Electron and Proton Heating in Transrelativistic Guide Field Reconnection

The plasma in low-luminosity accretion flows, such as the one around the black hole at the center of M87 or Sgr A* at our Galactic Center, is expected to be collisioness and two-temperature, with protons hotter than electrons. Here, particle heating is expected to be controlled by magnetic reconnection in the transrelativistic regime $sigma_{w}sim 0.1$-$1$, where the magnetization $sigma_{w}$ is the ratio of magnetic energy density to plasma enthalpy density. By means of large-scale 2D particle-in-cell simulations, we explore for a fiducial $sigma_w=0.1$ how the dissipated magnetic energy gets partitioned between electrons and protons, as a function of $beta_{rm i}$ (the ratio of proton thermal pressure to magnetic pressure) and of the strength of a guide field $B_{rm g}$ perpendicular to the reversing field $B_0$. At low $beta_{rm i};(lesssim 0.1)$, we find that the fraction of initial magnetic energy per particle converted into electron irreversible heat is nearly independent of $B_{rm g}/B_0$, whereas protons get heated much less with increasing $B_{rm g}/B_0$. As a result, for large $B_{rm g} /B_{0}$, electrons receive the overwhelming majority of irreversible particle heating (${sim}93%$ for $B_{rm g} /B_{0}=6$). This is significantly different than the antiparallel case $B_{rm g}/B_0=0$, in which electron irreversible heating accounts for only ${sim}18%$ of the total particle heating. At $beta_{rm i} sim 2$, when both species start already relativistically hot (for our fiducial $sigma_w=0.1$), electrons and protons each receive ${sim}50%$ of the irreversible particle heating, regardless of the guide field strength. Our results provide important insights into the plasma physics of electron and proton heating in hot accretion flows around supermassive black holes.