arXiv subjects

Mark R. Krumholz

Publications and source records attributed to Mark R. Krumholz.

At least 55 records · Page 3Linked to original sources

arXiv2025

The Molecular Cloud Lifecycle I: Constraining H2 formation and dissociation rates with observations

Molecular clouds (MCs) are the birthplaces of new stars in galaxies. A key component of MCs are photodissociation regions (PDRs), where far-ultraviolet radiation plays a crucial role in determining the gas's physical and chemical state. Traditional PDR models assume chemical steady state (CSS), where the rates of H$_2$ formation and photodissociation are balanced. However, real MCs are dynamic and can be out of CSS. In this study, we demonstrate that combining H$_2$ emission lines observed in the far-ultraviolet or infrared with column density observations can be used to derive the rates of H$_2$ formation and photodissociation. We derive analytical formulae that relate these rates to observable quantities, which we validate using synthetic H$_2$ line emission maps derived from the SILCC-Zoom hydrodynamical simulation. Our method estimates integrated H$_2$ formation and dissociation rates with an accuracy $\approx 30$ % (on top of uncertainties in observed H$_2$ emission maps and column densities). Our simulations, valid for column densities $N \leq 2 \times 10^{22}$ cm$^{-2}$, cover a wide dynamic range in H$_2$ formation and photodissociation rates, showing significant deviations from CSS, with 74 % of the MC's mass deviating from CSS by a factor greater than 2. Our analytical formulae can effectively distinguish between regions in and out of CSS. When applied to actual H$_2$ line observations, our method can assess the chemical state of MCs, providing insights into their evolutionary stages and lifetimes. A NASA Small Explorer mission concept, Eos, will be proposed in 2025 and is specifically designed to conduct the types of observations outlined in this study.

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arXiv2025

QUOKKA-based understanding of outflows (QED) -- III. Outflow loading and phase structure as a function of galactic environment

We present results from a suite of 3D high-resolution hydrodynamic simulations of supernova-driven outflows from galactic disc regions with a range of gas surface density, metallicity, and supernova scale height. We use this suite to quantify how outflow properties -- particularly the loading factors for mass, metallicity, and energy -- vary with these parameters. We find that the winds fall into three broad categories: steady and hot, multiphase and moderately bursty, and cool and highly bursty. The first of these is characterised by efficient metal and energy loading but weak mass loading, the second by moderate loading of mass, metals, and energy, and the third by negligible metal and energy loading but substantial mass loading. The most important factor in determining the kind of wind a galaxy will produce is the ratio of supernova to gas gas scale heights, with the latter set by a combination of supernova rate, metallicity-dependent cooling rate, and the gravitational potential. These often combine in counterintuitive ways -- for example increased cooling causes cold clouds to sink into the galactic midplane more rapidly, lowering the volume-filling factor of dense gas and making the environment more favourable for strong winds. Our findings suggest that the nature of galactic winds is likely highly sensitive to phenomena such as runaway stars occuring at a large height and dense gas and are poorly captured in most simulations, and that metal loading factors for type Ia supernovae may be substantially larger than those for type II, with important implications for galactic chemical evolution.

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arXiv2025

Understanding the Mechanisms Behind the Distribution of Galactic Metals

The evolution and distribution of metals within galaxies are critical for understanding galactic evolution and star formation processes, but the mechanisms responsible for shaping this distribution remain uncertain. In this study, we carry out high-resolution simulations of an isolated Milky Way-like galaxy, including a star-by-star treatment of both feedback and element injection. We include seven key isotopes of observational and physical interest, and which are distributed across different nucleosynthetic channels--primarily AGB stars (N, Ba, Ce), supernovae (O, Mg, S), and Wolf-Rayet stars (C) show measurably different correlation statistics in space and time and their fluctuations. This difference arises from the distinct ejection mechanisms associated with each nucleosynthetic process. The large-scale properties ensure that different elements, despite having different nucleosynthetic origins, are highly correlated with one another (>0.85 for all, >0.99 for same orgins), and their spatial correlations vary together in time. However small-scale variations naturally break elements into distinct nucleosynthetic familiars, with elements originating from the same channels correlating better with each other than with elements from different origins. Our findings suggest both challenges and opportunities for ongoing efforts to use chemical measurements of gas and stars to unravel the history and physics of galaxy assembly.

