Electron and proton acceleration in trans-relativistic magnetic reconnection: Dependence on plasma beta and magnetization

Non-Thermal electron acceleration via magnetic reconnection is thought to play an important role in powering the variable X-ray emission from radiatively ineficient accretion ows around black holes, such as Sgr A*at our Galactic center. The trans-relativistic regime of magnetic reconnection, where the magnetization, defined as the ratio of magnetic energy density to enthalpy density, is 1, is frequently encountered in such ows. By means of a large suite of two-dimensional particle-in-cell simulations, we investigate electron and proton acceleration in the trans-relativistic regime. We focus on the dependence of the electron energy spectrum on and the proton (i.e., the ratio of proton thermal pressure to magnetic pressure). We find that the electron spectrum in the reconnection region is non-Thermal and can be generally modeled as a power law. At . 3 103, the slope, p, is independent of and it hardens with increasing as p ' 1:8 + 0:7= p. Electrons are primarily accelerated by the non-ideal electric field at X-points, either in the initial current layer or in current sheets generated in between merging magnetic islands. At higher values of, the electron power law steepens and the electron spectrum eventually approaches a Maxwellian distribution for all values of. At values of near max 1=4, when both electrons and protons are relativistically hot prior to reconnection, the spectra of both species display an additional component at high energies, containing a few percent of particles. These particles are accelerated via a Fermi-like process by bouncing in between the reconnection outow and a stationary magnetic island. For the main population of non-thermal electrons that excludes this additional component, we provide an empirical prescription for the dependence of the power-law slope and the acceleration eficiency on and, which can be used in global simulations of collisionless accretion disks.