) highlighted a damping of magnetic helicity over the inertial range between 0.17 and 0.6 au suggesting that the solar wind develops into turbulence by a concurrent effect of large-scale convection of helicity and creation\/annihilation of helical wave structures. All these features shed new light onto the radial evolution of solar wind turbulence that urges to be considered in expanding models of the solar wind (Verdini et al. 2019; Grappin et al. 2021), and also to reproduce and investigate the role of proton heating and anisotropy of magnetic field fluctuations (Hellinger et al. 2015).","Citation Text":["Chen et al. 2020"],"Citation Start End":[[1374,1390]]}
+{"Identifier":"2019MNRAS.487.2474C__Sharma_et_al._2018_Instance_1","Paragraph":"In this work, we analyse a set of high-resolution stellar spectra that were acquired by the High Efficiency and Resolution Multi-Element Spectrograph (HERMES; Barden et al. 2010; Sheinis et al. 2015), a multifibre spectrograph mounted on the 3.9-metre Anglo-Australian Telescope (AAT). The spectrograph has a resolving power of R ${\\sim } 28\\, 000$ and covers four wavelength ranges (4713\u20134903, 5648\u20135873, 6478\u20136737, and 7585\u20137887\u2009\u00c5), frequently also referred to as \u2018spectral arms\u2019. Observations used in this study have been taken from multiple observing programmes that make use of the HERMES spectrograph: the main GALAH survey (De Silva et al. 2015), the K2-HERMES survey (Wittenmyer et al. 2018), and the TESS-HERMES survey (Sharma et al. 2018). Those observing programmes mostly observe stars at higher Galactic latitudes (|b| > 10\u00b0) and employ different selection functions, but share the same observing procedures, reduction, and analysis pipeline (internal version 5.3; Kos et al. 2017). All three programmes are magnitude-limited, with no colour cuts (except the K2-HERMES survey), and observations predominantly fall in the V magnitude range between 12 and 14. This leads to an unbiased sample of mostly southern stars that can be used for different population studies, such as multiple stellar systems in our case. Additionally, stellar atmospheric parameters and individual abundances derived from spectra acquired during different observing programmes are analysed with the same The Cannon procedure (internal version 182112 that uses parallax information to infer log\u2009g of a star; Ness et al. 2015; Buder et al. 2018), so they are intercomparable. The Cannon is a data-driven interpolation approach trained on a set of stellar spectra that span the majority of the stellar parameter space (for details, see Buder et al. 2018). Whenever we refer to valid or unflagged stellar parameters in the text, only stars with the quality flag flag_cannon equal to 0 were selected.","Citation Text":["Sharma et al. 2018"],"Citation Start End":[[771,789]]}
+{"Identifier":"2019MNRAS.487.2474CBarden_et_al._2010_Instance_1","Paragraph":"In this work, we analyse a set of high-resolution stellar spectra that were acquired by the High Efficiency and Resolution Multi-Element Spectrograph (HERMES; Barden et al. 2010; Sheinis et al. 2015), a multifibre spectrograph mounted on the 3.9-metre Anglo-Australian Telescope (AAT). The spectrograph has a resolving power of R ${\\sim } 28\\, 000$ and covers four wavelength ranges (4713\u20134903, 5648\u20135873, 6478\u20136737, and 7585\u20137887\u2009\u00c5), frequently also referred to as \u2018spectral arms\u2019. Observations used in this study have been taken from multiple observing programmes that make use of the HERMES spectrograph: the main GALAH survey (De Silva et al. 2015), the K2-HERMES survey (Wittenmyer et al. 2018), and the TESS-HERMES survey (Sharma et al. 2018). Those observing programmes mostly observe stars at higher Galactic latitudes (|b| > 10\u00b0) and employ different selection functions, but share the same observing procedures, reduction, and analysis pipeline (internal version 5.3; Kos et al. 2017). All three programmes are magnitude-limited, with no colour cuts (except the K2-HERMES survey), and observations predominantly fall in the V magnitude range between 12 and 14. This leads to an unbiased sample of mostly southern stars that can be used for different population studies, such as multiple stellar systems in our case. Additionally, stellar atmospheric parameters and individual abundances derived from spectra acquired during different observing programmes are analysed with the same The Cannon procedure (internal version 182112 that uses parallax information to infer log\u2009g of a star; Ness et al. 2015; Buder et al. 2018), so they are intercomparable. The Cannon is a data-driven interpolation approach trained on a set of stellar spectra that span the majority of the stellar parameter space (for details, see Buder et al. 2018). Whenever we refer to valid or unflagged stellar parameters in the text, only stars with the quality flag flag_cannon equal to 0 were selected.","Citation Text":["Barden et al. 2010"],"Citation Start End":[[201,219]]}
+{"Identifier":"2019MNRAS.487.2474CBuder_et_al._2018_Instance_1","Paragraph":"In this work, we analyse a set of high-resolution stellar spectra that were acquired by the High Efficiency and Resolution Multi-Element Spectrograph (HERMES; Barden et al. 2010; Sheinis et al. 2015), a multifibre spectrograph mounted on the 3.9-metre Anglo-Australian Telescope (AAT). The spectrograph has a resolving power of R ${\\sim } 28\\, 000$ and covers four wavelength ranges (4713\u20134903, 5648\u20135873, 6478\u20136737, and 7585\u20137887\u2009\u00c5), frequently also referred to as \u2018spectral arms\u2019. Observations used in this study have been taken from multiple observing programmes that make use of the HERMES spectrograph: the main GALAH survey (De Silva et al. 2015), the K2-HERMES survey (Wittenmyer et al. 2018), and the TESS-HERMES survey (Sharma et al. 2018). Those observing programmes mostly observe stars at higher Galactic latitudes (|b| > 10\u00b0) and employ different selection functions, but share the same observing procedures, reduction, and analysis pipeline (internal version 5.3; Kos et al. 2017). All three programmes are magnitude-limited, with no colour cuts (except the K2-HERMES survey), and observations predominantly fall in the V magnitude range between 12 and 14. This leads to an unbiased sample of mostly southern stars that can be used for different population studies, such as multiple stellar systems in our case. Additionally, stellar atmospheric parameters and individual abundances derived from spectra acquired during different observing programmes are analysed with the same The Cannon procedure (internal version 182112 that uses parallax information to infer log\u2009g of a star; Ness et al. 2015; Buder et al. 2018), so they are intercomparable. The Cannon is a data-driven interpolation approach trained on a set of stellar spectra that span the majority of the stellar parameter space (for details, see Buder et al. 2018). Whenever we refer to valid or unflagged stellar parameters in the text, only stars with the quality flag flag_cannon equal to 0 were selected.","Citation Text":["Buder et al. 2018"],"Citation Start End":[[1863,1880]]}
+{"Identifier":"2019MNRAS.487.2474CBuder_et_al._2018_Instance_1","Paragraph":"In this work, we analyse a set of high-resolution stellar spectra that were acquired by the High Efficiency and Resolution Multi-Element Spectrograph (HERMES; Barden et al. 2010; Sheinis et al. 2015), a multifibre spectrograph mounted on the 3.9-metre Anglo-Australian Telescope (AAT). The spectrograph has a resolving power of R ${\\sim } 28\\, 000$ and covers four wavelength ranges (4713\u20134903, 5648\u20135873, 6478\u20136737, and 7585\u20137887\u2009\u00c5), frequently also referred to as \u2018spectral arms\u2019. Observations used in this study have been taken from multiple observing programmes that make use of the HERMES spectrograph: the main GALAH survey (De Silva et al. 2015), the K2-HERMES survey (Wittenmyer et al. 2018), and the TESS-HERMES survey (Sharma et al. 2018). Those observing programmes mostly observe stars at higher Galactic latitudes (|b| > 10\u00b0) and employ different selection functions, but share the same observing procedures, reduction, and analysis pipeline (internal version 5.3; Kos et al. 2017). All three programmes are magnitude-limited, with no colour cuts (except the K2-HERMES survey), and observations predominantly fall in the V magnitude range between 12 and 14. This leads to an unbiased sample of mostly southern stars that can be used for different population studies, such as multiple stellar systems in our case. Additionally, stellar atmospheric parameters and individual abundances derived from spectra acquired during different observing programmes are analysed with the same The Cannon procedure (internal version 182112 that uses parallax information to infer log\u2009g of a star; Ness et al. 2015; Buder et al. 2018), so they are intercomparable. The Cannon is a data-driven interpolation approach trained on a set of stellar spectra that span the majority of the stellar parameter space (for details, see Buder et al. 2018). Whenever we refer to valid or unflagged stellar parameters in the text, only stars with the quality flag flag_cannon equal to 0 were selected.","Citation Text":["Buder et al. 2018"],"Citation Start End":[[1655,1672]]}
+{"Identifier":"2016MNRAS.455.2131L__Liu_&_Wei_2014_Instance_1","Paragraph":"As we have shown that the Ep\u2013E\u03b3 relation does not significantly evolve with redshift, we can use it to calibrate GRBs. To avoid the circularity problem, the Pad\u00e9 method proposed by Liu & Wei (2014) is applied. The main calibrating procedures are as follows: First, derive the distance-redshift relation of SNe Ia [here we use the Union2.1 (Suzuki et al. 2012) data set] using the Pad\u00e9 approximation of order (3,2), i.e.\n\n(17)\n\n\\begin{equation}\n\\mu (z)=\\frac{\\alpha _0+\\alpha _1z+\\alpha _2z^2+\\alpha _3z^3}{1+\\beta _1z+\\beta _2z^2},\n\\end{equation}\n\nwhere the coefficients (\u03b10, \u03b11, \u03b12, \u03b13, \u03b21, \u03b22) and the corresponding covariance matrix are derived by fitting equation (17) to the Union2.1 data set (see Liu & Wei 2014 for details). Assuming that the low-z GRBs trace the same Hubble diagram to SNe Ia, we can calculate the distance moduli of low-z GRBs directly from equation (17). The uncertainty of \u03bc propagates from the uncertainties of the coefficients (\u03b1i, \u03b2i). Then the luminosity distance of low-z GRBs can be obtained using the relation\n\n(18)\n\n\\begin{equation}\n\\mu (z)=5\\log \\frac{d_L(z)}{\\rm {Mpc}}+25.\n\\end{equation}\n\nAs dL is known, the collimation-corrected energy can be further calculated from equation (11). Note that there are only 12 low-z GRBs and 12 high-z GRBs available since the others have no measurement of jet opening angle. Then we fit the Ep\u2013E\u03b3 relation (i.e. equation (5)) to the 12 low-z GRBs, which gives the best-fitting parameters\n\n(19)\n\n\\begin{eqnarray}\n\\sigma _{\\rm int}=0.161\\pm 0.059,\\ \\ a=50.632\\pm 0.062,\\ \\ b=1.537\\pm 0.145.\\nonumber\\\\\n\\end{eqnarray}\n\nBy directly extrapolating the Ep\u2013E\u03b3 relation to high-z GRBs, we can inversely obtain the collimation-corrected energy for 12 high-z GRBs from equation (5). Finally, calculate the luminosity distance of high-z GRBs from equation (11), and then the distance moduli from equation (18). The uncertainty of distance moduli propagates from the uncertainties of E\u03b3, Sbolo and Fbeam, i.e. (Schaefer 2007),\n\n(20)\n\n\\begin{equation}\n\\sigma _{\\mu }^2=\\left(\\frac{5}{2\\ln 10}\\right)^2\\left[(\\ln 10)^2\\sigma _{\\log E_{\\gamma }}^2 + \\frac{\\sigma _{S_{\\rm bolo}}^2}{S_{\\rm bolo}^2} + \\frac{\\sigma _{F_{\\rm beam}}^2}{F_{\\rm beam}^2}\\right],\n\\end{equation}\n\nwhere\n\n(21)\n\n\\begin{eqnarray}\n\\sigma _{\\log E_{\\gamma }}^2=\\sigma _a^2 + \\left(\\sigma _b\\log \\frac{E_{p,i}}{300\\ {\\rm keV}}\\right)^2 + \\left(\\frac{b}{\\ln 10}\\frac{\\sigma _{E_{p,i}}}{E_{p,i}}\\right)^2 + \\sigma _{\\rm int}^2.\\nonumber\\\\\n\\end{eqnarray}\n\n","Citation Text":["Liu & Wei (2014)"],"Citation Start End":[[219,235]]}
+{"Identifier":"2016MNRAS.455.2131L__Liu_&_Wei_2014_Instance_2","Paragraph":"As we have shown that the Ep\u2013E\u03b3 relation does not significantly evolve with redshift, we can use it to calibrate GRBs. To avoid the circularity problem, the Pad\u00e9 method proposed by Liu & Wei (2014) is applied. The main calibrating procedures are as follows: First, derive the distance-redshift relation of SNe Ia [here we use the Union2.1 (Suzuki et al. 2012) data set] using the Pad\u00e9 approximation of order (3,2), i.e.\n\n(17)\n\n\\begin{equation}\n\\mu (z)=\\frac{\\alpha _0+\\alpha _1z+\\alpha _2z^2+\\alpha _3z^3}{1+\\beta _1z+\\beta _2z^2},\n\\end{equation}\n\nwhere the coefficients (\u03b10, \u03b11, \u03b12, \u03b13, \u03b21, \u03b22) and the corresponding covariance matrix are derived by fitting equation (17) to the Union2.1 data set (see Liu & Wei 2014 for details). Assuming that the low-z GRBs trace the same Hubble diagram to SNe Ia, we can calculate the distance moduli of low-z GRBs directly from equation (17). The uncertainty of \u03bc propagates from the uncertainties of the coefficients (\u03b1i, \u03b2i). Then the luminosity distance of low-z GRBs can be obtained using the relation\n\n(18)\n\n\\begin{equation}\n\\mu (z)=5\\log \\frac{d_L(z)}{\\rm {Mpc}}+25.\n\\end{equation}\n\nAs dL is known, the collimation-corrected energy can be further calculated from equation (11). Note that there are only 12 low-z GRBs and 12 high-z GRBs available since the others have no measurement of jet opening angle. Then we fit the Ep\u2013E\u03b3 relation (i.e. equation (5)) to the 12 low-z GRBs, which gives the best-fitting parameters\n\n(19)\n\n\\begin{eqnarray}\n\\sigma _{\\rm int}=0.161\\pm 0.059,\\ \\ a=50.632\\pm 0.062,\\ \\ b=1.537\\pm 0.145.\\nonumber\\\\\n\\end{eqnarray}\n\nBy directly extrapolating the Ep\u2013E\u03b3 relation to high-z GRBs, we can inversely obtain the collimation-corrected energy for 12 high-z GRBs from equation (5). Finally, calculate the luminosity distance of high-z GRBs from equation (11), and then the distance moduli from equation (18). The uncertainty of distance moduli propagates from the uncertainties of E\u03b3, Sbolo and Fbeam, i.e. (Schaefer 2007),\n\n(20)\n\n\\begin{equation}\n\\sigma _{\\mu }^2=\\left(\\frac{5}{2\\ln 10}\\right)^2\\left[(\\ln 10)^2\\sigma _{\\log E_{\\gamma }}^2 + \\frac{\\sigma _{S_{\\rm bolo}}^2}{S_{\\rm bolo}^2} + \\frac{\\sigma _{F_{\\rm beam}}^2}{F_{\\rm beam}^2}\\right],\n\\end{equation}\n\nwhere\n\n(21)\n\n\\begin{eqnarray}\n\\sigma _{\\log E_{\\gamma }}^2=\\sigma _a^2 + \\left(\\sigma _b\\log \\frac{E_{p,i}}{300\\ {\\rm keV}}\\right)^2 + \\left(\\frac{b}{\\ln 10}\\frac{\\sigma _{E_{p,i}}}{E_{p,i}}\\right)^2 + \\sigma _{\\rm int}^2.\\nonumber\\\\\n\\end{eqnarray}\n\n","Citation Text":["Liu & Wei 2014"],"Citation Start End":[[741,755]]}
+{"Identifier":"2021MNRAS.500.4004D__Truong_et_al._2020_Instance_1","Paragraph":"Several outcomes from the IllustrisTNG simulations have validated the model against observational constraints, making them suitable for the tasks at hand. Among them we highlight: the shape and width of the red sequence and the blue cloud of z = 0 galaxies (Nelson et al. 2018a), the existence and locus of the star formation main sequence (MS) at low redshifts (Donnari et al. 2019), the distribution of stellar mass across galaxy populations at z \u2272 4 (Pillepich et al. 2018), the galaxy size\u2013mass relation for star-forming and quiescent galaxies at 0 \u2264 z \u2264 2 (Genel et al. 2018), the evolution of the galaxy mass\u2013metallicity relation (Torrey et al. 2018), and quantitatively consistent optical morphologies in comparison to Pan-STARRS data (Rodriguez-Gomez et al. 2019) as far as galaxy properties are concerned. These come in addition to observationally-consistent results in relation to the properties of massive hosts and their intra-halo gas: e.g. the X-ray signals of the hot gaseous atmospheres (Davies et al. 2020; Truong et al. 2020), the amount and distribution of highly ionized Oxygen around galaxies (Nelson et al. 2018b), and the distributions of metals in the ICM at low redshifts (Vogelsberger et al. 2018). Importantly, the new physical mechanisms included in the TNG model have been shown to return galaxy populations whose star formation activity is in better agreement with observations than previous calculations like Illustris (Genel et al. 2014; Vogelsberger et al. 2014; Sijacki et al. 2015), in galaxy colours (Weinberger et al. 2018; Nelson et al. 2018a), atomic and molecular gas content of satellite galaxies (Stevens et al. 2019), and quenched fractions of central and satellite galaxies taken together with no distinction (z \u2272 2; Donnari et al. 2019). In a companion paper (Donnari et al. 2020), we discuss in detail the level of agreement between TNG results and observations when centrals and group and cluster satellites are considered separately and show that the quenched fractions of TNG galaxies are overall consistent with observational constraints and hence the results of this paper trustworthy.","Citation Text":["Truong et al. 2020"],"Citation Start End":[[1066,1084]]}
+{"Identifier":"2021MNRAS.500.4004DDonnari_et_al._2020_Instance_1","Paragraph":"Several outcomes from the IllustrisTNG simulations have validated the model against observational constraints, making them suitable for the tasks at hand. Among them we highlight: the shape and width of the red sequence and the blue cloud of z = 0 galaxies (Nelson et al. 2018a), the existence and locus of the star formation main sequence (MS) at low redshifts (Donnari et al. 2019), the distribution of stellar mass across galaxy populations at z \u2272 4 (Pillepich et al. 2018), the galaxy size\u2013mass relation for star-forming and quiescent galaxies at 0 \u2264 z \u2264 2 (Genel et al. 2018), the evolution of the galaxy mass\u2013metallicity relation (Torrey et al. 2018), and quantitatively consistent optical morphologies in comparison to Pan-STARRS data (Rodriguez-Gomez et al. 2019) as far as galaxy properties are concerned. These come in addition to observationally-consistent results in relation to the properties of massive hosts and their intra-halo gas: e.g. the X-ray signals of the hot gaseous atmospheres (Davies et al. 2020; Truong et al. 2020), the amount and distribution of highly ionized Oxygen around galaxies (Nelson et al. 2018b), and the distributions of metals in the ICM at low redshifts (Vogelsberger et al. 2018). Importantly, the new physical mechanisms included in the TNG model have been shown to return galaxy populations whose star formation activity is in better agreement with observations than previous calculations like Illustris (Genel et al. 2014; Vogelsberger et al. 2014; Sijacki et al. 2015), in galaxy colours (Weinberger et al. 2018; Nelson et al. 2018a), atomic and molecular gas content of satellite galaxies (Stevens et al. 2019), and quenched fractions of central and satellite galaxies taken together with no distinction (z \u2272 2; Donnari et al. 2019). In a companion paper (Donnari et al. 2020), we discuss in detail the level of agreement between TNG results and observations when centrals and group and cluster satellites are considered separately and show that the quenched fractions of TNG galaxies are overall consistent with observational constraints and hence the results of this paper trustworthy.","Citation Text":["Donnari et al. 2020"],"Citation Start End":[[1847,1866]]}