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arXiv2024

Comparing metallicity correlations in nearby non-AGN and AGN-host galaxies

The gas-phase metallicity distribution within galaxies records critical information about galactic evolution. In this work we investigate how active galactic nuclei (AGN) influence this distribution by measuring the two-point correlation functions of gas-phase metallicity in 95 non-AGN and 37 AGN-host galaxies from the Calar Alto Legacy Integral Field spectroscopy Area integral field spectrographic survey. We measure metallicity using a novel Bayesian method that properly includes both stellar and AGN contributions to emission line fluxes and allows us to measure metallicities in both AGN-host and non-AGN galaxies in a single, consistent framework. We find that the two-point correlation functions of both AGN-host and non-AGN galaxies are well-fit by a simple injection-diffusion model, and that the correlation lengths $l_\mathrm{corr}$ we derive for the non-AGN galaxies are reasonably consistent with those obtained in earlier work. The AGN-host galaxies generally have smaller $l_\mathrm{corr}$ than non-AGN galaxies at fixed stellar mass, but similar $l_\mathrm{corr}$ at fixed star formation rate (SFR), suggesting that the primary effect of hosting an AGN in this sample is a reduction in SFR at fixed stellar mass, and that this in turn suppresses the correlation length. Our findings further indicate that, while both SFR and stellar mass are positively correlated with metallicity correlation length $l_\mathrm{corr}$, the former is more fundamental, implying that fluctuations in the metallicity distribution within galaxies are driven more by short-term responses to physical processes such as star formation that can change much faster than a Hubble time.

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arXiv2024

A novel numerical method for mixed-frame multigroup radiation-hydrodynamics with GPU acceleration implemented in the QUOKKA code

Mixed-frame formulations of radiation-hydrodynamics (RHD), where the radiation quantities are computed in an inertial frame but matter quantities are in a comoving frame, are advantageous because they admit algorithms that conserve energy and momentum to machine precision and combine more naturally with adaptive mesh techniques, since unlike pure comoving-frame methods they do not face the problem that radiation quantities must change frame every time a cell is refined or coarsened. However, implementing multigroup RHD in a mixed-frame formulation presents challenges due to the complexity of handling frequency-dependent interactions and the Doppler shift of radiation boundaries. In this paper, we introduce a novel method for multigroup RHD that integrates a mixed-frame formulation with a piecewise powerlaw approximation for frequency dependence within groups. This approach ensures the exact conservation of total energy and momentum while effectively managing the Lorentz transformation of group boundaries and evaluation of group-averaged opacities. Our method takes advantage of the locality of matter-radiation coupling, allowing the source term for $N_g$ frequency groups to be handled with simple equations with a sparse Jacobian matrix of size $N_g + 1$, which can be inverted with $O(N_g)$ complexity. This results in a computational complexity that scales linearly with $N_g$ and requires no more communication than a pure hydrodynamics update, making it highly efficient for massively parallel and GPU-based systems. We implement our method in the GPU-accelerated RHD code QUOKKA and demonstrate that it passes a wide range of numerical tests, including preserving the asymptotic diffusion limit. We demonstrate that the piecewise powerlaw method shows significant advantages over traditional opacity averaging methods for handling rapidly variable opacities with modest frequency resolution.

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arXiv2024

An automated method to detect and characterise semi-resolved star clusters

We present a novel method for automatically detecting and characterising semi-resolved star clusters: clusters where the observational point-spread function (PSF) is smaller than the cluster's radius, but larger than the separations between individual stars. We apply our method to a 1.77 deg$^2$ field located in the Large Magellanic Cloud (LMC) using the VISTA survey of the Magellanic Clouds (VMC), which surveyed the LMC in the $YJK_\text{s}$ bands. Our approach first models the position-dependent PSF to detect and remove point sources from deep $K_\text{s}$ images; this leaves behind extended objects such as star clusters and background galaxies. We then analyse the isophotes of these extended objects to characterise their properties, perform integrated photometry, and finally remove any spurious objects this procedure identifies. We demonstrate our approach in practice on a deep VMC $K_\text{s}$ tile that contains the most active star-forming regions in the LMC: 30 Doradus, N158, N159, and N160. We select this tile because it is the most challenging for automated techniques due both to crowding and nebular emission. We detect 682 candidate star clusters, with an estimated contamination rate of 13% from background galaxies and chance blends of physically unrelated stars. We compare our candidates to publicly available James Webb Space Telescope data and find that at least 80% of our detections appear to be star clusters.

