arXiv subjects

C. Walsh

Publications and source records attributed to C. Walsh.

35 records · Page 2Linked to original sources

arXiv2019

VLA cm-wave survey of young stellar objects in the Oph A cluster: constraining extreme UV- and X-ray-driven disk photo-evaporation -- A pathfinder for Square Kilometre Array studies

Observations of young stellar objects (YSOs) in centimeter bands can probe the continuum emission from growing dust grains, ionized winds, and magnetospheric activity, which are intimately connected to the evolution of protoplanetary disks and the formation of planets. We have carried out sensitive continuum observations toward the Ophiuchus A star-forming region using the Karl G. Jansky Very Large Array (VLA) at 10 GHz over a field-of-view of 6$'$ with a spatial resolution of $θ_{maj}$ $\times$ $θ_{min}$ $\sim$ 0.4$''$ $\times$ 0.2$''$. We achieved a 5 $μ$Jy beam$^{-1}$ root-mean-square noise level at the center of our mosaic field of view. Among the eighteen sources we detected, sixteen are YSOs (three Class 0, five Class I, six Class II, and two Class III) and two are extragalactic candidates. We find that thermal dust emission generally contributes less that 30% of the emission at 10 GHz. The radio emission is dominated by other types of emission such as gyro-synchrotron radiation from active magnetospheres, free-free emission from thermal jets, free-free emission from the outflowing photo-evaporated disk material, and/or synchrotron emission from accelerated cosmic-rays in jet or protostellar surface shocks. These different types of emission could not be clearly disentangled. Our non-detections towards Class II/III disks suggest that extreme UV-driven photoevaporation is insufficient to explain the disk dispersal, assuming that the contribution of UV photoevaporating stellar winds to radio flux does not evolve with time. The sensitivity of our data cannot exclude photoevaporation due to X-ray photons as an efficient mechanism for disk dispersal. Deeper surveys with the Square Kilometre Array will be able to provide strong constraints on disk photoevaporation.

astro-ph.SR↗

arXiv2019

Critical Opalescence across the Doping Driven Mott Transition in Optical Lattices of Ultracold Atoms

Phase transitions and their associated crossovers are imprinted in the behavior of fluctuations. Motivated by recent experiments on ultracold atoms in optical lattices, we compute the thermodynamic density fluctuations $δN^2$ of the two-dimensional fermionic Hubbard model with plaquette cellular dynamical mean-field theory. To understand the length scale of these fluctuations, we separate the local from the nonlocal contributions to $δN^2$. We determine the effects of particle statistics, interaction strength $U$, temperature $T$ and density $n$. At high temperature, our theoretical framework reproduces the experimental observations in the doping-driven crossover regime between metal and Mott insulator. At low temperature, there is an increase of thermodynamic density fluctuations, analog to critical opalescence, accompanied by a surprising reduction of the absolute value of their nonlocal contributions. This is a precursory sign of an underlying phase transition between a pseudogap phase and a metallic phase in doped Mott insulators, which should play an important role in the cuprate high-temperature superconductors. Predictions for ultracold atom experiments are made.

cond-mat.quant-gas↗

arXiv2019

Upper limits on CH$_3$OH in the HD 163296 protoplanetary disk: evidence for a low gas-phase CH$_3$OH/H$_2$CO ratio

Methanol (CH$_3$OH) is at the root of organic ice chemistry in protoplanetary disks. However, its weak emission has made detections difficult. To date, gas-phase CH$_3$OH has been detected in only one Class II disk, TW Hya. We use the Atacama Large Millimeter/submillimeter Array (ALMA) to search for a total of four CH$_3$OH emission lines in bands 6 and 7 toward the disk around the young Herbig Ae star HD 163296. The disk-averaged column density of methanol and its related species formaldehyde (H$_2$CO) are estimated assuming optically thin emission in local thermodynamic equilibrium. We compare these results to the gas-phase column densities of the TW Hya disk. No targeted methanol lines were detected individually nor after line stacking. The 3$σ$ disk-integrated intensity upper limits are $< 51$ mJy km s$^{-1}$ for the band 6 lines and $< 26$ mJy km s$^{-1}$ for the band 7 lines. The band 7 lines provide the strictest 3$σ$ upper limit on disk-averaged column density with $N_{\mathrm{avg}} < 5.0 \times 10^{11}$ cm$^{-2}$. The methanol-to-formaldehyde ratio is CH$_3$OH/H$_2$CO $< 0.24$ in the HD 163296 disk compared to a ratio of $1.27$ in the TW Hya disk. Differences in the stellar irradiation of Herbig disks compared to T Tauri disks likely influence the gaseous methanol and formaldehyde content. Possible reasons for the lower HD 163296 methanol-to-formaldehyde ratio include: a higher than expected gas-phase formation of H$_2$CO in the HD 163296 disk, uncertainties in the grain surface formation efficiency of CH$_3$OH and H$_2$CO, and differences in the disk structure and/or CH$_3$OH and H$_2$CO desorption processes that release the molecules from ice mantles back into the gas phase. These results provide observational evidence that the gas-phase chemical complexity found in disks may be strongly influenced by the spectral type of the host star.

