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Aims. We introduce a new deep-learning approach for the reconstruction of 3D dust density and temperature distributions from multi-wavelength dust emission observations on the scale of individual star-forming cloud cores (<0.2 pc). Methods. We constructed a training data set by processing cloud cores from the Cloud Factory simulations with the POLARIS radiative transfer code to produce synthetic dust emission observations at 23 wavelengths between 12 and 1300 µm. We simplified the task by reconstructing the cloud structure along individual lines of sight (LoSs) and trained a conditional invertible neural network (cINN) for this purpose. The cINN belongs to the group of normalising flow methods and it is able to predict full posterior distributions for the target dust properties. We tested different cINN setups, ranging from a scenario that includes all 23 wavelengths down to a more realistically limited case with observations at only seven wavelengths. We evaluated the predictive performance of these models on synthetic test data. Results. We report an excellent reconstruction performance for the 23-wavelength cINN model, achieving median absolute relative errors of about 1.8% in log(n/m−3) and 1% in log(Tdust/K), respectively. We identify trends towards an overestimation at the low end of the density range and towards an underestimation at the high end of both the density and temperature values, which may be related to a bias in the training data. After limiting our coverage to a combination of only seven wavelengths, we still find a satisfactory performance with average absolute relative errors of about 2.8% and 1.7% in log(n/m−3) and log(Tdust/K). Conclusions. This proof-of-concept study shows that the cINN-based approach for 3D reconstruction of dust density and temperature is very promising and it is even compatible with a more realistically constrained wavelength coverage. [ABSTRACT FROM AUTHOR]

We present a numerical study of the evolution of power-law tails (PLTs) in the (column-)density distributions (N -PDF, ρ-PDF) in contracting star-forming clumps in primordial gas, without and with some initial rotational and/or turbulent support. In all considered runs multiple PLTs emerge shortly after the formation of the first protostar. The first PLT (PLT 1) in the ρ-PDF is a stable feature with slope q 1 ≃ −1.3 which corresponds – under the condition of preserved spherical symmetry – to the outer envelope of the protostellar object with density profile ρ ∝  l −2 in the classical Larson–Penston collapse model, where l is the radius. The second PLT (PLT 2) in the ρ-PDF is stable in the pure-infall runs but fluctuates significantly in the runs with initial support against gravity as dozens of protostars form and their mutual tidal forces change the density structure. Its mean slope, 〈 q 2〉 ≃ −2, corresponds to a density profile of ρ ∝  l −3/2 which describes a core in free fall in the classical Larson–Penston collapse model or an attractor solution at scales with dominating protostellar gravity. PLT 1 and PLT 2 in the N -PDFs are generally consistent with the observational data of Galactic low-mass star-forming regions from Herschel data. In the runs with initial support against gravity a third PLT (PLT 3) in the ρ-PDFs appears simultaneously with or after the emergence of PLT 2. It is very shallow, with mean slope of 〈 q 3〉 ≃ −1, and is associated with the formation of thin protostellar accretion discs. [ABSTRACT FROM AUTHOR]

Cosmic rays (CRs) are dynamically important in the evolution of galaxies by regulating star formation and powering galactic outflows. However, to what extent CRs regulate galaxy formation depends on the coupling strength of CRs with the ambient plasma and the effective CR transport speed. Moreover, both properties sensitively depend on the CR momentum, which is largely unexplored in three-dimensional hydrodynamical simulations. We perform magnetohydrodynamical simulations of entire galaxies with masses ranging from 1010 to |$10^{12}\, \mathrm{M}_\odot$| and compare dynamically coupled CRs in the grey approximation with a spectrally resolved model that includes CR momenta from |$0.1\, \mathrm{GeV} c^{-1}$| to |$100\, \mathrm{TeV} c^{-1}$|⁠. We find that hadronic cooling of CRs dominates over Alfvén cooling, with the latter emulating CR losses as a result of streaming of CRs down their pressure gradient. While star formation rates and galaxy morphologies are only mildly affected by the spectral CR modelling, mass loading factors of galactic outflows can differ by up to a factor of 4 in dwarf galaxies. All simulated low-mass haloes (M  = 1010, 1011, and |$3\times 10^{11}\, \mathrm{M}_\odot$|⁠) drive strong outflows, where CR transport is temporally dominated by advection. In contrast, the Milky Way-mass galaxy with |$M=10^{12}\, \mathrm{M}_\odot$| does not drive sustained outflows, so that CR transport is entirely dominated by diffusion. The effective energy weighted diffusion coefficients vary by two orders of magnitude from the canonical energy-weighted values of |$\langle {D}\rangle _{e_\mathrm{cr}}\sim 10^{28}\, \mathrm{cm^2\, s^{-1}}$| in the disc up to |$3\times 10^{29}\, \mathrm{cm^2\, s^{-1}}$| in the circumgalactic medium, where we observe substantial temperature and CR pressure differences between our grey and spectral CR models. [ABSTRACT FROM AUTHOR]

Cosmic rays (CRs) are ubiquitous in the interstellar medium (ISM) of nearby galaxies, but many of their properties are not well-constrained. Gamma-ray observations provide a powerful tool in this respect, allowing us to constrain both the interaction of CR protons with the ISM and their transport properties. To help better understand the link between observational signatures and CR physics, we use a series of magneto-hydrodynamical arepo simulations of isolated galaxies performed using spectrally resolved CR transport in every computational cell, with subsequent gamma-ray emission calculated using the Crayon + (Cosmic RAY emissiON) code. In each of our simulated haloes, modelling the energy-dependent spatial diffusion of CRs leads to a more extended distribution of high-energy (~100 GeV) gamma rays compared to that predicted by a 'grey' steady-state model, which is especially visible in the corresponding emission maps and radial profiles. Despite this, the total gamma-ray spectra can often be well approximated by the steady-state model, although recovering the same spectral index typically requires a minor variation of the energy dependence of the diffusion coefficient. Our simulations reproduce the observed shapes of the gamma-ray spectra of nearby star-forming galaxies and also match recent observations of the far infrared–gamma-ray relation. We find, however, that the spectrally resolved model yields marginally smaller luminosities for lower star formation rates compared to grey simulations of CRs. Our work highlights the importance of modelling spectrally resolved CR transport for an accurate prediction of spatially resolved high-energy gamma-ray emission, as will be probed by the upcoming Cherenkov Telescope Array observatory. [ABSTRACT FROM AUTHOR]