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arXiv2024

On the limitations of H alpha luminosity as a star formation tracer in spatially resolved observations

This study examines the limitations of H$α$ luminosity as a tracer of star formation rates (SFR) in spatially resolved observations. We carry out high-resolution simulations of a Milky Way-like galaxy including both supernova and photoionization feedback, and from these we generate synthetic H$α$ emission maps that we compare to maps of the true distribution of young stellar objects (YSOs) on scales from whole-galaxy to individual molecular clouds ($\lesssim 100$ pc). Our results reveal significant spatial mismatches between H$α$ and true YSO maps on sub-100 pc scales, primarily due to ionizing photon leakage, with a secondary contribution from young stars drifting away from their parent molecular clouds. On small scales these effect contribute significantly to the observed anti-correlation between gas and star formation, such that there is noticeably less anti-correlation if we replace an H$α$-based star formation map with a YSO-based one; this in turn implies that previous studies have underestimated the time it takes for young stars to disperse their parent molecular clouds. However, these effects are limited in dense regions with hydrogen columns $N_\mathrm{H} > 3 \times 10^{21}$ cm$^{-2}$, where the H$α$- and YSO-based SFR maps show better agreement. Based on this finding we propose a calibration model that can precisely measure the SFR of large molecular clouds (mean radius > 100 pc) with a combination of H$α$ and CO observations, which provides a foundation for future study of star formation processes in extragalactic molecular clouds.

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arXiv2024

The sub-critical illusion: synthetic Zeeman effect observations from galactic zoom-in simulations

Mass-to-flux ratios measured via the Zeeman effect suggest the existence of a transition from a magnetically sub-critical state in HI clouds to a super-critical state in molecular clouds. However, due to projection, chemical, and excitation effects, Zeeman measurements are subject to a number of biases, and may not reflect the true relations between gravitational and magnetic energies. In this paper, we carry out simulations of the formation of magnetised molecular clouds, zooming in from an entire galaxy to sub-pc scales, which we post-process to produce synthetic HI and OH Zeeman measurements. The mass-to-flux ratios we recover from the simulated observations show a transition in magnetic criticality that closely matches observations, but we find that the gravitational-magnetic energy ratios on corresponding scales are mostly super-critical, even in the HI regime. We conclude that HI clouds in the process of assembling to form molecular clouds are already super-critical even before H_2 forms, and that the apparent transition from sub- to super-criticality between HI and H_2 is primarily an illusion created by chemical and excitation biases affecting the Zeeman measurements.

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arXiv2024

Suppressed Cosmic Ray Energy Densities in Molecular Clouds From Streaming Instability-Regulated Transport

Cosmic rays (CRs) are the primary driver of ionization in star forming molecular clouds (MCs). Despite their potential impacts on gas dynamics and chemistry, no simulations of star cluster formation following the creation of individual stars have included explicit cosmic ray transport (CRT) to date. We conduct the first numerical simulations following the collapse of a $2000 M_{\odot}$ MC and the subsequent star formation including CRT using the STARFORGE framework implemented in the GIZMO code. We show that when CR-transport is streaming-dominated, the CR energy in the cloud is strongly attenuated due to energy losses from the streaming instability. Consequently, in a Milky Way like environment the median CR ionization rate (CRIR) in the cloud is low ($ ζ\lesssim 2 \times 10^{-19} \rm s^{-1}$) during the main star forming epoch of the calculation and the impact of CRs on the star formation in the cloud is limited. However, in high-CR environments, the CR distribution in the cloud is elevated ($ζ\lesssim 6 \times 10^{-18}$), and the relatively higher CR pressure outside the cloud causes slightly earlier cloud collapse and increases the star formation efficiency (SFE) by $50 \%$ to $\sim 13 \%$. The initial mass function (IMF) is similar in all cases except with possible variations in a high-CR environment. Further studies are needed to explain the range of ionization rates observed in MCs and explore star formation in extreme CR environments.

