Cosmic Ray Feedback Research Articles

Revisiting the role of cosmic-ray driven Alfven waves in pre-existing magnetohydrodynamic turbulence. I. Turbulent damping rates and feedback on background fluctuations

Alfv\'en waves (AWs) excited by the cosmic-ray (CR) streaming instability (CRSI) are a fundamental ingredient for CR confinement. The effectiveness of such self-confinement relies on a balance between the CRSI growth rate and the damping mechanisms acting on quasi-parallel AWs excited by CRs. One relevant mechanism is called turbulent damping, in which an AW packet injected in pre-existing turbulence undergoes a cascade process due to its nonlinear interaction with fluctuations of the background. The turbulent damping of an AW packet in pre-existing magnetohydrodynamic (MHD) turbulence is re-examined, revised, and extended to include the most recent theories of MHD turbulence that account for dynamic alignment and reconnection-mediated regimes. The case in which the role of feedback of CR-driven AWs on pre-existing turbulence is important is also discussed. The Els\"asser formalism is employed. Particular attention is given to the role of a nonlinearity parameter $ that estimates the strength of the nonlinear interaction between CR-driven AW packets and the background fluctuations. We point out the difference between $ and the parameter $ that instead describes the intrinsic strength of nonlinear interactions between pre-existing fluctuations. Turbulent damping rates of quasi-parallel AW packets and cosmic-ray feedback (CRF) are derived within this formalism. When the strength of the nonlinear interaction is properly taken into account, we find that (i) the turbulent damping rate of quasi-parallel AWs in sub-Alfv\'enic turbulence depends on the background-fluctuation amplitude to the third power, and hence is strongly suppressed; (ii) the dependence on the AW's wavelength (and thus on the CR gyro-radius from which it is excited) is different from what has been previously obtained; and (iii) when dynamic alignment of cascading fluctuations and the possibility of a reconnection-mediated range is included in the picture, the turbulent damping rate exhibits novel regimes and breaks. Finally, a criterion for CRF is derived and a simple phenomenological model of CR-modified scaling of background fluctuations is provided.

Effect of cosmic rays and ionizing radiation on observational ultraviolet plasma diagnostics in the circumgalactic medium

ABSTRACT The relevance of some galactic feedback mechanisms, in particular cosmic-ray (CR) feedback and the hydrogen ionizing radiation field, has been challenging to definitively describe in a galactic context, especially far outside the galaxy in the circumgalactic medium (CGM). Theoretical and observational uncertainties prevent conclusive interpretations of multiphase CGM properties derived from ultraviolet (UV) diagnostics. We conduct three-dimensional magnetohydrodynamic simulations of a section of a galactic disc with star formation and feedback, including radiative heating from stars, a UV background, and CR feedback. We utilize the temperature phases present in our simulations to generate Cloudy models to derive spatially and temporally varying synthetic UV diagnostics. We find that radiative effects without additional heating mechanisms are not able to produce synthetic diagnostics in the observed ranges. For low CR diffusivity $\kappa _{\rm {cr}}=10^{28} \rm {cm}^2 \rm {s}^{-1}$, CR streaming heating in the outflow helps our synthetic line ratios roughly match observed ranges by producing transitional temperature gas (T ∼ 105–106 K). High CR diffusivity $\kappa _{\rm {cr}}=10^{29} \rm {cm}^2 \rm {s}^{-1}$, with or without CR streaming heating, produced transitional temperature gas. The key parameter controlling the production of this gas phase remains unclear, as the different star formation history and outflow evolution itself influences these diagnostics. Our work demonstrates the use of UV plasma diagnostics to differentiate between galactic/circumgalactic feedback models.