+{"Identifier":"2021MNRAS.502.2922H__Hayward_et_al._2011_Instance_1","Paragraph":"As discussed in Section 1, to identify SMGs in the simulation, it is ideal to compute individual simulated galaxies\u2019 submm flux densities via dust radiative transfer. The mass and spatial resolution of Illustris and IllustrisTNG are insufficient to resolve the subkpc structure of the ISM, and owing to both the subgrid equation-of-state treatment of stellar feedback and resolution, such simulations tend to feature overly puffy discs and thus underestimate the attenuation (Trayford et al. 2017). Consequently, we do not perform radiative transfer directly. Instead, we use the following relation based on the results of performing radiative transfer on higher resolution hydrodynamical simulations of idealized isolated discs and mergers (Hayward et al. 2011, 2013a):\n(1)$$\\begin{eqnarray*}\r\n\\frac{S_{850}}{\\left(\\text{mJy}\\right)} = 0.81 \\left(\\frac{\\text{SFR}}{100 \\, \\left(\\text{M}_\\odot \\, \\text{yr}^{-1}\\right)} \\right)^{0.43} \\left(\\frac{M_{\\rm dust}}{10^8 \\, \\left(\\text{M}_\\odot \\right)} \\right)^{0.54},\r\n\\end{eqnarray*}$$where SFR is the \u2018instantaneous\u2019 SFR associated with the star-forming gas cells (for consistency with Hayward et al. 2011) and Mdust is the dust mass. When applying the relation, following Hayward et al. (2013b), we incorporate a scatter of 0.13 dex (independent of SFR and dust mass) assuming a Gaussian distribution (Hayward et al. 2011). The submm flux densities predicted using this relation also agree well with the results of performing dust radiative transfer directly on cosmological zoom simulations (Liang et al. 2018; Cochrane et al. 2019) and a semi-analytical model (\u2009Benson, private communication). Moreover, by combining the above with the observed SFR\u2013M\u22c6 and Mdust(M\u22c6, z) relations, one can derive an S850\u2013M\u22c6 relation (Hayward 2012; Hayward et al. 2013a) that agrees reasonably well with that observed for SMGs (Davies et al. 2013). Although given sufficient resolution and unlimited computing time, it would be preferred to perform radiative transfer directly, our approach has the advantage of trivial computational expense, and it may actually be more accurate than direct radiative transfer given the resolution of state-of-the-art large-volume simulations such as Illustris and IllustrisTNG .","Citation Text":["Hayward et al. 2011"],"Citation Start End":[[785,804]]}
+{"Identifier":"2021MNRAS.502.2922H__Hayward_et_al._2011_Instance_2","Paragraph":"As discussed in Section 1, to identify SMGs in the simulation, it is ideal to compute individual simulated galaxies\u2019 submm flux densities via dust radiative transfer. The mass and spatial resolution of Illustris and IllustrisTNG are insufficient to resolve the subkpc structure of the ISM, and owing to both the subgrid equation-of-state treatment of stellar feedback and resolution, such simulations tend to feature overly puffy discs and thus underestimate the attenuation (Trayford et al. 2017). Consequently, we do not perform radiative transfer directly. Instead, we use the following relation based on the results of performing radiative transfer on higher resolution hydrodynamical simulations of idealized isolated discs and mergers (Hayward et al. 2011, 2013a):\n(1)$$\\begin{eqnarray*}\r\n\\frac{S_{850}}{\\left(\\text{mJy}\\right)} = 0.81 \\left(\\frac{\\text{SFR}}{100 \\, \\left(\\text{M}_\\odot \\, \\text{yr}^{-1}\\right)} \\right)^{0.43} \\left(\\frac{M_{\\rm dust}}{10^8 \\, \\left(\\text{M}_\\odot \\right)} \\right)^{0.54},\r\n\\end{eqnarray*}$$where SFR is the \u2018instantaneous\u2019 SFR associated with the star-forming gas cells (for consistency with Hayward et al. 2011) and Mdust is the dust mass. When applying the relation, following Hayward et al. (2013b), we incorporate a scatter of 0.13 dex (independent of SFR and dust mass) assuming a Gaussian distribution (Hayward et al. 2011). The submm flux densities predicted using this relation also agree well with the results of performing dust radiative transfer directly on cosmological zoom simulations (Liang et al. 2018; Cochrane et al. 2019) and a semi-analytical model (\u2009Benson, private communication). Moreover, by combining the above with the observed SFR\u2013M\u22c6 and Mdust(M\u22c6, z) relations, one can derive an S850\u2013M\u22c6 relation (Hayward 2012; Hayward et al. 2013a) that agrees reasonably well with that observed for SMGs (Davies et al. 2013). Although given sufficient resolution and unlimited computing time, it would be preferred to perform radiative transfer directly, our approach has the advantage of trivial computational expense, and it may actually be more accurate than direct radiative transfer given the resolution of state-of-the-art large-volume simulations such as Illustris and IllustrisTNG .","Citation Text":["Hayward et al. 2011"],"Citation Start End":[[1178,1197]]}
+{"Identifier":"2021MNRAS.502.2922H__Hayward_et_al._2011_Instance_3","Paragraph":"As discussed in Section 1, to identify SMGs in the simulation, it is ideal to compute individual simulated galaxies\u2019 submm flux densities via dust radiative transfer. The mass and spatial resolution of Illustris and IllustrisTNG are insufficient to resolve the subkpc structure of the ISM, and owing to both the subgrid equation-of-state treatment of stellar feedback and resolution, such simulations tend to feature overly puffy discs and thus underestimate the attenuation (Trayford et al. 2017). Consequently, we do not perform radiative transfer directly. Instead, we use the following relation based on the results of performing radiative transfer on higher resolution hydrodynamical simulations of idealized isolated discs and mergers (Hayward et al. 2011, 2013a):\n(1)$$\\begin{eqnarray*}\r\n\\frac{S_{850}}{\\left(\\text{mJy}\\right)} = 0.81 \\left(\\frac{\\text{SFR}}{100 \\, \\left(\\text{M}_\\odot \\, \\text{yr}^{-1}\\right)} \\right)^{0.43} \\left(\\frac{M_{\\rm dust}}{10^8 \\, \\left(\\text{M}_\\odot \\right)} \\right)^{0.54},\r\n\\end{eqnarray*}$$where SFR is the \u2018instantaneous\u2019 SFR associated with the star-forming gas cells (for consistency with Hayward et al. 2011) and Mdust is the dust mass. When applying the relation, following Hayward et al. (2013b), we incorporate a scatter of 0.13 dex (independent of SFR and dust mass) assuming a Gaussian distribution (Hayward et al. 2011). The submm flux densities predicted using this relation also agree well with the results of performing dust radiative transfer directly on cosmological zoom simulations (Liang et al. 2018; Cochrane et al. 2019) and a semi-analytical model (\u2009Benson, private communication). Moreover, by combining the above with the observed SFR\u2013M\u22c6 and Mdust(M\u22c6, z) relations, one can derive an S850\u2013M\u22c6 relation (Hayward 2012; Hayward et al. 2013a) that agrees reasonably well with that observed for SMGs (Davies et al. 2013). Although given sufficient resolution and unlimited computing time, it would be preferred to perform radiative transfer directly, our approach has the advantage of trivial computational expense, and it may actually be more accurate than direct radiative transfer given the resolution of state-of-the-art large-volume simulations such as Illustris and IllustrisTNG .","Citation Text":["Hayward et al. 2011"],"Citation Start End":[[1395,1414]]}
 {"Identifier":"2017AandA...599A..19V__Farahani_et_al._2010_Instance_1","Paragraph":"Consider a rotating tornado with a straight magnetic field (\u03a90 \u2260 0,J0 = 0). In this case, the dispersion relation (14) reduces to (15)\\begin{eqnarray} \\lefteqn{(\\omega^{2}-C_{\\mathrm {A}}^{2}k^{2})(\\omega^{2}-C_{\\rm T}^{2}k^{2})}\\nonumber\\\\ & &+\\frac{a^2}{4(C_{\\mathrm {A}}^{2}+C_{\\rm s}^{2})}\\left[4\\Omega_{0}^{2}\\omega^{4}-2\\Omega_0^2k^2C_{\\rm s}^2\\omega^{2} -2\\Omega_0^2k^{4}C_{\\rm s}^{2}C_{\\mathrm {A}}^{2})\\right]\\nonumber\\\\ & &-\\frac{a^2}{4(C_{\\mathrm {A}}^{2}+C_{\\rm s}^{2})}\\left[(\\omega^{2}-C_{\\mathrm {A}}^{2}k^{2})^{2}(\\omega^{2}-C_{\\rm s}^{2}k^{2})\\right]=\\left(\\frac{\\rho_{0e}}{2\\rho_0}\\right)\\nonumber\\\\ & & \\times \\frac{(\\omega^2-k^2C_\\mathrm{A}^2)(\\omega^2-k^2C_{\\rm s}^2)(\\omega^2-k^2C_{\\mathrm{Ae}}^2)a}{(C_\\mathrm{A}^2+C_{\\rm s}^2)m_{\\rm e}}\\frac{K_0(m_{\\rm e}a)}{K_1(m_{\\rm e}a)}\\cdot \\label{rotationext} \\end{eqnarray}(\u03c92\u2212CA2k2)(\u03c92\u2212CT2k2)+a24(CA2+Cs2)[4\u03a902\u03c94\u22122\u03a902k2Cs2\u03c92\u22122\u03a902k4Cs2CA2)]\u2212a24(CA2+Cs2)[(\u03c92\u2212CA2k2)2(\u03c92\u2212Cs2k2)]=\u03c10e2\u03c10The second term on the left-hand side of Eq. (15) shows the effect of the internal rotation where the third term indicates the confinement of the tube. The term on the right-hand side of Eq. (15) shows the effect of the perturbations of the external medium. If we write the dispersion relation in terms of the fast and slow speeds we would have (16)\\begin{eqnarray} &&\\left(C_{\\mathrm {A}}^{2}+C_{\\rm s}^{2}+2{\\cal R}C_{\\mathrm {A}}^{2}\\right)\\left(\\omega^{2}-C_{+}^{2}k^{2}\\right)\\left(\\omega^{2}- C_{-}^{2}k^{2}\\right)\\nonumber\\\\ &&\\quad-\\frac{a^2}{4}\\left(\\omega^{2}-C_{\\mathrm {A}}^{2}k^{2}\\right)^{2}\\left(\\omega^{2}-C_{\\rm s}^{2}k^{2}\\right)= \\left(\\frac{\\rho_{0e}}{2\\rho_0}\\right)\\nonumber\\\\&&\\qquad\\times \\frac{\\left(\\omega^2-k^2C_\\mathrm{A}^2\\right)\\left(\\omega^2-k^2C_{\\rm s}^2\\right)\\left(\\omega^2-k^2C_{\\mathrm{Ae}}^2\\right)a}{m_{\\rm e}}\\frac{K_0(m_{\\rm e}a)}{K_1(m_{\\rm e}a)}, \\end{eqnarray}(CA2+Cs2+2\u211bCA2)(\u03c92\u2212C+2k2)(\u03c92\u2212C\u22122k2)\u2001\u2212a24(\u03c92\u2212CA2k2)2(\u03c92\u2212Cs2k2)=\u03c10e2\u03c10\u2001\u2001\u00d7(\u03c92\u2212k2CA2)(\u03c92\u2212k2Cs2)(\u03c92\u2212k2CAe2)ameK0(mea)K1(mea),where (17)\\begin{eqnarray} \\label{PhaseRotation} C_{\\pm}^{2}&=&C_{\\mathrm {A}}^{2}\\frac{(C_{\\mathrm {A}}^{2}+2C_{\\mathrm {s}}^{2})+{\\cal R}C_{\\mathrm {s}}^{2}\\pm\\sqrt{{\\cal P}}}{2(C_{\\mathrm {A}}^{2}+C_{\\mathrm {s}}^{2})+4C_{\\mathrm {A}}^{2}{\\cal R}},\\nonumber\\\\ {\\cal P}&=&C_{\\mathrm {A}}^{4}-2{\\cal R}C_{\\mathrm {s}}^{2}(C_{\\mathrm {A}}^{2}-4C_{\\mathrm {s}}^2)+{\\cal R}^{2}C_{\\mathrm {s}}^{2}(8C_{\\mathrm {A}}^{2}+C_{\\mathrm {s}}^{2}), \\end{eqnarray}C\u00b12=CA2(CA2+2Cs2)+\u211bCs2\u00b1\ud835\udcab2(CA2+Cs2)+4CA2\u211b,\ud835\udcab=CA4\u22122\u211bCs2(CA2\u22124Cs2)+\u211b2Cs2(8CA2+Cs2),and the dimensionless parameter, \u211b, representing the rotation is (18)\\begin{equation} {\\cal R}=\\frac{a^2\\Omega^{2}_{0}}{2\\,C_{\\mathrm {A}}^{2}}\\cdot \\end{equation}\u211b=a2\u03a9022\u2009CA2\u00b7Equation (17) indicates the modification of the Alfv\u00e9n speed and the tube speed by the equilibrium rotation to the fast (C+) and slow (C\u2212) magnetosonic speeds, respectively (see also Zhugzhda & Nakariakov 1999; Vasheghani Farahani et al. 2010). As such the torsional wave would propagate with the speed C+, and the longitudinal wave would propagate with the speed C\u2212. If we consider the dispersion to be weak (k2A0 \u226a 1), and take \\hbox{$\\omega^{2}\\approx\\,C_{\\pm}^{2}k^{2}$}\u03c92\u2248\u2009C\u00b12k2, an explicit expression for the dispersion relation could be obtained (19)\\begin{eqnarray} \\label{PhaseR} \\omega^{2}&\\approx&\\,C_{\\pm}^{2}k^{2}\\pm\\,\\frac{a^2}{4}\\frac{(C_{\\pm}^{2}-C_{\\mathrm {A}}^{2})^{2}(C_{\\pm}^{2}-C_{\\mathrm {s}}^{2})}{C_{\\mathrm {A}}^{2}\\,\\sqrt{{\\cal P}}}k^{4}+ \\left(\\frac{\\rho_{0e}}{2\\rho_0}\\right)\\nonumber\\\\&&\\quad\\times \\frac{(C_{\\pm}^2-C_\\mathrm{A}^2)(C_{\\pm}^2-C_{\\rm s}^2)(C_{\\pm}^2-C_{\\mathrm{Ae}}^2)a}{GC_{\\mathrm {A}}^{2}\\,\\sqrt{{\\cal P}}}\\nonumber\\\\&&\\quad\\times\\frac{K_0(Ga)}{K_1(Ga)}k^4, \\end{eqnarray}\u03c92\u2248\u2009C\u00b12k2\u00b1\u2009a24(C\u00b12\u2212CA2)2(C\u00b12\u2212Cs2)CA2\u2009\ud835\udcabk4+\u03c10e2\u03c10\u2001\u00d7(C\u00b12\u2212CA2)(C\u00b12\u2212Cs2)(C\u00b12\u2212CAe2)aGCA2\u2009\ud835\udcab\u2001\u00d7K0(Ga)K1(Ga)k4,where (20)\\begin{eqnarray} G^2=\\frac{\\left(k^2C^2_{\\mathrm{Ae}}-C_{\\pm}^2\\right)\\left(k^2C^2_{\\rm se}-C_{\\pm}^2\\right)} {\\left(C^2_{\\mathrm{Ae}}+C^2_{\\rm se}\\right)\\left(k^2C^2_{\\rm Te}-C_{\\pm}^2\\right)}, \\,\\mbox{ \\ } C_{\\rm Te}^{2}=\\frac{C_{\\mathrm {Ae}}^{2}C_{\\rm se}^{2}}{C_{\\mathrm {A}e}^{2}+C_{\\rm se}^{2}}\\cdot \\label{me} \\end{eqnarray}G2=(k2CAe2\u2212C\u00b12)(k2Cse2\u2212C\u00b12)(CAe2+Cse2)(k2CTe2\u2212C\u00b12),\u2009CTe2=CAe2Cse2CAe2+Cse2\u00b7The second term on the right-hand side of Eq. (19) is the dispersive correction term, while the third term on the right-hand side represents the effects of the perturbation of the external medium. Equation (19) clearly shows the interplay of the equilibrium rotation and the density contrast of the internal and external media. The modification of the speeds at k = 0 is clearly exhibited by both the rotation and the density contrast. Hence, the modification of the tube and Alfv\u00e9n speeds to the slow and fast magnetoacoustic speeds is clearly observed, see also Zhugzhda & Nakariakov (1999). In the long wavelength limit where the tube radius is much smaller than the wavelength, the dispersion would be week, therefore the arguments of the modified Bessel function of the second kind K would be small. In such a regime we are able to use the first terms of the expansions of the modified Bessel function of the second kind for small arguments (Abramowitz et al. 1988) which are (21)\\begin{eqnarray} K_{0}(Ga)=-\\mathrm{ln}\\left(\\frac{1}{2}Ga\\right),\\,\\,\\,\\,\\,\\,\\,\\,\\, K_{1}(Ga)=\\frac{1}{Ga}\\cdot \\label{K} \\end{eqnarray}K0(Ga)=\u2212ln12Ga,\u2009\u2009\u2009\u2009\u2009\u2009\u2009\u2009\u2009K1(Ga)=1Ga\u00b7By substituting the terms of Eq. (21) in Eq. (19) we obtain an explicit expression that is easier to read: (22)\\begin{eqnarray} \\omega^{2}\\approx\\,C_{\\pm}^{2}k^{2}\\pm\\,\\frac{a^2}{4}\\frac{(C_{\\pm}^{2}-C_{\\mathrm {A}}^{2})^{2}(C_{\\pm}^{2}-C_{\\mathrm {s}}^{2})}{C_{\\mathrm {A}}^{2}\\,\\sqrt{{\\cal P}}}k^{4}- \\left(\\frac{\\rho_{0e}}{\\rho_0}\\right)\\nonumber\\\\\\times \\frac{a^2}{2}\\frac{(C_{\\pm}^2-C_\\mathrm{A}^2)(C_{\\pm}^2-C_{\\rm s}^2)(C_{\\pm}^2-C_{\\mathrm{Ae}}^2)}{ C_{\\mathrm {A}}^{2}\\,\\sqrt{{\\cal P}}}\\mathrm{ln}\\left(\\frac{1}{2}Ga\\right)k^4. \\label{PhaseR2} \\end{eqnarray}\u03c92\u2248\u2009C\u00b12k2\u00b1\u2009a24(C\u00b12\u2212CA2)2(C\u00b12\u2212Cs2)CA2\u2009\ud835\udcabk4\u2212\u03c10e\u03c10\u00d7a22(C\u00b12\u2212CA2)(C\u00b12\u2212Cs2)(C\u00b12\u2212CAe2)CA2\u2009\ud835\udcabln12Gak4.Equation (22) represents the dispersion relation for magnetoacoustic waves propagating in a steadily rotating magnetic flux tube (e.g. a solar tornado), which is more convenient for observation purposes and coronal seismology. ","Citation Text":["Vasheghani Farahani et al. 2010"],"Citation Start End":[[3001,3032]]}
 {"Identifier":"2020ApJ...889..137M__Bhatawdekar_et_al._2019_Instance_1","Paragraph":"Evolution of the SMD (top) and SFRD (bottom) along the cosmic history (see top axis for the corresponding redshift). For these plots, we assumed all three BBG candidates without ALMA detection to be real passive galaxies at z \u223c 6. In the top panel, the SMD of our BBG sample at z \u223c 6 (red circle) is shown in conjunction with those of star-forming (cyan symbols) and passive (magenta symbols) galaxies at lower redshifts from the literature (M13: Muzzin et al. 2013; D14: Duncan et al. 2014; S14: Straatman et al. 2014; G15: Grazian et al. 2015; S16: Song et al. 2016; D17: Davidzon et al. 2017; B19: Bhatawdekar et al. 2019; K19: Kikuchihara et al. 2019). The vertical error bar associated with our BBG data corresponds to a 1\u03c3 uncertainty propagated from the Poisson error (Gehrels 1986) for the BBG number and the SED fitting uncertainty for the stellar mass. The horizontal error bar shows the redshift range expected from our BBG color selection. In the bottom panel, the red shaded region corresponds to the SFRD expected from the progenitors of the z \u223c 6 BBGs at a 99.7% confidence level (3\u03c3). The SFRD measurements at \n\n\n\n\n\n are collected from the literature (MD14: Madau & Dickinson 2014; O13: Oesch et al. 2013; O14: Oesch et al. 2014; F15: Finkelstein et al. 2015a; M16: McLeod et al. 2016; B16: Bouwens et al. 2016; I18: Ishigaki et al. 2018; O18: Oesch et al. 2018; B19: Bhatawdekar et al. 2019). All of them at \n\n\n\n\n\n are estimated by integrating the UVLFs down to MUV = \u221217 mag. The SFRD estimated at z \u223c 17 from an observed global 21 cm absorption trough (M18: Madau 2018; Bowman et al. 2018) is also shown in yellow. The functional fit to the MD14 data, which is proportional to (1 + z)\u22122.9 at high-z (Madau & Dickinson 2014), is superposed by the solid line. Two other power-law functions supporting an accelerated evolution at z \u2273 8 (\n\n\n\n\n\n Oesch et al. 2014) and a smooth evolution from lower redshift (\n\n\n\n\n\n Finkelstein et al. 2015a) are shown by dotted\u2013dashed and dotted lines, respectively. The SFRD derived assuming a universal relation among the halo mass, SFR, and dark matter accretion rate (Harikane et al. 2018) is also superposed by the gray shade in its 1\u03c3 uncertainty. All of the SMD and SFRD measurements from the literature are corrected for the stellar IMF and the cosmological model to match those in this work.","Citation Text":["Bhatawdekar et al. 2019"],"Citation Start End":[[648,671]]}
 {"Identifier":"2020ApJ...889..137M__Bhatawdekar_et_al._2019_Instance_2","Paragraph":"Evolution of the SMD (top) and SFRD (bottom) along the cosmic history (see top axis for the corresponding redshift). For these plots, we assumed all three BBG candidates without ALMA detection to be real passive galaxies at z \u223c 6. In the top panel, the SMD of our BBG sample at z \u223c 6 (red circle) is shown in conjunction with those of star-forming (cyan symbols) and passive (magenta symbols) galaxies at lower redshifts from the literature (M13: Muzzin et al. 2013; D14: Duncan et al. 2014; S14: Straatman et al. 2014; G15: Grazian et al. 2015; S16: Song et al. 2016; D17: Davidzon et al. 2017; B19: Bhatawdekar et al. 2019; K19: Kikuchihara et al. 2019). The vertical error bar associated with our BBG data corresponds to a 1\u03c3 uncertainty propagated from the Poisson error (Gehrels 1986) for the BBG number and the SED fitting uncertainty for the stellar mass. The horizontal error bar shows the redshift range expected from our BBG color selection. In the bottom panel, the red shaded region corresponds to the SFRD expected from the progenitors of the z \u223c 6 BBGs at a 99.7% confidence level (3\u03c3). The SFRD measurements at \n\n\n\n\n\n are collected from the literature (MD14: Madau & Dickinson 2014; O13: Oesch et al. 2013; O14: Oesch et al. 2014; F15: Finkelstein et al. 2015a; M16: McLeod et al. 2016; B16: Bouwens et al. 2016; I18: Ishigaki et al. 2018; O18: Oesch et al. 2018; B19: Bhatawdekar et al. 2019). All of them at \n\n\n\n\n\n are estimated by integrating the UVLFs down to MUV = \u221217 mag. The SFRD estimated at z \u223c 17 from an observed global 21 cm absorption trough (M18: Madau 2018; Bowman et al. 2018) is also shown in yellow. The functional fit to the MD14 data, which is proportional to (1 + z)\u22122.9 at high-z (Madau & Dickinson 2014), is superposed by the solid line. Two other power-law functions supporting an accelerated evolution at z \u2273 8 (\n\n\n\n\n\n Oesch et al. 2014) and a smooth evolution from lower redshift (\n\n\n\n\n\n Finkelstein et al. 2015a) are shown by dotted\u2013dashed and dotted lines, respectively. The SFRD derived assuming a universal relation among the halo mass, SFR, and dark matter accretion rate (Harikane et al. 2018) is also superposed by the gray shade in its 1\u03c3 uncertainty. All of the SMD and SFRD measurements from the literature are corrected for the stellar IMF and the cosmological model to match those in this work.","Citation Text":["Bhatawdekar et al. 2019"],"Citation Start End":[[1431,1454]]}
@@ -157,9 +170,6 @@
