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[MATH] . However, we expect that the intrinsic entropy perturbation of cosmic strings is negligible and will assume this in the following. The second part [MATH] |
comes from the relative entropy perturbation between different fluids [MATH] [EQUATION] where the relative entropy perturbation between different fluids |
[MATH] is given by [EQUATION] and the adiabatic sound speed for each component, [MATH] , is given by [MATH] with [MATH] and [MATH] being the energy density and pressure of the component. |
Now, let us estimate the amplitude of the curvature perturbation [MATH] for a comoving scale [MATH] . First, we consider a scale [MATH] which exits the Hubble radius during a radiation dominated era. We neglect the curvature perturbations which are generated when the corresponding scale is sub-Hubble. |
Thus, we just follow the evolution of the curvature perturbation from the epoch [MATH] when a comoving scale [MATH] exits the Hubble radius until the time [MATH] when the symmetry is restored and the strings disappear. |
The relative entropy perturbation between radiation and cosmic strings is [EQUATION] where we have used the fact that [MATH] is almost constant and much smaller than unity, and |
[MATH] is at most comparable to [MATH] . From the scaling solution, it follows that cosmic strings can be modeled as a random walk on scales larger than the Hubble radius with step length comparable to the Hubble radius. Then, the density fluctuations of cosmic strings for a super-Hubble scale can be easily estimated a... |
[EQUATION] where [MATH] is the mass per unit length of a string, [MATH] is the number of long strings crossing any given Hubble volume, and [MATH] . Notice that [MATH] can be different in radiation and matter dominated epochs although the difference is expected to be at most [MATH] . Inserting these equations to Eq. ( ... |
[EQUATION] As stated above, cosmic strings disappear at the time [MATH] due to symmetry restoration. Once cosmic strings disappear, the curvature perturbation is conserved at least until the bounce. Thus, the final curvature perturbation before the bounce is estimated as |
[EQUATION] Here we have made use of [MATH] (in the radiation era), and [MATH] is the value of [MATH] (in the radiation epoch) which is [MATH] . Thus, the curvature perturbations are independent of the comoving scale [MATH] and hence scale invariant at least before the bounce. In the same way, the curvature perturbation... |
[EQUATION] where [MATH] is the matter-radiation equality time in the contracting phase, we have made use of [MATH] (in the matter era), and [MATH] is the value of [MATH] in the matter epoch. Therefore, the curvature perturbation is scale invariant at least before the bounce also on these scales. |
According to the often-used Hwang-Vishniac (Deruelle-Mukhanov ) matching conditions for fluctuations across a space-like hypersurface, the curvature perturbation is conserved across the bounce. If we apply these matching condition, we conclude that the final curvature perturbations in the expanding phase are almost sca... |
there are problems with blindly applying these matching conditions. Subsequent studies have shown that the actual transfer of the fluctuations depends quite sensitively on the details of the bounce. There are cases where the curvature perturbation is conserved (see e.g. |
), but there are other examples where this does not hold . However, if the bounce time is short compared to the time scale of the fluctuations of interest, it can be rather rigorously shown that the spectrum of [MATH] is maintained through the bounce. This can be shown |
by modeling the background cosmology with three phases: the initial contracting radiation phase, the “bounce phase” during which [MATH] , where [MATH] is some constant, and the expanding radiation phase. The matching conditions at the two hypersurfaces between these phases can be consistently applied (since the backgro... |
Finally, we comment on some subtleties. First of all, cosmic strings may be formed again in the expanding phase. In this case, cosmic strings again produce isocurvature fluctuations in the expanding phase, which should be suppressed to less than [MATH] of the total curvature perturbations |
. Such a suppression may be realized in the case when the constant [MATH] for cosmic strings in the contracting phase is much larger than that in the expanding phase. The fact that the loop chopping efficiency [MATH] is smaller implies that the constant [MATH] might be larger. Therefore, it is plausible that the consta... |