We present magnetohydrodynamic (MHD) simulations of the star-forming multiphase interstellar medium (ISM) in stratified galactic patches with gas surface densities Σgas = 10, 30, 50, and 100 |$\mathrm{M_\odot \, pc^{-2}}$|⁠. The silcc project simulation framework accounts for non-equilibrium thermal and chemical processes in the warm and cold ISM. The sink-based star formation and feedback model includes stellar winds, hydrogen-ionizing UV radiation, core-collapse supernovae, and cosmic ray (CR) injection and diffusion. The simulations follow the observed relation between Σgas and the star formation rate surface density ΣSFR. CRs qualitatively change the outflow phase structure. Without CRs, the outflows transition from a two-phase (warm and hot at 1 kpc) to a single-phase (hot at 2 kpc) structure. With CRs, the outflow always has three phases (cold, warm, and hot), dominated in mass by the warm phase. The impact of CRs on mass loading decreases for higher Σgas and the mass loading factors of the CR-supported outflows are of order unity independent of ΣSFR. Similar to observations, vertical velocity dispersions of the warm ionized medium (WIM) and the cold neutral medium (CNM) correlate with the star formation rate as |$\sigma _\mathrm{z} \propto \Sigma _\mathrm{SFR}^a$|⁠ , with a ∼ 0.20. In the absence of stellar feedback, we find no correlation. The velocity dispersion of the WIM is a factor ∼2.2 higher than that of the CNM, in agreement with local observations. For |$\Sigma _\mathrm{SFR} \gtrsim 1.5 \times 10^{-2}\, \mathrm{M}_\odot \, \mathrm{yr}^{-1}\, \mathrm{kpc}^{-2}$| the WIM motions become supersonic. [ABSTRACT FROM AUTHOR]

Momentum-dependent cosmic ray diffusion drives powerful galactic winds The largest difference between the non-cooling and the correct model is the fraction of low energy CRs to the total CR energy. In the paper we present simulations with a new spectral cosmic ray (CR) solver, that includes energy dependent spatial diffusion and spectral cooling as introduced in Girichidis et al. ([1]). [Extracted from the article]

In star-forming galaxies, the far-infrared (FIR) and radio-continuum luminosities obey a tight empirical relation over a large range of star-formation rates (SFR). To understand the physics, we examine magnetohydrodynamic galaxy simulations, which follow the genesis of cosmic ray (CR) protons at supernovae and their advective and anisotropic diffusive transport. We show that gravitational collapse of the proto-galaxy generates a corrugated accretion shock, which injects turbulence and drives a small-scale magnetic dynamo. As the shock propagates outwards and the associated turbulence decays, the large velocity shear between the supersonically rotating cool disc with respect to the (partially) pressure-supported hot circumgalactic medium excites Kelvin–Helmholtz surface and body modes. Those interact non-linearly, inject additional turbulence and continuously drive multiple small-scale dynamos, which exponentially amplify weak seed magnetic fields. After saturation at small scales, they grow in scale to reach equipartition with thermal and CR energies in Milky Way-mass galaxies. In small galaxies, the magnetic energy saturates at the turbulent energy while it fails to reach equipartition with thermal and CR energies. We solve for steady-state spectra of CR protons, secondary electrons/positrons from hadronic CR-proton interactions with the interstellar medium, and primary shock-accelerated electrons at supernovae. The radio-synchrotron emission is dominated by primary electrons, irradiates the magnetized disc and bulge of our simulated Milky Way-mass galaxy and weakly traces bubble-shaped magnetically loaded outflows. Our star-forming and star-bursting galaxies with saturated magnetic fields match the global FIR-radio correlation (FRC) across four orders of magnitude. Its intrinsic scatter arises due to (i) different magnetic saturation levels that result from different seed magnetic fields, (ii) different radio synchrotron luminosities for different specific SFRs at fixed SFR, and (iii) a varying radio intensity with galactic inclination. In agreement with observations, several 100-pc-sized regions within star-forming galaxies also obey the FRC, while the centres of starbursts substantially exceed the FRC. [ABSTRACT FROM AUTHOR]

The interstellar medium (ISM) is a turbulent, highly structured multiphase medium. State-of-the-art cosmological simulations of the formation of galactic discs usually lack the resolution to accurately resolve those multiphase structures. However, small-scale density structures play an important role in the life cycle of the ISM, and determine the fraction of cold, dense gas, the amount of star formation, and the amount of radiation and momentum leakage from cloud-embedded sources. Here, we derive a statistical model to calculate the unresolved small-scale ISM density structure from coarse-grained, volume-averaged quantities such as the gas clumping factor , |$\mathcal {C}$|⁠ , and mean density 〈ρ〉 V . Assuming that the large-scale ISM density is statistically isotropic, we derive a relation between the three-dimensional clumping factor, |$\mathcal {C}_\rho$|⁠ , and the clumping factor of the 4 |$\pi$| column density distribution on the cloud surface, |$\mathcal {C}_\Sigma$|⁠ , and find |$\mathcal {C}_\Sigma =\mathcal {C}_\rho ^{2/3}$|⁠. Applying our model to calculate the covering fraction, i.e. the 4 |$\pi$| sky distribution of optically thick sightlines around sources inside interstellar gas clouds, we demonstrate that small-scale density structures lead to significant differences at fixed physical ISM density. Our model predicts that gas clumping increases the covering fraction by up to 30 per cent at low ISM densities compared to a uniform medium. On the other hand, at larger ISM densities, gas clumping suppresses the covering fraction and leads to increased scatter such that covering fractions can span a range from 20 per cent to 100 per cent at fixed ISM density. All data and example code are publicly available at GitHub. [ABSTRACT FROM AUTHOR]