Deciphering Lyman-α emission deep into the epoch of reionization

During the epoch of reionization, the first galaxies were enshrouded in pristine neutral gas, with one of the brightest emission lines in star-forming galaxies, Lyman α (Lyα), expected to remain undetected until the Universe became ionized. Providing an explanation for the surprising detection of Lyα in these early galaxies is a major challenge for extragalactic studies. Recent James Webb Space Telescope observations have reignited the debate about whether residence in an overdensity of galaxies is a sufficient and necessary condition for Lyα to escape. Here, we take unique advantage of both high-resolution and high-sensitivity images from the James Webb Space Telescope Near Infrared Camera to show that all galaxies in a sample of Lyα emitters with redshift >7 have close companions. We exploit on-the-fly radiative-transfer magnetohydrodynamical simulations with cosmic ray feedback to show that galaxies with frequent mergers have very bursty star formation histories that drives episodes of high intrinsic Lyα emission and facilitates the escape of Lyα photons along channels cleared of neutral gas. We conclude that the rapid buildup of stellar mass through mergers presents a compelling solution to the long-standing puzzle of the detection of Lyα emission deep in the epoch of reionization.

Disc settling and dynamical heating: histories of Milky Way-mass stellar discs across cosmic time in the FIRE simulations

ABSTRACT We study the kinematics of stars both at their formation and today within 14 Milky Way (MW)-mass galaxies from the FIRE-2 cosmological zoom-in simulations. We quantify the relative importance of cosmological disc settling and post-formation dynamical heating. We identify three eras: a Pre-Disc Era (typically ≳ 8 Gyr ago), when stars formed on dispersion-dominated orbits; an Early-Disc Era (≈8–4 Gyr ago), when stars started to form on rotation-dominated orbits but with high velocity dispersion, σform; and a Late-Disc Era (≲ 4 Gyr ago), when stars formed with low σform. σform increased with time during the Pre-Disc Era, peaking ≈8 Gyr ago, then decreased throughout the Early-Disc Era as the disc settled and remained low throughout the Late-Disc Era. By contrast, the dispersion measured today, σnow, increases monotonically with age because of stronger post-formation heating for Pre-Disc stars. Importantly, most of σnow was in place at formation, not added post-formation, for stars younger than ≈10 Gyr. We compare the evolution of the three velocity components: at all times, σR, form > σϕ, form > σZ, form. Post-formation heating primarily increased σR at ages ≲ 4 Gyr but acted nearly isotropically for older stars. The kinematics of young stars in FIRE-2 broadly agree with the range observed across the MW, M31, M33, and PHANGS-MUSE galaxies. The lookback time that the disc began to settle correlates with its dynamical state today: earlier-settling galaxies currently form colder discs. Including stellar cosmic-ray feedback does not significantly change disc rotational support at fixed stellar mass.

Exploring supermassive black hole physics and galaxy quenching across halo mass in FIRE cosmological zoom simulations

ABSTRACT Feedback from accreting supermassive black holes (SMBHs) is thought to be a primary driver of quenching in massive galaxies, but how to best implement SMBH physics into galaxy formation simulations remains ambiguous. As part of the Feedback in Realistic Environments (FIRE) project, we explore the effects of different modelling choices for SMBH accretion and feedback in a suite of ∼500 cosmological zoom-in simulations across a wide range of halo mass (1010–1013 M⊙). Within the suite, we vary the numerical schemes for BH accretion and feedback, accretion efficiency, and the strength of mechanical, radiative, and cosmic ray feedback independently. We then compare the outcomes to observed galaxy scaling relations. We find several models satisfying observational constraints for which the energetics in different feedback channels are physically plausible. Interestingly, cosmic rays accelerated by SMBHs play an important role in many plausible models. However, it is non-trivial to reproduce scaling relations across halo mass, and many model variations produce qualitatively incorrect results regardless of parameter choices. The growth of stellar and BH mass are closely related: for example, overmassive BHs tend to overquench galaxies. BH mass is most strongly affected by the choice of accretion efficiency in high-mass haloes, but by feedback efficiency in low-mass haloes. The amount of star formation suppression by SMBH feedback in low-mass haloes is determined primarily by the time-integrated feedback energy. For massive galaxies, the ‘responsiveness’ of a model (how quickly and powerfully the BH responds to gas available for accretion) is an additional important factor for quenching.