Another issue is that cosmic strings generate not only density perturbations but also vector and tensor perturbations (gravitational waves). Gravitational waves are produced by oscillations of loops as well as long strings. As explained before, the radius of a loop could become larger than the Hubble before there has b... |
. In particular, the metric perturbations always grow while the matter perturbations stay constant in the radiation dominated era. However, the vector perturbations will decrease in the expanding phase. If vector fluctuations are suppressed (even slightly) across the bounce (or the scalar fluctuations enhanced), then t... |
. As a final remark, we mention possible non-Gaussianities in the scenario. Since the distribution of cosmic string is highly non-Gaussian, the produced density fluctuations may give large non-Gaussianity, though the bispectrum for a simulated string model in the expanding universe is shown not to be so large for the d... |
. All these topics are worth investigating. Summary We have shown that adiabatic, super-Hubble, and almost scale invariant density fluctuations can be produced by cosmic strings in a contracting universe. Although cosmic strings can only generate isocurvature fluctuations in an expanding universe, they can produce adia... |
M.Y is grateful to M. Kawasaki for useful discussions. T.T. and M.Y would like to thank R. H. Brandenberger for kind hospitality at McGill University where this work was finished. This work is supported in part by a Canadian NSERC Discovery Grant and by the Canada Research Chair program (R.B.), and by the Sumitomo Foun... |
# Source: arxiv 0808.1292 # Title: High-Resolution Spectroscopy of Long-Periodic Eclipsing Binary Epsilon Aurigae # Sections: all # Downloaded: 2026-03-02T07:59:08.120644+00:00 |
HIGH-RESOLUTION SPECTROSCOPY OF LONG-PERIODIC ECLIPSING BINARY [MATH] AURIGAE ABSTRACT. The results of spectroscopic observations of long-periodic eclipsing binary [MATH] Aur are reported. The observations were carried out during 2 nights in 2007 at 2-meter telescope located at the peak Terskol, Northern Caucasus (Russ... |
Key words : Stars: binary: eclipsing; stars: individual: [MATH] Aur. 1. Introduction [MATH] Aur is well-observed long-periodic eclipsing binary, but still one of the most puzzling star. It is the eclipsing binary with longest known orbital period – 27.1 year. The main enigma is considered in the eclipsing object (it is... |
The eclipsing nature of [MATH] Aur was first mentioned by Fritsch (1824), where he discussed first ever-observed minimum in 1821. Since that [MATH] Aur’ eclipses were observed each 27.1 years (Ludendorff, 1904) (in 1848, 1875, 1902, 1929, 1956, 1983), the next is expected in 2010 (first contact – Aug, 06, 2009; mid-ecl... |
Recently (Carroll et al., 1991) [MATH] Aur secondary was interpreted as a protoplanetary system. So, spectroscopic monitoring before and during the eclipse is of great interest. |
2. Observations Spectroscopic observations were done at the Terskol Observatory (Russia, Northern Caucasus) during two nights, particularly at March, 30-31 and March, 31- April, 1 in 2007. 2-meter Zeiss telescope and coude-echelle spectrometer was used. The wavelength range covers from 3660 to 9500 Åin 80 orders. The r... |
3. Discussion Our research was focused on searching for the short-time variations of [MATH] line profile. [MATH] line was detected in absorption together with prominent blue and red emission wings symmetrical one to another, which is quite exciting (see Fig. 1 for the plot of [MATH] region of [MATH] Aur spectrum). |
The value variations of equivalent widths (EW) of the blue wing, the red wing and the absorption core of the [MATH] line profiles were calculated ( [MATH] – emission, [MATH] absorption) and given in Table 1. |
EW was calculated by direct numerical integration over the area under the line profile. As could be seen from Fig. 1, the blue wing of [MATH] line underwent a changes during the course of observations at March, 30-31, 2007. This changes reach up to 8%, that could be considered to be significant. During the next night n... |
Schanne, L. (2007) interpreted emission components of [MATH] as evidence of gas behind the star (for red-shifted component) and radial outward flows, attributed to instabilities in the star (blue-shifted component). |
Cha et al. (1994), Cha et al. (1995) attributed blue wing emission source to region region which contains an HII cloud with a short time scale variation. |
