Lepton Acceleration by Relativistic Collisionless Magnetic Reconnection

Abstract

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 $B_0$ is the typical magnetic field strength, ${\cal E}\equiv E_0/B_0$, with $E_0$ the reconnection electric field, $L$ 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 $dn/d\gamma \propto \gamma^{-1}$ for $\gamma \lesssim \Gamma_0$. The apparent distribution function may be steeper than $\gamma^{-1}$ due to the distribution of $\Gamma_0$ 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.Comment: submitted to ApJ; 6 figure

Thermalization in Relativistic Outflows and the Correlation between Spectral Hardness and Apparent Luminosity in Gamma‐Ray Bursts

“…Stochastic acceleration by turbulence (Dermer et al 1996;Thompson 2006) or by electrostatic acceleration in reconnection layers (Romanova & Lovelace 1992;Larrabee et al 2003) are possible heating mechanisms. This implies that the high-energy tail of the prompt GRB spectrum is generated near the scattering photosphere.…”

The termination shock in a striped pulsar wind

“…The magnetic reconnection might proceed in separate X-points but in average the process remains one-dimensional because the released energy is confined to a layer around the field reversal. Acceleration of relativistic electrons close to an X-point was considered by Romanova & Lovelace (1992); Zenitani & Hoshino (2001), Larrabee et al(2002) who found a powerlaw particle distribution with the slope β ∼ 1. Reconnection in a long current sheet at a time-scale large enough that particles pass many X-points has not been considered yet.…”

“…On the other hand, driven reconnection of the magnetic field within the shock radically alter the particle acceleration process. It follows from both analytical and numerical studies that particles are readily accelerated in the course of the magnetic field reconnection to form the energy distribution with the power-law index β ∼ 1 (Romanova & Lovelace 1992;Zenitani & Hoshino 2001;Larrabee, Lovelace & Romanova 2002). Electrons with such a distribution emit syn-chrotron radiation with a flat spectrum therefore Romanova & Lovelace (1992) and Birk, Crusius-Wätzel & Lesch (2001) suggested that reconnection plays a crucial role in flat spectrum extragalactic radio sources.…”

Polarization and Structure of Relativistic Parsec-Scale AGN Jets

“…(Recall that only electrons with γ e s m p /m e can be accelerated at a relativistic shock; here s is the shock Lorentz factor, and m p and m e are the proton and electron masses.) Thirdly, acceleration in reconnection layers can produce very-hard power-law spectra, dn/dγ ∼ γ −1 (Hoshino 2002;Larrabee et al 2003). The fact that reconnection models can produce spectra that are prohibitively hard for shock acceleration can serve as a distinctive property of electromagnetic models.…”