Radiation-magnetohydrodynamics simulations of cosmic ray feedback in disc galaxies

ABSTRACT Cosmic rays (CRs) are thought to play an important role in galaxy evolution. We study their effect when coupled to other important sources of feedback, namely supernovae (SNe) and stellar radiation, by including CR anisotropic diffusion and radiative losses but neglecting CR streaming. Using the ramses-rt code, we perform the first radiation-magnetohydrodynamics simulations of isolated disc galaxies with and without CRs. We study galaxies embedded in dark matter haloes of 1010, 1011, and $10^{12}\, \rm M_{\odot }$ with a maximum resolution of $9 \, \rm pc$. We find that CRs reduce the star formation (SF) rate in our two dwarf galaxies by a factor of 2, with decreasing efficiency with increasing galaxy mass. They increase significantly the outflow mass loading factor in all our galaxies and make the outflows colder. We study the impact of the CR diffusion coefficient, exploring values from κ = 1027 to $\rm 3\times 10^{29}\, cm^2\, s^{-1}$. With a lower κ, CRs remain confined for longer on small scales and are consequently efficient in suppressing SF, whereas a higher diffusion coefficient reduces the effect on SF and increases the generation of cold outflows. Finally, we compare CR feedback to a calibrated ’strong’ SN feedback model known to sufficiently regulate SF in high-redshift cosmological simulations. We find that CR feedback is not sufficiently strong to replace this strong SN feedback. As they tend to smooth out the ISM and fill it with denser gas, CRs also lower the escape fraction of Lyman continuum photons from galaxies.

Toward First-principles Characterization of Cosmic-Ray Transport Coefficients from Multiscale Kinetic Simulations

Abstract A major uncertainty in understanding the transport and feedback of cosmic rays (CRs) within and beyond our Galaxy lies in the unknown CR scattering rates, which are primarily determined by wave–particle interaction at microscopic gyroresonant scales. The source of the waves for the bulk CR population is believed to be self-driven by the CR streaming instability (CRSI), resulting from the streaming of CRs downward a CR pressure gradient. While a balance between driving by the CRSI and wave damping is expected to determine wave amplitudes and hence the CR scattering rates, the problem involves significant scale separation with substantial ambiguities based on quasi-linear theory (QLT). Here we propose a novel “streaming box” framework to study the CRSI with an imposed CR pressure gradient, enabling first-principles measurement of the CR scattering rates as a function of environmental parameters. By employing the magnetohydrodynamic particle-in-cell method with ion–neutral damping, we conduct a series of simulations with different resolutions and CR pressure gradients and precisely measure the resulting CR scattering rates in steady state. The measured rates show scalings consistent with QLT, but with a normalization smaller by a factor of several than typical estimates based on the single-fluid treatment of CRs. A momentum-by-momentum treatment provides better estimates when integrated over momentum but is also subject to substantial deviations, especially at small momentum. Our framework thus opens up the path toward providing comprehensive subgrid physics for macroscopic studies of CR transport and feedback in broad astrophysical contexts.