Also EW of the following absorption lines all of which exhibit long-term variability (Thompson et al. 1987) were mesured: Fe I (3922.9 Å), Ti II (4028.0 Å), Ti II (4443.85 Å), Ti II (4468.48 Å), [MATH] (4861.5 Å), Na DI (5889.953 Å), Na DII (5895.923 Å), O I (7772 Å). No short-time variability, reaching 5% limit, were ... |
Fig. 4 illustrates several portions of [MATH] Aur average spectra, with the most prominent lines being identified and denoted. Further photometrical and spectroscopical monitoring of this object is critically important for under- standing [MATH] Aur – the most puzzling eclipsing binary. |
References Cha G. et al.: 1994, A&A 284 , 874-882. Cha G. et al.: 1995, IBVS , No. 4149. Fritsch J.M.: 1824, Berl. Jahrb. , p. 252. Schanne L.: 2007, IBVS , No. 5747. Thompson D.T. et al.: 1987, ApJ 321 , 450-458. |
# Source: arxiv 0808.1302 # Title: Testing the Dark-Energy-Dominated Cosmology by the Solar-System Experiments # Sections: all # Downloaded: 2026-03-02T07:59:09.278685+00:00 |
TESTING THE DARK-ENERGY-DOMINATED COSMOLOGY BY THE SOLAR-SYSTEM EXPERIMENTS \bodymatter According to the recent astronomical data, the most part of energy in the Universe is in the ‘dark’ form, which is effectively described by [MATH] -term in Einstein equations. All arguments in favor of the dark energy were obtained ... |
inside the Solar system)? In general, such effects can be expected from the solution of the equations of General Relativity (GR) for a point-like mass [MATH] |
in the [MATH] -dominated (de Sitter) Universe, which was obtained by Kottler very long time ago. The presence of [MATH] -term should change, particularly, the standard relativistic shift of Mercury’s perihelion. This was the idea by Cardona & Tejeiro |
, who proposed using the measure of the uncertainty in our knowledge of Mercury’s perihelion shift to impose the upper bound on [MATH] . The result obtained was not so good as other cosmological estimates but, surprisingly, the accuracy was worse by only [MATH] orders of magnitude. A more skeptical viewpoint on the sam... |
Since accuracy of the above method is insufficient, it was proposed in our previous papers to utilize the data of radial (rather than angular) measurements of the Moon to reveal the anomalous increase in its distance from the Earth produced by the [MATH] -term, which looks formally as ‘local’ Hubble expansion. Why is i... |
Hubble dynamics at small scales is studied for a long time, starting from the pioneering work by McVittie . Although the results by various authors were quite contradictory ( e.g. review by Bonnor |
and references therein), the most popular point of view was that the Hubble expansion manifests itself only at the sufficiently large distances (from a few Mpc) and is absent at the less scales |
. There were a few arguments in favor of such conclusion, such as the so-called Einstein–Straus theorem a quasi-Newtonian treatment of Hubble effect in a small volume as a tidal-like action by distant matter ( e.g. the recent work by Domínguez & Gaite |
and references therein), and the Einstein–Infeld–Hoffmann (EIH) surface integral method, which was applied to the problem of local Hubble expansion by Anderson |
. Unfortunately, as is shown in Ref. \refcite dum05, all these approaches become inapplicable when the Universe evolution is governed by [MATH] -term, uniformly distributed in space. |
A frequent experimental argument against the Hubble expansion within Solar system is based on the available constraint on time variation in the gravitational constant derived from the lunar dynamics, which is now as strong as |
[MATH] yr -1 (Ref. \refcite wil04). Unfortunately, the equivalence between the effect of variable [MATH] and the cosmological expansion, stated by some authors, is based solely on the Newtonian arguments. A more accurate treatment of this problem in the GR framework |
shows that manifestation of [MATH] -term in some components of the metric tensor really looks like the influence of variable [MATH] |
if we assume that [MATH] , where [MATH] ; but such interpretation is not self-consistent: the [MATH] -dependence of a few other components is not expressible in terms of the variable coefficient of gravitational coupling. Therefore, the available limits on |
[MATH] , in general, cannot be reinterpreted as a constraint on local cosmological dynamics. Since all the commonly-used arguments against the local Hubble expansion fail in the case of dark energy, it becomes reasonable to seek for the corresponding effect; and the most sensitive tool seems to be the lunar laser rangi... |
