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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]

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]

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]

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]

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]

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]

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]

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]