We analyse observational signatures of magnetic fields for simulations of a Milky Way-like disc with supernova-driven interstellar turbulence and self-consistent chemical processes. In particular, we post-process two simulations data sets of the SILCC Project for two initial amplitudes of the magnetic field, B 0 = 3 and 6 μG, to study the evolution of Faraday rotation measures (RM) and synchrotron luminosity. For calculating the RM, three different models of the electron density n e are considered. A constant electron density, and two estimations based on the density of ionized species and the fraction of the total gas, respectively. Our results show that the RM profiles are extremely sensitive to the n e models, which assesses the importance of accurate electron distribution observations/estimations for the magnetic fields to be probed using Faraday RMs. As a second observable of the magnetic field, we estimate the synchrotron luminosity in the simulations using a semi-analytical cosmic ray model. We find that the synchrotron luminosity decreases over time, which is connected to the decay of magnetic energy in the simulations. The ratios between the magnetic, the cosmic ray, and the thermal energy density indicate that the assumption of equipartition does not hold for most regions of the ISM. In particular, for the ratio of the cosmic ray to the magnetic field energy the assumption of equipartition could lead to a wrong interpretation of the observed synchrotron emission. [ABSTRACT FROM AUTHOR]

An extinction-free estimator of the star formation rate (SFR) of galaxies is critical for understanding the high-redshift universe. To this end, the nearly linear, tight correlation of far-infrared (FIR), and radio luminosity of star-forming galaxies is widely used. While the FIR is linked to massive star formation, which also generates shock-accelerated cosmic-ray (CR) electrons and radio synchrotron emission, a detailed understanding of the underlying physics is still lacking. Hence, we perform three-dimensional magnetohydrodynamical (MHD) simulations of isolated galaxies over a broad range of halo masses and SFRs using the moving-mesh code arepo , and evolve the CR proton energy density self-consistently. In post-processing, we calculate the steady-state spectra of primary, shock-accelerated and secondary CR electrons, which result from hadronic CR proton interactions with the interstellar medium. The resulting total radio luminosities correlate with the FIR luminosities as observed and are dominated by primary CR electrons if we account for anisotropic CR diffusion. The increasing contribution of secondary emission up to 30 per cent in starbursts is compensated by the larger bremsstrahlung and Coulomb losses. CR electrons are in the calorimetric limit and lose most of their energy through inverse Compton interactions with star light and cosmic microwave background (CMB) photons while less energy is converted into synchrotron emission. This implies steep steady-state synchrotron spectra in starbursts. Interestingly, we find that thermal free–free emission flattens the total radio spectra at high radio frequencies and reconciles calorimetric theory with observations while free–free absorption explains the observed low-frequency flattening towards the central regions of starbursts. [ABSTRACT FROM AUTHOR]

Magnetic fields are an important component of the interstellar medium (ISM) and exhibit strongly varying field strengths and a non-trivial correlation with the gas density. Its dynamical impact varies between individual regions of the ISM and correlates with the orientation of the field with respect to the gas structures. Using high-resolution magneto-hydrodynamical simulations of the ISM, we explore the connection between the orientation of the field and the dynamical state of the gas. We find that the onset of gravitational instability in molecular gas above a density of |$\rho \sim 10^{-21}\, \mathrm{g\, cm}^{-3}$| |$(n\sim 400\, \mathrm{cm}^{-3})$| coincides with an alignment of the magnetic field lines and the gas flow. At this transition, the gradient of the density changes from mainly perpendicular to preferentially parallel to the field lines. A connection between the three-dimensional alignment and projected two-dimensional observables is non-trivial, because of a large dispersion of the magnetic field orientation along the line of sight. The turbulent correlation lengths can be small compared to the typical integration lengths. As a consequence, the small-scale signal of the orientation can sensitively depend on the line of sight or the dynamical state of the cloud can fluctuate stochastically or be completely averaged out. With higher spatial resolution more small-scale structures are resolved, which aggravates the link between magneto-hydrodynamical quantities and projected observables. [ABSTRACT FROM AUTHOR]

The γ-ray emission of star-forming (SF) galaxies is attributed to hadronic interactions of cosmic ray (CR) protons with the interstellar gas and contributions from CR electrons via bremsstrahlung and inverse Compton (IC) scattering. The relative importance of these processes in different galaxy types is still unclear. We model these processes in three-dimensional magnetohydrodynamical (MHD) simulations of the formation of isolated galactic discs using the moving-mesh code arepo , including dynamically coupled CR protons and adopting different CR transport models. We calculate steady-state CR spectra and also account for the emergence of secondary electrons and positrons. This allows us to produce detailed γ-ray maps, luminosities, and spectra of our simulated galaxies at different evolutionary stages. Our simulations with anisotropic CR diffusion and a low CR injection efficiency at supernovae (SNe; |$\zeta_\mathrm{SN}=0.05$|⁠) can successfully reproduce the observed far-infrared (FIR)–γ-ray relation. Starburst galaxies are close to the calorimetric limit, where CR protons lose most of their energy due to hadronic interactions and hence, their γ-ray emission is dominated by neutral pion decay. However, in low SF galaxies, the increasing diffusive losses soften the CR proton spectra due to energy-dependent diffusion, and likewise steepen the pionic γ-ray spectra. In turn, IC emission hardens the total spectra and can contribute up to ∼40 per cent of the total luminosity in low SF galaxies. Furthermore, in order to match the observed γ-ray spectra of starburst galaxies, we require a weaker energy dependence of the CR diffusion coefficient, |$D\propto E^{0.3}$|⁠ , in comparison to Milky Way-like galaxies. [ABSTRACT FROM AUTHOR]