For example, if we assume that planetary systems experience Hubble expansion with the same rate as everywhere in the Universe [MATH] km s -1 Mpc -1 ), then average radius of the lunar orbit [MATH] should increase by [MATH] cm for the period of 20 years. On the other hand, the accuracy of LLR during the last 20 years wa... |
The main problem is to exclude the effect of geophysical tides, which also contributes to the secular increase in the Earth–Moon distance as |
[MATH] where [MATH] is the Earth’s diurnal period, and [MATH] cm s -1 e.g. Ref. \refcite dum03). So, if [MATH] is known from independent astrometric measurements of the Earth’s rotation deceleration with respect to distant objects, then the above relation can be used to exclude the geophysical tides and, thereby, to re... |
The telescopic data, accumulated from the middle of the 17th century, were processed by a few researches; and one of the most detailed compilations was presented recently in Ref. \refcite sid02. Of course, the value of secular trend derived from the quite short time series can suffer from considerable periodic and quas... |
[MATH] (This value is appreciably less than in our previous work where it was taken from the older literature.) The entire analysis of LLR vs. the astrometric data is summarized in Table TESTING THE DARK-ENERGY-DOMINATED COSMOLOGY BY THE SOLAR-SYSTEM EXPERIMENTS . The excessive rate of increase in the lunar orbit, [MAT... |
[MATH] Next, it is reasonable to assume that the local Hubble expansion is formed only by the uniformly-distributed dark energy, while the irregularly-distributed (aggregated) forms of matter begin to affect the Hubble flow at the larger distances, thereby increasing its rate up to the standard intergalactic value. If ... |
respectively, then [EQUATION] So, if [MATH] is formed locally only by [MATH] while globally by both these terms, [MATH] and [MATH] (or, in terms of the relative densities, |
[MATH] and [MATH] ), then [EQUATION] At [MATH] and [MATH] , we get [MATH] . Therefore, [MATH] which is in reasonable agreement both with the well-known WMAP result, |
[MATH] km s -1 Mpc -1 , and with the recent Hubble diagram for type Ia supernovae , whose interpretation requires a slightly reduced value of [MATH] |
Therefore, the presence of local Hubble expansion, caused by the [MATH] -term, gives us a reasonable explanation of the anomalous increase in the lunar orbit, consistent with the ‘large-scale’ astronomical data. Thereby, this is one more argument in favor of the dark energy. Besides, if the local Hubble expansion reall... |
# Source: arxiv 0808.1341 # Title: A red supergiant nebula at 25 micron: arcsecond scale mass-loss asymmetries of mu Cep # Sections: all # Downloaded: 2026-03-02T07:59:10.480547+00:00 |
A red supergiant nebula at 25 micron: arcsecond scale mass-loss asymmetries of [MATH] Cep Abstract We present diffraction limited (0.6″) 24.5 µm Subaru/COMICS images of the red supergiant [MATH] Cep. We report the detection of a circumstellar nebula, that was not detected at shorter wavelengths. It extends to a radius ... |
[MATH] yr -1 . This work supports the idea that at least part of the asymmetries in shells of evolved massive stars and supernovae may be due to the mass-loss process in the red supergiant phase. |
Subject headings: (stars:) supergiants - stars: evolution - stars : individual [MATH] Cep - stars: mass-loss 1. Introduction Although the final stages of the post-main sequence evolution of massive stars do not last long, it is here where most of the mass is lost and the shaping of the pre-supernova ejecta takes place.... |
It is not only the study of the stars themselves that helps us understand the final stages of the evolution of massive stars. Investigating RSGs’ mass-loss and their circumstellar material helps us to understand the origin of the aspherical structures found around supernovae, such as SN 1987A’s rings, or gamma-ray burs... |
A third RSG that is found in the same location in the HR diagram as the above two objects is [MATH] Cep (Schuster et al 2006). Contrary to these two cooler objects, little is known about the material surrounding [MATH] Cep. This can be readily explained by its mass-loss, which is orders of magnitude lower than for NML ... |
2. Observations and data reduction [MATH] Cep was observed on 6 different occasions as a mid-IR standard star between June 2003 and July 2004 with the COMICS instrument mounted on the 8.2 meter Subaru telescope in Hawaii (Kataza et al. 2000; Okamoto et al. 2003; Sako et al. 2003). The star was imaged using the Q24.5-OL... |
[MATH] Cep is bright and therefore often used as a standard star, either for determining the instrumental point-spread-function (PSF) or for calibrating photometry. We observed the object for calibration purposes for a different project (as reported in de Wit et al. 2008b), and found that it was extended compared to ot... |