Morphology of supernova remnants and their halos

Context. Supernova remnants (SNRs) are known to accelerate particles to relativistic energies, on account of their nonthermal emission. The observational progress from radio to gamma-ray observations reveals more and more morphological features that need to be accounted for when modeling the emission from those objects. Aims. We use our time-dependent acceleration code RATPaC to study the formation of extended gamma-ray halos around supernova remnants and the morphological implications that arise when the high-energetic particles start to escape from the remnant. Methods. We performed spherically symmetric 1D simulations in which we simultaneously solved the transport equations for cosmic rays, magnetic turbulence, and the hydrodynamical flow of the thermal plasma in a volume large enough to keep all cosmic rays in the simulation. The transport equations for cosmic rays and magnetic turbulence were coupled via the cosmic-ray gradient and the spatial diffusion coefficient of the cosmic rays, while the cosmic-ray feedback onto the shock structure can be ignored. Our simulations span 25 000 yr, thus covering the free-expansion and the Sedov-Taylor phase of the remnant’s evolution. Results. We find a strong difference in the morphology of the gamma-ray emission from supernova remnants at later stages dependent on the emission process. At early times, both the inverse-Compton and the Pion-decay morphology are shell-like. However, as soon as the maximum-energy of the freshly accelerated particles starts to fall, the inverse-Compton morphology starts to become center-filled, whereas the Pion-decay morphology keeps its shell-like structure. Escaping high-energy electrons start to form an emission halo around the remnant at this time. There are good prospects for detecting this spectrally hard emission with the future Cerenkov Telescope Array, as there are for detecting variations in the gamma-ray spectral index across the interior of the remnant. Further, we find a constantly decreasing nonthermal X-ray flux that makes a detection of X-ray unlikely after the first few thousand years of the remnants’ evolution. The radio flux is increasing throughout the SNR’s lifetime and changes from a shell-like to a more center-filled morphology later on.

Cosmic ray feedback from supernovae in dwarf galaxies

The regulation of the baryonic content in dwarf galaxies is a long-standing problem. Supernovae (SNe) are supposed to play a key role in forming large-scale galactic winds by removing important amounts of gas from galaxies. SNe are efficient accelerators of non-thermal particles, so-called cosmic rays (CRs), which can substantially modify the dynamics of the gas and conditions to form large-scale galactic winds. We investigate how CR injection by SNe impacts the star formation and the formation of large-scale winds in dwarf galaxies, and whether it can produce galaxy star-formation rates (SFR) and wind properties closer to observations. We ran CR magneto-hydrodynamical simulations of dwarf galaxies at high resolution (9 pc) with the adaptive mesh refinement codeRAMSES. Those disc galaxies are embedded in isolated halos of mass of 1010and 1011 M⊙, and CRs are injected by SNe. We included CR isotropic and anisotropic diffusion with various diffusion coefficients, CR radiative losses, and CR streaming. The injection of CR energy into the interstellar medium smooths out the highest gas densities, which reduces the SFR by a factor of 2–3. Mass outflow rates are significantly greater with CR diffusion, by 2 orders of magnitudes for the higher diffusion coefficients. Without diffusion and streaming, CRs are inefficient at generating winds. CR streaming alone allows for the formation of winds but which are too weak to match observations. The formation of galactic winds strongly depends on the diffusion coefficient: for low coefficients, CR energy stays confined in high density regions where CR energy losses are highest, and higher coefficients, which allow for a more efficient leaking of CRs out of dense gas, produce stronger winds. CR diffusion leads to colder and denser winds than without CRs, and brings outflow rates and mass loading factors much closer to observations.

Cosmic-ray acceleration and escape from post-adiabatic supernova remnants

Context. Supernova remnants are known to accelerate cosmic rays on account of their nonthermal emission of radio waves, X-rays, and gamma rays. Although there are many models for the acceleration of cosmic rays in supernova remnants, the escape of cosmic rays from these sources has not yet been adequately studied. Aims. We aim to use our time-dependent acceleration code RATPaC to study the acceleration of cosmic rays and their escape in post-adiabatic supernova remnants and calculate the subsequent gamma-ray emission from inverse-Compton scattering and Pion decay. Methods. We performed spherically symmetric 1D simulations in which we simultaneously solved the transport equations for cosmic rays, magnetic turbulence, and the hydrodynamical flow of the thermal plasma in a volume large enough to keep all cosmic rays in the simulation. The transport equations for cosmic rays and magnetic turbulence were coupled via the cosmic-ray gradient and the spatial diffusion coefficient of the cosmic rays, while the cosmic-ray feedback onto the shock structure can be ignored. Our simulations span 100 000 years, thus covering the free-expansion, the Sedov–Taylor, and the beginning of the post-adiabatic phase of the remnant’s evolution. Results. At later stages of the evolution, cosmic rays over a wide range of energy can reside outside of the remnant, creating spectra that are softer than predicted by standard diffusive shock acceleration, and feature breaks in the 10 − 100 GeV-range. The total spectrum of cosmic rays released into the interstellar medium has a spectral index of s ≈ 2.4 above roughly 10 GeV which is close to that required by Galactic propagation models. We further find the gamma-ray luminosity to peak around an age of 4000 years for inverse-Compton-dominated high-energy emission. Remnants expanding in low-density media generally emit more inverse-Compton radiation, matching the fact that the brightest known supernova remnants – RCW86, Vela Jr., HESS J1731−347 and RX J1713.7−3946 – are all expanding in low density environments.