astro-ph.SR↗

arXiv2018

Thermodynamic and information-theoretic description of the Mott transition in the two-dimensional Hubbard model

At the Mott transition, electron-electron interaction changes a metal, in which electrons are itinerant, to an insulator, in which electrons are localized. This phenomenon is central to quantum materials. Here we contribute to its understanding by studying the two-dimensional Hubbard model at finite temperature with plaquette cellular dynamical mean-field theory. We provide an exhaustive thermodynamic description of the correlation-driven Mott transition of the half-filled model by calculating pressure, charge compressibility, entropy, kinetic energy, potential energy and free energy across the first-order Mott transition and its high-temperature crossover (Widom line). The entropy is extracted from the Gibbs-Duhem relation and shows complex behavior near the transition, marked by discontinuous jumps at the first-order boundary, singular behavior at the Mott endpoint and inflections marking sharp variations in the supercritical region. The free energy allows us to identify the thermodynamic phase boundary, to discuss phases stability and metastability, and to touch upon nucleation and spinodal decomposition mechanisms for the transition. We complement this thermodynamic description of the Mott transition by an information-theoretic description. We achieve this by calculating the local entropy, which is a measure of entanglement, and the single-site total mutual information, which quantifies quantum and classical correlations. These information-theoretic measures exhibit characteristic behaviors that allow us to identify the first-order coexistence regions, the Mott critical endpoint and the crossovers along the Widom line in the supercritical region.

cond-mat.str-el↗

arXiv2018

Entanglement entropy and mutual information across the Mott transition in the two-dimensional Hubbard model

Entanglement and information are powerful lenses to probe phases transitions in many-body systems. Motivated by recent cold atom experiments, which are now able to measure the corresponding information-theoretic quantities, we study the Mott transition in the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory, and focus on two key measures of quantum correlations: entanglement entropy and mutual information. We show that they detect the first-order nature of the transition, the universality class of the endpoint, and the crossover emanating from the endpoint.

cond-mat.str-el↗

arXiv2018

Complex cyanides as chemical clocks in hot cores

In the high-mass star-forming region G35.20-0.74N, small scale (about 800 AU) chemical segregation has been observed in which complex organic molecules containing the CN group are located in a small location. We aim to determine the physical origin of the large abundance difference (about 4 orders of magnitude) in complex cyanides within G35.20-0.74 B, and we explore variations in age, gas and dust temperature, and gas density. We performed gas-grain astrochemical modeling experiments with exponentially increasing (coupled) gas and dust temperature rising from 10 to 500 K at constant H$_2$ densities of 10$^7$, 10$^8$, and 10$^9$ cm$^{-3}$. We tested the effect of varying the initial ice composition, cosmic-ray ionization rate, warm-up time (over 50, 200, and 1000 kyr), and initial (10, 15, and 25 K) and final temperatures (300 and 500 K). Varying the initial ice compositions within the observed and expected ranges does not noticeably affect the modeled abundances indicating that the chemical make-up of hot cores is determined in the warm-up stage. Complex cyanides vinyl and ethyl cyanide (CH$_2$CHCN and C$_2$H$_5$CN, respectively) cannot be produced in abundances (versus H$_2$) greater than 5x10$^{-10}$ for CH$_2$CHCN and 2x10$^{-10}$ for C$_2$H$_5$CN with a fast warm-up time (52 kyr), while the lower limit for the observed abundance of C$_2$H$_5$CN toward source B3 is 3.4x10$^{-10}$. Complex cyanide abundances are reduced at higher initial temperatures and increased at higher cosmic-ray ionization rates. Reproducing the observed abundances toward G35.20-0.74 Core B3 requires a fast warm-up at a high cosmic-ray ionization rate (1x10$^{-16}$ s$^{-1}$) at a high gas density (>10$^9$ cm$^{-3}$). G35.20-0.74 source B3 only needs to be about 2000 years older than B1/B2 for the observed chemical difference to be present. (This abstract has been shortened)