3. Results 3.1. The 24.5 [MATH] m images: asymmetric dust distribution The highest SNR image (taken on 04/06/07) of [MATH] Cep is shown in the left panel of Fig. . We have subtracted from this image the scaled profile of the PSF standard asteroid 511 in order to enhance the features of [MATH] Cep’s circumstellar emissi... |
[MATH] Tau with again a PSF profile subtracted. It is clear that [MATH] Cep has extended circumstellar emission reaching distances from the star of at least 6″. The outer parts of the shell-like structure are roughly circular with indications of larger scale inhomogeneities. In contrast, the inner parts reveal a clearl... |
3.2. Dust radiative transfer modelling Emission at 24.5 µm stays optically thin for large columns of dust. Resolved images allow us to simultaneously model the dust emission as a function of distance from the star (the intensity profile) and the total dust emission as given by the SED. For this purpose, we employ DUSTY... |
[MATH] , solar metallicity and surface gravity corresponding to the supergiant nature of [MATH] Cep, i.e. [MATH] We use oxygen-rich dust with a condensation temperature of 1000 K. The dust particles follow a MRN size distribution (Mathis, Rumple, & Nordsieck 1977). Within the limitation of a spherical model, we experim... |
We build [MATH] Cep’s SED using a mid-IR spectrum taken with the short wavelength spectrometer (SWS, de Graauw et al. 1996) on board the ISO satellite (Kessler et al. 1996), near-IR [MATH] |
photometry from Heske (1990) and visual broadband [MATH] Johnson photometry from Lee (1970). The photometry is dereddened for an interstellar extinction of [MATH] |
(Levesque et al. 2005). The IRAS 60 [MATH] m and 100 [MATH] m data points lie above the extrapolated ISO-SWS spectrum. This excess flux is due to the much larger beam of IRAS and comes from extended cool dust emission. The origin of this emission is not obvious, it could be either due to the interstellar medium being h... |
The fit procedure initially estimates the [MATH] by matching the overall shape of the scaled model SED to the observed one. DUSTY’s output images are then accordingly scaled and convolved with the instrumental PSF. A comparison of model infrared excess and model intensity profile to the observed ones is made for all ge... |
The results of the 1D modelling are presented in Fig. Once the intensity profile is fit for a given nebular structure and stellar luminosity, the SED can be matched by increasing the amount of dust in the given nebula. The normalized intensity profile is quite insensitive to the total amount of dust for small optical d... |
4. Discussion We have presented the first high-resolution (0.6″) images of the circumstellar environment of the RSG [MATH] Cep. This material has not been seen in previous imaging campaigns. For a sample of massive evolved objects, Schuster et al. (2006) obtained deep optical images with the HST to search for scattered... |
One may speculate whether this geometry is due to a bipolar flow colliding with the spherically symmetric previous wind, or a slowly expanding torus. It is useful in this respect to consider the current findings for the more numerous lower-mass counterparts of RSGs, the Asymptotic Giant Branch (AGB) stars. Data on thes... |
[MATH] Cep indicate low velocities rather than high velocities, it is very well possible that we are now witnessing the same for a Red Supergiant. |
5. Concluding Remarks We have obtained the first diffraction-limited images of a Red Supergiant at 24.5 [MATH] m, and resolved the circumstellar material around [MATH] Cep out to 6″. The intensity profile and the SED were simultaneously fitted with a dust model. The main results can be summarized as follows: |
1. The outer parts of the shell are to first order circular with apparent inhomogeneities, the inner parts, tracing the mass lost in the past 1000 years display a flattened structure, which is possibly a slowly expanding, dense torus. The immediate conclusion from this is that any asymmetries in the shells of massive e... |
2. The mass-loss rate for [MATH] Cep is found to be a few times 10 -7 [MATH] yr -1 . This low mass-loss rate may explain the fact that [MATH] Cep is not detected in scattered light, as opposed to other RSGs which have mass-loss rates that are orders of magnitude larger. |
