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    Cosmic rays (CRs) with energies ≪ TeV comprise a significant component of the interstellar medium (ISM). Major uncertainties in CR behaviour on observable scales (much larger than CR gyroradii) stem from how magnetic fluctuations scatter CRs in pitch angle. Traditional first-principles models, which assume these magnetic fluctuations are weak and uniformly scatter CRs in a homogeneous ISM, struggle to reproduce basic observables such as the dependence of CR residence times and scattering rates on rigidity. We therefore explore a new category of ‘patchy’ CR scattering models, wherein CRs are pre-dominantly scattered by intermittent strong scattering structures with small volume-filling factors. These models produce the observed rigidity dependence with a simple size distribution constraint, such that larger scattering structures are rarer but can scatter a wider range of CR energies. To reproduce the empirically inferred CR scattering rates, the mean free path between scattering structures must be $\ell _{\rm mfp}\sim 10\, {\rm pc}$ at GeV energies. We derive constraints on the sizes, internal properties, mass/volume-filling factors, and the number density any such structures would need to be both physically and observationally consistent. We consider a range of candidate structures, both large scale (e.g. H ii regions) and small scale (e.g. intermittent turbulent structures, perhaps even associated with radio plasma scattering) and show that while many macroscopic candidates can be immediately ruled out as the primary CR scattering sites, many smaller structures remain viable and merit further theoretical study. We discuss future observational constraints that could test these models.

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    Cosmic rays (CRs) may drive outflows and alter the phase structure of the circumgalactic medium, with potentially important implications on galaxy formation. However, these effects ultimately depend on the dominant mode of transport of CRs within and around galaxies, which remains highly uncertain. To explore potential observable constraints on CR transport, we investigate a set of cosmological fire-2 CR-magnetohydrodynamic simulations of L* galaxies which evolve CRs with transport models motivated by self-confinement (SC) and extrinsic turbulence (ET) paradigms. To first order, the synchrotron properties diverge between SC and ET models due to a CR physics-driven hysteresis. SC models show a higher tendency to undergo ‘ejective’ feedback events due to a runaway buildup of CR pressure in dense gas due to the behaviour of SC transport scalings at extremal CR energy densities. The corresponding CR wind-driven hysteresis results in brighter, smoother, and more extended synchrotron emission in SC runs relative to ET and constant diffusion runs. The differences in synchrotron arise from different morphology, interstellar medium gas, and B properties, potentially ruling out SC as the dominant mode of CR transport in typical star-forming L* galaxies, and indicating the prospect for non-thermal radio continuum observations to constrain CR transport physics.

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    Synchrotron emission is one of few observable tracers of galactic magnetic fields (B) and cosmic rays (CRs). Much of our understanding of B in galaxies comes from utilizing synchrotron observations in conjunction with several simplifying assumptions of equipartition models, however, it remains unclear how well these assumptions hold, and what B these estimates physically represent. Using Feedback in Realistic Environments project simulations which self-consistently evolve CR proton, electron, and positron spectra from MeV to TeV energies, we present the first synthetic synchrotron emission predictions from simulated L* galaxies with ‘live’ spectrally resolved CR-magnetohydrodynamic. We find that synchrotron emission can be dominated by relatively cool and dense gas, resulting in equipartition estimates of B with fiducial assumptions underestimating the ‘true’ B in the gas that contributes the most emission by factors of 2–3 due to small volume-filling factors. Motivated by our results, we present an analytical framework that expands upon equipartition models for estimating B in a multiphase medium. Comparing our spectrally resolved synchrotron predictions to simpler spectral assumptions used in galaxy simulations with CRs, we find that spectral evolution can be crucial for accurate synchrotron calculations towards galactic centres, where loss terms are large.

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    Many recent numerical studies have argued that cosmic rays (CRs) from supernovae (SNe) or active galactic nuclei (AGNs) could play a crucial role in galaxy formation, in particular by establishing a CR-pressure-dominated circumgalactic medium (CGM). But explicit CR-magnetohydrodynamics (CR-MHD) remains computationally expensive, and it is not clear whether those results can be applied to simulations that do not explicitly treat magnetic fields or resolved interstellar medium phase structure. We therefore present an intentionally extremely simplified ‘sub-grid’ model for CRs, which attempts to capture the key qualitative behaviors of greatest interest for those interested in simulations or semi-analytical models including some approximate CR effects on galactic (≳ kpc) scales, while imposing negligible computational overhead. The model is numerically akin to some recently developed sub-grid models for radiative feedback, and allows for a simple constant parametrization of the CR diffusivity and/or streaming speed; it allows for an arbitrary distribution of sources (proportional to black hole accretion rates or star–particle SNe rates or gas/galaxy star formation rates), and interpolates between the limits where CRs escape the galaxies with negligible losses and those where CRs lose most of their energy catastrophically before escape (relevant in e.g. starburst galaxies). The numerical equations are solved trivially alongside gravity in most codes. We compare this to explicit CR-MHD simulations and discuss where the (many) sub-grid approximations break down, and what drives the major sources of uncertainty.