astro-ph.GA↗

arXiv2018

Probing midplane CO abundance and gas temperature with DCO$^+$ in the protoplanetary disk around HD 169142

This work aims to understand which midplane conditions are probed by the DCO$^+$ emission in the disk around the Herbig Ae star HD 169142. We explore the sensitivity of the DCO$^+$ formation pathways to the gas temperature and the CO abundance. The DCO$^+$ $J$=3-2 transition was observed with ALMA at a spatial resolution of 0.3". The HD 169142 DCO$^+$ radial intensity profile reveals a warm, inner component at radii <30 AU and a broad, ring-like structure from ~50-230 AU with a peak at 100 AU just beyond the millimeter grain edge. We modeled DCO$^+$ emission in HD 169142 with a physical disk structure adapted from the literature, and employed a simple deuterium chemical network to investigate the formation of DCO$^+$ through the cold deuterium fractionation pathway via H$_2$D$^+$. Contributions from the warm deuterium fractionation pathway via CH$_2$D$^+$ are approximated using a constant abundance in the intermediate disk layers. Parameterized models show that alterations to the midplane gas temperature and CO abundance of the literature model are both needed to recover the observed DCO$^+$ radial intensity profile. The best-fit model contains a shadowed, cold midplane in the region z/r < 0.1 with an 8 K decrease in gas temperature and a factor of five CO depletion just beyond the millimeter grain edge, and a 2 K decrease in gas temperature for r > 120 AU. The warm deuterium fractionation pathway is implemented as a constant DCO$^+$ abundance of 2.0$\times$10$^{-12}$ between 30-70 K. The DCO$^+$ emission probes a reservoir of cold material in the HD 169142 outer disk that is not revealed by the millimeter continuum, the SED, nor the emission from the 12CO, 13CO, or C18O $J$=2-1 lines.

astro-ph.SR↗

arXiv2018

A UV-to-NIR Study of Molecular Gas in the Dust Cavity Around RY Lupi

We present a study of molecular gas in the inner disk $\left(r < 20 \, \text{AU} \right)$ around RY Lupi, with spectra from HST-COS, HST-STIS, and VLT-CRIRES. We model the radial distribution of flux from hot gas in a surface layer between $r = 0.1-10$ AU, as traced by Ly$α$-pumped H$_2$. The result shows H$_2$ emission originating in a ring centered at $\sim$3 AU that declines within $r < 0.1$ AU, which is consistent with the behavior of disks with dust cavities. An analysis of the H$_2$ line shapes shows that a two-component Gaussian profile $\left(\text{FWHM}_{broad, H_2} = 105 \pm 15 \, \text{km s}^{-1}; \, \text{FWHM}_{narrow, H_2} = 43 \pm 13 \, \text{km s}^{-1} \right)$ is statistically preferred to a single-component Gaussian. We interpret this as tentative evidence for gas emitting from radially separated disk regions $\left( \left \langle r_{broad, H_2} \right \rangle \sim 0.4 \pm 0.1 \, \text{AU}; \, \left \langle r_{narrow, H_2} \right \rangle \sim 3 \pm 2 \, \text{AU} \right)$. The 4.7 $μ$m $^{12}$CO emission lines are also well fit by two-component profiles $\left( \left \langle r_{broad, CO} \right \rangle = 0.4 \pm 0.1 \, \text{AU}; \, \left \langle r_{narrow, CO} \right \rangle = 15 \pm 2 \, \text{AU} \right)$. We combine these results with 10 $μ$m observations to form a picture of gapped structure within the mm-imaged dust cavity, providing the first such overview of the inner regions of a young disk. The HST SED of RY Lupi is available online for use in modeling efforts.

astro-ph.SR↗

arXiv2018

Methanol ice co-desorption as a mechanism to explain cold methanol in the gas-phase