Impact of Cosmic-Ray Feedback on Accretion and Chemistry in Circumstellar Disks

Abstract We use the gas-grain chemistry code uclchem to explore the impact of cosmic-ray feedback on the chemistry of circumstellar disks. We model the attenuation and energy losses of the cosmic rays as they propagate outward from the star and also consider ionization due to stellar radiation and radionuclides. For accretion rates typical of young stars of M ⊙ yr−1, we show that cosmic rays accelerated by the stellar accretion shock produce an ionization rate at the disk surface ζ ≳ 10−15 s−1, at least an order of magnitude higher than the ionization rate associated with the Galactic cosmic-ray background. The incident cosmic-ray flux enhances the disk ionization at intermediate to high surface densities (Σ > 10 g cm−2), particularly within 10 au of the star. We find that the dominant ions are C+, S+, and Mg+ in the disk surface layers, while the ion dominates at surface densities above 1.0 g cm−2. We predict the radii and column densities at which the magnetorotational instability (MRI) is active in T Tauri disks and show that ionization by cosmic-ray feedback extends the MRI-active region toward the disk midplane. However, the MRI is only active at the midplane of a minimum-mass solar nebula disk if cosmic rays propagate diffusively (ζ ∝ r −1) away from the star. The relationship between accretion, which accelerates cosmic rays, the dense accretion columns, which attenuate cosmic rays, and the MRI, which facilitates accretion, creates a cosmic-ray feedback loop that mediates accretion and may produce variable luminosity.

Cosmic ray feedback in the FIRE simulations: constraining cosmic ray propagation with GeV γ-ray emission

ABSTRACT We present the implementation and the first results of cosmic ray (CR) feedback in the Feedback In Realistic Environments (FIRE) simulations. We investigate CR feedback in non-cosmological simulations of dwarf, sub-L⋆ starburst, and L⋆ galaxies with different propagation models, including advection, isotropic, and anisotropic diffusion, and streaming along field lines with different transport coefficients. We simulate CR diffusion and streaming simultaneously in galaxies with high resolution, using a two-moment method. We forward-model and compare to observations of γ-ray emission from nearby and starburst galaxies. We reproduce the γ-ray observations of dwarf and L⋆ galaxies with constant isotropic diffusion coefficient $\kappa \sim 3\times 10^{29}\, {\rm cm^{2}\, s^{-1}}$. Advection-only and streaming-only models produce order of magnitude too large γ-ray luminosities in dwarf and L⋆ galaxies. We show that in models that match the γ-ray observations, most CRs escape low-gas-density galaxies (e.g. dwarfs) before significant collisional losses, while starburst galaxies are CR proton calorimeters. While adiabatic losses can be significant, they occur only after CRs escape galaxies, so they are only of secondary importance for γ-ray emissivities. Models where CRs are ‘trapped’ in the star-forming disc have lower star formation efficiency, but these models are ruled out by γ-ray observations. For models with constant κ that match the γ-ray observations, CRs form extended haloes with scale heights of several kpc to several tens of kpc.