 {"Identifier":"2022MNRAS.510.3876LBouchez_et_al._2018_Instance_1","Paragraph":"Adaptive optics (AO; Beckers 1993) has become a key technology for all the main existing telescopes and is considered an enabling technology for future Extremely Large Telescopes (ELTs; Ramsay et al. 2016; Boyer 2018; Bouchez et al. 2018). AO requires sufficiently bright reference sources for the measurement of the wavefront (WF) distortions introduced by the atmospheric turbulence: Sodium laser guide stars (LGS; Foy & Labeyrie 1985; Tallon & Foy 1990) are currently the only valid option to increase the low sky coverage allowed by the use of natural stars (Ellerbroek & Andersen 2008). A Sodium LGS is generated by a laser beam at 589 nm wavelength that excites the Sodium atoms concentrated in a \u223c13 km thick layer at about 90 km above the ground (Pfrommer & Hickson 2014), returning a photon flux at the same wavelength (Happer et al. 1994; Thomas et al. 2008). The Sodium layer vertical extension and its variable density profile (Pfrommer, Hickson & She 2009; Holzl\u00f6hner et al. 2016) lead to some peculiar complications of the WF sensing process (Lombini 2011). The Shack\u2013Hartmann WF Sensor (SHWS) is the current baseline for the LGS WF sensors (WSs) for the future ELT AO instruments  (Boyer & Ellerbroek 2016; Stuik et al. 2016; Males et al. 2018; Sauvage et al. 2018). The LGS spots appear elongated in the sub-apertures located off-axis with respect to the upward laser beam, due to the parallactic effect; the elongation points at the laser launch location and its amplitude increases with the distance from the launcher itself (Fig. 1). The LGS angular elongation \u03f5 can be approximated by\n(1)$$\\begin{eqnarray}\r\n\\epsilon \\approx r \\frac{\\Delta H}{H^2} \\text{cos}(\\xi) ,\r\n\\end{eqnarray}$$where r is the sub-aperture distance from the launcher, H is the Sodium layer mean altitude, \u0394H is the layer vertical extension, and \u03be is the Zenith angle. The spot position angle \u03c9 is\n(2)$$\\begin{eqnarray}\r\n\\omega = \\text{atan}\\left(\\frac{y_l-y_{s}}{x_l - x_{s}}\\right) ,\r\n\\end{eqnarray}$$","Citation Text":["Bouchez et al. 2018"],"Citation Start End":[[268,287]]}
 {"Identifier":"2022MNRAS.510.3876LPfrommer_&_Hickson_2014_Instance_1","Paragraph":"Adaptive optics (AO; Beckers 1993) has become a key technology for all the main existing telescopes and is considered an enabling technology for future Extremely Large Telescopes (ELTs; Ramsay et al. 2016; Boyer 2018; Bouchez et al. 2018). AO requires sufficiently bright reference sources for the measurement of the wavefront (WF) distortions introduced by the atmospheric turbulence: Sodium laser guide stars (LGS; Foy & Labeyrie 1985; Tallon & Foy 1990) are currently the only valid option to increase the low sky coverage allowed by the use of natural stars (Ellerbroek & Andersen 2008). A Sodium LGS is generated by a laser beam at 589 nm wavelength that excites the Sodium atoms concentrated in a \u223c13 km thick layer at about 90 km above the ground (Pfrommer & Hickson 2014), returning a photon flux at the same wavelength (Happer et al. 1994; Thomas et al. 2008). The Sodium layer vertical extension and its variable density profile (Pfrommer, Hickson & She 2009; Holzl\u00f6hner et al. 2016) lead to some peculiar complications of the WF sensing process (Lombini 2011). The Shack\u2013Hartmann WF Sensor (SHWS) is the current baseline for the LGS WF sensors (WSs) for the future ELT AO instruments  (Boyer & Ellerbroek 2016; Stuik et al. 2016; Males et al. 2018; Sauvage et al. 2018). The LGS spots appear elongated in the sub-apertures located off-axis with respect to the upward laser beam, due to the parallactic effect; the elongation points at the laser launch location and its amplitude increases with the distance from the launcher itself (Fig. 1). The LGS angular elongation \u03f5 can be approximated by\n(1)$$\\begin{eqnarray}\r\n\\epsilon \\approx r \\frac{\\Delta H}{H^2} \\text{cos}(\\xi) ,\r\n\\end{eqnarray}$$where r is the sub-aperture distance from the launcher, H is the Sodium layer mean altitude, \u0394H is the layer vertical extension, and \u03be is the Zenith angle. The spot position angle \u03c9 is\n(2)$$\\begin{eqnarray}\r\n\\omega = \\text{atan}\\left(\\frac{y_l-y_{s}}{x_l - x_{s}}\\right) ,\r\n\\end{eqnarray}$$","Citation Text":["Pfrommer & Hickson 2014"],"Citation Start End":[[805,828]]}
 {"Identifier":"2022MNRAS.510.3876LStuik_et_al._2016_Instance_1","Paragraph":"Adaptive optics (AO; Beckers 1993) has become a key technology for all the main existing telescopes and is considered an enabling technology for future Extremely Large Telescopes (ELTs; Ramsay et al. 2016; Boyer 2018; Bouchez et al. 2018). AO requires sufficiently bright reference sources for the measurement of the wavefront (WF) distortions introduced by the atmospheric turbulence: Sodium laser guide stars (LGS; Foy & Labeyrie 1985; Tallon & Foy 1990) are currently the only valid option to increase the low sky coverage allowed by the use of natural stars (Ellerbroek & Andersen 2008). A Sodium LGS is generated by a laser beam at 589 nm wavelength that excites the Sodium atoms concentrated in a \u223c13 km thick layer at about 90 km above the ground (Pfrommer & Hickson 2014), returning a photon flux at the same wavelength (Happer et al. 1994; Thomas et al. 2008). The Sodium layer vertical extension and its variable density profile (Pfrommer, Hickson & She 2009; Holzl\u00f6hner et al. 2016) lead to some peculiar complications of the WF sensing process (Lombini 2011). The Shack\u2013Hartmann WF Sensor (SHWS) is the current baseline for the LGS WF sensors (WSs) for the future ELT AO instruments  (Boyer & Ellerbroek 2016; Stuik et al. 2016; Males et al. 2018; Sauvage et al. 2018). The LGS spots appear elongated in the sub-apertures located off-axis with respect to the upward laser beam, due to the parallactic effect; the elongation points at the laser launch location and its amplitude increases with the distance from the launcher itself (Fig. 1). The LGS angular elongation \u03f5 can be approximated by\n(1)$$\\begin{eqnarray}\r\n\\epsilon \\approx r \\frac{\\Delta H}{H^2} \\text{cos}(\\xi) ,\r\n\\end{eqnarray}$$where r is the sub-aperture distance from the launcher, H is the Sodium layer mean altitude, \u0394H is the layer vertical extension, and \u03be is the Zenith angle. The spot position angle \u03c9 is\n(2)$$\\begin{eqnarray}\r\n\\omega = \\text{atan}\\left(\\frac{y_l-y_{s}}{x_l - x_{s}}\\right) ,\r\n\\end{eqnarray}$$","Citation Text":["Stuik et al. 2016"],"Citation Start End":[[1272,1289]]}
-{"Identifier":"2021MNRAS.502.2922H__Hayward_et_al._2011_Instance_1","Paragraph":"As discussed in Section 1, to identify SMGs in the simulation, it is ideal to compute individual simulated galaxies\u2019 submm flux densities via dust radiative transfer. The mass and spatial resolution of Illustris and IllustrisTNG are insufficient to resolve the subkpc structure of the ISM, and owing to both the subgrid equation-of-state treatment of stellar feedback and resolution, such simulations tend to feature overly puffy discs and thus underestimate the attenuation (Trayford et al. 2017). Consequently, we do not perform radiative transfer directly. Instead, we use the following relation based on the results of performing radiative transfer on higher resolution hydrodynamical simulations of idealized isolated discs and mergers (Hayward et al. 2011, 2013a):\n(1)$$\\begin{eqnarray*}\r\n\\frac{S_{850}}{\\left(\\text{mJy}\\right)} = 0.81 \\left(\\frac{\\text{SFR}}{100 \\, \\left(\\text{M}_\\odot \\, \\text{yr}^{-1}\\right)} \\right)^{0.43} \\left(\\frac{M_{\\rm dust}}{10^8 \\, \\left(\\text{M}_\\odot \\right)} \\right)^{0.54},\r\n\\end{eqnarray*}$$where SFR is the \u2018instantaneous\u2019 SFR associated with the star-forming gas cells (for consistency with Hayward et al. 2011) and Mdust is the dust mass. When applying the relation, following Hayward et al. (2013b), we incorporate a scatter of 0.13 dex (independent of SFR and dust mass) assuming a Gaussian distribution (Hayward et al. 2011). The submm flux densities predicted using this relation also agree well with the results of performing dust radiative transfer directly on cosmological zoom simulations (Liang et al. 2018; Cochrane et al. 2019) and a semi-analytical model (\u2009Benson, private communication). Moreover, by combining the above with the observed SFR\u2013M\u22c6 and Mdust(M\u22c6, z) relations, one can derive an S850\u2013M\u22c6 relation (Hayward 2012; Hayward et al. 2013a) that agrees reasonably well with that observed for SMGs (Davies et al. 2013). Although given sufficient resolution and unlimited computing time, it would be preferred to perform radiative transfer directly, our approach has the advantage of trivial computational expense, and it may actually be more accurate than direct radiative transfer given the resolution of state-of-the-art large-volume simulations such as Illustris and IllustrisTNG .","Citation Text":["Hayward et al. 2011","Hayward et al. 2011"],"Citation Start End":[[785,804],[1178,1197]]}
-{"Identifier":"2021MNRAS.502.2922H__Hayward_et_al._2011_Instance_3","Paragraph":"As discussed in Section 1, to identify SMGs in the simulation, it is ideal to compute individual simulated galaxies\u2019 submm flux densities via dust radiative transfer. The mass and spatial resolution of Illustris and IllustrisTNG are insufficient to resolve the subkpc structure of the ISM, and owing to both the subgrid equation-of-state treatment of stellar feedback and resolution, such simulations tend to feature overly puffy discs and thus underestimate the attenuation (Trayford et al. 2017). Consequently, we do not perform radiative transfer directly. Instead, we use the following relation based on the results of performing radiative transfer on higher resolution hydrodynamical simulations of idealized isolated discs and mergers (Hayward et al. 2011, 2013a):\n(1)$$\\begin{eqnarray*}\r\n\\frac{S_{850}}{\\left(\\text{mJy}\\right)} = 0.81 \\left(\\frac{\\text{SFR}}{100 \\, \\left(\\text{M}_\\odot \\, \\text{yr}^{-1}\\right)} \\right)^{0.43} \\left(\\frac{M_{\\rm dust}}{10^8 \\, \\left(\\text{M}_\\odot \\right)} \\right)^{0.54},\r\n\\end{eqnarray*}$$where SFR is the \u2018instantaneous\u2019 SFR associated with the star-forming gas cells (for consistency with Hayward et al. 2011) and Mdust is the dust mass. When applying the relation, following Hayward et al. (2013b), we incorporate a scatter of 0.13 dex (independent of SFR and dust mass) assuming a Gaussian distribution (Hayward et al. 2011). The submm flux densities predicted using this relation also agree well with the results of performing dust radiative transfer directly on cosmological zoom simulations (Liang et al. 2018; Cochrane et al. 2019) and a semi-analytical model (\u2009Benson, private communication). Moreover, by combining the above with the observed SFR\u2013M\u22c6 and Mdust(M\u22c6, z) relations, one can derive an S850\u2013M\u22c6 relation (Hayward 2012; Hayward et al. 2013a) that agrees reasonably well with that observed for SMGs (Davies et al. 2013). Although given sufficient resolution and unlimited computing time, it would be preferred to perform radiative transfer directly, our approach has the advantage of trivial computational expense, and it may actually be more accurate than direct radiative transfer given the resolution of state-of-the-art large-volume simulations such as Illustris and IllustrisTNG .","Citation Text":["Hayward et al. 2011"],"Citation Start End":[[1395,1414]]}
-{"Identifier":"2021MNRAS.502.2922H__Hayward_et_al._2011_Instance_2","Paragraph":"As discussed in Section 1, to identify SMGs in the simulation, it is ideal to compute individual simulated galaxies\u2019 submm flux densities via dust radiative transfer. The mass and spatial resolution of Illustris and IllustrisTNG are insufficient to resolve the subkpc structure of the ISM, and owing to both the subgrid equation-of-state treatment of stellar feedback and resolution, such simulations tend to feature overly puffy discs and thus underestimate the attenuation (Trayford et al. 2017). Consequently, we do not perform radiative transfer directly. Instead, we use the following relation based on the results of performing radiative transfer on higher resolution hydrodynamical simulations of idealized isolated discs and mergers (Hayward et al. 2011, 2013a):\n(1)$$\\begin{eqnarray*}\r\n\\frac{S_{850}}{\\left(\\text{mJy}\\right)} = 0.81 \\left(\\frac{\\text{SFR}}{100 \\, \\left(\\text{M}_\\odot \\, \\text{yr}^{-1}\\right)} \\right)^{0.43} \\left(\\frac{M_{\\rm dust}}{10^8 \\, \\left(\\text{M}_\\odot \\right)} \\right)^{0.54},\r\n\\end{eqnarray*}$$where SFR is the \u2018instantaneous\u2019 SFR associated with the star-forming gas cells (for consistency with Hayward et al. 2011) and Mdust is the dust mass. When applying the relation, following Hayward et al. (2013b), we incorporate a scatter of 0.13 dex (independent of SFR and dust mass) assuming a Gaussian distribution (Hayward et al. 2011). The submm flux densities predicted using this relation also agree well with the results of performing dust radiative transfer directly on cosmological zoom simulations (Liang et al. 2018; Cochrane et al. 2019) and a semi-analytical model (\u2009Benson, private communication). Moreover, by combining the above with the observed SFR\u2013M\u22c6 and Mdust(M\u22c6, z) relations, one can derive an S850\u2013M\u22c6 relation (Hayward 2012; Hayward et al. 2013a) that agrees reasonably well with that observed for SMGs (Davies et al. 2013). Although given sufficient resolution and unlimited computing time, it would be preferred to perform radiative transfer directly, our approach has the advantage of trivial computational expense, and it may actually be more accurate than direct radiative transfer given the resolution of state-of-the-art large-volume simulations such as Illustris and IllustrisTNG .","Citation Text":[],"Citation Start End":[]}
 {"Identifier":"2016ApJ...832...27A__Emslie_et_al._2012_Instance_1","Paragraph":"The energy partition study of Emslie et al. (2012) was restricted to 38 large solar eruptive events. In a more comprehensive study of the global flare energetics we choose a data set that contains the 400 largest (GOES M- and X-class) flare events observed during the first 3.5 years of the SDO era. Previously, we determined the dissipated magnetic energies Emag in these flares based on fitting the vertical-current approximation of a nonlinear force-free field (NLFFF) solution to the loop geometries detected in EUV images from SDO\/AIA, a new method that could be applied to 177 events with a heliographic longitude of \n\n\n\n\n\n (Paper I). We also determined the thermal energy Eth in the soft X-ray and EUV-emitting plasma during the flare peak times based on a multi-temperature DEM forward-fitting method to SDO\/AIA image pixels with spatial synthesis, which was applicable to 391 events (Paper II). In the present study, we determined the nonthermal energy Ent contained in accelerated electrons based on spectral fits to RHESSI data using the OSPEX software, which was applicable to 191 events. The major conclusions of the new results emerging from this study are as follows.\n\n1.\nThe (logarithmic) mean energy ratio of the nonthermal energy to the total magnetically dissipated flare energy is found to be \n\n\n\n\n\n, with a logarithmic standard deviation corresponding to a factor of \n\n\n\n\n\n, which yields an uncertainty of \n\n\n\n\n\n for the mean, i.e., \n\n\n\n\n\n. The majority (\n\n\n\n\n\n) of the flare events fulfill the inequality \n\n\n\n\n\n, which suggests that magnetic energy dissipation (most likely by a magnetic reconnection process) provides sufficient energy to accelerate the nonthermal electrons detected by bremsstrahlung in hard X-rays. Our results yield an order of magnitude higher electron acceleration efficiency than previous estimates, i.e., \n\n\n\n\n\n (with N = 37, Emslie et al. 2012).\n\n\n2.\nThe (logarithmic) mean of the thermal energy Eth to the nonthermal energy Ent is found to be \n\n\n\n\n\n, with a logarithmic standard deviation corresponding to a factor of \n\n\n\n\n\n. The fraction of flares with thermal energy smaller than the nonthermal energy, as expected in the thick-target model, is found to be the case for \n\n\n\n\n\n only. Therefore, the thick-target model is sufficient to explain the full amount of thermal energy in most flares, in the framework of the warm-target model. The cross-over method shows the opposite tendency, but we suspect that the cross-over method overestimates the low-energy cutoff and underestimates the nonthermal energies. Previous estimates yielded a similar ratio, i.e., \n\n\n\n\n\n (Emslie et al. 2012).\n\n\n3.\nA corollary of the two previous conclusions is that the thermal to magnetic energy ratio is \n\n\n\n\n\n. A total of 95% of flares fulfills the inequality \n\n\n\n\n\n, indicating that all thermal energy in flares is supplied by magnetic energy. Previous estimates were a factor of 17 lower, i.e., \n\n\n\n\n\n (Emslie et al. 2012), which would imply a very inefficient magnetic to thermal energy conversion process.\n\n\n4.\nThe largest uncertainty in the calculation of nonthermal energies, the low-energy cutoff, is found to yield different values for two used methods, i.e., \n\n\n\n\n\n keV for the warm thick-target model, versus \n\n\n\n\n\n for the thermal\/nonthermal cross-over method. The calculation of the nonthermal energies is highly sensitive to the value of the low-energy cutoff, which strongly depends on the assumed (warm-target) temperature.\n\n\n5.\nThe flare temperature can be characterized with three different definitions, for which we found the following (67%-standard deviation) ranges: \n\n\n\n\n\n MK for the AIA DEM peak temperature, \n\n\n\n\n\n MK for the emission measure-weighted temperatures, and \n\n\n\n\n\n MK for the RHESSI high-temperature DEM tails. The median ratios are found to be \n\n\n\n\n\n and \n\n\n\n\n\n. The mean active region temperature evaluated from DEMs with AIA, Te = 8.6 MK, is used to estimate the low-energy cutoff ec of the nonthermal component according to the warm-target model, i.e., \n\n\n\n\n\n. The low-energy cutoff ec of the nonthermal spectrum has a strong functional dependence on the temperature TR.\n\n\n","Citation Text":["Emslie et al. (2012)"],"Citation Start End":[[72,92]]}
 {"Identifier":"2016ApJ...832...27A__Emslie_et_al._2012_Instance_2","Paragraph":"The energy partition study of Emslie et al. (2012) was restricted to 38 large solar eruptive events. In a more comprehensive study of the global flare energetics we choose a data set that contains the 400 largest (GOES M- and X-class) flare events observed during the first 3.5 years of the SDO era. Previously, we determined the dissipated magnetic energies Emag in these flares based on fitting the vertical-current approximation of a nonlinear force-free field (NLFFF) solution to the loop geometries detected in EUV images from SDO\/AIA, a new method that could be applied to 177 events with a heliographic longitude of \n\n\n\n\n\n (Paper I). We also determined the thermal energy Eth in the soft X-ray and EUV-emitting plasma during the flare peak times based on a multi-temperature DEM forward-fitting method to SDO\/AIA image pixels with spatial synthesis, which was applicable to 391 events (Paper II). In the present study, we determined the nonthermal energy Ent contained in accelerated electrons based on spectral fits to RHESSI data using the OSPEX software, which was applicable to 191 events. The major conclusions of the new results emerging from this study are as follows.\n\n1.\nThe (logarithmic) mean energy ratio of the nonthermal energy to the total magnetically dissipated flare energy is found to be \n\n\n\n\n\n, with a logarithmic standard deviation corresponding to a factor of \n\n\n\n\n\n, which yields an uncertainty of \n\n\n\n\n\n for the mean, i.e., \n\n\n\n\n\n. The majority (\n\n\n\n\n\n) of the flare events fulfill the inequality \n\n\n\n\n\n, which suggests that magnetic energy dissipation (most likely by a magnetic reconnection process) provides sufficient energy to accelerate the nonthermal electrons detected by bremsstrahlung in hard X-rays. Our results yield an order of magnitude higher electron acceleration efficiency than previous estimates, i.e., \n\n\n\n\n\n (with N = 37, Emslie et al. 2012).\n\n\n2.\nThe (logarithmic) mean of the thermal energy Eth to the nonthermal energy Ent is found to be \n\n\n\n\n\n, with a logarithmic standard deviation corresponding to a factor of \n\n\n\n\n\n. The fraction of flares with thermal energy smaller than the nonthermal energy, as expected in the thick-target model, is found to be the case for \n\n\n\n\n\n only. Therefore, the thick-target model is sufficient to explain the full amount of thermal energy in most flares, in the framework of the warm-target model. The cross-over method shows the opposite tendency, but we suspect that the cross-over method overestimates the low-energy cutoff and underestimates the nonthermal energies. Previous estimates yielded a similar ratio, i.e., \n\n\n\n\n\n (Emslie et al. 2012).\n\n\n3.\nA corollary of the two previous conclusions is that the thermal to magnetic energy ratio is \n\n\n\n\n\n. A total of 95% of flares fulfills the inequality \n\n\n\n\n\n, indicating that all thermal energy in flares is supplied by magnetic energy. Previous estimates were a factor of 17 lower, i.e., \n\n\n\n\n\n (Emslie et al. 2012), which would imply a very inefficient magnetic to thermal energy conversion process.\n\n\n4.\nThe largest uncertainty in the calculation of nonthermal energies, the low-energy cutoff, is found to yield different values for two used methods, i.e., \n\n\n\n\n\n keV for the warm thick-target model, versus \n\n\n\n\n\n for the thermal\/nonthermal cross-over method. The calculation of the nonthermal energies is highly sensitive to the value of the low-energy cutoff, which strongly depends on the assumed (warm-target) temperature.\n\n\n5.\nThe flare temperature can be characterized with three different definitions, for which we found the following (67%-standard deviation) ranges: \n\n\n\n\n\n MK for the AIA DEM peak temperature, \n\n\n\n\n\n MK for the emission measure-weighted temperatures, and \n\n\n\n\n\n MK for the RHESSI high-temperature DEM tails. The median ratios are found to be \n\n\n\n\n\n and \n\n\n\n\n\n. The mean active region temperature evaluated from DEMs with AIA, Te = 8.6 MK, is used to estimate the low-energy cutoff ec of the nonthermal component according to the warm-target model, i.e., \n\n\n\n\n\n. The low-energy cutoff ec of the nonthermal spectrum has a strong functional dependence on the temperature TR.\n\n\n","Citation Text":["Emslie et al. 2012"],"Citation Start End":[[1915,1933]]}
