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Cosmic rays (CRs) are dynamically important for the formation and evolution of galaxies by regulating star formation and by 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 along the magnetic field. Moreover, both properties sensitively depend on the CR momentum, which is largely unexplored in three-dimensional hydrodynamical simulations. We perform magneto-hydrodynamical simulations of entire galaxies with masses ranging from $10^{10}$ 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 Alfv\'{e}n 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 four in dwarf galaxies. All simulated low-mass halos ($M=10^{10}$, $10^{11}$, and $3\times10^{11}\,\mathrm{M}_\odot$) 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 $\langle{D}\rangle_{e_\mathrm{cr}}\sim10^{28}\,\mathrm{cm^2\,s^{-1}}$ in the disc up to $3\times10^{29}\,\mathrm{cm^2\,s^{-1}}$ in the circumgalactic medium, where we observe substantial temperature and CR pressure differences between our grey and spectral CR models., Comment: 28 pages, MNRAS, accepted

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 (MHD) 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 halos, 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 spectral indices and 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., Comment: 18 pages, 11 figures, submitted to MNRAS, comments are welcome!

Recently, cosmic ray (CR) feedback has been identified as a critical process in galaxy formation but most previous simulations have integrated out the energy-dependence of the CR distribution, despite its large extent over more than twelve decades in particle energy. To improve upon this simplification, we present the implementation and first application of spectrally resolved CRs which are coupled to the magneto-hydrodynamics in simulations of galaxy formation. The spectral model for the CRs enables more accurate cooling of CRs and allows for an energy-dependent spatial diffusion, for which we introduce a new stable numerical algorithm that proves essential in highly dynamical systems. We perform galaxy formation simulations with this new model and compare the results to a grey CR approach with a simplified diffusive transport and effective cooling that assumes steady-state spectra. We find that the galaxies with spectrally resolved CRs differ in morphology, star formation rate, and strength and structure of the outflows. Interestingly, the first outflow front is driven by CRs with average momenta of $\sim200-600\,\mathrm{Gev}~c^{-1}$. The subsequent formation of outflows, which reach mass loading factors of order unity, are primarily launched by CRs of progressively smaller average momenta of $\sim8-15\,\mathrm{GeV}~c^{-1}$. The CR spectra in the galactic centre quickly approach a steady state, which does not significantly vary over time. In the outer disc and outflow regions, the spectral shape approaches steady state only after $\sim2\,\mathrm{Gyr}$ of evolution. Furthermore, the shapes of the approximate steady state spectra differ for individual regions of the galaxy, which highlights the importance of actively including the full CR spectrum., Comment: 21 pages, 13 figures, published in MNRAS, erratum added

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 magneto-hydrodynamical (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 to synchrotron emission. This implies steep steady-state synchrotron spectra in starbursts. Interestingly, we find that thermal free-free emission hardens 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., Comment: 24 pages, 15 figures, submitted to MNRAS, comments are welcome

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). We examine magneto-hydrodynamic galaxy simulations with cosmic rays (CRs), accounting for 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 inject turbulence and drive multiple small-scale dynamos, which exponentially amplify magnetic fields. 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 magnetised disc, bulge, and bubble-shaped magnetically-loaded outflows of our simulated Milky Way-mass galaxy. 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. (abridged), Comment: 37 pages, 26 figures, accepted for publication in MNRAS

The $\gamma$-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 magneto-hydrodynamical (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 $\gamma$-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)-$\gamma$-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 $\gamma$-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 $\gamma$-ray spectra. In turn, IC emission hardens the total spectra and can contribute up to $\sim40$ per cent of the total luminosity in low SF galaxies. Furthermore, in order to match the observed $\gamma$-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., Comment: 20 pages, 11 figures, accepted to MNRAS

Current-day cosmic ray (CR) propagation studies use static Milky-Way models and fit parametrized source distributions to data. Instead, we use three-dimensional magneto-hydrodynamical (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 turn-over 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 modeling 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., Comment: 23 pages, 17 figures, accepted to MNRAS