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    Recent theoretical studies predict that the circumgalactic medium (CGM) around low-redshift, ∼L* galaxies could have substantial non-thermal pressure support in the form of cosmic rays. However, these predictions are sensitive to the specific model of cosmic ray transport employed, which is theoretically and observationally underconstrained. In this work, we propose a novel observational constraint for calculating the lower limit of the radially averaged, effective cosmic ray transport rate, ${\kappa _{\rm eff}^{\rm min}}$. Under a wide range of assumptions (so long as cosmic rays do not lose a significant fraction of their energy in the galactic disc, regardless of whether the cosmic ray pressure is important or not in the CGM), we demonstrate a well-defined relationship between ${\kappa _{\rm eff}^{\rm min}}$ and three observable galaxy properties: the total hydrogen column density, the average star formation rate, and the gas circular velocity. We use a suite of Feedback in Realistic Environments 2 galaxy simulations with a variety of cosmic ray transport physics to demonstrate that our analytical model of ${\kappa _{\rm eff}^{\rm min}}$ is a robust lower limit of the true cosmic ray transport rate. We then apply our new model to calculate ${\kappa _{\rm eff}^{\rm min}}$ for galaxies in the COS-Halos sample, and confirm this already reveals strong evidence for an effective transport rate that rises rapidly away from the interstellar medium to values ${\kappa _{\rm eff}^{\rm min}}\gtrsim 10^{30\!-\!31}\, {\rm cm}^2\, {\rm s}^{-1}$ (corresponding to anisotropic streaming velocities of $v^{\rm stream}_{\rm eff} \gtrsim 1000\, {\rm km}\, {\rm s}^{-1}$) in the diffuse CGM, at impact parameters larger than 50–100 kpc. We discuss how future observations can provide qualitatively new constraints in our understanding of cosmic rays in the CGM and intergalactic medium.

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    Models for cosmic ray (CR) dynamics fundamentally depend on the rate of CR scattering from magnetic fluctuations. In the ISM, for CRs with energies ∼MeV-TeV, these fluctuations are usually attributed either to ‘extrinsic turbulence’ (ET) – a cascade from larger scales – or ‘self-confinement’ (SC) – self-generated fluctuations from CR streaming. Using simple analytic arguments and detailed ‘live’ numerical CR transport calculations in galaxy simulations, we show that both of these, in standard form, cannot explain even basic qualitative features of observed CR spectra. For ET, any spectrum that obeys critical balance or features realistic anisotropy, or any spectrum that accounts for finite damping below the dissipation scale, predicts qualitatively incorrect spectral shapes and scalings of B/C and other species. Even if somehow one ignored both anisotropy and damping, observationally required scattering rates disagree with ET predictions by orders of magnitude. For SC, the dependence of driving on CR energy density means that it is nearly impossible to recover observed CR spectral shapes and scalings, and again there is an orders-of-magnitude normalization problem. But more severely, SC solutions with super-Alfvénic streaming are unstable. In live simulations, they revert to either arbitrarily rapid CR escape with zero secondary production, or to bottleneck solutions with far-too-strong CR confinement and secondary production. Resolving these fundamental issues without discarding basic plasma processes requires invoking different drivers for scattering fluctuations. These must act on a broad range of scales with a power spectrum obeying several specific (but plausible) constraints.

