The Impact of Cosmic Ray Transport on the $γ$-Ray Luminosity of Diffuse Gas

TL;DR

This work addresses how cosmic-ray transport influences γ-ray luminosity from diffuse, multiphase gas in environments like the CGM and ICM. Using Athena++ with a two-moment CR transport framework, the authors demonstrate that fast transport (diffusion or streaming) decouples CRs from dense gas, reducing $L_\gamma$ by about two orders of magnitude, while slow transport enhances CR energization via turbulent and cloud-driven reacceleration, increasing emissivity. A key finding is that reacceleration by condensing cold clouds can dominate CR energy growth, and although the correlation between CRs and dense gas, quantified by $\mathcal{C}$, affects $L_\gamma$, it is secondary to reacceleration in determining the luminosity when transport is slow. The results imply that to remain consistent with null detections of diffuse γ-ray emission, CR transport in the CGM/ICM must be fast or streaming-dominated, and they highlight that γ-ray measurements primarily probe CR energy density in dense gas rather than the diffuse component. Overall, the study provides a framework to interpret γ-ray limits in terms of CR transport, reacceleration processes, and the $E_c$–$n$ phase-space distribution in turbulent multiphase media.

Abstract

Observations of $γ$-rays from diffuse gas provide the opportunity to study the distribution of high energy particles in different astrophysical environments. In the circumgalactic medium (CGM) and the intracluster medium (ICM), it is expected that relativistic cosmic rays collide with thermal particles and produce $γ$-rays through pion decay. The $γ$-ray luminosity of a plasma depends on where cosmic rays are: if they are in denser gas, they produce more $γ$-rays. In this work, we study how different cosmic-ray transport mechanisms impact the $γ$-ray luminosity of a turbulent, multiphase medium formed from an initially diffuse medium. Two quantities set the luminosity: the average cosmic-ray energy density and the correlation of cosmic-ray energy and gas density. Overall, cosmic rays must escape cold dense regions in order to produce less $γ$-ray emission and be consistent with observations. Our simulations with fast transport mechanisms (either diffusion or streaming) are degenerate: they each produce a lower $γ$-ray luminosity than slow transport simulations by two orders of magnitude. This result means that fast transport (particularly in dense clumps) is necessary for simulations to agree with the dearth of observations of $γ$-ray emission from diffuse gas like the CGM and ICM. We also show the significant difference in luminosity is the result of cosmic-ray reacceleration. This reacceleration is different from the turbulent reacceleration described by Ptuskin (1988). Instead, condensing, cold clouds drive a significant increase in the average cosmic-ray energy and, as a result, the $γ$-ray luminosity.

Figures (13)

• Figure 1: Contours of the critical outer length scale $L_\mathrm{crit}$, where cosmic-ray reacceleration by long-wavelength turbulence is optimal. Green contours show the dependence of this length scale on the cosmic ray diffusion coefficient $\kappa$ and the phase velocity of the turbulence $v$. The solid black line shows the outer scale of turbulent driving used in this work $(24\mathrm{kpc})$, and the dotted black line shows the sound speed of the initial homogeneous medium. The dashed lines correspond to each of the diffusion cases we examine (a different hue of red for each diffusion coefficient we examine). The smallest diffusion coefficient we use, $10^{29}\, \mathrm{cm}^{2}\mathrm{s}^{-1}$, is at the optimal value for our simulation setup.
• Figure 2: $\gamma$-ray emissivity as a function of cosmic-ray energy density $E_c$ and plasma density $n$. The emissivity is proportional to the product of these quantities. The transport of cosmic rays determines the polytropic relationship between $E_c$ and $n$. Advective transport, when cosmic rays are locked to the gas, leads to a $n^{4/3}$ dependence, illustrated with a solid gray line. More diffusive, decoupled cosmic ray transport leads to a $n^{0}$ dependence which is shown as a dashed black line. Streaming along magnetic flux tubes would produce a $n^{4/3}$ dependence. As gas compresses and density increases, different cosmic-ray transport mechanisms produce significantly different $\gamma$-ray emissivity. Specifically, more advective (slower) transport leads to more $\gamma$-ray production.
• Figure 3: Evolution of $\gamma$-ray luminosity over time for each simulation. Left side shows the evolution of the logarithm of $L_\gamma$ relative to the initial state. Right side shows a zoomed in, linear scale version to highlight the differences between the various fast transport cases. While slow transport (lighter red lines) leads to a nearly $100$ times larger $L_\gamma$ (left plot), there are order unity discrepancies between the different fast transport results (right plot).
• Figure 4: Line-of-sight averaged gas density and cosmic-ray energy density adjacent to integrated $\gamma$-ray luminosity for each simulation. As diffusion coefficient increases, cosmic rays de-correlate from the dense gas and the diffuse $\gamma$-ray luminosity decreases. Note that the cosmic-ray energy density contours are normalized by the total cosmic-ray energy in the simulation to account for the effects of reacceleration, which cause the total luminosity in the 1e29 run to be 100 times larger than the fast transport runs (see Figure \ref{['fig:Lgamma']}). For the streaming runs, the $\gamma$-ray luminosity is low, but the cosmic rays are even more de-correlated from dense gas when the effects of ion-neutral damping are included.
• Figure 5: Evolution of total kinetic energy (upper left), total magnetic energy (middle left), total cosmic-ray energy (lower left), total thermal energy (middle right), and total energy change (lower right) for each simulation. The simulations have similar kinetic and magnetic energy evolution. The cosmic-ray energy evolution differs across the simulations because of the different cosmic ray transport in each simulation. Similarly, the thermal energy barely changes, except for in the slow cosmic ray transport cases. This change is clearer in the total energy loss plot (bottom right). The total energy decreases because of $\gamma$-ray emission, which increases proportionally with the cosmic-ray energy density. So, when the cosmic-ray energy density increases (bottom left plot), the total energy loss also increases.