Particle-in-cell study of the tearing instability for relativistic pair plasmas

Two-dimensional particle-in-cell (PIC) simulations explore the collisionless tearing instability from a Harris equilibrium of a pair (electron-positron) plasma, with no guide field, for a range of parameters from non-relativistic to relativistic temperatures and drift velocities. Growth rates match the predictions of Zelenyi & Krasnosel'skikh (1979) modified for relativistic drifts by Hoshino (2020) as long as the assumption holds that the thickness of the current sheet is larger than the Larmor radius. Aside from confirming these predictions, we explore the transitions from thick to thin current sheets and from classical to relativistic temperatures. We determine a limit for the minimum current thickness to which a current sheet can evolve before the tearing instability sets in. Large-scale astronomical environmental parameters imply significant reconnection of system size current sheets is most likely in regimes with relativistic temperatures, e.g. active galactic nuclei. We also explore the nonlinear evolution of the modes that move to lower wave numbers (especially for thick current sheets with low growth rates) and eventually increase to faster growth rates associated with thinner current sheets before saturating.