Lepton Acceleration by Relativistic Collisionless Magnetic Reconnection

We have calculated self-consistent equilibria of a collisionless relativistic electron-positron gas in the vicinity of a magnetic $X-$point. For the considered conditions, pertinent to extra-galactic jets, we find that leptons are accelerated up to Lorentz factors $\Gamma_0 = \kappa e B_0L {\cal E}^2 /mc^2 \gg 1$,where$B_0$isthetypicalmagneticfieldstrength,${\cal E}\equiv E_0/B_0$,with$E_0$thereconnectionelectricfield,$L$ is the length scale of the magnetic field, and $\kappa \approx 12$. The acceleration is due to the dominance of the electric field over the magnetic field in a region around the $X-$point. The distribution function of the accelerated leptons is found to be approximately $dn\mathrm{/}d\gamma \propto {\gamma }^{-1}$ for $\gamma \lesssim {\mathrm{\Gamma }}_0$. The apparent distribution function may be steeper than ${\gamma }^{-1}$ due to the distribution of ${\mathrm{\Gamma }}_0$ values and/or the radiative losses. Self-consistent equilibria are found only for plasma inflow rates to the $X-$point less than a critical value.