Evidence for Cosmic-Ray Escape in the Small Magellanic Cloud Using Fermi Gamma Rays

Abstract Galaxy formation simulations demonstrate that cosmic-ray (CR) feedback may be important in the launching of galactic-scale winds. CR protons dominate the bulk of the CR population, yet most observational constraints of CR feedback come from synchrotron emission of CR electrons. In this paper, we analyze 105 months of Fermi Gamma-ray Space Telescope observations of the Small Magellanic Cloud (SMC), with the aim of exploring CR feedback and transport in an external galaxy. We produce maps of the 2–300 GeV emission and detect statistically significant extended emission along the “Bar” and the “Wing,” where active star formation is occurring. Gamma-ray emission is not detected above 13 GeV, and we set stringent upper limits on the flux above this energy. We find the best fit to the gamma-ray spectrum is a single-component model with a power law of index and an exponential cutoff energy of GeV. We assess the relative contribution of pulsars and CRs to the emission, and we find that pulsars may produce up to 10 % of the flux above 100 MeV. Thus, we attribute most of the gamma-ray emission (based on its spectrum and morphology) to CR interactions with the interstellar medium. We show that the gamma-ray emissivity of the SMC is at least five times smaller than that of the Milky Way and that the SMC is far below the “calorimetric limit,” where all CR protons experience pion losses. We interpret these findings as evidence that CRs are escaping the SMC via advection and diffusion.

The Parker Instability with Cosmic-Ray Streaming

Abstract Recent studies have found that cosmic-ray transport plays an important role in feedback processes such as star formation and the launching of galactic winds. Although cosmic-ray buoyancy is widely held to be a destabilizing force in galactic disks, the effect of cosmic-ray transport on the stability of stratified systems has yet to be analyzed. We perform a stability analysis of a stratified layer for three different cosmic-ray transport models: decoupled (Classic Parker), coupled with γ c = 4/3 but not streaming (Modified Parker), and finally coupled with streaming at the Alfvén speed. When the compressibility of the cosmic rays is decreased the system becomes much more stable, but the addition of cosmic-ray streaming to the Parker instability severely destabilizes it. Through comparison of these three cases and analysis of the work contributions for the perturbed quantities of each system, we demonstrate that cosmic-ray heating of the gas is responsible for the destabilization of the system. We find that a 3D system is unstable over a larger range of wavelengths than the 2D system. Therefore, the Parker instability with cosmic-ray streaming may play an important role in cosmic-ray feedback.

Radiative transfer calculations of the diffuse ionized gas in disc galaxies with cosmic ray feedback

The large vertical scale heights of the diffuse ionised 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 (SILCC) 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 ionising sources to get an appropriate ionising 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.

Stellar feedback strongly alters the amplification and morphology of galactic magnetic fields

Abstract Using high-resolution magnetohydrodynamic simulations of idealized, non-cosmological galaxies, we investigate how cooling, star formation and stellar feedback affect galactic magnetic fields. We find that the amplification histories, saturation values and morphologies of the magnetic fields vary considerably depending on the baryonic physics employed, primarily because of differences in the gas density distribution. In particular, adiabatic runs and runs with a subgrid (effective equation of state) stellar feedback model yield lower saturation values and morphologies that exhibit greater large-scale order compared with runs that adopt explicit stellar feedback and runs with cooling and star formation but no feedback. The discrepancies mostly lie in gas denser than the galactic average, which requires cooling and explicit fragmentation to capture. Independent of the baryonic physics included, the magnetic field strength scales with gas density as B ∝ n2/3, suggesting isotropic flux freezing or equipartition between the magnetic and gravitational energies during the field amplification. We conclude that accurate treatments of cooling, star formation and stellar feedback are crucial for obtaining the correct magnetic field strength and morphology in dense gas, which, in turn, is essential for properly modelling other physical processes that depend on the magnetic field, such as cosmic ray feedback.

The basis for cosmic ray feedback: Written on the wind.

Star formation and supermassive black hole growth in galaxies appear to be self-limiting. The mechanisms for self-regulation are known as feedback. Cosmic rays, the relativistic particle component of interstellar and intergalactic plasma, are among the agents of feedback. Because cosmic rays are virtually collisionless in the plasma environments of interest, their interaction with the ambient medium is primarily mediated by large scale magnetic fields and kinetic scale plasma waves. Because kinetic scales are much smaller than global scales, this interaction is most conveniently described by fluid models. In this paper, I discuss the kinetic theory and the classical theory of cosmic ray hydrodynamics (CCRH) which follows from assuming cosmic rays interact only with self-excited waves. I generalize CCRH to generalized cosmic ray hydrodynamics, which accommodates interactions with extrinsic turbulence, present examples of cosmic ray feedback, and assess where progress is needed.