 {"Identifier":"2016ApJ...832...27A__Emslie_et_al._2012_Instance_3","Paragraph":"The energy partition study of Emslie et al. (2012) was restricted to 38 large solar eruptive events. In a more comprehensive study of the global flare energetics we choose a data set that contains the 400 largest (GOES M- and X-class) flare events observed during the first 3.5 years of the SDO era. Previously, we determined the dissipated magnetic energies Emag in these flares based on fitting the vertical-current approximation of a nonlinear force-free field (NLFFF) solution to the loop geometries detected in EUV images from SDO\/AIA, a new method that could be applied to 177 events with a heliographic longitude of \n\n\n\n\n\n (Paper I). We also determined the thermal energy Eth in the soft X-ray and EUV-emitting plasma during the flare peak times based on a multi-temperature DEM forward-fitting method to SDO\/AIA image pixels with spatial synthesis, which was applicable to 391 events (Paper II). In the present study, we determined the nonthermal energy Ent contained in accelerated electrons based on spectral fits to RHESSI data using the OSPEX software, which was applicable to 191 events. The major conclusions of the new results emerging from this study are as follows.\n\n1.\nThe (logarithmic) mean energy ratio of the nonthermal energy to the total magnetically dissipated flare energy is found to be \n\n\n\n\n\n, with a logarithmic standard deviation corresponding to a factor of \n\n\n\n\n\n, which yields an uncertainty of \n\n\n\n\n\n for the mean, i.e., \n\n\n\n\n\n. The majority (\n\n\n\n\n\n) of the flare events fulfill the inequality \n\n\n\n\n\n, which suggests that magnetic energy dissipation (most likely by a magnetic reconnection process) provides sufficient energy to accelerate the nonthermal electrons detected by bremsstrahlung in hard X-rays. Our results yield an order of magnitude higher electron acceleration efficiency than previous estimates, i.e., \n\n\n\n\n\n (with N = 37, Emslie et al. 2012).\n\n\n2.\nThe (logarithmic) mean of the thermal energy Eth to the nonthermal energy Ent is found to be \n\n\n\n\n\n, with a logarithmic standard deviation corresponding to a factor of \n\n\n\n\n\n. The fraction of flares with thermal energy smaller than the nonthermal energy, as expected in the thick-target model, is found to be the case for \n\n\n\n\n\n only. Therefore, the thick-target model is sufficient to explain the full amount of thermal energy in most flares, in the framework of the warm-target model. The cross-over method shows the opposite tendency, but we suspect that the cross-over method overestimates the low-energy cutoff and underestimates the nonthermal energies. Previous estimates yielded a similar ratio, i.e., \n\n\n\n\n\n (Emslie et al. 2012).\n\n\n3.\nA corollary of the two previous conclusions is that the thermal to magnetic energy ratio is \n\n\n\n\n\n. A total of 95% of flares fulfills the inequality \n\n\n\n\n\n, indicating that all thermal energy in flares is supplied by magnetic energy. Previous estimates were a factor of 17 lower, i.e., \n\n\n\n\n\n (Emslie et al. 2012), which would imply a very inefficient magnetic to thermal energy conversion process.\n\n\n4.\nThe largest uncertainty in the calculation of nonthermal energies, the low-energy cutoff, is found to yield different values for two used methods, i.e., \n\n\n\n\n\n keV for the warm thick-target model, versus \n\n\n\n\n\n for the thermal\/nonthermal cross-over method. The calculation of the nonthermal energies is highly sensitive to the value of the low-energy cutoff, which strongly depends on the assumed (warm-target) temperature.\n\n\n5.\nThe flare temperature can be characterized with three different definitions, for which we found the following (67%-standard deviation) ranges: \n\n\n\n\n\n MK for the AIA DEM peak temperature, \n\n\n\n\n\n MK for the emission measure-weighted temperatures, and \n\n\n\n\n\n MK for the RHESSI high-temperature DEM tails. The median ratios are found to be \n\n\n\n\n\n and \n\n\n\n\n\n. The mean active region temperature evaluated from DEMs with AIA, Te = 8.6 MK, is used to estimate the low-energy cutoff ec of the nonthermal component according to the warm-target model, i.e., \n\n\n\n\n\n. The low-energy cutoff ec of the nonthermal spectrum has a strong functional dependence on the temperature TR.\n\n\n","Citation Text":["Emslie et al. 2012"],"Citation Start End":[[2659,2677]]}
@@ -203,8 +213,6 @@
 {"Identifier":"2022ApJ...925...30L__Liu_et_al._2021_Instance_4","Paragraph":"The angular dispersion function method (hereafter the ADF method; Falceta-Gon\u00e7alves et al. 2008; Hildebrand et al. 2009; Houde et al. 2009, 2016) analytically accounts for various of effects that may affect the measured angular dispersion. Based on different effects considered, the ADF methods can be divided into the structure function method (hereafter the Hil09 method; Hildebrand et al. 2009), the autocorrelation function method for single-dish observations (hereafter the Hou09 method; Houde et al. 2009), and the autocorrelation function method for interferometer observations (hereafter the Hou16 method; Houde et al. 2016). Similarly, we adopt the correction factors in Liu et al. (2021) for strong field models. For the Hil09 method, the corrected plane-of-sky uniform magnetic field strength is estimated as\n6\n\n\n\nBposu,Hil09,est\u223c0.1\u03bc0\u03c1\u03b4vlos\u3008Bt2\u3009\u3008B02\u3009\u221212Hil09\n\nand the corrected plane-of-sky total magnetic field strength is estimated as\n7\n\n\n\nBpostot,Hil09,est\u223c0.21\u03bc0\u03c1\u03b4vlos\u3008Bt2\u3009\u3008B2\u3009\u221212Hil09,\n\nwhere \n\n\n\n((\u3008Bt2\u3009\/\u3008B02\u3009)0.5)Hil09\n\n is the turbulent-to-ordered field strength ratio and \n\n\n\n((\u3008Bt2\u3009\/\u3008B2\u3009)0.5)Hil09\n\n is the turbulent-to-total field strength ratio derived from this method. We do not calculate \n\n\n\nBposu,Hil09,est\n\n if \n\n\n\n((\u3008Bt2\u3009\/\u3008B02\u3009)0.5)Hil09>0.1\n\n (Liu et al. 2021). For the Hou09 and Hou16 methods, the corrected plane-of-sky uniform magnetic field strength is estimated as\n8\n\n\n\nBposu,Hou,est\u223c0.19\u03bc0\u03c1\u03b4vlos\u3008Bt2\u3009\u3008B02\u3009\u221212Hou\n\nand the corrected plane-of-sky total magnetic field strength is estimated as\n9\n\n\n\nBpostot,Hou,est\u223c0.39\u03bc0\u03c1\u03b4vlos\u3008Bt2\u3009\u3008B2\u3009\u221212Hou,\n\nwhere \n\n\n\n((\u3008Bt2\u3009\/\u3008B02\u3009)0.5)Hou\n\n is the turbulent-to-ordered field strength ratio and \n\n\n\n((\u3008Bt2\u3009\/\u3008B2\u3009)0.5)Hou\n\n is the turbulent-to-total field strength ratio derived from the two methods. Due to the limitation that the angular dispersion cannot exceed the value expected for a random field, the maximum derivable turbulent-to-ordered field strength ratio from the ADF methods is 0.76 (Liu et al. 2021). Thus, if the derived \n\n\n\n((\u3008Bt2\u3009\/\u3008B02\u3009)0.5)Hou\n\n is greater than 0.76, the assumptions underlying the ADF methods on accounting for the line-of-sight signal integration may not be valid, which could lead to overestimation of the turbulent-to-ordered field strength ratio and underestimation of the field strength. In this situation, we adopt the turbulent-to-ordered field strength ratio \n\n\n\n((\u3008Bt2\u3009\/\u3008B02\u3009)0.5)nosiHou\n\n and the turbulent-to-total field strength ratio \n\n\n\n((\u3008Bt2\u3009\/\u3008B2\u3009)0.5)nosiHou\n\n without accounting for the line-of-sight signal integration and apply the same correction factors as those for the Hil09 method. Then the corrected plane-of-sky uniform magnetic field strength is estimated as\n10\n\n\n\nBposu,Hou,est\u223c0.1\u03bc0\u03c1\u03b4vlos(\u3008Bt2\u3009\u3008B02\u3009\u221212)nosiHou\n\nand the corrected plane-of-sky total magnetic field strength is estimated as\n11\n\n\n\nBpostot,Hou,est\u223c0.21\u03bc0\u03c1\u03b4vlos(\u3008Bt2\u3009\u3008B2\u3009\u221212)nosiHou,\n\nwhere \n\n\n\n((\u3008Bt2\u3009\/\u3008B02\u3009)0.5)nosiHou=((\u3008Bt2\u3009\/\u3008B02\u3009)0.5)Hou\/Nadf\n\n. N\nadf is the number of turbulent fluid elements along the line of sight. Similarly, we do not calculate \n\n\n\nBposu,Hou,est\n\n if \n\n\n\n((\u3008Bt2\u3009\/\u3008B02\u3009)0.5)nosiHou>0.1\n\n (Liu et al. 2021).","Citation Text":["Liu et al. 2021"],"Citation Start End":[[3151,3166]]}
 {"Identifier":"2021AandA...647A.177D__Mozunder_et_al._1968_Instance_1","Paragraph":"An estimate of a sputtering cross-section can be inferred from our measurements with \u03c3s \u2248 V\u2215d, where V is the volume occupied by \n\n${Y}_{\\textrm{s}}^{\\infty}$Ys\u221e\n molecules and d the depth of sputtering. \n\n$\\sigma_{\\textrm{s}}\\approx {Y}_{\\textrm{s}}^{\\infty}\/l_{\\textrm{d}}\/\\textrm{ml}$\u03c3s\u2248Ys\u221e\/ld\/ml\n, where ml is the number of CO or CO2 molecules cm\u22122 in a monolayer (about 6.7 \u00d7 1014 cm\u22122 and 5.7 \u00d7 1014 cm\u22122, respectively,with the adopted ice densities). As is shown in Table 1, the sputtering radius rs would therefore be about 1.26 to 2.12 times larger than the radiolysis destruction radius rd in the case of the CO2 ice, and 2.03 to 2.36 for CO in the considered energy range (~0.5-1 MeV\/u). The net radiolysis is the combined effect of the direct primary excitations and ionisations, the core of the energy deposition by the ion, and the so-called delta rays (energetic secondary electrons) travelling at much larger distances from the core; that is, several hundreds of nanometres at the considered energies in this work (e.g. Mozunder et al. 1968; Magee & Chatterjee 1980; Katz et al. 1990; Moribayashi 2014; Awad & Abu-Shady 2020). The effective radiolysis track radius that we calculate is lower than the sputtering one, which points towards a large fraction of the energy deposited in the core of the track. The scatter on the ratio of these radii is due to the lack of more precise data. It nevertheless allows to put a rough constraint on the estimate of Nd in the absence of additional depth measurements, with \n\n${N}_{\\textrm{d}} \\lesssim {Y}_{\\textrm{s}}^{\\infty}\/\\sigma_{\\textrm{d}}$Nd\u2272Ys\u221e\/\u03c3d\n. If the rs\u2215rd ratio is high, a large amount of species come from the thermal sublimation of an ice spot less affected by radiolysis, and the fraction of ejected intact molecules is higher. The aspect ratio corresponding to these experiments evolves between about ten and twenty for CO2 and CO, whereas for water ice at a stopping power of Se \u2248 3.6 \u00d7 103eV\u22151015 H2 O molecules cm\u22122, we show that it is closer to one (Dartois et al. 2018). The depth of sputtering is much larger for CO and CO2 than for H2O at the same energy deposition, not only because their sublimation rate is higher, but also because they do not form OH bonds. For complex organic molecules embedded in ice mantles dominated by a CO or CO2 ice matrix, with the lack of OH bonding and the sputtering for trace species being driven by that of the matrix (in the astrophysical context), the co-desorption of complex organic molecules present in low proportions with respect to CO\/CO2 cannot only be more efficient, but will thus arise from deeper layers.","Citation Text":["Mozunder et al. 1968"],"Citation Start End":[[1082,1102]]}
 {"Identifier":"2021AandA...647A.17Dartois_et_al._2018_Instance_1","Paragraph":"An estimate of a sputtering cross-section can be inferred from our measurements with \u03c3s \u2248 V\u2215d, where V is the volume occupied by \n\n${Y}_{\\textrm{s}}^{\\infty}$Ys\u221e\n molecules and d the depth of sputtering. \n\n$\\sigma_{\\textrm{s}}\\approx {Y}_{\\textrm{s}}^{\\infty}\/l_{\\textrm{d}}\/\\textrm{ml}$\u03c3s\u2248Ys\u221e\/ld\/ml\n, where ml is the number of CO or CO2 molecules cm\u22122 in a monolayer (about 6.7 \u00d7 1014 cm\u22122 and 5.7 \u00d7 1014 cm\u22122, respectively,with the adopted ice densities). As is shown in Table 1, the sputtering radius rs would therefore be about 1.26 to 2.12 times larger than the radiolysis destruction radius rd in the case of the CO2 ice, and 2.03 to 2.36 for CO in the considered energy range (~0.5-1 MeV\/u). The net radiolysis is the combined effect of the direct primary excitations and ionisations, the core of the energy deposition by the ion, and the so-called delta rays (energetic secondary electrons) travelling at much larger distances from the core; that is, several hundreds of nanometres at the considered energies in this work (e.g. Mozunder et al. 1968; Magee & Chatterjee 1980; Katz et al. 1990; Moribayashi 2014; Awad & Abu-Shady 2020). The effective radiolysis track radius that we calculate is lower than the sputtering one, which points towards a large fraction of the energy deposited in the core of the track. The scatter on the ratio of these radii is due to the lack of more precise data. It nevertheless allows to put a rough constraint on the estimate of Nd in the absence of additional depth measurements, with \n\n${N}_{\\textrm{d}} \\lesssim {Y}_{\\textrm{s}}^{\\infty}\/\\sigma_{\\textrm{d}}$Nd\u2272Ys\u221e\/\u03c3d\n. If the rs\u2215rd ratio is high, a large amount of species come from the thermal sublimation of an ice spot less affected by radiolysis, and the fraction of ejected intact molecules is higher. The aspect ratio corresponding to these experiments evolves between about ten and twenty for CO2 and CO, whereas for water ice at a stopping power of Se \u2248 3.6 \u00d7 103eV\u22151015 H2 O molecules cm\u22122, we show that it is closer to one (Dartois et al. 2018). The depth of sputtering is much larger for CO and CO2 than for H2O at the same energy deposition, not only because their sublimation rate is higher, but also because they do not form OH bonds. For complex organic molecules embedded in ice mantles dominated by a CO or CO2 ice matrix, with the lack of OH bonding and the sputtering for trace species being driven by that of the matrix (in the astrophysical context), the co-desorption of complex organic molecules present in low proportions with respect to CO\/CO2 cannot only be more efficient, but will thus arise from deeper layers.","Citation Text":["Dartois et al. 2018"],"Citation Start End":[[2075,2094]]}
-{"Identifier":"2021MNRAS.500.4004D__Truong_et_al._2020_Instance_1","Paragraph":"Several outcomes from the IllustrisTNG simulations have validated the model against observational constraints, making them suitable for the tasks at hand. Among them we highlight: the shape and width of the red sequence and the blue cloud of z = 0 galaxies (Nelson et al. 2018a), the existence and locus of the star formation main sequence (MS) at low redshifts (Donnari et al. 2019), the distribution of stellar mass across galaxy populations at z \u2272 4 (Pillepich et al. 2018), the galaxy size\u2013mass relation for star-forming and quiescent galaxies at 0 \u2264 z \u2264 2 (Genel et al. 2018), the evolution of the galaxy mass\u2013metallicity relation (Torrey et al. 2018), and quantitatively consistent optical morphologies in comparison to Pan-STARRS data (Rodriguez-Gomez et al. 2019) as far as galaxy properties are concerned. These come in addition to observationally-consistent results in relation to the properties of massive hosts and their intra-halo gas: e.g. the X-ray signals of the hot gaseous atmospheres (Davies et al. 2020; Truong et al. 2020), the amount and distribution of highly ionized Oxygen around galaxies (Nelson et al. 2018b), and the distributions of metals in the ICM at low redshifts (Vogelsberger et al. 2018). Importantly, the new physical mechanisms included in the TNG model have been shown to return galaxy populations whose star formation activity is in better agreement with observations than previous calculations like Illustris (Genel et al. 2014; Vogelsberger et al. 2014; Sijacki et al. 2015), in galaxy colours (Weinberger et al. 2018; Nelson et al. 2018a), atomic and molecular gas content of satellite galaxies (Stevens et al. 2019), and quenched fractions of central and satellite galaxies taken together with no distinction (z \u2272 2; Donnari et al. 2019). In a companion paper (Donnari et al. 2020), we discuss in detail the level of agreement between TNG results and observations when centrals and group and cluster satellites are considered separately and show that the quenched fractions of TNG galaxies are overall consistent with observational constraints and hence the results of this paper trustworthy.","Citation Text":["Truong et al. 2020"],"Citation Start End":[[1066,1084]]}
-{"Identifier":"2021MNRAS.500.4004D_Instance_1","Paragraph":"Several outcomes from the IllustrisTNG simulations have validated the model against observational constraints, making them suitable for the tasks at hand. Among them we highlight: the shape and width of the red sequence and the blue cloud of z = 0 galaxies (Nelson et al. 2018a), the existence and locus of the star formation main sequence (MS) at low redshifts (Donnari et al. 2019), the distribution of stellar mass across galaxy populations at z \u2272 4 (Pillepich et al. 2018), the galaxy size\u2013mass relation for star-forming and quiescent galaxies at 0 \u2264 z \u2264 2 (Genel et al. 2018), the evolution of the galaxy mass\u2013metallicity relation (Torrey et al. 2018), and quantitatively consistent optical morphologies in comparison to Pan-STARRS data (Rodriguez-Gomez et al. 2019) as far as galaxy properties are concerned. These come in addition to observationally-consistent results in relation to the properties of massive hosts and their intra-halo gas: e.g. the X-ray signals of the hot gaseous atmospheres (Davies et al. 2020; Truong et al. 2020), the amount and distribution of highly ionized Oxygen around galaxies (Nelson et al. 2018b), and the distributions of metals in the ICM at low redshifts (Vogelsberger et al. 2018). Importantly, the new physical mechanisms included in the TNG model have been shown to return galaxy populations whose star formation activity is in better agreement with observations than previous calculations like Illustris (Genel et al. 2014; Vogelsberger et al. 2014; Sijacki et al. 2015), in galaxy colours (Weinberger et al. 2018; Nelson et al. 2018a), atomic and molecular gas content of satellite galaxies (Stevens et al. 2019), and quenched fractions of central and satellite galaxies taken together with no distinction (z \u2272 2; Donnari et al. 2019). In a companion paper (Donnari et al. 2020), we discuss in detail the level of agreement between TNG results and observations when centrals and group and cluster satellites are considered separately and show that the quenched fractions of TNG galaxies are overall consistent with observational constraints and hence the results of this paper trustworthy.","Citation Text":[],"Citation Start End":[]}
