Transition to Petschek Reconnection in Subrelativistic Pair Plasmas: Implications for Particle Acceleration

TL;DR

This study demonstrates that subrelativistic pair-plasma reconnection ($\sigma<1$) tends to form Petschek-like laminar exhausts rather than plasmoid-dominated chains, due to a reduced plasmoid production rate. By introducing the plasmoid parameter $\mathcal{P}$ and identifying a critical threshold near $\mathcal{P}_c \approx 0.075$, the authors predict the transition between single- and multi-X-point reconnection and link this geometry to distinct particle energization pathways. High-$\sigma$ reconnection yields broad, hard power-law spectra due to stochastic acceleration across multiple X-points and plasmoids, while low-$\sigma$ reconnection primarily heats the inflow, producing Maxwellian exhaust distributions with only a weak nonthermal tail. The findings provide a kinetic-scale justification for Petschek-like reconnection in collisionless plasmas and offer a framework for predicting current-sheet geometry and energy spectra in diverse astrophysical environments.

Abstract

While relativistic magnetic reconnection in pair plasmas has emerged in recent years as a candidate for the origin of radiation from extreme astrophysical environments, the corresponding subrelativistic pair plasma regime has remained less explored, leaving open the question of how relativistic physics affects reconnection. In this paper, we investigate the differences between these regimes by contrasting 2D particle-in-cell simulations of reconnection in pair plasmas with relativistic magnetization ($σ\gg 1$) and subrelativistic magnetization ($σ< 1$). By utilizing unprecedentedly large domain sizes and outflow boundary conditions, we demonstrate that lowering the magnetization results in a change in the reconnection geometry from a plasmoid chain to a Petschek geometry, where laminar exhausts bounded by slow-mode shocks emanate from a single diffusion region. We attribute this change to the reduced plasmoid production rate in the low-$σ$ case: when the secondary tearing rate is sufficiently low, plasmoids are too few in number to prevent the system from relaxing into a stable Petschek configuration. This geometric change also affects particle energization: we show that while high-$σ$ plasmoid chains generate power-law energy spectra, low-$σ$ Petschek exhausts merely heat incoming plasma and yield negligible nonthermal acceleration. These results have implications for predicting the global current sheet geometry and the resulting energy spectrum in a variety of systems.

Figures (9)

• Figure 1: Density profiles for Runs III and IV, respectively, once steady state is achieved. The density scale is cut off at five times the inflow density.
• Figure 2: Density profile for the $\sigma = 0.3$ Run V spanning $6000 \; c/\omega_p$ in the $y$-direction once it has reached steady state. Note that while plasmoids near the X-point have comparable widths to the width of the exhaust, by the time the plasmoids move farther away from the X-point their width becomes much smaller than that of the exhaust, and they become comparatively insignificant. Two plasmoids can be seen at $y \approx 1440$ and $1760 \; c / \omega_p$. An animated https://youtube.com/playlist?list=PL-1sbkerHVc_Cxk0X2DX6jZhpSMV1ktlM&si=hcuGYkDMQXw76oGL of this figure shows the steady-state evolution over several Alfvén-crossing times.
• Figure 3: Plots (a) - (h) show selected quantities for a cut along $y = 1600 \; c/\omega_p$ in Run V. Plots (a) and (b) show the normalized density and normal bulk velocity, respectively. Plots (c) - (h) show the Rankine-Hugoniot jump quantities, normalized to their upstream values. Plot (i) shows general quantities plotted along that same $y$-value; the transition region depicted in plots (a) - (h) is shaded in gray. The upstream magnetic pressure $P_{B0} \equiv B_0^2 / 8 \pi$.
• Figure 4: Spacetime plots of the midline ($x = L_x / 2 = 60 \; c / \omega_p$) for Runs I and II respectively after they have reached equilibrium. The areas with the lowest density (the darkest blue) are the diffusion regions and the high-density streaks of yellow are the plasmoids---thus these plots show the life journey of plasmoids as they are born and leave the domain. As one can see in the $\sigma = 0.3$ case, plasmoid production, while regular, is sufficiently infrequent to allow most plasmoids to escape the the X-point at the center without ever merging with another plasmoid (though one prominent collision can be seen near (190, 180)). The case in Run I is quite different - here we see rapid plasmoid production and, crucially, many mergers. This results in large, slow plasmoids which themselves are more susceptible to further mergers. This feedback mechanism fills the domain with large, massive plasmoids.
• Figure 5: Electron energy spectra for Runs III and IV for the entire domain, normalized by the magnetization. The dashed blue line indicates the expected pickup energy, $m v_A^2$. The transition between the exhaust component and the plasmoid component is indicated by the yellow line. Note that the first structures on the far left for each case represent the inflow which has acquired a small thermal temperature due to wave heating. As the domain size ($L_y$) grows for $\sigma = 0.3$, the shape of the plot looks the same, however the magnitude of the plasmoid component in the spectrum decreases relative to that of the exhaust due to the decreasing fraction of the domain occupied by plasmoids.