Transport of magnetic turbulence in supernova remnants

Context. Supernova remnants are known as sources of galactic cosmic rays for their non-thermal emission of radio waves, X-rays, and gamma-rays. However, the observed soft broken power-law spectra are hard to reproduce within standard acceleration theory based on the assumption of Bohm diffusion and steady-state calculations. Aims. We point out that a time-dependent treatment of the acceleration process together with a self-consistent treatment of the scattering turbulence amplification is necessary. Methods. We numerically solve the coupled system of transport equations for cosmic rays and isotropic Alfvenic turbulence. The equations are coupled through the growth rate of turbulence determined by the cosmic-ray gradient and the spatial diffusion coefficient of cosmic rays determined by the energy density of the turbulence. The system is solved on a co-moving expanding grid extending upstream for dozens of shock radii, allowing for the self-consistent study of cosmic-ray diffusion in the vicinity of their acceleration site. The transport equation for cosmic rays is solved in a test-particle approach. Results. We demonstrate that the system is typically not in a steady state. In fact, even after several thousand years of evolution, no equilibrium situation is reached. The resulting time-dependent particle spectra strongly differ from those derived assuming a steady state and Bohm diffusion. Our results indicate that proper accounting for the evolution of the scattering turbulence and hence the particle diffusion coefficient is crucial for the formation of the observed soft spectra. In any case, the need to continuously develop magnetic turbulence upstream of the shock introduces non-linearity in addition to that imposed by cosmic-ray feedback.

Cosmological simulations of dwarf galaxies with cosmic ray feedback

We perform zoom-in cosmological simulations of a suite of dwarf galaxies, examining the impact of cosmic rays (CRs) generated by supernovae, including the effect of diffusion. We first look at the effect of varying the uncertain CR parameters by repeatedly simulating a single galaxy. Then we fix the comic ray model and simulate five dwarf systems with virial masses range from 8 to 30 × 1010 M⊙. We find that including CR feedback (with diffusion) consistently leads to disc-dominated systems with relatively flat rotation curves and constant star formation rates. In contrast, our purely thermal feedback case results in a hot stellar system and bursty star formation. The CR simulations very well match the observed baryonic Tully–Fisher relation, but have a lower gas fraction than in real systems. We also find that the dark matter cores of the CR feedback galaxies are cuspy, while the purely thermal feedback case results in a substantial core.

The first stars: formation under cosmic ray feedback

We explore the impact of a cosmic ray (CR) background generated by supernova explosions from the first stars on star-forming metal-free gas in a minihalo at $z\sim25$. Starting from cosmological initial conditions, we use the smoothed particle hydrodynamics code GADGET-2 to follow gas collapsing under the influence of a CR background up to densities of $n=10^{12}\,{\rm cm}^{-3}$, at which point we form sink particles. Using a suite of simulations with two sets of initial conditions and employing a range of CR background models, we follow each simulation for $5000\,$yr after the first sink forms. CRs both heat and ionise the gas, boosting ${\rm H}_2$ formation. Additional ${\rm H}_2$ enhances the cooling efficiency of the gas, allowing it to fulfil the Rees-Ostriker criterion sooner and expediting the collapse, such that each simulation reaches high densities at a different epoch. As it exits the loitering phase, the thermodynamic path of the collapsing gas converges to that seen in the absence of any CR background. By the time the gas approaches sink formation densities, the thermodynamic state of the gas is thus remarkably similar across all simulations. This leads to a robust characteristic mass that is largely independent of the CR background, of order $\sim$ a few $\times10\,{\rm M}_{\odot}$ even as the CR background strength varies by five orders of magnitude.