A Simple Sub-Grid Model For Cosmic Ray Effects on Galactic Scales

Many recent numerical studies have argued that cosmic rays (CRs) from supernovae (SNe) or active galactic nuclei (AGN) could play a crucial role in galaxy formation, in particular by establishing a CR-pressure dominated circum-galactic medium (CGM). But explicit CR-magneto-hydrodynamics (CR-MHD) remains computationally expensive, and it is not clear whether it even makes physical sense in simulations that do not explicitly treat magnetic fields or resolved ISM 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-analytic 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 parameterization 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.Comment: 12 pages, 4 figures. Submitted to MNRAS. Comments welcom

Standard Self-Confinement and Extrinsic Turbulence Models for Cosmic Ray Transport are Fundamentally Incompatible with Observations

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-Alfvenic 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.Comment: 36 pages, 7 figures. Updated to match published version, added section discussing 'meso-scale' phenomenolog

Galactic Cosmic-ray Scattering due to Intermittent Structures

Cosmic rays (CRs) with energies $\ll$ TeV comprise a significant component of the interstellar medium (ISM). Major uncertainties in CR behavior 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 predominantly 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 $\ell_{\rm mfp} \sim 10$ 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.Comment: 9 pages, 3 figures, submitted to MNRA

Constraining Cosmic-ray Transport with Observations of the Circumgalactic Medium

Recent theoretical studies predict that the circumgalactic medium (CGM) around low-redshift, $\sim L_*$ galaxies could have substantial nonthermal 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, $\kappa_{\rm min}^{\rm eff}$. Under a wide range of assumptions (so long as cosmic rays do not lose a significant fraction of their energy in the galactic disk, regardless of whether the cosmic-ray pressure is important or not in the CGM), we demonstrate a well-defined relationship between $\kappa_{\rm min}^{\rm eff}$ 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 FIRE-2 galaxy simulations with a variety of cosmic-ray transport physics to demonstrate that our analytic model of $\kappa_{\rm min}^{\rm eff}$ is a robust lower limit of the true cosmic-ray transport rate. We then apply our new model to calculate $\kappa_{\rm min}^{\rm eff}$ for galaxies in the COS-Halos sample, and confirm this already reveals strong evidence for an effective transport rate which rises rapidly away from the interstellar medium to values $\kappa_{\rm min}^{\rm eff}\gtrsim 10^{30-31}\,{\rm cm}^2\,{\rm s}^{-1}$ (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.Comment: 9 pages, 2 figures, accepted to MNRA

NIHAO project II: Halo shape, phase-space density and velocity distribution of dark matter in galaxy formation simulations

We use the NIHAO (Numerical Investigation of Hundred Astrophysical Objects) cosmological simulations to study the effects of galaxy formation on key properties of dark matter (DM) haloes. NIHAO consists of $\simeq 90$ high-resolution SPH simulations that include (metal-line) cooling, star formation, and feedback from massive stars and SuperNovae, and cover a wide stellar and halo mass range: $10^6 < M_* / M_{\odot} < 10^{11}$ ( $10^{9.5} < M_{\rm halo} / M_{\odot} < 10^{12.5}$). When compared to DM-only simulations, the NIHAO haloes have similar shapes at the virial radius, R_{\rm vir}, but are substantially rounder inside $\simeq 0.1R_{\rm vir}$. In NIHAO simulations $c/a$ increases with halo mass and integrated star formation efficiency, reaching $\sim 0.8$ at the Milky Way mass (compared to 0.5 in DM-only), providing a plausible solution to the long-standing conflict between observations and DM-only simulations. The radial profile of the phase-space $Q$ parameter ($\rho/\sigma^3$) is best fit with a single power law in DM-only simulations, but shows a flattening within $\simeq 0.1R_{\rm vir}$ for NIHAO for total masses $M>10^{11} M_{\odot}$. Finally, the global velocity distribution of DM is similar in both DM-only and NIHAO simulations, but in the solar neighborhood, NIHAO galaxies deviate substantially from Maxwellian. The distribution is more symmetric, roughly Gaussian, with a peak that shifts to higher velocities for Milky Way mass haloes. We provide the distribution parameters which can be used for predictions for direct DM detection experiments. Our results underline the ability of the galaxy formation processes to modify the properties of dark matter haloes.Comment: 19 pages, 17 figures, analysis strongly improved, main conclusions unchanged, accepted for publication in MNRA

Impact of Cosmic Rays on Thermal Instability in the Circumgalactic Medium

Large reservoirs of cold (~10⁴ K) gas exist out to and beyond the virial radius in the circumgalactic medium (CGM) of all types of galaxies. Photoionization modeling suggests that cold CGM gas has significantly lower densities than expected by theoretical predictions based on thermal pressure equilibrium with hot CGM gas. In this work, we investigate the impact of cosmic-ray physics on the formation of cold gas via thermal instability. We use idealized three-dimensional magnetohydrodynamic simulations to follow the evolution of thermally unstable gas in a gravitationally stratified medium. We find that cosmic-ray pressure lowers the density and increases the size of cold gas clouds formed through thermal instability. We develop a simple model for how the cold cloud sizes and the relative densities of cold and hot gas depend on cosmic-ray pressure. Cosmic-ray pressure can help counteract gravity to keep cold gas in the CGM for longer, thereby increasing the predicted cold mass fraction and decreasing the predicted cold gas inflow rates. Efficient cosmic-ray transport, by streaming or diffusion, redistributes cosmic-ray pressure from the cold gas to the background medium, resulting in cold gas properties that are in between those predicted by simulations with inefficient transport and simulations without cosmic rays. We show that cosmic rays can significantly reduce galactic accretion rates and resolve the tension between theoretical models and observational constraints on the properties of cold CGM gas

Synchrotron Signatures of Cosmic Ray Transport Physics in Galaxies

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-MHD simulations of L$_{\ast}$ 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 behavior 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, ISM gas and \textbf{B} properties, potentially ruling out SC as the dominant mode of CR transport in typical star-forming L$_{\ast}$ galaxies, and indicating the potential for non-thermal radio continuum observations to constrain CR transport physics.Comment: 5 pages, 3 figures. Accepted versio