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 $\gamma$-ray emission. The remnant SN 1006 is an ideal particle acceleration laboratory because it is observed across all electromagnetic wavelengths from radio to $\gamma$-rays. We perform three-dimensional (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 $\gamma$-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 $\gamma$-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 one-dimensional plasma particle-in-cell simulations of shock acceleration to realistic SNR conditions. 3. To match the radial emission profiles and the $\gamma$-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 micro-scale plasma physics simulations to the scale of SNRs., Comment: 18 pages, 18 figures, published in MNRAS

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 $\gamma$-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., Comment: Submitted to Space Science Reviews topical collection Star formation

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 ionisation. This allows for more accurate models for astrophysical plasmas, like the interstellar medium, and direct comparisons with observations., Comment: 16 pages, MNRAS accepted, corrected typo in eq. (63)

Cosmic ray (CR) electrons reveal key insights into the non-thermal physics of the interstellar medium, galaxies, galaxy clusters, and active galactic nuclei by means of their inverse Compton {\gamma}-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 inverse Compton, bremsstrahlung and synchrotron processes, diffusive shock acceleration and reacceleration, and Fermi-II reacceleration. 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., Comment: 19 pages, 14 figures, 11 pages, 9 figures, published in MNRAS

The halo of the Milky Way contains a hot plasma with a surface brightness in soft X-rays of the order $10^{-12}$erg cm$^{-2}$ s$^{-1}$ deg$^{-2}$. The origin of this gas is unclear, but so far numerical models of galactic star formation have failed to reproduce such a large surface brightness by several orders of magnitude. In this paper, we analyze simulations of the turbulent, magnetized, multi-phase interstellar medium including thermal feedback by supernova explosions as well as cosmic-ray feedback. We include a time-dependent chemical network, self-shielding by gas and dust, and self-gravity. Pure thermal feedback alone is sufficient to produce the observed surface brightness, although it is very sensitive to the supernova rate. Cosmic rays suppress this sensitivity and reduce the surface brightness because they drive cooler outflows. Self-gravity has by far the largest effect because it accumulates the diffuse gas in the disk in dense clumps and filaments, so that supernovae exploding in voids can eject a large amount of hot gas into the halo. This can boost the surface brightness by several orders of magnitude. Although our simulations do not reach a steady state, all simulations produce surface brightness values of the same order of magnitude as the observations, with the exact value depending sensitively on the simulation parameters. We conclude that star formation feedback alone is sufficient to explain the origin of the hot halo gas, but measurements of the surface brightness alone do not provide useful diagnostics for the study of galactic star formation., Comment: ApJ Letters in press

We present a novel implementation of cosmic rays (CR) in the magneto-hydrodynamic code FLASH. CRs are described as separate fluids with different energies. CR advection, energy dependent anisotropic diffusion with respect to the magnetic field and adiabatic losses to follow the evolution of spectra are taken into account. We present a first study of the transport and immediate (~150 kyr) dynamical impact of CRs on the turbulent magnetised interstellar medium around supernova remnants on scales up to 80 pc. CR diffusion quickly leads to an efficient acceleration of low-density gas (mainly perpendicular to the magnetic field) with accelerations up to two orders of magnitude above the thermal values. Peaked (at 1 GeV) CR injection spectra have a stronger impact on the dynamics than power-law spectra. For realistic magnetic field configurations low energy CRs (with smaller diffusion coefficients) distribute anisotropically with large spatial variations of a factor of ten and more. Adiabatic losses can change the local spectra perceptibly but do not have an integral effect on the dynamics at the spatial and temporal scales considered here. We discuss the potential global impact of CRs and anisotropic transport on the dynamical structure of the ISM and also detail the limitations of the model., Comment: 22 pages, submitted to MNRAS, comments welcome