Methanol is formed via surface reactions on icy dust grains. Methanol is also detected in the gas-phase at temperatures below its thermal desorption temperature and at levels higher than can be explained by pure gas-phase chemistry. The process that controls the transition from solid state to gas-phase methanol in cold environments is not understood. The goal of this work is to investigate whether thermal CO desorption provides an indirect pathway for methanol to co-desorb at low temperatures. Mixed CH$_{3}$OH:CO/CH$_{4}$ ices were heated under UHV (ultra-high vacuum) conditions and ice contents are traced using RAIRS (reflection absorption IR spectroscopy), while desorbing species were detected mass spectrometrically. An updated gas-grain chemical network was used to test the impact of the results of these experiments. The physical model used is applicable for TW Hya, a protoplanetary disk in which cold gas-phase methanol has recently been detected. Methanol release together with thermal CO desorption is found to be an ineffective process in the experiments, resulting in an upper limit of $\leq$ 7.3 $\times$ 10$^{-7}$ CH3OH molecules per CO molecule over all ice mixtures considered. Chemical modelling based on the upper limits shows that co-desorption rates as low as 10$^{-6}$ CH$_{3}$OH molecules per CO molecule are high enough to release substantial amounts of methanol to the gas-phase at and around the location of the CO thermal desorption front in a protoplanetary disk. The impact of thermal co-desorption of CH3OH with CO as a grain-gas bridge mechanism is compared with that of UV induced photodesorption and chemisorption.

astro-ph.SR↗

arXiv2017

ALMA unveils rings and gaps in the protoplanetary system HD 169142: signatures of two giant protoplanets

The protoplanetary system HD 169142 is one of the few cases where a potential candidate protoplanet has been recently detected via direct imaging. To study the interaction between the protoplanet and the disk itself observations of the gas and dust surface density structure are needed. This paper reports new ALMA observations of the dust continuum at 1.3\,mm, $^{12}$CO, $^{13}$CO and C$^{18}$O $J=2-1$ emission from the system HD 169142 at angular resolution of $\sim 0".18 - 0".28$ ($\sim 20\,$au$ - 33\,$au). The dust continuum emission reveals a double-ring structure with an inner ring between $0".17-0".28$ ($\sim 20 - 35\,$au) and an outer ring between $0".48-0".64$ ($\sim 56 - 83\,$au). The size and position of the inner ring is in good agreement with previous polarimetric observations in the near-infrared and is consistent with dust trapping by a massive planet. No dust emission is detected inside the inner dust cavity ($R \lesssim 20\,$au) or within the dust gap ($\sim 35 - 56\,$au). In contrast, the channel maps of the $J=2-1$ line of the three CO isotopologues reveal the presence of gas inside the dust cavity and dust gap. The gaseous disk is also much larger than the compact dust emission extending to $\sim 1'.5$ ($\sim 180\,$au) in radius. This difference and the sharp drop of the continuum emission at large radii point to radial drift of large dust grains ($>$ \micron-size). Using the thermo-chemical disk code \textsc{dali}, the continuum and the CO isotopologues emission are modelled to quantitatively measure the gas and dust surface densities. The resulting gas surface density is reduced by a factor of $\sim 30-40$ inward of the dust gap. The gas and dust distribution hint at the presence of multiple planets shaping the disk structure via dynamical clearing (dust cavity and gap) and dust trapping (double ring dust distribution).

astro-ph.SR↗

arXiv2016

Water delivery from cores to disks: deuteration as a probe of the prestellar inheritance of H2O