Current-day cosmic ray (CR) propagation studies use static Milky Way models and fit parametrized source distributions to data. Instead, we use three-dimensional magnetohydrodynamic (MHD) simulations of isolated galaxies with the moving-mesh code arepo that self-consistently accounts for hydrodynamic effects of CR protons. In post-processing, we calculate their steady-state spectra, taking into account all relevant loss processes. We show that this steady-state assumption is well justified in the disc and generally for regions that emit non-thermal radio and gamma rays. Additionally, we model the spectra of primary electrons, accelerated by supernova remnants, and secondary electrons and positrons produced in hadronic CR proton interactions with the gas. We find that proton spectra above 10 GeV only weakly depend on galactic radius, while they acquire a radial dependence at lower energies due to Coulomb interactions. Radiative losses steepen the spectra of primary CR electrons in the central galactic regions, while diffusive losses dominate in the outskirts. Secondary electrons exhibit a steeper spectrum than primaries because they originate from the transported steeper CR proton spectra. Consistent with Voyager-1 and AMS-02 data, our models (i) show a turnover of proton spectra below GeV energies due to Coulomb interactions so that electrons start to dominate the total particle spectra and (ii) match the shape of the positron fraction up to 10 GeV. We conclude that our steady-state CR modelling in MHD CR galaxy simulations is sufficiently realistic to capture the dominant transport effects shaping their spectra, arguing for a full MHD treatment to accurately model CR transport in the future. [ABSTRACT FROM AUTHOR]

We review numerical methods for simulations of cosmic ray (CR) propagation on galactic and larger scales. We present the development of algorithms designed for phenomenological and self-consistent models of CR propagation in kinetic description based on numerical solutions of the Fokker–Planck equation. The phenomenological models assume a stationary structure of the galactic interstellar medium and incorporate diffusion of particles in physical and momentum space together with advection, spallation, production of secondaries and various radiation mechanisms. The self-consistent propagation models of CRs include the dynamical coupling of the CR population to the thermal plasma. The CR transport equation is discretized and solved numerically together with the set of MHD equations in various approaches treating the CR population as a separate relativistic fluid within the two-fluid approach or as a spectrally resolved population of particles evolving in physical and momentum space. The relevant processes incorporated in self-consistent models include advection, diffusion and streaming propagation as well as adiabatic compression and several radiative loss mechanisms. We discuss, applications of the numerical models for the interpretation of CR data collected by various instruments. We present example models of astrophysical processes influencing galactic evolution such as galactic winds, the amplification of large-scale magnetic fields and instabilities of the interstellar medium. [ABSTRACT FROM AUTHOR]

We review numerical methods for simulations of cosmic ray (CR) propagation on galactic and larger scales. We present the development of algorithms designed for phenomenological and self-consistent models of CR propagation in kinetic description based on numerical solutions of the Fokker–Planck equation. The phenomenological models assume a stationary structure of the galactic interstellar medium and incorporate diffusion of particles in physical and momentum space together with advection, spallation, production of secondaries and various radiation mechanisms. The self-consistent propagation models of CRs include the dynamical coupling of the CR population to the thermal plasma. The CR transport equation is discretized and solved numerically together with the set of MHD equations in various approaches treating the CR population as a separate relativistic fluid within the two-fluid approach or as a spectrally resolved population of particles evolving in physical and momentum space. The relevant processes incorporated in self-consistent models include advection, diffusion and streaming propagation as well as adiabatic compression and several radiative loss mechanisms. We discuss, applications of the numerical models for the interpretation of CR data collected by various instruments. We present example models of astrophysical processes influencing galactic evolution such as galactic winds, the amplification of large-scale magnetic fields and instabilities of the interstellar medium. [ABSTRACT FROM AUTHOR]

The emergence and development of a power‐law tail (PLT) at the high‐density end of the observed column‐density distribution are thought to be indicative for advanced evolution of star‐forming molecular clouds. As shown from many numerical simulations, it corresponds to a morphologically analogous evolution of the mass‐density distribution (ρ‐PDF). The latter may display also a second, shallower PLT at the stage of collapse of the first formed protostellar cores. It is difficult to estimate the parameters of a possible second PLT due to resolution constraints. To address the issue, we extend the method for the extraction of single PLTs from arbitrary density distributions suggested by Veltchev et al. (MNRAS, 489, 788, 2019) to detect a second PLT. The technique is elaborated through tests on an analytic ρ‐PDF and applied to a set of hydrodynamical high‐resolution simulations of isothermal self‐gravitating clouds. In all but one case two PLTs were detected—the first slope is always steeper and the second one is typically ∂lnV/lnρ∼−1. These results are in a good agreement with numerical and theoretical works and do suggest that the technique extracts correctly double PLTs from smooth PDFs. [ABSTRACT FROM AUTHOR]

