Electron and proton heating in trans-relativistic magnetic reconnection

Abstract

Hot collisionless accretion flows, such as the one in Sgr A${}^{\ast }$ at our Galactic center, provide a unique setting for the investigation of magnetic reconnection. Here, protons are non-relativistic while electrons can be ultra-relativistic. By means of two-dimensional particle-in-cell simulations, we investigate electron and proton heating in the outflows of trans-relativistic reconnection (i.e., ${\sigma }_w\sim 0.1-1$, where the magnetization ${\sigma }_w$ is the ratio of magnetic energy density to enthalpy density). For both electrons and protons, we find that heating at high ${\beta }_{\mathrm{i}}$ (here, ${\beta }_{\mathrm{i}}$ is the ratio of proton thermal pressure to magnetic pressure) is dominated by adiabatic compression ('adiabatic heating'), while at low ${\beta }_{\mathrm{i}}$ it is accompanied by a genuine increase in entropy ('irreversible heating'). For our fiducial ${\sigma }_w=0.1$, the irreversible heating efficiency at ${\beta }_{\mathrm{i}}\lesssim 1$ is nearly independent of the electron-to-proton temperature ratio $T_{\mathrm{e}}/T_{\mathrm{i}}$ (which we vary from $0.1$ up to $1$), and it asymptotes to $\sim 2\%$ of the inflowing magnetic energy in the low-${\beta }_{\mathrm{i}}$ limit. Protons are heated more efficiently than electrons at low and moderate ${\beta }_{\mathrm{i}}$ (by a factor of $\sim 7$), whereas the electron and proton heating efficiencies become comparable at ${\beta }_{\mathrm{i}}\sim 2$ if $T_{\mathrm{e}}/T_{\mathrm{i}}=1$, when both species start already relativistically hot. We find comparable heating efficiencies between the two species also in the limit of relativistic reconnection (${\sigma }_w\gtrsim 1$). Our results have important implications for the two-temperature nature of collisionless accretion flows, and may provide the sub-grid physics needed in general relativistic MHD simulations.

arXiv comment29 pages, 27 figures, 7 appendices; accepted to ApJ

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