Microphysical Plasma Relations from Special-relativistic Turbulence

The microphysical, kinetic properties of astrophysical plasmas near accreting compact objects are still poorly understood. For instance, in modern general-relativistic magnetohydrodynamic simulations, the relation between the temperature of electrons $T_{e}$ and protons $T_{p}$ is prescribed in terms of simplified phenomenological models where the electron temperature is related to the proton temperature in terms of the ratio between the gas and magnetic pressures, or $\beta$ parameter. We here present a very comprehensive campaign of {two-dimensional} kinetic Particle-In-Cell (PIC) simulations of special-relativistic turbulence to investigate systematically the microphysical properties of the plasma in the trans-relativistic regime. Using a realistic mass ratio between electrons and protons, we analyze how the index of the electron energy distributions $\kappa$, the efficiency of nonthermal particle production $\mathcal{E}$, and the temperature ratio $\mathcal{T}:=T_{e}/T_{p}$, vary over a wide range of values of $\beta$ and $\sigma$. For each of these quantities, we provide two-dimensional fitting functions that describe their behaviour in the relevant space of parameters, thus connecting the microphysical properties of the plasma, $\kappa$, $\mathcal{E}$, and $\mathcal{T}$, with the macrophysical ones $\beta$ and $\sigma$. In this way, our results can find application in wide range of astrophysical scenarios, including the accretion and the jet emission onto supermassive black holes, such as M87* and Sgr A*.