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arXiv2024

Cluster Population Demographics in NGC 628 Derived from Stochastic Population Synthesis Models

The physical properties of star cluster populations offer valuable insights into their birth, evolution, and disruption. However, individual stars in clusters beyond the nearest neighbours of the Milky Way are unresolved, forcing analyses of star cluster demographics to rely on integrated light, a process fraught with uncertainty. Here we infer the demographics of the cluster population in the benchmark galaxy NGC 628 using data from the Legacy Extra-galactic UV Survey (LEGUS) coupled to a novel Bayesian forward-modelling technique. Our method analyzes all 1178 clusters in the LEGUS catalogue, $\sim4$ times more than prior studies severely affected by completeness cuts. Our results indicate that the cluster mass function is either significantly steeper than the commonly-observed slope of $-2$ or is truncated at $\approx 10^{4.5}$ M$_\odot$; the latter possibility is consistent with proposed relations between truncation mass and star formation surface density. We find that cluster disruption is relatively mild for the first $\approx 200$ Myr of cluster evolution; no evidence for mass-dependent disruption is found. We find suggestive but not incontrovertible evidence that inner galaxy clusters may be more prone to disruption and outer galaxy clusters have a more truncated mass function, but confirming or refuting these findings will require larger samples from future observations of outer galaxy clusters. Finally, we find that current stellar track and atmosphere models, along with common forms for cluster mass and age distributions, cannot fully capture all features in the multidimensional photometric distribution of star clusters. While our forward-modelling approach outperforms earlier backward-modeling approaches, some systematic differences persist between observed and modelled photometric distributions.

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arXiv2024

TeV $γ$-ray emission near globular cluster Terzan 5 as a probe of cosmic ray transport

Cosmic rays travelling through interstellar space have their propagation directions repeatedly scattered by fluctuating interstellar magnetic fields. The nature of this scattering is a major unsolved problem in astrophysics, one that has resisted solution largely due to a lack of direct observational constraints on the scattering rate. Here we show that very high-energy $γ$-ray emission from the globular cluster Terzan 5, which has unexpectedly been found to be displaced from the cluster, presents a direct probe of this process. We show that this displacement is naturally explained by cosmic rays accelerated in the bow shock around the cluster propagating a finite distance before scattering processes re-orient enough of them towards Earth to produce a detectable $γ$-ray signal. The angular distance between the cluster and the signal places tight constraints on the scattering rate, which we show are consistent with a model whereby scattering is primarily due to excitation of magnetic waves by the cosmic rays themselves. The analysis method we develop here will make it possible to use sources with similarly displaced non-thermal X-ray and TeV $γ$-ray signals as direct probes of cosmic ray scattering across a range of Galactic environments.

astro-ph.HE↗

arXiv2024

CONGRuENTS (COsmic-ray, Neutrino, Gamma-ray and Radio Non-Thermal Spectra). II. Population-level correlations between galactic infrared, radio, and γ-ray emission

Galaxies obey a number of empirical correlations between their radio, γ-ray, and infrared emission, but the physical origins of these correlations remain uncertain. Here we use the CONGRuENTS model for broadband non-thermal emission from star-forming galaxies, which self-consistently calculates energy-dependent transport and non-thermal emission from cosmic ray hadrons and leptons, to predict radio and γ-ray emission for a synthetic galaxy population with properties drawn from a large deep-field survey. We show that our synthetic galaxies reproduce observed relations such as the FIR-radio correlation, the FIR-γ correlation, and the distribution of radio spectral indices, and we use the model to explain the physical origins of these relations. Our results show that the FIR-radio correlation arises because the amount of cosmic ray electron power ultimately radiated as synchrotron emission varies only weakly with galaxy star formation rate as a result of the constraints imposed on gas properties by hydrostatic balance and turbulent dynamo action; the same physics dictates the extent of proton calorimetry in different galaxies, and thus sets the FIR-γ-ray correlation. We further show that galactic radio spectral indices result primarily from competition between thermal free-free emission and energy-dependent loss of cosmic ray electrons to bremsstrahlung and escape into galactic halos, with shaping of the spectrum by inverse Compton, synchrotron, and ionisation processes typically playing a sub-dominant role. In addition to explaining existing observations, we use our analysis to predict a heretofore unseen correlation between the curvature of galaxies' radio spectra and their pion-driven γ-ray emission, a prediction that will be testable with upcoming facilities.