 {"Identifier":"2018ApJ...860....8X__Liang_&_Zhang_2005_Instance_1","Paragraph":"For GRB 140629A, our analysis suggests that the optical and X-ray afterglows are from a narrow jet (\n\n\n\n\n\n rad) with a low B \n\n\n\n\n\n in a dense medium (n = 60 cm\u22123). In addition, the radiation efficiency of GRB 140629A is extremely low. We test whether or not it satisfies various empirical relations reported in the literature derived from observations of the prompt gamma-ray phase and the multi-wavelength afterglows. By estimating the jet opening angle with a jet-like break time tj in late multi-wavelength light curves, Ghirlanda et al. (2004a) derived a tight correlation between geometrically corrected jet energy \n\n\n\n\n\n and the peak energy \n\n\n\n\n\n of \n\n\n\n\n\n spectrum in the burst frame, i.e., \n\n\n\n\n\n. The \n\n\n\n\n\n value inferred from the Ghirlanda relation is 46 keV for GRB 140629A, which is definitely inconsistent with the data, i.e., \n\n\n\n\n\n. Liang & Zhang (2005) derived an empirical relation between \n\n\n\n\n\n, \n\n\n\n\n\n, and the jet break time (\n\n\n\n\n\n) in the burst frame, i.e., \n\n\n\n\n\n\/\n\n\n\n\n\n\/\n\n\n\n\n\n\/\n\n\n\n\n\nBased on this relation, an isotropic energy \n\n\n\n\n\n erg is obtained, which is larger than that observed by more than one order of magnitude. These results suggest that GRB 140629A does not follow these two relations (Ghirlanda et al. 2004a; Liang & Zhang 2005), although both tight correlations have been used for measuring the cosmological parameters with GRBs (e.g., Dai et al. 2004; Ghirlanda et al. 2004b; Liang & Zhang 2005; Wang et al. 2015a). Note that the observed jet break time of GRB 140629A is much earlier, hence the inferred \u03b8j is much lower than those of the GRBs used to derive these relations (e.g., Frail et al. 2001; Bloom et al. 2003). It is unclear whether the violation of GRB 140629A is due to the selection effect or other physical reasons. For example, two-component jet models composed of a narrow and a wide component have been proposed to explain the data of some GRBs (e.g., Huang et al. 2004; Racusin et al. 2008). In these cases, the high-energy emission was proposed to be emitted by the narrow jet. However, one cannot exclude the possibility that the observed gamma-ray energy would be dominated by the wide jet component under certain conditions. Meanwhile, the early break time for GRB 140629A is likely due to the effect of the narrow jet component but not the wide one. If this is the case, the inconsistency between the jet energy and the opening angle would result in this violation of GRB 140629A. Liang et al. (2015) discovered a tight empirical correlation between Liso, \n\n\n\n\n\n, and \u03930 to reveal the direct connection between the gamma-ray and afterglows,\n7\n\n\n\n\n\nBased on the equation above, we get \n\n\n\n\n\n for GRB 140629A, where the error is calculated from the uncertainties in \n\n\n\n\n\n and \u03930 only. The derived \n\n\n\n\n\n is well consistent with the observed one, \n\n\n\n\n\n erg s\u22121, as shown in Figure 6. Note that the initial Lorentz factor of the ejecta \u03930 is sensitive to the deceleration time (the peak time of the onset bump), but not strongly related to the jet break time. The onset of the afterglow bump is usually bright (Liang et al. 2010, 2013; Li et al. 2012; Wang et al. 2013), and it is easier to identify than the jet break time from an observed light curve.10\n\n10\nThe jet break is usually detected in late optical afterglow light curves. It is dim and also contaminated by emission from the host galaxy and\/or associated supernovae (e.g., Li et al. 2012). This is also an issue in identifying an observed jet break as the narrow or the wide component in the case of a two-component jet.\n The consistency of GRB 140629A with \n\n\n\n\n\n suggests that this relation is more robust than the Ghirlanda or Liang\u2013Zhang relations, since it is not sensitive to the jet opening angle \u03b8j.","Citation Text":["Liang & Zhang (2005)"],"Citation Start End":[[893,913]]}
 {"Identifier":"2018ApJ...860....8X__Liang_&_Zhang_2005_Instance_2","Paragraph":"For GRB 140629A, our analysis suggests that the optical and X-ray afterglows are from a narrow jet (\n\n\n\n\n\n rad) with a low B \n\n\n\n\n\n in a dense medium (n = 60 cm\u22123). In addition, the radiation efficiency of GRB 140629A is extremely low. We test whether or not it satisfies various empirical relations reported in the literature derived from observations of the prompt gamma-ray phase and the multi-wavelength afterglows. By estimating the jet opening angle with a jet-like break time tj in late multi-wavelength light curves, Ghirlanda et al. (2004a) derived a tight correlation between geometrically corrected jet energy \n\n\n\n\n\n and the peak energy \n\n\n\n\n\n of \n\n\n\n\n\n spectrum in the burst frame, i.e., \n\n\n\n\n\n. The \n\n\n\n\n\n value inferred from the Ghirlanda relation is 46 keV for GRB 140629A, which is definitely inconsistent with the data, i.e., \n\n\n\n\n\n. Liang & Zhang (2005) derived an empirical relation between \n\n\n\n\n\n, \n\n\n\n\n\n, and the jet break time (\n\n\n\n\n\n) in the burst frame, i.e., \n\n\n\n\n\n\/\n\n\n\n\n\n\/\n\n\n\n\n\n\/\n\n\n\n\n\nBased on this relation, an isotropic energy \n\n\n\n\n\n erg is obtained, which is larger than that observed by more than one order of magnitude. These results suggest that GRB 140629A does not follow these two relations (Ghirlanda et al. 2004a; Liang & Zhang 2005), although both tight correlations have been used for measuring the cosmological parameters with GRBs (e.g., Dai et al. 2004; Ghirlanda et al. 2004b; Liang & Zhang 2005; Wang et al. 2015a). Note that the observed jet break time of GRB 140629A is much earlier, hence the inferred \u03b8j is much lower than those of the GRBs used to derive these relations (e.g., Frail et al. 2001; Bloom et al. 2003). It is unclear whether the violation of GRB 140629A is due to the selection effect or other physical reasons. For example, two-component jet models composed of a narrow and a wide component have been proposed to explain the data of some GRBs (e.g., Huang et al. 2004; Racusin et al. 2008). In these cases, the high-energy emission was proposed to be emitted by the narrow jet. However, one cannot exclude the possibility that the observed gamma-ray energy would be dominated by the wide jet component under certain conditions. Meanwhile, the early break time for GRB 140629A is likely due to the effect of the narrow jet component but not the wide one. If this is the case, the inconsistency between the jet energy and the opening angle would result in this violation of GRB 140629A. Liang et al. (2015) discovered a tight empirical correlation between Liso, \n\n\n\n\n\n, and \u03930 to reveal the direct connection between the gamma-ray and afterglows,\n7\n\n\n\n\n\nBased on the equation above, we get \n\n\n\n\n\n for GRB 140629A, where the error is calculated from the uncertainties in \n\n\n\n\n\n and \u03930 only. The derived \n\n\n\n\n\n is well consistent with the observed one, \n\n\n\n\n\n erg s\u22121, as shown in Figure 6. Note that the initial Lorentz factor of the ejecta \u03930 is sensitive to the deceleration time (the peak time of the onset bump), but not strongly related to the jet break time. The onset of the afterglow bump is usually bright (Liang et al. 2010, 2013; Li et al. 2012; Wang et al. 2013), and it is easier to identify than the jet break time from an observed light curve.10\n\n10\nThe jet break is usually detected in late optical afterglow light curves. It is dim and also contaminated by emission from the host galaxy and\/or associated supernovae (e.g., Li et al. 2012). This is also an issue in identifying an observed jet break as the narrow or the wide component in the case of a two-component jet.\n The consistency of GRB 140629A with \n\n\n\n\n\n suggests that this relation is more robust than the Ghirlanda or Liang\u2013Zhang relations, since it is not sensitive to the jet opening angle \u03b8j.","Citation Text":["Liang & Zhang 2005"],"Citation Start End":[[1293,1311]]}
 {"Identifier":"2017ApJ...836...65M___2014_Instance_2","Paragraph":"Bolometric magnitudes, \n\n\n\n\n\n, are estimated as the sum of the \n\n\n\n\n\n-band magnitudes, \n\n\n\n\n\n, bolometric correction (\n\n\n\n\n\n), and DMs, i.e., \n\n\n\n\n\n = \n\n\n\n\n\n\u2212\n\n\n\n\n\n+\n\n\n\n\n\n-DM. \n\n\n\n\n\n are adopted from the work of Levesque et al. (2005), which is based on MARCS models. The new temperature scale by Davies et al. (2013) agrees within \u00b1100 K with that of Levesque et al. (2005). Errors in the \n\n\n\n\n\n values are calculated by propagation. \n\n\n\n\n\n magnitude errors are provided in the 2MASS catalog (0.02 mag in average); errors in \n\n\n\n\n\n are described in Section 3.2 (0.02 mag on average); errors in \n\n\n\n\n\n are conservatively assumed to be 0.5 mag\u2014the difference between the \n\n\n\n\n\n values provided by Levesque et al. (2005) for an M0Iab and M2Iab star amounts to \u22480.1 mag, while the typical difference between their \n\n\n\n\n\n values is 0.5 mag (e.g., Verhoelst et al. 2009); rare supergiant Ia can be more than 1 mag brighter. Adopted distance moduli, DMs, are those of Messineo et al. (2016), who estimated distances of 68 (out of 94) targets using extinction as indicator of distance, and calibrating the extinction\u2013distance relation with clump stars surrounding the target (see also Drimmel et al. 2003; Messineo et al. 2014). Errors in the DM values range from 0.12 to 0.36 mag; they have been estimated as a sum of three terms: the uncertainty of the absolute magnitude of clump stars (\u22480.11 mag), the error of the centroid of the Gaussian (0.04\u20130.25 mag, \n\n\n\n\n\n of the Gaussian divided by the square-root of the number of enclosed stars), and the uncertainty in the reddening of clump stars (\n\n\n\n\n\n \u2248 0.06 mag, taken as the half-width of the J \u2212 K bin times 0.537); only CMDs with a well visible trace were considered. To verify these bolometric magnitudes, which are based only on one magnitude (\n\n\n\n\n\n) plus the bolometric corrections by Levesque et al. (2005), we calculated estimates of bolometric magnitudes (\n\n\n\n\n\n) by directly integrating under their stellar energy distribution with the collected infrared measurements (see also Ortiz et al. 2002; Messineo et al. 2004, 2014). We extrapolated to zero the flux on the blue part (from 0 to 1.2 \u03bcm) of the spectrum with a blackbody, and to the red part (beyond 12\u201325 \u03bcm) with a linear fit passing through the last two available flux measurements. The differences between the two estimates of bolometric magnitudes yield an average of 0.09 mag with a \u03c3 = 0.03 mag. We obtained that the red extrapolation contributed only \u22120.004 to 0.002 mag to the total \n\n\n\n\n\n; the blue extrapolation added \u22120.85 mag (for the direct integration only JHKs magnitudes were used and not the DENIS I magnitudes). When including the DENIS I magnitudes, i.e., blue from 0 to 0.8 \u03bcm and green from 0.8 to 12\u201325 \u03bcm, we obtained that the contribution of the blue extrapolation to the total \n\n\n\n\n\n would drop to \u22120.18 mag\u2014extinction in the I-band \n\n\n\n\n\n is assumed to be 6.8 times \n\n\n\n\n\n(Messineo et al. 2005). Table 7 lists the inferred values of \n\n\n\n\n\n, bolometric magnitudes, and adopted DM values.","Citation Text":["Messineo et al.","2014"],"Citation Start End":[[2083,2098],[2105,2109]]}
@@ -283,8 +291,6 @@
 {"Identifier":"2017ApJ...840..118L__Mu_et_al._2016_Instance_3","Paragraph":"Our formula can be used to confront the curvature effect with observations and estimate the decay timescale of the steep decay phase. In observations, the steep decay phase has been observed in the decay phase of the prompt emission phase and flares in GRBs. Since the value of E0 (\n\n\n\n\n\u223c\n0.3\n\u2013\n1\n\nMeV\n\n\n) in the prompt emission phase is significantly larger than \n\n\n\n\n10\n\nkeV\n\n\n, the \u03b2 in the steep decay phase of prompt emission would be a linear function of observer time based on Equation (38). This behavior has been observed in a number of bursts, such as GRBs 050814 (Zhang et al. 2009, please see the spectral evolution in the \n\n\n\n\n\u03b2\n\u2212\n\n\nt\n\n\nobs\n\n\n\n\n space), 051001 etc. The linear relation between \u03b2 and \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n\n\n is also found in the steep decay of flares (e.g., Mu et al. 2016). For a linear function \u03b2 of \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n\n\n, one can obtain the slope of the linear function, which is equal to \n\n\n\n\n7.9\n\n\n\u03ba\n\n\n\u02c6\n\n\n\n\/\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n=\n2.37\n\nkeV\n\n\/\n\n[\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n]\n\n\n based on Equations (38) or (39). Then, the decay timescale \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n\n\n of our studying phase can be estimated if the value of \n\n\n\n\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n\n\n is known. We fit the spectral evolution in the decay phase of a flare (\n\n\n\n\n\u223c\n172\n\ns\n\n\n) in GRB 060904B (Mu et al. 2016) with a linear function. The fitting result, i.e., \n\n\n\n\n\u03b2\n=\n0.84\n+\n0.020\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n\n\n with \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n\n\nt\n\n\nobs\n\n\n\u2212\n\n\nt\n\n\np\n\n\n\n\n, is shown in the left panel of Figure 4 with  a red solid line. Then, we have \n\n\n\n\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n=\n119\n\nkeV\n\ns\n\n\n, which is around that found in Mu et al. (2016), i.e., \n\n\n\n\n2.54\n\nkeV\n\u00d7\n65.39\n\ns\n\n\n. For a flare (\n\n\n\n\n\u223c\n116\n\ns\n\n\n) in GRB 131030A, the spectrum at the beginning of the steep decay phase can be fitted with a Band function. With the fitting result found in Mu et al. (2016), i.e., \n\n\n\n\n\n\n\u03b1\n\n\n\u02c6\n\n\n=\n\u2212\n0.91\n\n\n, \n\n\n\n\n\n\n\u03b2\n\n\n\u02c6\n\n\n=\n\u2212\n3.19\n\n\n, and \n\n\n\n\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n=\n1.95\n\n\n, we plot the evolution of \u03b2 based on Equation (38) in the right panel of Figure 4 with a red solid line. Here, we adopt \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n=\n54\n\ns\n\n\n (Mu et al. 2016), which can also be roughly estimated based on the flux evolution. It can be found that Equation (38) describes the spectral evolution approximately, which may reveal that a more appropriate value of parameters (e.g., \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n\n\n) may be required for this source. The agreement of our analytical formula and observational data shows that the assumption (2) given at the beginning of Section 2 (i.e., the jet shell has no \u03b8-dependent spectral parameters or Lorentz factor) is applicable in reality.","Citation Text":["Mu et al. (2016)"],"Citation Start End":[[1726,1742]]}
 {"Identifier":"2017ApJ...840..118L__Mu_et_al._2016_Instance_2","Paragraph":"Our formula can be used to confront the curvature effect with observations and estimate the decay timescale of the steep decay phase. In observations, the steep decay phase has been observed in the decay phase of the prompt emission phase and flares in GRBs. Since the value of E0 (\n\n\n\n\n\u223c\n0.3\n\u2013\n1\n\nMeV\n\n\n) in the prompt emission phase is significantly larger than \n\n\n\n\n10\n\nkeV\n\n\n, the \u03b2 in the steep decay phase of prompt emission would be a linear function of observer time based on Equation (38). This behavior has been observed in a number of bursts, such as GRBs 050814 (Zhang et al. 2009, please see the spectral evolution in the \n\n\n\n\n\u03b2\n\u2212\n\n\nt\n\n\nobs\n\n\n\n\n space), 051001 etc. The linear relation between \u03b2 and \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n\n\n is also found in the steep decay of flares (e.g., Mu et al. 2016). For a linear function \u03b2 of \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n\n\n, one can obtain the slope of the linear function, which is equal to \n\n\n\n\n7.9\n\n\n\u03ba\n\n\n\u02c6\n\n\n\n\/\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n=\n2.37\n\nkeV\n\n\/\n\n[\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n]\n\n\n based on Equations (38) or (39). Then, the decay timescale \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n\n\n of our studying phase can be estimated if the value of \n\n\n\n\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n\n\n is known. We fit the spectral evolution in the decay phase of a flare (\n\n\n\n\n\u223c\n172\n\ns\n\n\n) in GRB 060904B (Mu et al. 2016) with a linear function. The fitting result, i.e., \n\n\n\n\n\u03b2\n=\n0.84\n+\n0.020\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n\n\n with \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n\n\nt\n\n\nobs\n\n\n\u2212\n\n\nt\n\n\np\n\n\n\n\n, is shown in the left panel of Figure 4 with  a red solid line. Then, we have \n\n\n\n\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n=\n119\n\nkeV\n\ns\n\n\n, which is around that found in Mu et al. (2016), i.e., \n\n\n\n\n2.54\n\nkeV\n\u00d7\n65.39\n\ns\n\n\n. For a flare (\n\n\n\n\n\u223c\n116\n\ns\n\n\n) in GRB 131030A, the spectrum at the beginning of the steep decay phase can be fitted with a Band function. With the fitting result found in Mu et al. (2016), i.e., \n\n\n\n\n\n\n\u03b1\n\n\n\u02c6\n\n\n=\n\u2212\n0.91\n\n\n, \n\n\n\n\n\n\n\u03b2\n\n\n\u02c6\n\n\n=\n\u2212\n3.19\n\n\n, and \n\n\n\n\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n=\n1.95\n\n\n, we plot the evolution of \u03b2 based on Equation (38) in the right panel of Figure 4 with a red solid line. Here, we adopt \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n=\n54\n\ns\n\n\n (Mu et al. 2016), which can also be roughly estimated based on the flux evolution. It can be found that Equation (38) describes the spectral evolution approximately, which may reveal that a more appropriate value of parameters (e.g., \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n\n\n) may be required for this source. The agreement of our analytical formula and observational data shows that the assumption (2) given at the beginning of Section 2 (i.e., the jet shell has no \u03b8-dependent spectral parameters or Lorentz factor) is applicable in reality.","Citation Text":["Mu et al. 2016"],"Citation Start End":[[1373,1387]]}
 {"Identifier":"2017ApJ...840..118L__Mu_et_al._2016_Instance_1","Paragraph":"Our formula can be used to confront the curvature effect with observations and estimate the decay timescale of the steep decay phase. In observations, the steep decay phase has been observed in the decay phase of the prompt emission phase and flares in GRBs. Since the value of E0 (\n\n\n\n\n\u223c\n0.3\n\u2013\n1\n\nMeV\n\n\n) in the prompt emission phase is significantly larger than \n\n\n\n\n10\n\nkeV\n\n\n, the \u03b2 in the steep decay phase of prompt emission would be a linear function of observer time based on Equation (38). This behavior has been observed in a number of bursts, such as GRBs 050814 (Zhang et al. 2009, please see the spectral evolution in the \n\n\n\n\n\u03b2\n\u2212\n\n\nt\n\n\nobs\n\n\n\n\n space), 051001 etc. The linear relation between \u03b2 and \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n\n\n is also found in the steep decay of flares (e.g., Mu et al. 2016). For a linear function \u03b2 of \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n\n\n, one can obtain the slope of the linear function, which is equal to \n\n\n\n\n7.9\n\n\n\u03ba\n\n\n\u02c6\n\n\n\n\/\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n=\n2.37\n\nkeV\n\n\/\n\n[\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n]\n\n\n based on Equations (38) or (39). Then, the decay timescale \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n\n\n of our studying phase can be estimated if the value of \n\n\n\n\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n\n\n is known. We fit the spectral evolution in the decay phase of a flare (\n\n\n\n\n\u223c\n172\n\ns\n\n\n) in GRB 060904B (Mu et al. 2016) with a linear function. The fitting result, i.e., \n\n\n\n\n\u03b2\n=\n0.84\n+\n0.020\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n\n\n with \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n\n\nt\n\n\nobs\n\n\n\u2212\n\n\nt\n\n\np\n\n\n\n\n, is shown in the left panel of Figure 4 with  a red solid line. Then, we have \n\n\n\n\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n=\n119\n\nkeV\n\ns\n\n\n, which is around that found in Mu et al. (2016), i.e., \n\n\n\n\n2.54\n\nkeV\n\u00d7\n65.39\n\ns\n\n\n. For a flare (\n\n\n\n\n\u223c\n116\n\ns\n\n\n) in GRB 131030A, the spectrum at the beginning of the steep decay phase can be fitted with a Band function. With the fitting result found in Mu et al. (2016), i.e., \n\n\n\n\n\n\n\u03b1\n\n\n\u02c6\n\n\n=\n\u2212\n0.91\n\n\n, \n\n\n\n\n\n\n\u03b2\n\n\n\u02c6\n\n\n=\n\u2212\n3.19\n\n\n, and \n\n\n\n\n\n\nE\n\n\n0\n\n\n(\n\n\n\n\nt\n\n\n\n\n\n\n\nobs\n\n\n=\n0\n)\n=\n1.95\n\n\n, we plot the evolution of \u03b2 based on Equation (38) in the right panel of Figure 4 with a red solid line. Here, we adopt \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n=\n54\n\ns\n\n\n (Mu et al. 2016), which can also be roughly estimated based on the flux evolution. It can be found that Equation (38) describes the spectral evolution approximately, which may reveal that a more appropriate value of parameters (e.g., \n\n\n\n\n\n\n\n\nt\n\n\n\n\n\n\n\nc\n\n\n\n\n) may be required for this source. The agreement of our analytical formula and observational data shows that the assumption (2) given at the beginning of Section 2 (i.e., the jet shell has no \u03b8-dependent spectral parameters or Lorentz factor) is applicable in reality.","Citation Text":["Mu et al. 2016"],"Citation Start End":[[828,842]]}
