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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]

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]

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]

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]

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]

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]

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]