Particle Acceleration Driven by Null Electromagnetic Fields Near a Kerr Black Hole

Abstract

Short timescale variability is often associated with a black hole system. The consequence of an electromagnetic outflow suddenly generated near a Kerr black hole is considered assuming that it is described by a solution of a force-free field with a null electric current. We compute charged particle acceleration induced by the burst field. We show that the particle is instantaneously accelerated to the relativistic regime by the field with a very large amplitude, which is characterized by a dimensionless number κ. Our numerical calculation demonstrates how the trajectory of the particle changes with κ. We also show that the maximum energy increases with κ2/3. The typical maximum energy attained by a proton for an event near a super massive black hole is Emax∼100 TeV, which is enough observed high-energy flares.

The non-null and force-free electromagnetic field

“…Theorem 6. Let F 2R be a field sheet foliation for an electrically dominated force free field on M. Let (e 0 , e 1 , e 2 , e 3 ) be a foliation adapted frame F 2R on some starlike chart on U p centered about p ∈ M with an associated field F E as given by equation (24). Suppose e 0 and e 1 form an involutive distribution, then F M given by equation ( 6) is a magnetically dominated solution for u = ũ in U p .…”

“…which coincides with the angular velocity of F M (see [23]). In a recent paper [24], the authors discuss the acceleration of charged particles in a null and force-free field, and show that particles can easily reach relativistic speeds under the right circumstance. Since we are focused on fields rather than particles in this work, we do not perform a detailed analysis here, but it is worth mentioning that similar effects can take place even in our magnetically dominated field given by F M in equation (41).…”