-{"Identifier":"2016MNRAS.455.2131L__Liu_&_Wei_2014_Instance_1","Paragraph":"As we have shown that the Ep\u2013E\u03b3 relation does not significantly evolve with redshift, we can use it to calibrate GRBs. To avoid the circularity problem, the Pad\u00e9 method proposed by Liu & Wei (2014) is applied. The main calibrating procedures are as follows: First, derive the distance-redshift relation of SNe Ia [here we use the Union2.1 (Suzuki et al. 2012) data set] using the Pad\u00e9 approximation of order (3,2), i.e.\n\n(17)\n\n\\begin{equation}\n\\mu (z)=\\frac{\\alpha _0+\\alpha _1z+\\alpha _2z^2+\\alpha _3z^3}{1+\\beta _1z+\\beta _2z^2},\n\\end{equation}\n\nwhere the coefficients (\u03b10, \u03b11, \u03b12, \u03b13, \u03b21, \u03b22) and the corresponding covariance matrix are derived by fitting equation (17) to the Union2.1 data set (see Liu & Wei 2014 for details). Assuming that the low-z GRBs trace the same Hubble diagram to SNe Ia, we can calculate the distance moduli of low-z GRBs directly from equation (17). The uncertainty of \u03bc propagates from the uncertainties of the coefficients (\u03b1i, \u03b2i). Then the luminosity distance of low-z GRBs can be obtained using the relation\n\n(18)\n\n\\begin{equation}\n\\mu (z)=5\\log \\frac{d_L(z)}{\\rm {Mpc}}+25.\n\\end{equation}\n\nAs dL is known, the collimation-corrected energy can be further calculated from equation (11). Note that there are only 12 low-z GRBs and 12 high-z GRBs available since the others have no measurement of jet opening angle. Then we fit the Ep\u2013E\u03b3 relation (i.e. equation (5)) to the 12 low-z GRBs, which gives the best-fitting parameters\n\n(19)\n\n\\begin{eqnarray}\n\\sigma _{\\rm int}=0.161\\pm 0.059,\\ \\ a=50.632\\pm 0.062,\\ \\ b=1.537\\pm 0.145.\\nonumber\\\\\n\\end{eqnarray}\n\nBy directly extrapolating the Ep\u2013E\u03b3 relation to high-z GRBs, we can inversely obtain the collimation-corrected energy for 12 high-z GRBs from equation (5). Finally, calculate the luminosity distance of high-z GRBs from equation (11), and then the distance moduli from equation (18). The uncertainty of distance moduli propagates from the uncertainties of E\u03b3, Sbolo and Fbeam, i.e. (Schaefer 2007),\n\n(20)\n\n\\begin{equation}\n\\sigma _{\\mu }^2=\\left(\\frac{5}{2\\ln 10}\\right)^2\\left[(\\ln 10)^2\\sigma _{\\log E_{\\gamma }}^2 + \\frac{\\sigma _{S_{\\rm bolo}}^2}{S_{\\rm bolo}^2} + \\frac{\\sigma _{F_{\\rm beam}}^2}{F_{\\rm beam}^2}\\right],\n\\end{equation}\n\nwhere\n\n(21)\n\n\\begin{eqnarray}\n\\sigma _{\\log E_{\\gamma }}^2=\\sigma _a^2 + \\left(\\sigma _b\\log \\frac{E_{p,i}}{300\\ {\\rm keV}}\\right)^2 + \\left(\\frac{b}{\\ln 10}\\frac{\\sigma _{E_{p,i}}}{E_{p,i}}\\right)^2 + \\sigma _{\\rm int}^2.\\nonumber\\\\\n\\end{eqnarray}\n\n","Citation Text":["Liu & Wei (2014)","Liu & Wei 2014"],"Citation Start End":[[219,235],[741,755]]}
-{"Identifier":"2016MNRAS.455.2131L__Liu_&_Wei_2014_Instance_2","Paragraph":"As we have shown that the Ep\u2013E\u03b3 relation does not significantly evolve with redshift, we can use it to calibrate GRBs. To avoid the circularity problem, the Pad\u00e9 method proposed by Liu & Wei (2014) is applied. The main calibrating procedures are as follows: First, derive the distance-redshift relation of SNe Ia [here we use the Union2.1 (Suzuki et al. 2012) data set] using the Pad\u00e9 approximation of order (3,2), i.e.\n\n(17)\n\n\\begin{equation}\n\\mu (z)=\\frac{\\alpha _0+\\alpha _1z+\\alpha _2z^2+\\alpha _3z^3}{1+\\beta _1z+\\beta _2z^2},\n\\end{equation}\n\nwhere the coefficients (\u03b10, \u03b11, \u03b12, \u03b13, \u03b21, \u03b22) and the corresponding covariance matrix are derived by fitting equation (17) to the Union2.1 data set (see Liu & Wei 2014 for details). Assuming that the low-z GRBs trace the same Hubble diagram to SNe Ia, we can calculate the distance moduli of low-z GRBs directly from equation (17). The uncertainty of \u03bc propagates from the uncertainties of the coefficients (\u03b1i, \u03b2i). Then the luminosity distance of low-z GRBs can be obtained using the relation\n\n(18)\n\n\\begin{equation}\n\\mu (z)=5\\log \\frac{d_L(z)}{\\rm {Mpc}}+25.\n\\end{equation}\n\nAs dL is known, the collimation-corrected energy can be further calculated from equation (11). Note that there are only 12 low-z GRBs and 12 high-z GRBs available since the others have no measurement of jet opening angle. Then we fit the Ep\u2013E\u03b3 relation (i.e. equation (5)) to the 12 low-z GRBs, which gives the best-fitting parameters\n\n(19)\n\n\\begin{eqnarray}\n\\sigma _{\\rm int}=0.161\\pm 0.059,\\ \\ a=50.632\\pm 0.062,\\ \\ b=1.537\\pm 0.145.\\nonumber\\\\\n\\end{eqnarray}\n\nBy directly extrapolating the Ep\u2013E\u03b3 relation to high-z GRBs, we can inversely obtain the collimation-corrected energy for 12 high-z GRBs from equation (5). Finally, calculate the luminosity distance of high-z GRBs from equation (11), and then the distance moduli from equation (18). The uncertainty of distance moduli propagates from the uncertainties of E\u03b3, Sbolo and Fbeam, i.e. (Schaefer 2007),\n\n(20)\n\n\\begin{equation}\n\\sigma _{\\mu }^2=\\left(\\frac{5}{2\\ln 10}\\right)^2\\left[(\\ln 10)^2\\sigma _{\\log E_{\\gamma }}^2 + \\frac{\\sigma _{S_{\\rm bolo}}^2}{S_{\\rm bolo}^2} + \\frac{\\sigma _{F_{\\rm beam}}^2}{F_{\\rm beam}^2}\\right],\n\\end{equation}\n\nwhere\n\n(21)\n\n\\begin{eqnarray}\n\\sigma _{\\log E_{\\gamma }}^2=\\sigma _a^2 + \\left(\\sigma _b\\log \\frac{E_{p,i}}{300\\ {\\rm keV}}\\right)^2 + \\left(\\frac{b}{\\ln 10}\\frac{\\sigma _{E_{p,i}}}{E_{p,i}}\\right)^2 + \\sigma _{\\rm int}^2.\\nonumber\\\\\n\\end{eqnarray}\n\n","Citation Text":[],"Citation Start End":[]}
 {"Identifier":"2018MNRAS.479.3438G__Dabringhausen,_Hilker_&_Kroupa_2008_Instance_1","Paragraph":"In the single cloud simulations presented in Paper I and Paper II, the system was treated in isolation, i.e. with no external forces acting upon it. In reality, such a binary would be placed deep in the potential well of a galaxy, where stars and dark matter exert their gravitational influence. To mimic the presence of the galactic spheroid, we include an external potential with a Hernquist profile (Hernquist 1990), which can be written as\n(1)\r\n\\begin{eqnarray*}\r\n\\rho (r) = \\frac{M_*}{2\\pi}\\frac{a_*}{r}\\frac{1}{(r+a_*)^3},\r\n\\end{eqnarray*}\r\nand an enclosed mass given by\n(2)\r\n\\begin{eqnarray*}\r\nm(r) = M_*\\frac{r^2}{(r+a_*)^2},\r\n\\end{eqnarray*}\r\nwhere M* and a* are scaling constants that represent the total mass of the spheroid and the size of core, respectively. Based on a typical MBH\u2013Mbulge relation (Magorrian et al. 1998) and a radius-to-stellar-mass relation (Dabringhausen, Hilker & Kroupa 2008), we choose MH = 4.78 \u00d7 102M0 and rH = 3.24 \u00d7 102a0, thus implying\n(3)\r\n\\begin{eqnarray*}\r\nm(a_0) \\approx 5\\times 10^{-3} M_0.\r\n\\end{eqnarray*}\r\nAs a consequence, this external force represents only a small perturbation to the dynamics of the interaction that is still dominated by the binary\u2019s gravitational potential. Moreover, because this external potential is spherically symmetric, orbits experience precession only, where energy and angular momentum are conserved. In principle, this precession could enhance stream collisions, prompting more gas onto the binary, although the time-scales are too long with respect to the frequency of cloud infall, which is the dominant effect in our models. Based on this, we do not expect the oscillations induced by this potential to have a secular effect in the overall evolution of the system during the stages modelled. In practice, this potential maintains the binary close to the centre of the reference frame by applying a restoring force when it drifts away due to the interaction with the incoming material. It is important to mention that the gas also feels this external force.","Citation Text":["Dabringhausen, Hilker & Kroupa 2008"],"Citation Start End":[[933,968]]}
 {"Identifier":"2018AandA...614A..76J__Vollmann_&_Eversberg_(2006)_Instance_1","Paragraph":"For the new observations described in Sect. 3, the spectra are renormalised by applying a linear fit to two wavelength regions, 6455\u20136559 \u212b and 6567\u20136580 \u212b, on either side of the H\u03b1 line. The value for pEW (H\u03b1) is measured over the wavelength range 6560\u20136565 \u212b. The selected wavelength range is sufficiently narrow to exclude nearby spectral lines and sufficiently broad to measure the H\u03b1 line of a fast rotating star. The value of pEW(H\u03b1) is calculated from\n\n(1)\n\n${\\rm{pEW}(H\\alpha)} = \\int^{\\lambda_2}_{\\lambda_1}\n\\left(1-\\frac{F(\\lambda)}{F_{\\rm{pc}}}\\right){\\rm{d}}\\lambda,$pEW(H\u03b1)= \u222b \u03bb1\u03bb2 1-F(\u03bb)Fpc d\u03bb, \n\n\nwhere Fpc is the average of the median flux in the pseudo-continuum in the ranges [6545:6559] and [6567:6580], \u03bb1  = 6560\u212b, \u03bb2  = 6565\u212b, and the error is determined with the method of Vollmann & Eversberg (2006), which is applied as follows:\n\n(2)\n\n$\\sigma_{\\rm{pEW}} = \\frac{\\mathrm\\Delta \\lambda -\n\\rm{pEW(H\\alpha)}}{\\rm{S\/N}} \\sqrt{1 + \\frac{F_{\\rm{pc}}}{F_{1,2}}},$\u03c3pEW=\u0394\u03bb-pEW(H\u03b1)S\u2215N1+  Fpc   F1,2, \n\nwhere \u0394\u03bb = \u03bb2 \u2212 \u03bb1 and F1,2  is the mean flux in the wavelength range between \u03bb1 and \u03bb2. For H\u03b1 active stars, i.e. where pEW(H\u03b1) is negative, the normalised H\u03b1 luminosity can be expressed as\n\n(3)\n\n$\\log \\left(\\frac{L_{{\\rm{H}}\\alpha}}{L_{\\rm{bol}}}\\right) = \\log \\chi\n+ \\log (-{\\rm{pEW}}({\\rm{H}}\\alpha)),$logLH\u03b1Lbol = log\u03c7+ log(-pEW(H\u03b1)), \n\nwhere log \u03c7 is given as a function of the effective temperature (e.g. Reiners & Basri 2008). Lines with H\u03b1 in absorption have positive pEW(H\u03b1) values and lines with H\u03b1 in emission have negative pEW(H\u03b1) values. The minimum level of emission in H\u03b1 that we are sensitive to is pEW(H\u03b1) \u2264\u22120.5\u212b, which is the definition for an active star in this work and is indicated by the term H\u03b1 active. This detection threshold was determined by visually inspecting the spectra and is consistent with values obtained by Newton et al. (2017) and West et al. (2015). The values derived from the new observations are tabulated in Table A.2.","Citation Text":["Vollmann & Eversberg (2006)"],"Citation Start End":[[849,876]]}
 {"Identifier":"2020MNRAS.499..462S__Navarro,_Frenk_&_White_1996_Instance_1","Paragraph":"In this work, we consider four different galaxy models from Smirnov & Sotnikova (2018). Full details of the simulations can be found in that work and we refer an interested reader to it. Here, we briefly describe some important aspects of the simulations. Initially, each model consists of an axisymmetric exponential disc:\n(11)$$\\begin{eqnarray}\r\n\\rho (R,z) = \\frac{M_\\mathrm{d}}{4\\pi R_\\mathrm{d}^2 z_\\mathrm{d}} \\exp \\left(-\\frac{R}{R_\\mathrm{d}}\\right) \\operatorname{sech}^2\\left(\\frac{z}{z_\\mathrm{d}}\\right) \\, ,\r\n\\end{eqnarray}$$where Md is the total mass of the disc, Rd is the disc scale length, and zd is the disc scale height, plus spherically symmetric dark halo of NFW-type (Navarro, Frenk & White 1996). The halo is characterized by the ratio Mh(r  4Rd)\/Md, where Mh(r  4Rd) is the dark halo mass inside the sphere with a radius of 4Rd. One model also includes a Hernquist type bulge (Hernquist 1990):\n(12)$$\\begin{eqnarray}\r\n\\rho _\\mathrm{b}(r) = \\frac{M_\\mathrm{b}\\, r_\\mathrm{b}}{2\\pi \\, r\\, (r_\\mathrm{b} + r)^3} \\, ,\r\n\\end{eqnarray}$$where rb is the scale parameter and Mb is the total bulge mass. Disc and halo components are represented by several millions of particles (see Table 1). Bulge particle number is chosen such that the mass of one particle from the bulge is equal to the mass of one particle from the disc. Some important physical parameters of the models are specified in Table 1. The initial equilibrium state of each multicomponent model was prepared via script mkgalaxy (McMillan & Dehnen 2007) from the toolbox for N-body simulation NEMO (Teuben 1995). Evolution of the models was followed for about 8\u2009Gyr using the fastest N-body code for one CPU gyrfalcON (Dehnen 2002). Each model gives rise to a bar after 1\u22122\u2009Gyr from the beginning of the simulation. Each bar gradually thickens in the vertical direction (clear buckling events can occur depending on the model) and takes a B\/PS shape if seen side-on. Fig. 1 shows the end-state of the bulgeless model with \u03bc = 1.5 and Q(2Rd) = 1.2. This model is our fiducial or \u2018main\u2019 model. On the example of this model, we consider below how various projection effects affect the extracted parameters of the B\/PS bulge. For each of the models, we prepared a set of Flexible Image Transport System (FITS) images obtained from the corresponding density distribution of disc\/bulge particles. Such images can then be decomposed using a usual decomposition procedure analogous to that used for images of real galaxies.","Citation Text":["Navarro, Frenk & White 1996"],"Citation Start End":[[739,766]]}
@@ -443,10 +449,6 @@
 {"Identifier":"2016AandA...585A.125B__Voevodkin_et_al._(2010)_Instance_1","Paragraph":"To investigate this further, we performed an additional test where we froze the slopes for both the fossils and groups to 3.0 and only fit the normalisation for both samples. The value of 3.0 for the slope was chosen as generally most groups and clusters can be described well by this particular slope, after factoring in selection effects. The fossils now have a normalisation of 0.38 \u00b1 0.11 and the groups sample have a normalisation of 0.22 \u00b1 0.13. We now proceeded to remove the influence of selection effects on the normalisation of the scaling relation for both samples by generating mock samples of objects as in Bharadwaj et al. (2015) by varying the input normalisations. For each mock sample, the slope was always fixed to 3 and the intrinsic scatter was fixed to the observed values. Flux and luminosity cuts were applied to both the 400d sample and the groups sample to match the true sample of objects. For the 400d fossil sample, the selection criteria were taken from Voevodkin et al. (2010), and can be described as follows: a lower flux cut of 1.4 \u00d7  10-13 erg \/ s \/ cm2, an upper redshift cut of 0.2, and a lower luminosity cut of 1043 erg\/s. Here, fluxes and luminosities are in the ROSAT (0.5\u20132.0 keV) band. After performing the bias corrections, the fossils scaling relation has a normalisation of 0.30 \u00b1 0.10 vs. 0.0078 \u00b1 0.13 for the groups, indicating that the large normalisations seem to persist even after accounting for selection effects. Despite a nearly 2.3\u03c3 higher normalisation for fossils with respect to non-fossils, we still only treat this finding as an indication because on top of the statistical uncertainties in both quantities (which is large currently for the 400d fossils), there could also be an additional systematic uncertainty introduced due to differences in the luminosity determination in the different parent catalogues. Secondly, the archival nature of this subsample of 400d objects is biased towards systems lacking a SCC (Table 2) and, assuming that the remaining systems are SCC, then adding these objects could potentially increase the normalisation for the scaling relation, and the difference between the fossils and the groups sample would be higher than what we demonstrate here. We plan to explore this in greater detail in a future study of fossils scaling relations. ","Citation Text":["Voevodkin et al. (2010)"],"Citation Start End":[[1032,1055]]}
 {"Identifier":"2017MNRAS.464.3679K__Webb_et_al._1999_Instance_1","Paragraph":"In this work, we focus on constraining the variability of the fine-structure constant, \u03b1 \u2261 e2\/\u210fc, which represents the coupling strength of the electromagnetic force. In the last 15 years, there have been many attempts to measure this constant in absorption systems along the lines of sight to distant quasars. The approach called the \u2018Many Multiplet\u2019 (MM) method, pioneered by Dzuba, Flambaum & Webb (1999) and Webb et al. (1999), compares the relative velocity spacing between different metal ion transitions and relates it to possible variation in \u03b1. For example, considering just a single transition, variation in \u03b1 is related to the velocity shift \u0394vi of a transition\n\n(1)\n\r\n\\begin{equation}\r\n\\Delta \\alpha \/\\alpha \\equiv \\frac{\\alpha _{\\rm obs}-\\alpha _{\\rm lab}}{\\alpha _{\\rm lab}}\\approx \\frac{-\\Delta v_i}{2c}\\frac{\\omega _i}{q_i},\r\n\\end{equation}\r\n\nwhere c is the speed of light, qi is sensitivity of the transition to \u03b1-variation, calculated from many body-relativistic corrections to the energy levels of ions and \u03c9i is its wavenumber measured in the laboratory. There have been two MM method studies of large absorber samples: the Keck High Resolution Echelle Spectrometer (HIRES\/Keck) sample of 143 absorption systems (Webb et al. 1999, 2001; Murphy et al. 2001a, 2004; Murphy, Webb & Flambaum 2003b) and the Ultraviolet and Visual Echelle Spectrograph on the Very Large Telescope (UVES\/VLT) sample of 154 absorption systems (Webb et al. 2011; King et al. 2012). These studies reported weighted mean values of \u0394\u03b1\/\u03b1 = \u22125.7 \u00b1 1.1 parts per million (ppm) and 2.29 \u00b1 0.95 ppm, respectively. Webb et al. (2011) and King et al. (2012) also combined both samples and found a 4.1\u03c3 statistical preference for a dipole-like variation in \u03b1 across the sky. Contrary to these studies, several other attempts to measure \u03b1 from individual absorbers (Quast, Reimers & Levshakov 2004; Levshakov et al. 2005, 2006, 2007; Chand et al. 2006) or smaller samples of absorption systems (Chand et al. 2004; Srianand et al. 2004) reported \u0394\u03b1\/\u03b1 consistent with zero. However, these analyses contained shortcomings that produced biased values and\/or considerably underestimated error bars (Murphy, Webb & Flambaum 2007a, 2008b; cf. Srianand et al., 2007). For example, a reanalysis, including remodelling of the Chand et al. (2004) spectra by Wilczynska et al. (2015), yielded a weighted mean of \u0394\u03b1\/\u03b1 = 2.2 \u00b1 2.3 ppm which, given the distribution of the 18 quasars across the sky, was not inconsistent with the evidence for dipole-like \u03b1-variation.","Citation Text":["Webb et al. (1999)"],"Citation Start End":[[452,470]]}