Molecular outflows contributing to the matter cycle of star-forming galaxies are now observed in small and large systems at low and high redshift. Their physical origin is still unclear. In most theoretical studies, only warm ionized/neutral and hot gas outflowing from the interstellar medium is generated by star formation. We investigate an in situ H2 formation scenario in the outflow using high-resolution simulations, including non-equilibrium chemistry and self-gravity, of turbulent, warm, and atomic clouds with densities 0.1, 0.5, and |$1\, \mathrm{cm}^{-3}$| exposed to a magnetized hot wind. For cloud densities |$\gtrsim 0.5\, \mathrm{cm}^{-3}$|⁠ , a magnetized wind triggers H2 formation before cloud dispersal. Up to 3 per cent of the initial cloud mass can become molecular on |$\sim \! 10\, \mathrm{Myr}$| time-scales. The effect is stronger for winds with perpendicular B -fields and intermediate density clouds (⁠|$n_\mathrm{c}\sim 0.5\, \mathrm{cm}^{-3}$|⁠). Here, H2 formation can be boosted by up to one order of magnitude compared to isolated cooling clouds independent of self-gravity. Self-gravity preserves the densest clouds well past their |$\sim \! 15\, \mathrm{Myr}$| cloud crushing time-scales. This model could provide a plausible in situ origin for the observed molecular gas. All simulations form warm ionized gas, which represents an important observable phase. The amount of warm ionized gas is almost independent of the cloud density but solely depends on the magnetic field configuration in the wind. For low-density clouds (⁠|$0.1\, \mathrm{cm}^{-3}$|⁠), up to 60 per cent of the initially atomic cloud mass can become warm and ionized. [ABSTRACT FROM AUTHOR]

Supernova remnants (SNRs) are believed to be the source of Galactic cosmic rays (CRs). SNR shocks accelerate CR protons and electrons which reveal key insights into the non-thermal physics by means of their synchrotron and γ-ray emission. The remnant SN 1006 is an ideal particle acceleration laboratory because it is observed across all electromagnetic wavelengths from radio to γ-rays. We perform 3D magnetohydrodynamics (MHD) simulations where we include CR protons and follow the CR electron spectrum. By matching the observed morphology and non-thermal spectrum of SN 1006 in radio, X-rays, and γ-rays, we gain new insight into CR electron acceleration and magnetic field amplification. (1) We show that a mixed leptonic–hadronic model is responsible for the γ-ray radiation: while leptonic inverse-Compton emission and hadronic pion-decay emission contribute equally at GeV energies observed by Fermi , TeV energies observed by imaging air Cherenkov telescopes are hadronically dominated. (2) We show that quasi-parallel acceleration (i.e. when the shock propagates at a narrow angle to the upstream magnetic field) is preferred for CR electrons and that the electron acceleration efficiency of radio-emitting GeV electrons at quasi-perpendicular shocks is suppressed at least by a factor ten. This precludes extrapolation of current 1D plasma particle-in-cell simulations of shock acceleration to realistic SNR conditions. (3) To match the radial emission profiles and the γ-ray spectrum, we require a volume-filling, turbulently amplified magnetic field and that the Bell-amplified magnetic field is damped in the immediate post-shock region. Our work connects microscale plasma physics simulations to the scale of SNRs. [ABSTRACT FROM AUTHOR]

Star clusters form in dense, hierarchically collapsing gas clouds. Bulk kinetic energy is transformed to turbulence with stars forming from cores fed by filaments. In the most compact regions, stellar feedback is least effective in removing the gas and stars may form very efficiently. These are also the regions where, in high-mass clusters, ejecta from some kind of high-mass stars are effectively captured during the formation phase of some of the low mass stars and channeled into the latter to form multiple populations. Star formation epochs in star clusters are generally set by gas flows that determine the abundance of gas in the cluster. We argue that there is likely only one star formation epoch after which clusters remain essentially clear of gas by cluster winds. Collisional dynamics is important in this phase leading to core collapse, expansion and eventual dispersion of every cluster. We review recent developments in the field with a focus on theoretical work. [ABSTRACT FROM AUTHOR]

Star formation is a complex multi-scale phenomenon that is of significant importance for astrophysics in general. Stars and star formation are key pillars in observational astronomy from local star forming regions in the Milky Way up to high-redshift galaxies. From a theoretical perspective, star formation and feedback processes (radiation, winds, and supernovae) play a pivotal role in advancing our understanding of the physical processes at work, both individually and of their interactions. In this review we will give an overview of the main processes that are important for the understanding of star formation. We start with an observationally motivated view on star formation from a global perspective and outline the general paradigm of the life-cycle of molecular clouds, in which star formation is the key process to close the cycle. After that we focus on the thermal and chemical aspects in star forming regions, discuss turbulence and magnetic fields as well as gravitational forces. Finally, we review the most important stellar feedback mechanisms. [ABSTRACT FROM AUTHOR]

In recent years, exciting developments have taken place in the identification of the role of cosmic rays in star-forming environments. Observations from radio to infrared wavelengths and theoretical modelling have shown that low-energy cosmic rays (< 1 TeV ) play a fundamental role in shaping the chemical richness of the interstellar medium, determining the dynamical evolution of molecular clouds. In this review we summarise in a coherent picture the main results obtained by observations and by theoretical models of propagation and generation of cosmic rays, from the smallest scales of protostars and circumstellar discs, to young stellar clusters, up to Galactic and extragalactic scales. We also discuss the new fields that will be explored in the near future thanks to new generation instruments, such as: CTA, for the γ -ray emission from high-mass protostars; SKA and precursors, for the synchrotron emission at different scales; and ELT/HIRES, JWST, and ARIEL, for the impact of cosmic rays on exoplanetary atmospheres and habitability. [ABSTRACT FROM AUTHOR]

