Electron and Proton Acceleration in Trans-relativistic Magnetic Reconnection: Dependence on Plasma Beta and Magnetization

Nonthermal electron acceleration via magnetic reconnection is thought to play an important role in powering the variable X-ray emission from radiatively inefficient accretion flows around black holes. The trans-relativistic regime of magnetic reconnection—where the magnetization σ, defined as the ratio of magnetic energy density to enthalpy density, is ∼1—is frequently encountered in such flows. 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 σ and the proton β (the ratio of proton thermal pressure to magnetic pressure). We find that the electron spectrum in the reconnection region is nonthermal and can be modeled as a power law. At low β, the slope, p, is independent of β and hardens with increasing σ as p≃ 1.8+0.7/\sqrt{σ }. Electrons are primarily accelerated by the nonideal electric field at X-points, either in the initial current layer or in current sheets generated between merging magnetic islands. At higher values of β, the electron power law steepens, and the electron spectrum eventually approaches a Maxwellian distribution for all values of σ. At values of β near β _max ≈ 1/4σ, 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 between the reconnection outflow and a stationary magnetic island