astro-ph.HE↗

arXiv2024

Formation of Giant Clumps in High-$z$ Disc Galaxies by Compressive Turbulence

We address the formation of giant clumps in violently unstable gas-rich disc galaxies at cosmic noon. While these are commonly thought to originate from gravitational Toomre instability, cosmological simulations have indicated that clumps form even in regions where the Toomre $Q$ parameter is well above unity, which should be stable according to linear Toomre theory (Inoue et al., 2016). Examining one of these cosmological simulations, we find that it exhibits an excess in compressive modes of turbulence with converging motions. The energy in converging motions within proto-clump regions is $\sim 70\%$ of the total turbulent energy, compared to $\sim 17\%$ expected in equipartition. When averaged over the whole disc, $\sim 32\%$ of the turbulent energy is in converging motions, with a further $\sim 8\%$ in diverging motions. Thus, a total of $\sim 40\%$ of the turbulent energy is in compressive modes, with the rest in solenoidal modes, compared to the $(1/3)-(2/3)$ division expected in equipartition. By contrast, we find that in an isolated-disc simulation with similar properties, resembling high-$z$ star-forming galaxies, the energy in the different turbulence modes are in equipartition, both in proto-clump regions and over the whole disc. We conclude that the origin of the excessive converging motions in proto-clump regions is external to the disc, and propose several mechanisms that can induce them. This is an additional mechanism for clump formation, complementary to and possibly preceding gravitational instability.

astro-ph.GA↗

arXiv2024

Feedback in Emerging Extragalactic Star Clusters (JWST--FEAST): Calibration of Star Formation Rates in the Mid-Infrared with NGC 628

New JWST near-infrared imaging of the nearby galaxy NGC 628 from the Cycle 1 program JWST-FEAST is combined with archival JWST mid-infrared imaging to calibrate the 21 $μ$m emission as a star formation rate indicator (SFR) at $\sim$120 pc scales. The Pa$α$ ($λ$1.8756 $μ$m) hydrogen recombination emission line targeted by FEAST provides a reference SFR indicator that is relatively insensitive to dust attenuation, as demonstrated by combining this tracer with the HST H$α$ imaging. Our analysis is restricted to regions that appear compact in nebular line emission and are sufficiently bright to mitigate effects of both age and stochastic sampling of the stellar initial mass function. We find that the 21 $μ$m emission closely correlates with the nebular line emission, with a power-law with exponent=1.07$\pm$0.01, in agreement with past results. We calibrate a hybrid SFR indicator using a combination of H$α$ and 24 $μ$m (extrapolated from 21 $μ$m) tracers and derive the proportionality constant between the two tracers $b=0.095\pm0.007$, which is $\sim$ 3-5 times larger than previous derivations using large regions/entire galaxies. We model these discrepancies as an increasing contribution to the dust heating by progressively older stellar populations for increasing spatial scales, in agreement with earlier findings that star formation is hierarchically distributed in galaxies. Thus, use of hybrid SFR indicators requires prior knowledge of the mean age of the stellar populations dominating the dust heating, which makes their application uncertain. Conversely, non-linear calibrations of SFRs from L(24) alone are more robust, with a factor $\lesssim$2.5 variation across the entire range of L(24) luminosities from HII regions to galaxies.

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arXiv2024

Feedback in emerging extragalactic star clusters, FEAST: The relation between 3.3 $μ$m PAH emission and Star Formation Rate traced by ionized gas in NGC 628

We present maps of ionized gas (traced by Pa$α$ and Br$α$) and 3.3 $μ$m Polycyclic Aromatic Hydrocarbon (PAH) emission in the nearby spiral galaxy NGC 628, derived from new JWST/NIRCam data from the FEAST survey. With this data, we investigate and calibrate the relation between 3.3 $μ$m PAH emission and star formation rate (SFR) in and around emerging young star clusters (eYSCs) on a scale of ${\sim}40$ pc. We find a tight (correlation coefficient $ρ$${\sim}$0.9) sub-linear (power-law exponent $α$${\sim}$0.75) relation between the 3.3 $μ$m PAH luminosity surface density and SFR traced by Br$α$ for compact, cospatial (within 0.16$''$ or ${\sim}$7 pc) peaks in Pa$α$, Br$α$, and 3.3 $μ$m (eYSC-I). The scatter in the relationship does not correlate well with variations in local interstellar medium (ISM) metallicity due to a radial metallicity gradient, but rather is likely due to stochastic sampling of the stellar initial mass function (IMF) and variations in the PAH heating and age of our sources. The deviation from a linear relation may be explained by PAH destruction in more intense ionizing environments, variations in age, and IMF stochasticity at intermediate to low luminosities. We test our results with various continuum subtraction techniques using combinations of NIRCam bands and find that they remain robust with only minor differences in the derived slope and intercept. An unexpected discrepancy is identified between the relations of hydrogen recombination lines (Pa$α$ versus Br$α$; H$α$ versus Br$α$).

