The Role of Electric Dominance for Particle Injection in Relativistic Reconnection

Magnetic reconnection in relativistic plasmas -- where the magnetization $\sigma\gg1$ -- is regarded as an efficient particle accelerator, capable of explaining the most dramatic astrophysical flares. We employ two-dimensional (2D) particle-in-cell simulations of relativistic pair-plasma reconnection with vanishing guide field and outflow boundaries to quantify the impact of the energy gain occurring in regions of electric dominance ($E>B$) for the early stages of particle acceleration (i.e., the ``injection'' stage). We calculate the mean fractional contribution $\zeta(\epsilon^\ast,\epsilon_{\rm T}$) by $E>B$ fields to particle energization up to the injection threshold energy, $\epsilon^\ast=\sigma/4$; here, $\epsilon_{\rm T}$ is the particle energy at time $T$. We find that $\zeta$ monotonically increases with $\sigma$ and $\epsilon_{\rm T}$; for $\sigma\gtrsim 50$ and $\epsilon_{\rm T}/\sigma\gtrsim 8$, we find that $\gtrsim 80\%$ of the energy gain obtained before reaching $\epsilon^\ast=\sigma/4$ occurs in $E>B$ regions. We find that $\zeta$ is independent of simulation box size $L_x$, as long as $\epsilon_{\rm T}$ is normalized to the maximum particle energy, which scales as $\epsilon_{\rm max}\propto L_{\rm x}^{1/2}$ in 2D. The distribution of energy gains $\epsilon_{\chi}$ acquired in $E>B$ regions can be modeled as $dN/d\epsilon_{\chi}\propto\epsilon_{\chi}^{-0.35}\exp[-(\epsilon_{\chi}/0.06\,\sigma)^{0.5}]$. Our results help assess the role of electric dominance in relativistic reconnection with vanishing guide fields, which may be realized in the magnetospheres of black holes and neutron stars.