Non-thermal 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 , such as Sgr A* at our Galactic center .
The trans-relativistic regime of magnetic reconnection , where the magnetization \sigma , defined as the ratio of magnetic energy density to enthalpy density , is \sim 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 \sigma and the proton \beta ( 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 \beta \lesssim 3 \times 10 ^ { -3 } , the slope , p , is independent of \beta and it hardens with increasing \sigma as p \simeq 1.8 + 0.7 / \sqrt { \sigma } .
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 \beta , the electron power law steepens and the electron spectrum eventually approaches a Maxwellian distribution for all values of \sigma .
At values of \beta near \beta _ { max } \approx 1 / 4 \sigma , 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 outflow 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 efficiency on \beta and \sigma , which can be used in global simulations of collisionless accretion disks .