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arXiv2024

The Interplay between the IMF and Star Formation Efficiency through Radiative Feedback at High Stellar Surface Densities

The observed rest-UV luminosity function at cosmic dawn ($z \sim 8-14$) measured by JWST revealed an excess of UV-luminous galaxies relative to many pre-launch theoretical predictions. A high star-formation efficiency (SFE) and a top-heavy initial mass function (IMF) are among the mechanisms proposed for explaining this excess. Although a top-heavy IMF has been proposed for its ability to increase the light-to-mass ratio ($Ψ_{\mathrm{UV}}$), the resulting enhanced radiative pressure from young stars could decrease the star formation efficiency (SFE), potentially driving galaxy luminosities back down. In this Letter, we use idealized radiation hydrodynamic simulations of star cluster formation to explore the effects of a top-heavy IMF on the SFE of clouds typical of the high pressure conditions found at these redshifts. We find that the SFE in star clusters with solar neighbourhood-like dust abundance decreases with increasingly top-heavy IMF's -- by $\sim 20 \%$ for an increase of factor 4 in $Ψ_{\mathrm{UV}}$, and by $50 \%$ for a factor $ \sim 10$ in $Ψ_{\mathrm{UV}}$. However, we find that an expected decrease in the dust-to-gas ratio ($\sim 0.01 \times \mathrm{Solar}$) at these redshifts can completely compensate for the enhanced light output. This leads to a (cloud-scale; $\sim 10 \, \mathrm{pc}$) SFE that is $\gtrsim 70\%$ even for a factor 10 increase in $Ψ_{\mathrm{UV}}$, implying that highly efficient star formation is unavoidable for high surface density and low metallicity conditions. Our results suggest that a top-heavy IMF, if present, likely coexists with efficient star formation in these galaxies.

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arXiv2024

When are galactic winds molecular?

The molecular phase of supernova-driven outflows originates from the cold, molecular gas in the disc of a star-forming galaxy, and may carry a substantial fraction of the wind mass flux in some galaxies, but it remains poorly understood. Observations of this phase come mostly from very nearby galaxies due its low surface brightness and covering fraction, and simulations often lack the spatial resolution necessary to resolve it. Here we analytically estimate the survivability of this phase in order to understand under what conditions an galactic wind can contain a significant molecular phase. We show that the molecular content of outflows is primarily determined by two dimensionless numbers: a generalised Eddington ratio describing the strength of the outflow and an ionisation parameter-like quantity describing the strength of the radiation field per baryon. We apply this model to a sample of galaxies and show that, while any molecules entrained in the winds of normal star-forming galaxies should be destroyed close to the galactic disc, the outflows of strong starburst should become increasingly dominated by molecules.

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arXiv2024

An Asymptotically-Correct Implicit-Explicit Time Integration Scheme for Finite Volume Radiation-Hydrodynamics

Numerical radiation-hydrodynamics (RHD) for non-relativistic flows is a challenging problem because it encompasses processes acting over a very broad range of timescales, and where the relative importance of these processes often varies by orders of magnitude across the computational domain. Here we present a new implicit-explicit (IMEX) method for numerical RHD that has a number of desirable properties that have not previously been combined in a single method. Our scheme is based on moments and allows machine-precision conservation of energy and momentum, making it highly suitable for adaptive mesh refinement applications; it requires no more communication than hydrodynamics and includes no non-local iterative steps, making it highly suitable for massively parallel and GPU-based systems where communication is a bottleneck; and we show that it is asymptotically-accurate in the streaming, static diffusion, and dynamic diffusion limits, including in the so-called asymptotic diffusion regime where the computational grid does not resolve the photon mean free path. We implement our method in the GPU-accelerated RHD code QUOKKA and show that it passes a wide range of numerical tests.

astro-ph.IM↗