Pair Production in Low-Luminosity Galactic Nuclei

Electron-positron pairs may be produced near accreting black holes by a variety of physical processes, and the resulting pair plasma may be accelerated and collimated into a relativistic jet. Here we use a self-consistent dynamical and radiative model to investigate pair production by collisions in weakly radiative accretion flows around a black hole of mass M and accretion rate Ṁ. Our flow model is drawn from general relativistic magnetohydrodynamic simulations, and our radiation field is computed by a Monte Carlo transport scheme assuming the electron distribution function is thermal. We argue that the pair production rate scales as r^-6 M^-1 Ṁ^6. We confirm this numerically and calibrate the scaling relation. This relation is self-consistent in a wedge in M, Ṁ parameter space. If Ṁ is too low the implied pair density over the poles of the black hole is below the Goldreich-Julian density and pair production is relatively unimportant; if Ṁ is too high the models are radiatively efficient. We also argue that for a power-law spectrum the pair production rate should scale with the observables LX X-ray luminosity and M as LX² M^-4. We confirm this numerically and argue that this relation likely holds even for radiatively efficient flows. The pair production rates are sensitive to black hole spin and to the ion-electron temperature ratio which are fixed in this exploratory calculation. We finish with a brief discussion of the implications for Sgr A* and M87.