Cosmic ray (CR) protons are an important component in many astrophysical systems. Processes like CR injection, cooling, adiabatic changes as well as active CR transport through the medium strongly modify the CR momentum distribution and have to be taken into account in hydrodynamical simulations. We present an efficient novel numerical scheme to accurately compute the evolution of the particle distribution function by solving the Fokker–Planck equation with a low number of spectral bins (10–20), which is required to include a full spectrum for every computational fluid element. The distribution function is represented by piecewise power laws and is not forced to be continuous, which enables an optimal representation of the spectrum. The Fokker–Planck equation is solved with a two-moment approach evolving the CR number and energy density. The low numerical diffusion of the scheme reduces the numerical errors by orders of magnitude in comparison to classical schemes with piecewise constant spectral representations. With this method not only the spectral evolution of CRs can be computed accurately in magnetohydrodynamic simulations but also their dynamical impact as well as CR ionization. This allows for more accurate models for astrophysical plasmas, like the interstellar medium, and direct comparisons with observations. [ABSTRACT FROM AUTHOR]

We present a new approach to extract the power-law part of a density/column-density probability density function (ρ-pdf/ N -pdf) in star-forming clouds. This approach is based on the mathematical method bPlfit of Virkar & Clauset (2014, Annals of Applied Statistics, 8, 89) and it assesses the power-law part of an arbitrary distribution, without any assumptions about the other parts of this distribution. The slope and deviation point are derived as averaged values as the number of bins is varied. Neither parameter is sensitive to spikes and other local features of the tail. This adapted bPlfit method is applied to two different sets of data from numerical simulations of star-forming clouds at scales 0.5 and 500 pc, and it displays ρ-pdf and N -pdf evolution in agreement with a number of numerical and theoretical studies. Applied to Herschel data on the regions Aquila and Rosette, the method extracts pronounced power-law tails, consistent with those seen in simulations of evolved clouds. [ABSTRACT FROM AUTHOR]

Cosmic ray (CR) electrons reveal key insights into the non-thermal physics of the interstellar medium (ISM), galaxies, galaxy clusters, and active galactic nuclei by means of their inverse Compton (IC) γ-ray emission and synchrotron emission in magnetic fields. While magnetohydrodynamical (MHD) simulations with CR protons capture their dynamical impact on these systems, only few computational studies include CR electron physics because of the short cooling time-scales and complex hysteresis effects, which require a numerically expensive, high-resolution spectral treatment. Since CR electrons produce important non-thermal observational signatures, such a spectral CR electron treatment is important to link MHD simulations to observations. We present an efficient post-processing code for Cosmic Ray Electron Spectra that are evolved in Time (crest) on Lagrangian tracer particles. The CR electron spectra are very accurately evolved on comparably large MHD time-steps owing to an innovative hybrid numerical-analytical scheme. crest is coupled to the cosmological MHD code arepo and treats all important aspects of spectral CR electron evolution such as adiabatic expansion and compression, Coulomb losses, radiative losses in form of IC, bremsstrahlung and synchrotron processes, diffusive shock acceleration and reacceleration, Fermi-II reacceleration, and secondary electron injection. After showing various code validations of idealized one-zone simulations, we study the coupling of crest to MHD simulations. We demonstrate that the CR electron spectra are efficiently and accurately evolved in shock-tube and Sedov–Taylor blast wave simulations. This opens up the possibility to produce self-consistent synthetic observables of non-thermal emission processes in various astrophysical environments. [ABSTRACT FROM AUTHOR]

Context. Mrk 71/NGC 2366 is the closest green pea (GP) analog and candidate Lyman Continuum (LyC) emitter. Recently, 11 LyC-leaking GPs have been detected through direct observations of the ionizing continuum, making this the most abundant class of confirmed LyC-emitters at any redshift. High resolution, multiwavelength studies of GPs can lead to an understanding of the method(s), through which LyC escapes from these galaxies. Aims. The proximity of Mrk 71/NCG 2366 offers unprecedented detail on the inner workings of a GP analog, and enables us to identify the mechanisms of LyC escape. Methods. We used 5825–7650 Å integral field unit PMAS observations to study the kinematics and physical conditions in Mrk 71. An electron density map was obtained from the [S II] ratio. A fortuitous second order contamination by the [O II] λ3727 doublet enabled the construction of an electron temperature map. Resolved maps of sound speed, thermal broadening, "true" velocity dispersion, and Mach number were obtained and compared to the high resolution magnetohydrodynamic SImulating the LifeCycle of molecular Clouds (SILCC) simulations. Results. Two regions of increased velocity dispersion indicative of outflows are detected to the north and south of the super star cluster, knot B, with redshifted and blueshifted velocities, respectively. We confirm the presence of a faint broad kinematical component, which is seemingly decoupled from the outflow regions, and is fainter and narrower than previously reported in the literature. Within uncertainties, the low- and high-ionization gasses move together. Outside of the core of Mrk 71, an increase in Mach numbers is detected, implying a decrease in gas density. Simulations suggest this drop in density can be as high as ∼4 dex, down to almost optically thin levels, which would imply a nonzero LyC escape fraction along the outflows even when assuming all of the detected H I gas is located in front of Mrk 71 in the line of sight. Conclusions. Our results strongly indicate that kinematical feedback is an important ingredient for LyC leakage in GPs. [ABSTRACT FROM AUTHOR]

