Double Power-law Electron Spectra in Solar Flares Due to Temperature Anisotropy Instabilities

Abstract

Despite extensive observational and theoretical efforts, the physical processes responsible for shaping the diversity of accelerated electron spectra observed in solar flares remain poorly understood. We use 2D particle-in-cell (PIC) simulations of magnetized plasmas subject to continuous shear-driven magnetic amplification to investigate whether electron temperature anisotropy instabilities in above-the-loop-top (ALT) regions can account for this diversity. We explore how the resulting spectra depend on key plasma parameters: the initial electron temperature $T_e$ and the initial ratio of electron cyclotron to plasma frequencies, $f_e = ω_{ce}/ω_{pe}$. In our simulations, the adiabatic evolution of the plasma generates electron temperature anisotropy with the electron temperature perpendicular to the magnetic field being larger than the parallel temperature. This eventually drives electromagnetic instabilities capable of scattering and accelerating electrons. The simulations consistently produce nonthermal tails in the electron spectra whose hardness increases with the initial value of $f_e$, while depending only weakly on $T_e$. For runs in which $f_e \lesssim 1.2$, the spectra exhibit double power-law shapes with downward (knee-like) breaks, and the electron scattering is dominated by OQES modes. In runs with $f_e\gtrsim 1.5$, PEMZ modes dominate and produce harder double power-law spectra with upward (elbow-like) breaks. Cases that include the $f_e\sim 1.2-1.5$ transition yield nearly single power-laws that end with bump-like breaks. Our results support the role of temperature anisotropy instabilities in accelerating electrons in ALT regions, offering a promising framework to help explain the wide range of nonthermal electron spectra reported in solar flare observations.