The effect of inverse Compton losses on particle acceleration in three-dimensional relativistic reconnection

TL;DR

This paper investigates how inverse Compton cooling affects particle acceleration in three-dimensional relativistic magnetic reconnection. Using large-scale 3D PIC simulations, the authors show that cooling in the weak regime ($\gamma_{\rm rad} > \sigma$) does not alter the reconnection rate or the free-phase acceleration physics, maintaining a $dN_{\rm free}/d\gamma \propto \gamma^{-1}$ spectrum, while the trapped-phase spectrum above the cooling break follows $dN/d\gamma \propto \gamma^{-3}$. These results validate the two-zone acceleration model proposed for 3D reconnection and imply that radiative emission models should treat free, rapidly accelerating particles separately from trapped, cooling particles. The findings have direct implications for interpreting high-energy emission from blazar jets and GRB prompt emission, suggesting observable signatures from the beaming of free particles and the cooled plasmoid-dominated population. Overall, the work strengthens the role of radiative reconnection models in shaping nonthermal astrophysical spectra and provides a practical framework for incorporating cooling effects into emission calculations.

Abstract

Relativistic magnetic reconnection is a key mechanism for dissipating magnetic energy and accelerating particles in astrophysics. In the absence of radiative cooling, recent particle-in-cell (PIC) simulations have shown that high-energy particles gain most of their energy in the upstream region, during a short-lived "free phase" where they meander between the two sides of the layer; when they get captured/trapped by the downstream flux ropes, they undergo a "trapped phase", where no significant energization occurs. Here, we perform a suite of 3D PIC simulations of relativistic reconnection including inverse Compton (IC) losses in the weakly cooled regime in which the radiation-reaction-limited Lorentz factor $γ_{\rm rad}$ exceeds the magnetization $σ$. We show that electron cooling losses do not appreciably alter the reconnection rate, the structure of the layer, and the physics of particle acceleration in the free phase, so the spectrum of free electrons is $dN_{\rm free}/dγ\propto γ^{-1}$, as in the uncooled case. The spectrum of trapped electrons above the cooling break $γ_{\rm cool}$ (in the range $γ_{\rm cool}<γ<γ_{\rm rad}$) is $dN/dγ\propto γ^{-3}$, steeper than the scaling $dN/dγ\propto γ^{-2}$ of uncooled simulations. This confirms that no significant particle energization occurs during the trapped phase. Our results validate the model by arXiv:2302.12269 for particle acceleration in 3D relativistic reconnection, and imply that radiative emission models of reconnection-powered astrophysical sources should employ a two-zone structure, that differentiates between free, rapidly accelerating particles and trapped, passively cooling particles.

Figures (7)

• Figure 1: Time evolution of the reconnection rate $\eta_{\rm rec}=v_{\rm in}/c$ for different values of $\gamma_{\rm rad}$, as described in the legend.
• Figure 2: Representative cross sections of the density structure of the reconnection layer, taken at $t= 7.9\, L/c$, for different $\gamma_{\rm rad}$, as marked on the panels. The density $n$ is normalized to the initial upstream density $n_0$. To enhance contrast, we show $(n/n_0)^5$. Left: Cross sections taken at $z=0$ in the $x-y$ plane, with the inflow direction on the vertical axis and the outflow direction on the horizontal axis. Right: Cross sections taken at $x=0$ in the $y-z$ plane, with the inflow direction on the vertical axis and the guide-field direction on the horizontal axis.
• Figure 3: 2D histograms of the acceleration rate $\dot{\gamma}_{\rm acc}/\omega_{\rm c}$ for free electrons (left) and trapped electrons (right), for different $\gamma_{\rm rad}$, as marked in the panels. The Lorentz factor $\gamma$ on the horizontal axis is the instantaneous value. The histograms are normalized to their respective maxima, and colors span the range $[10^{-3},1]$ in logarithmic increments. Horizontal dashed red lines show the optimal acceleration rate $\dot{\gamma}_{\rm acc}/\omega_{\rm c}\simeq \eta_{\rm rec}\simeq 0.05$.
• Figure 4: 2D histograms of acceleration time $t_{\rm acc}=\gamma/\dot{\gamma}_{\rm acc}$ (left) and escape time $t_{\rm esc}$ (right) of free electrons, for different $\gamma_{\rm rad}$, as marked in the panels. The Lorentz factor $\gamma$ on the horizontal axis is the instantaneous value on the left, while it is the value at the end of the free phase on the right. The histograms are normalized to their respective maxima, and colors span the range $[10^{-3},1]$ in logarithmic increments. Dashed lines are given by $\omega_{\rm c}t_{\rm acc} = 19 \,\gamma$ in the left column, and $\omega_{\rm c}t_{\rm esc} = 13 \,\gamma$ in the right column.
• Figure 5: Particle energy spectra averaged during the steady state, $t\gtrsim 4\, L/c$. We show the total spectra (solid; including free and trapped particles) and the spectra of free particles (dashed; shown only for $\gamma>\sigma$). Since free particles are always a minority (apart from the upper spectral cutoff, where they contribute as much as the trapped population), total spectra are nearly the same as the spectra of trapped particles. Top: total and free spectra of positrons. Middle: total and free spectra of electrons. Bottom: total spectra of electrons, and predicted shape of the total spectra based on the measured free spectra and the analytical scalings in Eq. \ref{['eq:13nocooldiff']} (for the uncooled case, yellow dotted curve) or Eq. \ref{['eq:14cooldiff']} (for the cooled cases, green dotted curves). In each panel, the vertical gray line is $\gamma=\sigma$, dotted lines show $\gamma_{\rm rad}$, and dot-dashed lines show $\gamma_{\rm cool}$.