We investigate the delivery of regular and deuterated forms of water from prestellar cores to circumstellar disks. We adopt a semi-analytical axisymmetric two-dimensional collapsing core model with post-processing gas-ice astrochemical simulations, in which a layered ice structure is considered. The physical and chemical evolutions are followed until the end of the main accretion phase. When mass averaged over the whole disk, a forming disk has a similar H2O abundance and HDO/H2O abundance ratio as their precollapse values (within a factor of 2), regardless of time in our models. Consistent with previous studies, our models suggest that interstellar water ice is delivered to forming disks without significant alteration. On the other hand, the local vertically averaged H2O ice abundance and HDO/H2O ice ratio can differ more, by up to a factor of several, depending on time and distance from a central star. Key parameters for the local variations are the fluence of stellar UV photons en route into the disk and the ice layered structure, the latter of which is mostly established in the prestellar stages. We also find that even if interstellar water ice is destroyed by stellar UV and (partly) reformed prior to disk entry, the HDO/H2O ratio in reformed water ice is similar to the original value. This finding indicates that some caution is needed in discussions on the prestellar inheritance of H2O based on comparisons between the observationally derived HDO/H2O ratio in clouds/cores and that in disks/comets. Alternatively, we propose that the ratio of D2O/HDO to HDO/H2O better probes the prestellar inheritance of H2O. It is also found that icy organics are more enriched in deuterium than water ice in forming disks. The differential deuterium fractionation in water and organics is inherited from the prestellar stages.

astro-ph.GA↗

arXiv2016

ALMA-resolved salt emission traces the chemical footprint and inner wind morphology of VY CMa

(abreviated) We aim to study the inner-wind structure (R<250 Rstar) of the well-known red supergiant VY CMa. We analyse high spatial resolution (~0".24x0".13) ALMA Science Verification (SV) data in band 7 in which four thermal emission lines of gaseous sodium chloride (NaCl) are present at high signal-to-noise ratio. For the first time, the NaCl emission in the inner wind region of VY CMa is spatially resolved. The ALMA observations reveal the contribution of up to four different spatial regions. The NaCl emission pattern is different compared to the dust continuum and TiO2 emission already analysed from the ALMA SV data. The emission can be reconciled with an axisymmetric geometry, where the lower density polar/rotation axis has a position angle of ~50 degrees measured from north to east. However, this picture can not capture the full morphological diversity, and discrete mass ejection events need to be invoked to explain localized higher-density regions. The velocity traced by the gaseous NaCl line profiles is significantly lower than the average wind terminal velocity, and much slower than some of the fastest mass ejections, signalling a wide range of characteristic speeds for the mass loss. Gaseous NaCl is detected far beyond the main dust condensation region. Realising the refractory nature of this metal halide, this hints at a chemical process preventing all NaCl from condensing onto dust grains. We show that in the case of the ratio of the surface binding temperature to the grain temperature being ~50, only some 10% of NaCl remains in gaseous form, while for lower values of this ratio thermal desorption efficiently evaporates NaCl. Photodesorption by stellar photons seems not to be a viable explanation for the detection of gaseous NaCl at 220 Rstar from the central star, and instead, we propose shock-induced sputtering driven by localized mass ejection events as alternative.

astro-ph.SR↗

arXiv2015

Sequential planet formation in the HD 100546 protoplanetary disk?

Context. The disk around the Herbig Ae star, HD 100546, shows structures that suggest the presence of two companions in the disk at $\sim10$ and $\sim70$ AU. The outer companion seems to be in the act of formation. Aims. Our aims are to provide constraints on the age of the planets in HD 100546 and to explore the potential evidence for sequential planet formation in transition disks such as HD 100546. Methods. We compare the recent resolved continuum observations of the disk around HD 100546 with the results of dust evolution simulations using an analytical prescription for the shapes of gaps carved by massive planets. Results. An inner pressure bump must have been present since early in the disk lifetime to have good agreement between the dust evolution models and the continuum observations of HD 100546. This pressure bump may have resulted from the presence of a very massive planet ($\sim20 M_{\rm{Jup}}$), which formed early in the inner disk ($r\sim$10 AU). If only this single planet exists, the disk is likely to be old, comparable to the stellar age ($\sim$5-10 Myr). Another possible explanation is an additional massive planet in the outer disk ($r\sim70$ AU): either a low-mass outer planet ($\lesssim5 M_{\rm{Jup}}$) injected at early times, or a higher mass outer planet ($\gtrsim15 M_{\rm{Jup}}$) formed very recently, traps the right amount of dust in pressure bumps to reproduce the observations. In the latter case, the disk could be much younger ($\sim3.0$ Myr). Conclusions. In the case in which two massive companions are embedded in the disk around HD 100546, as suggested in the literature, the outer companion could be at least $\gtrsim$2.5 Myr younger than the inner companion.

astro-ph.EP↗

arXiv2014

Water in Low-Mass Star-Forming Regions with Herschel: The Link Between Water Gas and Ice in Protostellar Envelopes

