Comparing subgrid models for cosmic ray diffusion in a magnetized isolated galaxy simulation

TL;DR

This work develops two physically motivated subgrid diffusion models for cosmic ray transport—one microscopic (pitch-angle-averaged) and one macroscopic (turbulence-driven streaming)—plus a superdiffusive extension, and applies them in post-processing to a RAMSES-simulated Milky Way–like galaxy. The diffusion coefficients are computed from local plasma properties, notably density $\rho$, ionization $\chi$, and Alfvén Mach number $\mathcal{M}_A$, and crucially depend on the magnetic-field tilt via $\kappa_z = \kappa_\parallel \sin^2\theta + \kappa_\perp \cos^2\theta$. Results show diffusion coefficients spanning $10^{26}$–$10^{31}$ cm$^2$ s$^{-1}$ and midplane CR energy densities from ~0.7 to ~70 eV cm$^{-3}$, with gamma-ray outputs that vary across models and ISM phases. These findings highlight the strong influence of ISM multiphase structure and magnetic topology on CR transport and the importance of incorporating self-consistent, locally adaptive diffusion in galaxy evolution models for realistic CR feedback and high-energy emission predictions.

Abstract

Galactic cosmic rays (CRs) play a crucial role in galaxy formation and evolution by altering gas dynamics and chemistry across multiple scales. Typical numerical simulations of CR transport assume a constant diffusion coefficient for the entire galaxy, despite both numerical and theoretical studies showing that it can change by orders of magnitude depending on the phase of the interstellar medium. Only a few simulations exist that self-consistently calculate CR transport with diffusion, streaming, and advection by the background gas. In this study we explore three subgrid models for CR diffusion, based on popular theories of CR transport. We post-process an isolated, star-forming MHD galactic disk simulated using the RAMSES code. The resulting diffusion coefficients depend solely on the subgrid turbulent kinetic energy and the MHD state variables of the plasma. We use these models to calculate coefficients for vertical transport. We find that they depend critically on the local magnetic field tilt angle. Across models, our resulting diffusion coefficients range from $10^{26}~\rm cm^2s^{-1}$ to $10^{31}~\rm cm^2s^{-1}$, and yield CR energy densities at the midplane from $1$ to $100 ~\rm eV cm^{-3}$, suggesting varied degrees of backreaction on their environment. Using simple approximations, we show that the gamma ray luminosity of the galaxy depends primarily on the gas surface density and the turbulent confinement of CRs by the galactic corona.

Figures (12)

• Figure 1: Spatial maps of physical properties in and around our galactic disk. The galaxy is an isolated MHD disk simulated using RAMSES. In each row the left panel shows a face-on view, the right an edge-on view, of the galaxy, coloured by a given quantity shown on each colorbar. From top to bottom we have gas surface density $\Sigma_{\rm{gas}}$, temperature $T$, ionization fraction $\chi$, one-dimensional turbulent velocity dispersion $\sigma_{\rm{1D}}$, magnetic field magnitude $B$, and Alfvén mach number $\mathcal{M}_{A}$. In general the disk is dominated in mass by cold and warm, neutral, dense gas compared to the warm and hot ionized gas that makes up the circumgalactic medium.
• Figure 2: Continuation of Figure 1.
• Figure 3: Spatial distributions of the diffusion coefficient for our macroscopic model. The three rows show, from top to bottom respectively, the diffusion coefficient parallel to the magnetic field, the ratio of the perpendicular to parallel diffusion coefficients, and the diffusion coefficient in the $z$-direction (out of the plane of the disk). The latter is derived in Sect. \ref{['sec:kappaz']}. The highest values of $\kappa_\parallel$ and $\kappa_z$ can be found in the disk, especially near the galactic center, and decrease with radius and with height $z$. The CR diffusion is the most anisotropic ($\kappa_\perp/\kappa_\parallel \ll 1$) in this plane of the disk as well, and quickly becomes isotropic everywhere outside of the disk.
• Figure 4: Density--temperature histograms binned in log-space. The histograms are coloured by the average value of a given parameter in that $\log\rho$--$\log T$ bin. The top two panels are $\mathcal{M}_{A}$ and $\chi$, and the middle left shows $\sigma_{\rm{1D}}$. All of the gas above $\log T\sim 20,000$ K is completely ionized, with a transition zone of partially ionized (the band of teal around $\log T\sim 10^4$), and then predominantly neutral at lower temperatures, with higher density being associated with lower neutral gas. Behind this histogram we have coloured the temperature regimes for the five phases we define in Table \ref{['tab:phases']}. All bins above the red dashed line has $\chi>0.5$; this boundary is also marked by a red line on the $\chi$ colorbar. The middle right panel shows a measure of the magnetic field orientation $b_z^2$. The bottom panels are slightly different, instead showing $\log\rho$ on the x-axis but $\log \mathcal{M}_{A}$ and $\log v_{A}$ on the y-axis instead. This rows's histograms are coloured by the total mass contained in the bin.
• Figure 5: Average values of various parameters in the galactic disk as a function of radius. The top row shows the RMS average of magnetic field $B$ and ionization fraction $\chi$. The left lower panel shows the RMS average of the turbulent velocity dispersion $\sigma_{\rm{1D}}$. Each of the three panels shows a volume-weighted and mass-weighted average, with the former shown as a solid teal line and the latter as a dashed dark blue line. We also show a weighted confidence interval for the three panels for each weighting, calculated as discussed in Sect. \ref{['sec:radial']}. Each weighting is associated with either a physically-motivated integral, or an average that highlights a particular phase of the ISM (see Sections \ref{['sec:avg']} and \ref{['sec:ingredients']}). The bottom right panel combines the physically-motivated averages to calculate an average Alfvén mach number $\mathcal{M}_{A}$. $B$ and $\sigma_{\rm{1D}}$ both drop with radius, but the magnetic field has a higher mass-weighted average in contrast to the velocity dispersion having a higher volume-weighted average. The ionization fraction $\chi$ conversely increases with radius for the mass-weighted average and remains approximately constant and around $\chi\sim 1$ for the volume-weighted average. The Alfvén mach number also drops with radius from the center to the disk's edge by about an order of magnitude.