We investigate the impact of cosmic rays (CRs) on galactic outflows from a multiphase interstellar medium with solar neighbourhood conditions. The three-dimensional magnetohydrodynamical simulations include CRs as a relativistic fluid in the advection-diffusion approximation. The thermal and chemical state of the interstellar medium is computed with a non-equilibrium chemical network. We find that CRs [injected with 10  per cent of the supernova (SN) energy] efficiently support the launching of outflows and strongly affect their phase structure. Outflows leaving the midplane are denser ($$\rho \sim 10^{-26}\, \mathrm{g\, cm}^{-3}$$), colder ($${\sim } 10^4\, \mathrm{K}$$) and slower ($${\sim } 30\, \mathrm{km\, s}^{-1}$$) if CRs are considered in addition to thermal SNe. The CR-supported outflows are also smoother, in particular at larger heights (> $$1\, \mathrm{kpc}$$ above the midplane) without the direct impact of SN explosions. Approximately, 5 per cent − 25 per cent of the injected CR energy is lost via hadronic cooling. Smaller diffusion coefficients lead to slightly larger hadronic losses but allow for steeper CR pressure gradients, stronger outflows and larger accelerations. Up to a height of $$z \sim 1\, \mathrm{kpc,}$$ there are large volumes in approximate pressure equilibrium between the thermal and the CR component. At larger altitudes, the CR pressure is 10–100 times as large as the thermal counterpart. More than $${\sim } 1\, \mathrm{kpc}$$ away from the midplane, CRs provide the dominant gas acceleration mechanism. [ABSTRACT FROM AUTHOR]

The large vertical scale heights of the diffuse ionized gas (DIG) in disc galaxies are challenging to model, as hydrodynamical models including only thermal feedback seem to be unable to support gas at these heights. In this paper, we use a three-dimensional Monte Carlo radiation transfer code to post-process disc simulations of the Simulating the Life-Cycle of Molecular Clouds project that include feedback by cosmic rays. We show that the more extended discs in simulations including cosmic ray feedback naturally lead to larger scale heights for the DIG which are more in line with observed scale heights. We also show that including a fiducial cosmic ray heating term in our model can help to increase the temperature as a function of disc scale height, but fails to reproduce observed DIG nitrogen and sulphur forbidden line intensities. We show that, to reproduce these line emissions, we require a heating mechanism that affects gas over a larger density range than is achieved by cosmic ray heating, which can be achieved by fine tuning the total luminosity of ionizing sources to get an appropriate ionizing spectrum as a function of scale height. This result sheds a new light on the relation between forbidden line emissions and temperature profiles for realistic DIG gas distributions. [ABSTRACT FROM AUTHOR]

We present three-dimensional radiation-hydrodynamical simulations of the impact of stellar winds, photoelectric heating, photodissociating and photoionizing radiation, and supernovae on the chemical composition and star formation in a stratified disc model. This is followed by a sink-based model for star clusters with populations of individual massive stars. Stellar winds and ionizing radiation regulate the star formation rate at a factor of ~10 below the simulation with only supernova feedback due to their immediate impact on the ambient interstellar medium after star formation. Ionizing radiation (with winds and supernovae) significantly reduces the ambient densities for most supernova explosions to ρ < 10-25 g cm-3, compared to 10-23g cm-3 for the model with only winds and supernovae. Radiation from massive stars reduces the amount of molecular hydrogen and increases the neutral hydrogen mass and volume filling fraction. Only this model results in a molecular gas depletion time-scale of 2 Gyr and shows the best agreement with observations. In the radiative models, the Hα emission is dominated by radiative recombination as opposed to collisional excitation (the dominant emission in non-radiative models), which only contributes ~1-10 per cent to the total Hα emission. Individual massive stars (M ≥ 30M☉) with short lifetimes are responsible for significant fluctuations in the Hα luminosities. The corresponding inferred star formation rates can underestimate the true instantaneous star formation rate by a factor of ~10. [ABSTRACT FROM AUTHOR]

We present three-dimensional radiation-hydrodynamical simulations of the impact of stellar winds, photoelectric heating, photodissociating and photoionizing radiation, and supernovae on the chemical composition and star formation in a stratified disc model. This is followed by a sink-based model for star clusters with populations of individual massive stars. Stellar winds and ionizing radiation regulate the star formation rate at a factor of ~10 below the simulation with only supernova feedback due to their immediate impact on the ambient interstellar medium after star formation. Ionizing radiation (with winds and supernovae) significantly reduces the ambient densities for most supernova explosions to ρ < 10-25 g cm-3, compared to 10-23g cm-3 for the model with only winds and supernovae. Radiation from massive stars reduces the amount of molecular hydrogen and increases the neutral hydrogen mass and volume filling fraction. Only this model results in a molecular gas depletion time-scale of 2 Gyr and shows the best agreement with observations. In the radiative models, the Hα emission is dominated by radiative recombination as opposed to collisional excitation (the dominant emission in non-radiative models), which only contributes ~1-10 per cent to the total Hα emission. Individual massive stars (M ≥ 30M☉) with short lifetimes are responsible for significant fluctuations in the Hα luminosities. The corresponding inferred star formation rates can underestimate the true instantaneous star formation rate by a factor of ~10. [ABSTRACT FROM AUTHOR]

We present three-dimensional radiation-hydrodynamical simulations of the impact of stellar winds, photoelectric heating, photodissociating and photoionizing radiation, and supernovae on the chemical composition and star formation in a stratified disc model. This is followed by a sink-based model for star clusters with populations of individual massive stars. Stellar winds and ionizing radiation regulate the star formation rate at a factor of ∼10 below the simulation with only supernova feedback due to their immediate impact on the ambient interstellar medium after star formation. Ionizing radiation (with winds and supernovae) significantly reduces the ambient densities for most supernova explosions to ρ < 10-25 g cm-3, compared to 10-23g cm-3 for the model with only winds and supernovae. Radiation from massive stars reduces the amount of molecular hydrogen and increases the neutral hydrogen mass and volume filling fraction. Only this model results in a molecular gas depletion time-scale of 2 Gyr and shows the best agreement with observations. In the radiative models, the Hα emission is dominated by radiative recombination as opposed to collisional excitation (the dominant emission in non-radiative models), which only contributes ∼1-10 per cent to the total Hα emission. Individual massive stars (M ≥ 30M☉) with short lifetimes are responsible for significant fluctuations in the Hα luminosities. The corresponding inferred star formation rates can underestimate the true instantaneous star formation rate by a factor of ∼10. [ABSTRACT FROM AUTHOR]