Aims: Our aim is to determine the critical parameters in water chemistry and the contribution of water to the oxygen budget by observing and modelling water gas and ice for a sample of eleven low-mass protostars, for which both forms of water have been observed. Methods: A simplified chemistry network, which is benchmarked against more sophisticated chemical networks, is developed that includes the necessary ingredients to determine the water vapour and ice abundance profiles in the cold, outer envelope in which the temperature increases towards the protostar. Comparing the results from this chemical network to observations of water emission lines and previously published water ice column densities, allows us to probe the influence of various agents (e.g., FUV field, initial abundances, timescales, and kinematics). Results: The observed water ice abundances with respect to hydrogen nuclei in our sample are 30-80ppm, and therefore contain only 10-30% of the volatile oxygen budget of 320ppm. The keys to reproduce this result are a low initial water ice abundance after the pre-collapse phase together with the fact that atomic oxygen cannot freeze-out and form water ice in regions with T(dust)>15 K. This requires short prestellar core lifetimes of less than about 0.1Myr. The water vapour profile is shaped through the interplay of FUV photodesorption, photodissociation, and freeze-out. The water vapour line profiles are an invaluable tracer for the FUV photon flux and envelope kinematics. Conclusions: The finding that only a fraction of the oxygen budget is locked in water ice can be explained either by a short pre-collapse time of less than 0.1 Myr at densities of n(H)~1e4 cm-3, or by some other process that resets the initial water ice abundance for the post-collapse phase. A key for the understanding of the water ice abundance is the binding energy of atomic oxygen on ice.

astro-ph.GA↗

arXiv2012

The UMIST database for astrochemistry 2012

We present the fifth release of the UMIST Database for Astrochemistry (UDfA). The new reaction network contains 6173 gas-phase reactions, involving 467 species, 47 of which are new to this release. We have updated rate coefficients across all reaction types. We have included 1171 new anion reactions and updated and reviewed all photorates. In addition to the usual reaction network, we also now include, for download, state-specific deuterated rate coefficients, deuterium exchange reactions and a list of surface binding energies for many neutral species. Where possible, we have referenced the original source of all new and existing data. We have tested the main reaction network using a dark cloud model and a carbon-rich circumstellar envelope model. We present and briefly discuss the results of these models.

astro-ph.SR↗

arXiv2011

Discovery of interstellar anions in Cepheus star-forming region

We report the detection of microwave emission lines from the hydrocarbon anion C6H- and its parent neutral C6H in the star-forming region L1251A (in Cepheus), and the pre-stellar core L1512 (in Auriga). The carbon-chain-bearing species C4H, HC3N, HC5N, HC7N and C3S are also detected in large abundances. The observations of L1251A constitute the first detections of anions and long-chain polyynes and cyanopolyynes (with more than 5 carbon atoms) in the Cepheus Flare star-forming region, and the first detection of anions in the vicinity of a protostar outside of the Taurus molecular cloud complex, highlighting a wider importance for anions in the chemistry of star formation. Rotational excitation temperatures have been derived from the HC3N hyperfine structure lines, and are found to be 6.2 K for L1251A and 8.7 K for L1512. The anion-to-neutral ratios are 3.6% and 4.1%, respectively, which are within the range of values previously observed in the interstellar medium, and suggest a relative uniformity in the processes governing anion abundances in different dense interstellar clouds. This research contributes towards the growing body of evidence that carbon chain anions are relatively abundant in interstellar clouds throughout the Galaxy, but especially in the regions of relatively high density and high depletion surrounding pre-stellar cores and young, embedded protostars.

astro-ph.GA↗

arXiv2007

Hydrocarbon anions in interstellar clouds and circumstellar envelopes

The recent detection of the hydrocarbon anion C6H- in the interstellar medium has led us to investigate the synthesis of hydrocarbon anions in a variety of interstellar and circumstellar environments. We find that the anion/neutral abundance ratio can be quite large, on the order of at least a few percent, once the neutral has more than five carbon atoms. Detailed modeling shows that the column densities of C6H- observed in IRC+10216 and TMC-1 can be reproduced. Our calculations also predict that other hydrocarbon anions, such as C4H- and C8H-, are viable candidates for detection in IRC+10216, TMC-1 and photon-dominated regions such as the Horsehead Nebula.

astro-ph↗