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  7. ABSTRACT We derive a consistent set of moment equations for cosmic ray (CR)-magnetohydrodynamics, assuming a gyrotropic distribution function (DF). Unlike previous efforts, we derive a closure, akin to the M1 closure in radiation hydrodynamics (RHD), that is valid in both the nearly isotropic DF and/or strong-scattering regimes, and the arbitrarily anisotropic DF or free-streaming regimes, as well as allowing for anisotropic scattering and transport/magnetic field structure. We present the appropriate two-moment closure and equations for various choices of evolved variables, including the CR phase space DF f, number density n, total energy e, kinetic energy ϵ, and their fluxes or higher moments, and the appropriate coupling terms to the gas. We show that this naturally includes and generalizes a variety of terms including convection/fluid motion, anisotropic CR pressure, streaming, diffusion, gyro-resonant/streaming losses, and re-acceleration. We discuss how this extends previous treatments of CR transport including diffusion and moment methods and popular forms of the Fokker–Planck equation, as well as how this differs from the analogous M1-RHD equations. We also present two different methods for incorporating a reduced speed of light (RSOL) to reduce time-step limitations: In both, we carefully address where the RSOL (versus true c) must appear for the correct behaviour to be recovered in all interesting limits, and show how current implementations of CRs with an RSOL neglect some additional terms. 
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    We present the first simulations evolving resolved spectra of cosmic rays (CRs) from MeV–TeV energies (including electrons, positrons, (anti)protons, and heavier nuclei), in live kinetic-magnetohydrodynamics galaxy simulations with star formation and feedback. We utilize new numerical methods including terms often neglected in historical models, comparing Milky Way analogues with phenomenological scattering coefficients ν to Solar-neighbourhood [Local interstellar medium (LISM)] observations (spectra, B/C, e+/e−, $\mathrm{\bar{p}}/\mathrm{p}$, 10Be/9Be, ionization, and γ-rays). We show it is possible to reproduce observations with simple single-power-law injection and scattering coefficients (scaling with rigidity R), similar to previous (non-dynamical) calculations. We also find: (1) The circumgalactic medium in realistic galaxies necessarily imposes an $\sim 10\,$ kpc CR scattering halo, influencing the required ν(R). (2) Increasing the normalization of ν(R) re-normalizes CR secondary spectra but also changes primary spectral slopes, owing to source distribution and loss effects. (3) Diffusive/turbulent reacceleration is unimportant and generally sub-dominant to gyroresonant/streaming losses, which are sub-dominant to adiabatic/convective terms dominated by $\sim 0.1-1\,$ kpc turbulent/fountain motions. (4) CR spectra vary considerably across galaxies; certain features can arise from local structure rather than transport physics. (5) Systematic variation in CR ionization rates between LISM and molecular clouds (or Galactic position) arises naturally without invoking alternative sources. (6) Abundances of CNO nuclei require most CR acceleration occurs around when reverse shocks form in SNe, not in OB wind bubbles or later Sedov–Taylor stages of SNe remnants.

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    The physics of magnetic fields (B) and cosmic rays (CRs) have recently been included in simulations of galaxy formation. However, significant uncertainties remain in how these components affect galaxy evolution. To understand their common observational tracers, we analyse the magnetic fields in a set of high-resolution, magnetohydrodynamic, cosmological simulations of Milky-Way-like galaxies from the FIRE-2 project. We compare mock observables of magnetic field tracers for simulations with and without CRs to observations of Zeeman splitting and rotation/dispersion measures. We find reasonable agreement between simulations and observations in both the neutral and the ionized interstellar medium (ISM). We find that the simulated galaxies with CRs show weaker ISM |B| fields on average compared to their magnetic-field-only counterparts. This is a manifestation of the effects of CRs in the diffuse, low density inner circumgalactic medium (CGM). We find that equipartition between magnetic and cosmic ray energy densities may be valid at large (> 1 kpc) scales for typical ISM densities of Milky-Way-like galaxies, but not in their haloes. Within the ISM, the magnetic fields in our simulated galaxies follow a power-law scaling with gas density. The scaling extends down to neutral hydrogen number densities < 300 cm−3, in contrast to observationally derived models, but consistent with the observational measurements. Finally, we generate synthetic rotation measure (RM) profiles for projections of the simulated galaxies and compare to observational constraints in the CGM. While consistent with upper limits, improved data are needed to detect the predicted CGM RMs at 10–200 kpc and better constrain theoretical predictions.

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  10. Abstract

    We use hydrodynamical simulations of two Milky Way–mass galaxies to demonstrate the impact of cosmic-ray pressure on the kinematics of cool and warm circumgalactic gas. Consistent with previous studies, we find that cosmic-ray pressure can dominate over thermal pressure in the inner 50 kpc of the circumgalactic medium (CGM), creating an overall cooler CGM than that of similar galaxy simulations run without cosmic rays. We generate synthetic sight lines of the simulated galaxies’ CGM and use Voigt profile-fitting methods to extract ion column densities, Doppler-bparameters, and velocity centroids of individual absorbers. We directly compare these synthetic spectral line fits with HST/COS CGM absorption-line data analyses, which tend to show that metallic species with a wide range of ionization potential energies are often kinematically aligned. Compared to the Milky Way simulation run without cosmic rays, the presence of cosmic-ray pressure in the inner CGM creates narrower Oviabsorption features and broader Siiiiabsorption features, a quality that is more consistent with observational data. Additionally, because the cool gas is buoyant due to nonthermal cosmic-ray pressure support, the velocity centroids of both cool and warm gas tend to align in the simulated Milky Way with feedback from cosmic rays. Our study demonstrates that detailed, direct comparisons between simulations and observations, focused on gas kinematics, have the potential to reveal the dominant physical mechanisms that shape the CGM.

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