Synchrotron Pair Production Equilibrium in Relativistic Magnetic Reconnection

Magnetic reconnection is ubiquitous in astrophysical systems, and in many such systems, the plasma suffers from significant cooling due to synchrotron radiation. We study relativistic magnetic reconnection in the presence of strong synchrotron cooling, where the ambient magnetization $\sigma$ is high and the magnetic compactness $\ell_{B}$ of the system is of order unity. In this regime, $e^{\pm}$ pair production from synchrotron photons is inevitable, and this process can regulate the magnetization $\sigma$ surrounding the current sheet. We investigate this self-regulation analytically and find a self-consistent steady state for a given magnetic compactness of the system and initial magnetization. This result helps estimate the self-consistent upstream magnetization in systems where plasma density is poorly constrained, and can be useful for a variety of astrophysical systems. As illustrative examples, we apply it to study the properties of reconnecting current sheets near the supermassive black hole of M87, as well as the equatorial current sheet outside the light cylinder of the Crab pulsar.Comment: 11 pages, 2 figures, submitted to ApJ. Comments welcome