The SILCC project (SImulating the Life-Cycle of molecular Clouds) aims at a more selfconsistent understanding of the interstellar medium (ISM) on small scales and its link to galaxy evolution. We present three-dimensional (magneto)hydrodynamic simulations of the ISM in a vertically stratified box including self-gravity, an external potential due to the stellar component of the galactic disc, and stellar feedback in the form of an interstellar radiation field and supernovae (SNe). The cooling of the gas is based on a chemical network that follows the abundances of H+, H, H2, C+, and CO and takes shielding into account consistently. We vary the SN feedback by comparing different SN rates, clustering and different positioning, in particular SNe in density peaks and at random positions, which has a major impact on the dynamics. Only for random SN positions the energy is injected in sufficiently low-density environments to reduce energy losses and enhance the effective kinetic coupling of the SNe with the gas. This leads to more realistic velocity dispersions (sHI 0.8s300-8000K ~ 10-20 km s-1, sHa 0.6s8000-3 105 K ~ 20-30 km s-1), and strong outflows with mass loading factors (ratio of outflow to star formation rate) of up to 10 even for solar neighbourhood conditions. Clustered SNe abet the onset of outflows compared to individual SNe but do not influence the net outflow rate. The outflows do not contain any molecular gas and are mainly composed of atomic hydrogen. The bulk of the outflowing mass is dense (~ 10-25-10-24 g cm-3) and slow (v ~ 20-40 km s-1) but there is a high-velocity tail of up to v ~ 500 km s-1 with ~ 10-28-10-27 g cm-3. [ABSTRACT FROM AUTHOR]

The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form PV(ρ)∝ρ–1.54 for the (volume-weighted) PDF and PM(ρ)∝ρ–0.54 for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall. [ABSTRACT FROM AUTHOR]

ABSTRACT We investigate the formation of protostellar clusters during the collapse of dense molecular cloud cores with a focus on the evolution of potential and kinetic energy, the degree of substructure and the early phase of mass segregation. Our study is based on a series of hydrodynamic simulations of dense cores, where we vary the initial density profile and the initial turbulent velocity. In the three-dimensional adaptive mesh refinement simulations, we follow the dynamical formation of filaments and protostars until a star formation efficiency of 20 per cent. Despite the different initial configurations, the global ensemble of all protostars in a setup shows a similar energy evolution and forms sub-virial clusters with an energy ratio Ekin/| Epot|∼ 0.2. Concentrating on the innermost central region, the clusters show a roughly virialized energy balance. However, the region of virial balance only covers the innermost ∼10-30 per cent of all the protostars. In all simulations with multiple protostars, the total kinetic energy of the protostars is higher than the kinetic energy of the gas cloud, although the protostars only contain 20 per cent of the total mass. The clusters vary significantly in size, mass and number of protostars, and show different degrees of substructure and mass segregation. Flat density profiles and compressive turbulent modes produce more subclusters than centrally concentrated profiles and solenoidal turbulence. We find that dynamical relaxation and hence dynamical mass segregation is very efficient in all cases from the very beginning of the nascent cluster, i.e. during a phase when protostars constantly form and accrete. [ABSTRACT FROM AUTHOR]

ABSTRACT We investigate the impact of different initial conditions for the initial density profile and the initial turbulence on the formation process of protostellar clusters. We study the collapse of dense molecular cloud cores with three-dimensional adaptive mesh refinement simulations. We focus our discussion on the distribution of the gas among the protostellar objects in the turbulent dynamical cores. Despite the large variations in the initial configurations and the resulting gas and cluster morphology we find that all stellar clusters follow a very similar gas accretion behaviour. Once secondary protostars begin to form, the central region of a cluster is efficiently shielded from further accretion. Hence, objects located close to the centre are starved of material, as indicated by a strong decrease of the central accretion rate. This fragmentation-induced starvation occurs not only in rotationally supported discs and filaments, but also in more spherically symmetric clusters with complex chaotic motions. [ABSTRACT FROM AUTHOR]

We present a detailed parameter study of collapsing turbulent cloud cores, varying the initial density profile and the initial turbulent velocity field. We systematically investigate the influence of different initial conditions on the star formation process, mainly focusing on the fragmentation, the number of formed stars and the resulting mass distributions. Our study compares four different density profiles (uniform, Bonnor-Ebert type, and ), combined with six different supersonic turbulent velocity fields (compressive, mixed and solenoidal, initialized with two different random seeds each) in three-dimensional simulations using the adaptive-mesh refinement, hydrodynamics code . The simulations show that density profiles with flat cores produce hundreds of low-mass stars, either distributed throughout the entire cloud or found in subclusters, depending on the initial turbulence. Concentrated density profiles always lead to the formation of one high-mass star in the centre of the cloud and, if at all, low-mass stars surrounding the central one. In uniform and Bonnor-Ebert type density distributions, compressive initial turbulence leads to local collapse about 25 per cent earlier than solenoidal turbulence. However, central collapse in the steep power-law profiles is too fast for the turbulence to have any significant influence. We conclude that (i) the initial density profile and turbulence mainly determine the cloud evolution and the formation of clusters, (ii) the initial mass function (IMF) is not universal for all setups and (iii) that massive stars are much less likely to form in flat density distributions. The IMFs obtained in the uniform and Bonnor-Ebert type density profiles are more consistent with the observed IMF, but shifted to lower masses. [ABSTRACT FROM AUTHOR]