3. A general conclusion is that imaging thermal dust emission at 24.5 [MATH] m is a viable manner to spatially resolve the circumstellar material around evolved objects with low mass-loss rates and as a consequence are otherwise not detected with maser observations, CO imaging or scattered light imaging. |
RDO is grateful for the support from the Leverhulme Trust for awarding a Research Fellowship. We thank Martin Groenewegen for fruitful discussions. The version of the ISO data presented in this paper correspond to the Highly Processed Data Product (HPDP) set called hpdp_39802402_5 by W.F. Frieswijk et al., available fo... |
# Source: arxiv 0808.1441 # Title: Injection of Short-Lived Radionuclides into the Early Solar System from a Faint Supernova with Mixing-Fallback # Sections: all # Downloaded: 2026-03-02T07:59:20.702033+00:00 |
Injection of Short-Lived Radionuclides into the Early Solar System from a Faint Supernova with Mixing-Fallback Abstract Several short-lived radionuclides (SLRs) were present in the early solar system, some of which should have formed just prior to or soon after the solar system formation. Stellar nucleosynthesis has be... |
In this study, we propose a faint supernova with mixing and fallback as a stellar source of SLRs with mean lives of [MATH] 5 Myr ( 26 Al, 41 Ca, 53 Mn, and 60 Fe) in the solar system. In such a supernova, the inner region of the exploding star experiences mixing, a small fraction of mixed materials is ejected, and the ... |
methods: analytical — nuclear reactions, nucleosynthesis, abundances — solar system: formation Introduction The former presence of short-lived radionuclides (SLRs) in the early solar system ( 10 Be, 26 Al, 36 Cl, 41 Ca, 53 Mn, 60 Fe, 107 Pd, 129 I, and 182 Hf) has been inferred from excesses in the abundances of their ... |
The SLRs with relatively long mean-lives such as 107 Pd, 129 I, 182 Hf, and perhaps 53 Mn may have been products of steady-state nucleosynthesis in the galaxy (Jacobsen, 2005 , while those with mean-lives ( [MATH] ) of [MATH] 5 Myr, 10 Be ( [MATH] =2.2 Myr), 26 Al ( [MATH] =1.03 Myr), 36 Cl ( [MATH] =0.43 Myr), 41 Ca (... |
There have been several attempts to find a plausible stellar source(s) for the abundances of SLRs in the early solar system. A low-mass (1.5 M ) thermally-pulsing asymptotic-giant-branch (TP-AGB) star cannot produce enough 60 Fe to match the initial abundance of 60 Fe in the solar system (e.g., Busso et al., 2003 ; Was... |
Type II core-collapse supernovae have also been considered as plausible sources for SLRs. However, most supernova models imply that if a supernova provided 26 Al and 41 Ca into the solar system, it would also supply 10-100 times more 53 Mn than its estimated initial abundance in the solar system (e.g., Goswami and Vanh... |
Another problem with supernovae as sources of SLRs is overproduction of 60 Fe if all the 26 Al in the solar system was derived from supernovae. Although the yield of 60 Fe depends the mass loss and initial mass (e.g., Limongi & Chieffi, 2006 , the expected amount of 60 Fe injected from a supernova would be, in general,... |
In this study, we propose a supernova with mixing and fallback, with a kinetic energy of explosion slightly less than that for a typical supernova ( [MATH] 10 51 erg) as a potential source of 26 Al, 41 Ca, 53 Mn, and 60 Fe in the early solar system. Faint supernovae such as SN1997D and SN1999br have such kinetic energi... |
Injection of supernova ejecta into the solar system materials The abundance of a SLR injected into preexisting solar system materials can be expressed as follows, assuming that injected materials are well-mixed with preexisting materials (e.g., Wasserburg et al., 2006 ; Sahijpal & Soni, 2006 .: |
[EQUATION] where SLR and SI are the numbers of SLR and a stable isotope (SI) for the initial solar system, respectively. Time-zero for the solar system is, in practice, considered to be the time of formation of CAIs, the oldest solid materials formed in the solar system. [MATH] and [MATH] are the numbers of SLR and SI ... |
Nuclides ejected from supernovae with mixing-fallback In the standard model for a supernova almost all the materials are ejected, but materials in the very inner-most region, which is typically deeper than the incomplete Si-burning layer, fall back onto the star. In the model for a supernova with fallback (Meyer & Clay... |
In the model for a supernova with mixing-fallback, we assume two mass-cut boundaries at different depths of a pre-supernova star. The deeper boundary is defined as the initial mass-cut boundary ( cut ) corresponding to the mass-cut boundary in previous models. The shallower boundary is defined as the outer boundary of ... |
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