 {"Identifier":"2017MNRAS.464.3679K__Webb_et_al._1999_Instance_2","Paragraph":"In this work, we focus on constraining the variability of the fine-structure constant, \u03b1 \u2261 e2\/\u210fc, which represents the coupling strength of the electromagnetic force. In the last 15 years, there have been many attempts to measure this constant in absorption systems along the lines of sight to distant quasars. The approach called the \u2018Many Multiplet\u2019 (MM) method, pioneered by Dzuba, Flambaum & Webb (1999) and Webb et al. (1999), compares the relative velocity spacing between different metal ion transitions and relates it to possible variation in \u03b1. For example, considering just a single transition, variation in \u03b1 is related to the velocity shift \u0394vi of a transition\n\n(1)\n\r\n\\begin{equation}\r\n\\Delta \\alpha \/\\alpha \\equiv \\frac{\\alpha _{\\rm obs}-\\alpha _{\\rm lab}}{\\alpha _{\\rm lab}}\\approx \\frac{-\\Delta v_i}{2c}\\frac{\\omega _i}{q_i},\r\n\\end{equation}\r\n\nwhere c is the speed of light, qi is sensitivity of the transition to \u03b1-variation, calculated from many body-relativistic corrections to the energy levels of ions and \u03c9i is its wavenumber measured in the laboratory. There have been two MM method studies of large absorber samples: the Keck High Resolution Echelle Spectrometer (HIRES\/Keck) sample of 143 absorption systems (Webb et al. 1999, 2001; Murphy et al. 2001a, 2004; Murphy, Webb & Flambaum 2003b) and the Ultraviolet and Visual Echelle Spectrograph on the Very Large Telescope (UVES\/VLT) sample of 154 absorption systems (Webb et al. 2011; King et al. 2012). These studies reported weighted mean values of \u0394\u03b1\/\u03b1 = \u22125.7 \u00b1 1.1 parts per million (ppm) and 2.29 \u00b1 0.95 ppm, respectively. Webb et al. (2011) and King et al. (2012) also combined both samples and found a 4.1\u03c3 statistical preference for a dipole-like variation in \u03b1 across the sky. Contrary to these studies, several other attempts to measure \u03b1 from individual absorbers (Quast, Reimers & Levshakov 2004; Levshakov et al. 2005, 2006, 2007; Chand et al. 2006) or smaller samples of absorption systems (Chand et al. 2004; Srianand et al. 2004) reported \u0394\u03b1\/\u03b1 consistent with zero. However, these analyses contained shortcomings that produced biased values and\/or considerably underestimated error bars (Murphy, Webb & Flambaum 2007a, 2008b; cf. Srianand et al., 2007). For example, a reanalysis, including remodelling of the Chand et al. (2004) spectra by Wilczynska et al. (2015), yielded a weighted mean of \u0394\u03b1\/\u03b1 = 2.2 \u00b1 2.3 ppm which, given the distribution of the 18 quasars across the sky, was not inconsistent with the evidence for dipole-like \u03b1-variation.","Citation Text":["Webb et al. 1999"],"Citation Start End":[[1273,1289]]}
-{"Identifier":"2019MNRAS.487.2474C__Sharma_et_al._2018_Instance_1","Paragraph":"In this work, we analyse a set of high-resolution stellar spectra that were acquired by the High Efficiency and Resolution Multi-Element Spectrograph (HERMES; Barden et al. 2010; Sheinis et al. 2015), a multifibre spectrograph mounted on the 3.9-metre Anglo-Australian Telescope (AAT). The spectrograph has a resolving power of R ${\\sim } 28\\, 000$ and covers four wavelength ranges (4713\u20134903, 5648\u20135873, 6478\u20136737, and 7585\u20137887\u2009\u00c5), frequently also referred to as \u2018spectral arms\u2019. Observations used in this study have been taken from multiple observing programmes that make use of the HERMES spectrograph: the main GALAH survey (De Silva et al. 2015), the K2-HERMES survey (Wittenmyer et al. 2018), and the TESS-HERMES survey (Sharma et al. 2018). Those observing programmes mostly observe stars at higher Galactic latitudes (|b| > 10\u00b0) and employ different selection functions, but share the same observing procedures, reduction, and analysis pipeline (internal version 5.3; Kos et al. 2017). All three programmes are magnitude-limited, with no colour cuts (except the K2-HERMES survey), and observations predominantly fall in the V magnitude range between 12 and 14. This leads to an unbiased sample of mostly southern stars that can be used for different population studies, such as multiple stellar systems in our case. Additionally, stellar atmospheric parameters and individual abundances derived from spectra acquired during different observing programmes are analysed with the same The Cannon procedure (internal version 182112 that uses parallax information to infer log\u2009g of a star; Ness et al. 2015; Buder et al. 2018), so they are intercomparable. The Cannon is a data-driven interpolation approach trained on a set of stellar spectra that span the majority of the stellar parameter space (for details, see Buder et al. 2018). Whenever we refer to valid or unflagged stellar parameters in the text, only stars with the quality flag flag_cannon equal to 0 were selected.","Citation Text":["Sharma et al. 2018"],"Citation Start End":[[771,789]]}
-{"Identifier":"2019MNRAS.487.2474CBarden_et_al._2010_Instance_1","Paragraph":"In this work, we analyse a set of high-resolution stellar spectra that were acquired by the High Efficiency and Resolution Multi-Element Spectrograph (HERMES; Barden et al. 2010; Sheinis et al. 2015), a multifibre spectrograph mounted on the 3.9-metre Anglo-Australian Telescope (AAT). The spectrograph has a resolving power of R ${\\sim } 28\\, 000$ and covers four wavelength ranges (4713\u20134903, 5648\u20135873, 6478\u20136737, and 7585\u20137887\u2009\u00c5), frequently also referred to as \u2018spectral arms\u2019. Observations used in this study have been taken from multiple observing programmes that make use of the HERMES spectrograph: the main GALAH survey (De Silva et al. 2015), the K2-HERMES survey (Wittenmyer et al. 2018), and the TESS-HERMES survey (Sharma et al. 2018). Those observing programmes mostly observe stars at higher Galactic latitudes (|b| > 10\u00b0) and employ different selection functions, but share the same observing procedures, reduction, and analysis pipeline (internal version 5.3; Kos et al. 2017). All three programmes are magnitude-limited, with no colour cuts (except the K2-HERMES survey), and observations predominantly fall in the V magnitude range between 12 and 14. This leads to an unbiased sample of mostly southern stars that can be used for different population studies, such as multiple stellar systems in our case. Additionally, stellar atmospheric parameters and individual abundances derived from spectra acquired during different observing programmes are analysed with the same The Cannon procedure (internal version 182112 that uses parallax information to infer log\u2009g of a star; Ness et al. 2015; Buder et al. 2018), so they are intercomparable. The Cannon is a data-driven interpolation approach trained on a set of stellar spectra that span the majority of the stellar parameter space (for details, see Buder et al. 2018). Whenever we refer to valid or unflagged stellar parameters in the text, only stars with the quality flag flag_cannon equal to 0 were selected.","Citation Text":["Barden et al. 2010"],"Citation Start End":[[201,219]]}
-{"Identifier":"2019MNRAS.487.2474CBuder_et_al._2018_Instance_1","Paragraph":"In this work, we analyse a set of high-resolution stellar spectra that were acquired by the High Efficiency and Resolution Multi-Element Spectrograph (HERMES; Barden et al. 2010; Sheinis et al. 2015), a multifibre spectrograph mounted on the 3.9-metre Anglo-Australian Telescope (AAT). The spectrograph has a resolving power of R ${\\sim } 28\\, 000$ and covers four wavelength ranges (4713\u20134903, 5648\u20135873, 6478\u20136737, and 7585\u20137887\u2009\u00c5), frequently also referred to as \u2018spectral arms\u2019. Observations used in this study have been taken from multiple observing programmes that make use of the HERMES spectrograph: the main GALAH survey (De Silva et al. 2015), the K2-HERMES survey (Wittenmyer et al. 2018), and the TESS-HERMES survey (Sharma et al. 2018). Those observing programmes mostly observe stars at higher Galactic latitudes (|b| > 10\u00b0) and employ different selection functions, but share the same observing procedures, reduction, and analysis pipeline (internal version 5.3; Kos et al. 2017). All three programmes are magnitude-limited, with no colour cuts (except the K2-HERMES survey), and observations predominantly fall in the V magnitude range between 12 and 14. This leads to an unbiased sample of mostly southern stars that can be used for different population studies, such as multiple stellar systems in our case. Additionally, stellar atmospheric parameters and individual abundances derived from spectra acquired during different observing programmes are analysed with the same The Cannon procedure (internal version 182112 that uses parallax information to infer log\u2009g of a star; Ness et al. 2015; Buder et al. 2018), so they are intercomparable. The Cannon is a data-driven interpolation approach trained on a set of stellar spectra that span the majority of the stellar parameter space (for details, see Buder et al. 2018). Whenever we refer to valid or unflagged stellar parameters in the text, only stars with the quality flag flag_cannon equal to 0 were selected.","Citation Text":["Buder et al. 2018"],"Citation Start End":[[1863,1880]]}
-{"Identifier":"2019MNRAS.487.2474CBuder_et_al._2018_Instance_1","Paragraph":"In this work, we analyse a set of high-resolution stellar spectra that were acquired by the High Efficiency and Resolution Multi-Element Spectrograph (HERMES; Barden et al. 2010; Sheinis et al. 2015), a multifibre spectrograph mounted on the 3.9-metre Anglo-Australian Telescope (AAT). The spectrograph has a resolving power of R ${\\sim } 28\\, 000$ and covers four wavelength ranges (4713\u20134903, 5648\u20135873, 6478\u20136737, and 7585\u20137887\u2009\u00c5), frequently also referred to as \u2018spectral arms\u2019. Observations used in this study have been taken from multiple observing programmes that make use of the HERMES spectrograph: the main GALAH survey (De Silva et al. 2015), the K2-HERMES survey (Wittenmyer et al. 2018), and the TESS-HERMES survey (Sharma et al. 2018). Those observing programmes mostly observe stars at higher Galactic latitudes (|b| > 10\u00b0) and employ different selection functions, but share the same observing procedures, reduction, and analysis pipeline (internal version 5.3; Kos et al. 2017). All three programmes are magnitude-limited, with no colour cuts (except the K2-HERMES survey), and observations predominantly fall in the V magnitude range between 12 and 14. This leads to an unbiased sample of mostly southern stars that can be used for different population studies, such as multiple stellar systems in our case. Additionally, stellar atmospheric parameters and individual abundances derived from spectra acquired during different observing programmes are analysed with the same The Cannon procedure (internal version 182112 that uses parallax information to infer log\u2009g of a star; Ness et al. 2015; Buder et al. 2018), so they are intercomparable. The Cannon is a data-driven interpolation approach trained on a set of stellar spectra that span the majority of the stellar parameter space (for details, see Buder et al. 2018). Whenever we refer to valid or unflagged stellar parameters in the text, only stars with the quality flag flag_cannon equal to 0 were selected.","Citation Text":["Buder et al. 2018"],"Citation Start End":[[1655,1672]]}
 {"Identifier":"2017ApJ...845..170B__Emsellem_et_al._2004_Instance_1","Paragraph":"Even when imaged into 40 km s\u22121 channels, CO(2\u22121) absorption is apparent in NGC 4374 and IC 4296 against their strong nuclear continuum sources. While extragalactic CO absorption is not frequently observed due to low equivalent widths, ALMA\u2019s high angular resolution and sensitivity allow its detection against some nearby active nuclei (e.g., Davis et al. 2014; Rangwala et al. 2015). To better characterize the central absorption features, we also imaged their visibility data (without continuum subtraction) into cubes with 1.28 km s\u22121 channels. The primary absorption in IC 4296 is consistent with the galaxy\u2019s assumed systemic velocity (Table 1), although there may be a small secondary absorption feature \u223c15 km s\u22121 redward of \n\n\n\n\n\n. The CO(1\u22122) transition seen in the nucleus of NGC 4374, however, is redshifted by \u223c100 km s\u22121 from the \n\n\n\n\n\n value derived using stellar kinematics (Emsellem et al. 2004) and by \u223c50 km s\u22121 with respect to the best-fitting \n\n\n\n\n\n from ionized gas dynamical modeling (e.g., Walsh et al. 2010). The absorption lines in these two galaxies have narrow widths (\u22727 km s\u22121 FWHM) that are only slightly smaller than the minimum line widths in our CO-bright subsample. Maximum absorption depths are (\u22123.26 \u00b1 0.74) and (\u22125.25 \u00b1 0.35) K with integrated absorption intensities \n\n\n\n\n\n of (19.4 \u00b1 2.5) and (44.3 \u00b1 1.4) K km s\u22121 for NGC 4374 and IC 4296, respectively. From these \n\n\n\n\n\n measurements, we estimate corresponding H2 column densities \n\n\n\n\n\n of \n\n\n\n\n\n and \n\n\n\n\n\n cm\u22122 after assuming an absorption depth ratio CO(1\u22122)\/CO(0\u22121) \u2248 0.6 (based on 13CO absorption line ratios; e.g., see Eckart et al. 1990) and a CO-to-H2 conversion factor \n\n\n\n\n\n corresponding to \n\n\n\n\n\n M pc\u22122 (K km s\u22121)\u22121 (see Section 3.1.2; Sandstrom et al. 2013). These \n\n\n\n\n\n estimates are much more uncertain than indicated by the formal associated uncertainties, since the \n\n\n\n\n\n and CO(1\u22122)\/CO(1\u22120) values carry large systematic uncertainties, and faint nuclear CO emission may somewhat dilute these equivalent widths.","Citation Text":["Emsellem et al. 2004"],"Citation Start End":[[935,955]]}
 {"Identifier":"2016ApJ...821...67S__Ruiter_et_al._2013_Instance_1","Paragraph":"In order to examine how our qcr(M1) would affect the brightness distribution of the violent merger scenario, we adopt the same assumptions as in Ruiter et al. (2013) except for qcr(M1). For the primary at the time of merging, we use the same WD mass distribution as Ruiter et al. (2013; see also Ruiter et al. 2011), although it is highly uncertain whether the WD can increase its mass by avoiding the formation of a common envelope during the very rapid accretion from the He star companion. We also assume the same \n\n\n\n\n\n\nm\n\n\nWD\n\n\n\u2013\n\n\nM\n\n\nbol\n\n\n\n\n relation of SNe Ia as Ruiter et al. (2013; see Figure 4 in Ruiter et al. 2013; Sim et al. 2010) and a flat mass ratio distribution of DD systems for simplicity. Using either our critical mass ratio or theirs, we calculated the brightness distribution and compared them with each other (Figure 11). We find that there is no significant difference between them qualitatively. This result implies that the qcr of the violent merger-induced explosion is not so crucial for the brightness distribution of SNe Ia, as mentioned in Ruiter et al. (2013). Our results are closest to the \u03b7 = 1.5 case among Ruiter et al.'s three cases. In the cases of our qcr and Ruiter et al.'s \u03b7 = 1.5, the brightness distribution concentrates around \u221219.0 mag. In Figure 11, we add the observational volume-limited brightness distributions of SNe Ia. One in panel (a) is derived by the Lick Observatory Supernova Search (LOSS; Li et al. 2011), and the other in panel (b) is obtained by ROTSE-IIIb (see Table 1 in Quimby et al. 2012). The fraction of faint events in our models is lower than the observation of LOSS. This discrepancy might decrease if we consider the viewing angle effects (see also the discussion in Ruiter et al. 2013), which might be increasingly important especially for a large value of qcr. On the other hand, the results of ROTSE-IIIb are consistent with ours, except most luminous (\u2272\u221219.5 mag) events. It should be noted, however, that there are large uncertainties for the observational brightness distribution (e.g., Quimby et al. 2012) and our models are too simple to be compared with the observational results. More detailed studies are required to reach a definitive conclusion.","Citation Text":["Ruiter et al. (2013)"],"Citation Start End":[[187,207]]}
 {"Identifier":"2016ApJ...821...67S__Ruiter_et_al._2013_Instance_2","Paragraph":"In order to examine how our qcr(M1) would affect the brightness distribution of the violent merger scenario, we adopt the same assumptions as in Ruiter et al. (2013) except for qcr(M1). For the primary at the time of merging, we use the same WD mass distribution as Ruiter et al. (2013; see also Ruiter et al. 2011), although it is highly uncertain whether the WD can increase its mass by avoiding the formation of a common envelope during the very rapid accretion from the He star companion. We also assume the same \n\n\n\n\n\n\nm\n\n\nWD\n\n\n\u2013\n\n\nM\n\n\nbol\n\n\n\n\n relation of SNe Ia as Ruiter et al. (2013; see Figure 4 in Ruiter et al. 2013; Sim et al. 2010) and a flat mass ratio distribution of DD systems for simplicity. Using either our critical mass ratio or theirs, we calculated the brightness distribution and compared them with each other (Figure 11). We find that there is no significant difference between them qualitatively. This result implies that the qcr of the violent merger-induced explosion is not so crucial for the brightness distribution of SNe Ia, as mentioned in Ruiter et al. (2013). Our results are closest to the \u03b7 = 1.5 case among Ruiter et al.'s three cases. In the cases of our qcr and Ruiter et al.'s \u03b7 = 1.5, the brightness distribution concentrates around \u221219.0 mag. In Figure 11, we add the observational volume-limited brightness distributions of SNe Ia. One in panel (a) is derived by the Lick Observatory Supernova Search (LOSS; Li et al. 2011), and the other in panel (b) is obtained by ROTSE-IIIb (see Table 1 in Quimby et al. 2012). The fraction of faint events in our models is lower than the observation of LOSS. This discrepancy might decrease if we consider the viewing angle effects (see also the discussion in Ruiter et al. 2013), which might be increasingly important especially for a large value of qcr. On the other hand, the results of ROTSE-IIIb are consistent with ours, except most luminous (\u2272\u221219.5 mag) events. It should be noted, however, that there are large uncertainties for the observational brightness distribution (e.g., Quimby et al. 2012) and our models are too simple to be compared with the observational results. More detailed studies are required to reach a definitive conclusion.","Citation Text":["Ruiter et al. (2013"],"Citation Start End":[[308,327]]}
@@ -710,8 +712,6 @@
 {"Identifier":"2016ApJ...819...25K__Verhamme_et_al._2012_Instance_1","Paragraph":"In the interpretation of clumpy star formation in a disk-like galaxy, as usually observed in high-z galaxies (e.g., Elmegreen et al. 2009; F\u00f6rster Schreiber et al. 2011; Murata et al. 2014; Tadaki et al. 2014), the ellipticity of a source may be an intrinsic property related to the viewing angle of the disk. That is, large ellipticity implies that its viewing angle is close to edge-on and that the stellar disk lies in the elongated direction. If we consider that Ly\u03b1 is emitted in directions perpendicular to the disk, as predicted by the recent theoretical studies for Ly\u03b1 line transfer (e.g., Verhamme et al. 2012; Yajima et al. 2012b), the pitch angle of Ly\u03b1 emission will be at right angles to that of UV continuum. Moreover, in such a case, it is also expected that the size in Ly\u03b1 emission aHL(NB711) shows a positive correlation with ellipticity measured in rest-frame UV continuum because the Ly\u03b1-emitting region in bipolar directions perpendicular to the disk can be viewed from longer distances if the viewing angle of the disk is closer to edge-on, that is, larger ellipticity. However, as presented in the top panel of Figure 17, we do not find such positive correlation between aHL(NB711) and ellipticity for the 54 ACS-detected LAEs. Furthermore, as shown in the bottom panel of Figure 17,14 the observed distribution of the LAEs in the EW0\u2013 plane seems not to be quantitatively consistent with the interpretation of clumpy star formation in a disk-like galaxy, where EW0 is expected to decrease significantly toward the edge-on direction (i.e., larger ellipticity) via radiative transfer effects for Ly\u03b1 resonance photons (e.g., Verhamme et al. 2012; Yajima et al. 2012b); this result is consistent with Shibuya et al. (2014). Therefore, the interpretation of clumpy star formation in a disk-like galaxy seems not to be preferred for our LAE sample. This conclusion can be reinforced with the absence of an ACS source with a large size and round shape; if there are multiple clumpy star-forming regions in a disk-like galaxy, some such galaxies will be viewed face-on, resulting in alarge size and round shape. We emphasize again that this result is not affected by a selection bias against them if they are bright enough (i.e., I814 \u2272 26 mag), as shown in Figures 7 and 18.\n14\nNote that, considering the strong positive correlation between aHL and  shown in Figure 8, this plot is qualitatively identical to the distribution in the EW0\u2013aHL plane shown in the top panel of Figure 16.\n\n","Citation Text":["Verhamme et al. 2012","Verhamme et al. 2012"],"Citation Start End":[[643,663],[1692,1712]]}
 {"Identifier":"2016ApJ...819...25KElmegreen_et_al._2009_Instance_1","Paragraph":"In the interpretation of clumpy star formation in a disk-like galaxy, as usually observed in high-z galaxies (e.g., Elmegreen et al. 2009; F\u00f6rster Schreiber et al. 2011; Murata et al. 2014; Tadaki et al. 2014), the ellipticity of a source may be an intrinsic property related to the viewing angle of the disk. That is, large ellipticity implies that its viewing angle is close to edge-on and that the stellar disk lies in the elongated direction. If we consider that Ly\u03b1 is emitted in directions perpendicular to the disk, as predicted by the recent theoretical studies for Ly\u03b1 line transfer (e.g., Verhamme et al. 2012; Yajima et al. 2012b), the pitch angle of Ly\u03b1 emission will be at right angles to that of UV continuum. Moreover, in such a case, it is also expected that the size in Ly\u03b1 emission aHL(NB711) shows a positive correlation with ellipticity measured in rest-frame UV continuum because the Ly\u03b1-emitting region in bipolar directions perpendicular to the disk can be viewed from longer distances if the viewing angle of the disk is closer to edge-on, that is, larger ellipticity. However, as presented in the top panel of Figure 17, we do not find such positive correlation between aHL(NB711) and ellipticity for the 54 ACS-detected LAEs. Furthermore, as shown in the bottom panel of Figure 17,14 the observed distribution of the LAEs in the EW0\u2013 plane seems not to be quantitatively consistent with the interpretation of clumpy star formation in a disk-like galaxy, where EW0 is expected to decrease significantly toward the edge-on direction (i.e., larger ellipticity) via radiative transfer effects for Ly\u03b1 resonance photons (e.g., Verhamme et al. 2012; Yajima et al. 2012b); this result is consistent with Shibuya et al. (2014). Therefore, the interpretation of clumpy star formation in a disk-like galaxy seems not to be preferred for our LAE sample. This conclusion can be reinforced with the absence of an ACS source with a large size and round shape; if there are multiple clumpy star-forming regions in a disk-like galaxy, some such galaxies will be viewed face-on, resulting in alarge size and round shape. We emphasize again that this result is not affected by a selection bias against them if they are bright enough (i.e., I814 \u2272 26 mag), as shown in Figures 7 and 18.\n14\nNote that, considering the strong positive correlation between aHL and  shown in Figure 8, this plot is qualitatively identical to the distribution in the EW0\u2013aHL plane shown in the top panel of Figure 16.\n\n","Citation Text":["Elmegreen et al. 2009"],"Citation Start End":[[160,181]]}
 {"Identifier":"2015ApJ...810...69M__Hockney_&_Eastwood_1988_Instance_1","Paragraph":"On the basis of the absolute PM estimate derived in the previous section, we performed a numerical integration of the orbit of Terzan 5 in the Galactic potential. We used the three-component (bulge, disk, and halo) axisymmetric model from Allen & Santillan (1991), which has been extensively used and discussed in the literature to study orbits and dynamical environmental effects on Galactic stellar systems (e.g., Allen et al. 2006; Montuori et al. 2007; Ortolani et al. 2011; Moreno et al. 2014; Zonoozi et al. 2014), thanks to its relative simplicity and fully analytic nature. We adjusted the various model parameters to make the rotation velocity curve match the value of 243 km s\u22121 measured at the Solar Galactocentric distance of 8.4 kpc (see above). The cluster PMs were reported in the Cartesian Galactocentric reference frame, resulting in a velocity vector (vx, vy, vz) = (\u221260.4 \u00b1 1.3, 85.7 \u00b1 11.1, 35.0 \u00b1 6.0) km s\u22121 at the position (x, y, z) = (\u22122.51 \u00b1 0.30, 0.39 \u00b1 0.02, 0.17 \u00b1 0.01) kpc. We adopted the convention in which the X axis points opposite to the Sun (i.e., the Sun position is (\u22128.4,0,0)). The orbit was then time-integrated backwards for 12 Gyr, starting from the given initial (current) conditions and using a second-order leapfrog integrator (e.g., Hockney & Eastwood 1988) with a rather small and constant time step (\u223c100 kyr, corresponding to \n\n\n\n\n\n of the dynamical time at the Sun distance, computed as \n\n\n\n\n\n, where \n\n\n\n\n\n is a characteristic Galactic mass parameter). During the >105 time steps used to describe the entire orbit evolution, the errors on the conservation of both the energy and the Z component of angular momentum were kept under control and never exceeded one part over 105 and 1013, respectively. To take into account the uncertainties on the kinematic data, we generated a set of 1,000 orbits starting from the phase-space initial conditions normally distributed within a 3\u03c3 range around the cluster velocity vector components and the current position, with \u03c3 being equal to the quoted uncertainties on these parameters. For all of these orbits we repeated the backward time integration. The probability densities of the resulting orbits projected on the equatorial and meridional Galactic planes are shown in Figures 13 and 14, respectively. Darker colors correspond to more probable regions of the space, that is, to Galactic coordinates crossed more frequently by the simulated orbits. As is apparent, the larger distances reached by the system during its evolution are R = 3.5 kpc and \n\n\n\n\n\n kpc at a 3\u03c3 level of significance, which roughly correspond to a region having the current size of the bulge.","Citation Text":["Hockney & Eastwood 1988"],"Citation Start End":[[1326,1349]]}
-{"Identifier":"2022ApJ...940L..13A__Chen_et_al._2020_Instance_1","Paragraph":"Since 2018 the Parker Solar Probe (PSP) mission is collecting solar wind plasma and magnetic field data through the inner heliosphere, reaching the closest distance to the Sun ever reached by any previous mission (Fox et al. 2016; Kasper et al. 2021). Thanks to the PSP journey around the Sun (it has completed 11 orbits) a different picture has been drawn for the near-Sun solar wind with respect to the near-Earth one (Bale et al. 2019; Kasper et al. 2019; Chhiber et al. 2020; Malaspina et al. 2020; Bandyopadhyay et al. 2022; Zank et al. 2022). Different near-Sun phenomena have been frequently encountered, with the emergence of magnetic field flips, i.e., the so-called switchbacks (Dudok de Wit et al. 2020; Zank et al. 2020), kinetic-scale current sheets (Lotekar et al. 2022), and a scale-invariant population of current sheets between ion and electron inertial scales (Chhiber et al. 2021). Going away from the Sun (from 0.17 to 0.8 au), evidence of radial evolution of different properties of solar wind turbulence (Chen et al. 2020) as the spectral slope of the inertial range (from \u22123\/2 close to the Sun to \u22125\/3, at distances larger than 0.4 au), an increase of the outer scale of turbulence, a decrease of the Alfv\u00e9nic flux, and a decrease of the imbalance between outward (z\n+) and inward (z\n\u2212) propagating components (Chen et al. 2020) has been provided. Although the near-Sun solar wind shares different properties with the near-Earth one (Allen et al. 2020; Cuesta et al. 2022), significant differences have been also found in the variance of magnetic fluctuations (about 2 orders of magnitude) and in the compressive component of inertial range turbulence. In a similar way, Alberti et al. (2020) first reported a breakdown of the scaling properties of the energy transfer rate, likely related to the breaking of the phase-coherence of inertial range fluctuations. These findings, also highlighted by Telloni et al. (2021) and Alberti et al. (2022) analyzing a radial alignment between PSP and Solar Orbiter, and PSP and BepiColombo, respectively, have been interpreted as an increase in the efficiency of the nonlinear energy cascade mechanism when moving away from the Sun. More recently, by investigating the helical content of turbulence Alberti et al. (2022) highlighted a damping of magnetic helicity over the inertial range between 0.17 and 0.6 au suggesting that the solar wind develops into turbulence by a concurrent effect of large-scale convection of helicity and creation\/annihilation of helical wave structures. All these features shed new light onto the radial evolution of solar wind turbulence that urges to be considered in expanding models of the solar wind (Verdini et al. 2019; Grappin et al. 2021), and also to reproduce and investigate the role of proton heating and anisotropy of magnetic field fluctuations (Hellinger et al. 2015).","Citation Text":["Chen et al. 2020","Chen et al. 2020"],"Citation Start End":[[1067,1083],[1374,1390]]}
-{"Identifier":"2022ApJ...940L..13A__Chen_et_al._2020_Instance_2","Paragraph":"Since 2018 the Parker Solar Probe (PSP) mission is collecting solar wind plasma and magnetic field data through the inner heliosphere, reaching the closest distance to the Sun ever reached by any previous mission (Fox et al. 2016; Kasper et al. 2021). Thanks to the PSP journey around the Sun (it has completed 11 orbits) a different picture has been drawn for the near-Sun solar wind with respect to the near-Earth one (Bale et al. 2019; Kasper et al. 2019; Chhiber et al. 2020; Malaspina et al. 2020; Bandyopadhyay et al. 2022; Zank et al. 2022). Different near-Sun phenomena have been frequently encountered, with the emergence of magnetic field flips, i.e., the so-called switchbacks (Dudok de Wit et al. 2020; Zank et al. 2020), kinetic-scale current sheets (Lotekar et al. 2022), and a scale-invariant population of current sheets between ion and electron inertial scales (Chhiber et al. 2021). Going away from the Sun (from 0.17 to 0.8 au), evidence of radial evolution of different properties of solar wind turbulence (Chen et al. 2020) as the spectral slope of the inertial range (from \u22123\/2 close to the Sun to \u22125\/3, at distances larger than 0.4 au), an increase of the outer scale of turbulence, a decrease of the Alfv\u00e9nic flux, and a decrease of the imbalance between outward (z\n+) and inward (z\n\u2212) propagating components (Chen et al. 2020) has been provided. Although the near-Sun solar wind shares different properties with the near-Earth one (Allen et al. 2020; Cuesta et al. 2022), significant differences have been also found in the variance of magnetic fluctuations (about 2 orders of magnitude) and in the compressive component of inertial range turbulence. In a similar way, Alberti et al. (2020) first reported a breakdown of the scaling properties of the energy transfer rate, likely related to the breaking of the phase-coherence of inertial range fluctuations. These findings, also highlighted by Telloni et al. (2021) and Alberti et al. (2022) analyzing a radial alignment between PSP and Solar Orbiter, and PSP and BepiColombo, respectively, have been interpreted as an increase in the efficiency of the nonlinear energy cascade mechanism when moving away from the Sun. More recently, by investigating the helical content of turbulence Alberti et al. (2022) highlighted a damping of magnetic helicity over the inertial range between 0.17 and 0.6 au suggesting that the solar wind develops into turbulence by a concurrent effect of large-scale convection of helicity and creation\/annihilation of helical wave structures. All these features shed new light onto the radial evolution of solar wind turbulence that urges to be considered in expanding models of the solar wind (Verdini et al. 2019; Grappin et al. 2021), and also to reproduce and investigate the role of proton heating and anisotropy of magnetic field fluctuations (Hellinger et al. 2015).","Citation Text":[],"Citation Start End":[]}
 {"Identifier":"2022ApJ...930..125L__Cartwright_&_Moldwin_2010_Instance_1","Paragraph":"A scenario that could potentially support superdiffusive parallel transport for energetic ions interacting with SMFRs in the large-scale solar wind is when (1) these structures can be viewed as coherent, quasi-helical magnetic field structures with a typical width L\n\nI\n of intermediate size and sharp boundaries (Greco et al. 2009), and (2) energetic particles have gyroradii r\n\ng\n that are small compared to the typical SMFR width L\n\nI\n. There is observational support at 1 au for all these assumptions (e.g., Greco et al. 2009; Cartwright & Moldwin 2010; le Roux et al. 2015). Thus, it is reasonable to envisage that the particle guiding centers follow the helical magnetic field lines (negligible cross-field drifts) to propagate through SMFR structures in a coherent fashion for a considerable distance before scattering during exit of the structure through the narrow magnetic boundaries. To be more specific, SMFRs identified at 1 au typically have widths L\n\nI\n \u2248 0.01 \u2212 0.001 au (Cartwright & Moldwin 2010; Khabarova et al. 2015), while data analysis of low-frequency 2D turbulence suggests elongated SMFR structures with an average length L\n\nI\u2223\u2223 so that L\n\nI\u2223\u2223\/L\n\nI\n \u2248 2 \u2212 3 (Weygand et al. 2011). Based on the expression for the path length s\n\nI\n of a SMFR helical field line (Equation (9)), we estimate that the distance a particle guiding center travel through a SMFR structure by following magnetic field lines can be considerable because s\n\nI\n \u2248 0.004 \u2212 0.04 au. Furthermore, the protons accelerated by SMFRs reach kinetic energies of \u22725 MeV (Khabarova & Zank 2017) in the solar wind at 1 au, thus easily fulfilling the requirement r\n\ng\n \u226a L\n\nI\n. Consequently, the transport through SMFRs can be characterized as involving an enhanced probability of relatively long transport distances or step sizes along the background\/guide field perpendicular to the shock surface (in the z-direction) between scattering events indicating L\u00e9vy walks as discussed by Zimbardo & Perri (2020) and Zimbardo et al. (2021).","Citation Text":["Cartwright & Moldwin 2010"],"Citation Start End":[[580,605]]}
 {"Identifier":"2022ApJ...930..125L__Cartwright_&_Moldwin_2010_Instance_2","Paragraph":"A scenario that could potentially support superdiffusive parallel transport for energetic ions interacting with SMFRs in the large-scale solar wind is when (1) these structures can be viewed as coherent, quasi-helical magnetic field structures with a typical width L\n\nI\n of intermediate size and sharp boundaries (Greco et al. 2009), and (2) energetic particles have gyroradii r\n\ng\n that are small compared to the typical SMFR width L\n\nI\n. There is observational support at 1 au for all these assumptions (e.g., Greco et al. 2009; Cartwright & Moldwin 2010; le Roux et al. 2015). Thus, it is reasonable to envisage that the particle guiding centers follow the helical magnetic field lines (negligible cross-field drifts) to propagate through SMFR structures in a coherent fashion for a considerable distance before scattering during exit of the structure through the narrow magnetic boundaries. To be more specific, SMFRs identified at 1 au typically have widths L\n\nI\n \u2248 0.01 \u2212 0.001 au (Cartwright & Moldwin 2010; Khabarova et al. 2015), while data analysis of low-frequency 2D turbulence suggests elongated SMFR structures with an average length L\n\nI\u2223\u2223 so that L\n\nI\u2223\u2223\/L\n\nI\n \u2248 2 \u2212 3 (Weygand et al. 2011). Based on the expression for the path length s\n\nI\n of a SMFR helical field line (Equation (9)), we estimate that the distance a particle guiding center travel through a SMFR structure by following magnetic field lines can be considerable because s\n\nI\n \u2248 0.004 \u2212 0.04 au. Furthermore, the protons accelerated by SMFRs reach kinetic energies of \u22725 MeV (Khabarova & Zank 2017) in the solar wind at 1 au, thus easily fulfilling the requirement r\n\ng\n \u226a L\n\nI\n. Consequently, the transport through SMFRs can be characterized as involving an enhanced probability of relatively long transport distances or step sizes along the background\/guide field perpendicular to the shock surface (in the z-direction) between scattering events indicating L\u00e9vy walks as discussed by Zimbardo & Perri (2020) and Zimbardo et al. (2021).","Citation Text":["Cartwright & Moldwin 2010"],"Citation Start End":[[1037,1062]]}
 {"Identifier":"2017ApJ...848...51D__Andr\u00e9_et_al._2010_Instance_2","Paragraph":"In recent years, there has been an increasing interest in identifying embedded filaments at an early stage of fragmentation, where star formation activities have not yet started. Kainulainen et al. (2016) studied the Musca molecular cloud using the NIR, 870 \u03bcm dust continuum and molecular line data, and suggested that the Musca cloud is a very promising candidate for a filament at an early stage of fragmentation and shows very few signs of ongoing star formation. However, the identification of such filaments is still limited in the literature (e.g., Kainulainen et al. 2016). In the I05463+2652 site, we have selected two elongated filamentary features (\u201cs-fl\u201d and \u201cnw-fl\u201d). The Herschel temperature map reveals these filaments with a temperature of \u223c11 K. It has been suggested that the thermally supercritical filaments (i.e., \n\n\n\n\n\n\nM\n\n\nline\n\n\n>\n\n\nM\n\n\nline\n,\ncrit\n\n\n\n\n) can be unstable to radial collapse and fragmentation (Andr\u00e9 et al. 2010). However, thermally subcritical filaments (i.e., \n\n\n\n\n\n\nM\n\n\nline\n\n\n\n\n\nM\n\n\nline\n,\ncrit\n\n\n\n\n) may lack prestellar clumps\/cores and embedded protostars (Andr\u00e9 et al. 2010). In the I05463+2652 site, the observed masses per unit length of the filaments are computed to be \n\n\n\n\n\u223c\n60\n\n\n\nM\n\n\n\u2299\n\n\n\n\n pc\u22121 (for filament \u201cs-fl\u201d) and \n\n\n\n\n\u223c\n200\n\n\n\nM\n\n\n\u2299\n\n\n\n\n pc\u22121 (for filament \u201cnw-fl\u201d), which are much higher than the critical mass per unit length at T = 10 K (i.e., \n\n\n\n\n\n\nM\n\n\nline\n,\ncrit\n\n\n=\n16\n\n\n\nM\n\n\n\u2299\n\n\n\n\n pc\u22121; see Section 3.2). For the purpose of comparison, we also provide the observed masses per unit length of some well known filaments (such as DR21 (\n\n\n\n\n\n\nM\n\n\nline\n\n\n\u223c\n4500\n\n\n\nM\n\n\n\u2299\n\n\n\n\n pc\u22121), Serpens South (\n\n\n\n\n\n\nM\n\n\nline\n\n\n\u223c\n290\n\n\n\nM\n\n\n\u2299\n\n\n\n\n pc\u22121), Taurus B211\/B213 (\n\n\n\n\n\n\nM\n\n\nline\n\n\n\u223c\n50\n\n\n\nM\n\n\n\u2299\n\n\n\n\n pc\u22121), and Musca (\n\n\n\n\n\n\nM\n\n\nline\n\n\n\u223c\n20\n\n\n\nM\n\n\n\u2299\n\n\n\n\n pc\u22121)) (see Table 1 in Andr\u00e9 et al. 2016). Based on the analysis of masses per unit length, the elongated filaments (\u201cs-fl\u201d and \u201cnw-fl\u201d) are thermally supercritical (see Section 3.2). Furthermore, these two filaments contain clumps (or fragments), indicating the signature of gravitational fragmentation. Arzoumanian et al. (2013) pointed out that supercritical filaments may undergo gravitational contraction and increase in mass per unit length through the accretion of background material.","Citation Text":["Andr\u00e9 et al. 2010"],"Citation Start End":[[1143,1160]]}