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Abstract Identifying the physical mechanism driving blazar flares remains a central challenge in high-energy astrophysics. We show that the energy dependence of the standard deviation of the polarization angle variability (σ_PA) provides a powerful and robust discriminator of blazar flaring mechanisms. Using particle-in-cell-integrated polarized radiative transfer simulations, we perform the most rigorous statistical analyses of polarization variability to date. We demonstrate that magnetic reconnection and magnetized turbulence imprint qualitatively distinct energy dependence ofσ_PAthat directly reflects their different magnetic field evolution and particle transport. Reconnection predicts higherσ_PAwith higher photon energy until the synchrotron spectral peak, whereas turbulence produces nearly flatσ_PAacross the synchrotron spectral component. These trends are resilient to realistic observational limitations. Applying our results to optical and IXPE data of Mrk 421 and 1ES 1959+650, we find strong evidence for reconnection-driven flares embedded in a turbulent blazar zone. Energy-dependentσ_PAemerges as a decisive new probe of particle acceleration in relativistic jets. 

Abstract Certain solar flares exhibit a distinctive candle-flame or cusp-shaped feature above the bright flare arcade visible in extreme ultraviolet (EUV) and X-ray channels sensitive to high-temperature plasma. The presence of a cusp-like structure is generally regarded as a key piece of morphological evidence for magnetic reconnection to power explosive energy release in solar flares. In addition, downward-propagating plasma flows above the flare arcade have often been interpreted as outflows driven by magnetic reconnection. However, the relationship between the observed candle-flame-shaped morphology and the underlying magnetic field geometry for reconnection remains unclear. Likewise, the observed speed of the plasma downflows has been found to be too low compared to the upstream Alfvén speed predicted by reconnection theories. With the help of a recently developed three-dimensional magnetohydrodynamics model, we examine the locations where magnetic topology changes from antiparallel to closed (Y-points) in a candle-flame-shaped flare, compare the observational emission features with synthetic EUV images generated from the model, and analyze their time evolutions. We also investigate the role of projection effects and line-of-sight integration in the measurements of plasma downflow speeds. Our analysis reveals that the Y-points do not necessarily coincide with the apparent cusp tip. Also, the apparent speeds of the supra-arcade downflows, as derived from tracks in the time–distance plots, underestimate the true Alfvén speeds in the reconnection inflow region by at least a factor of 2 up to an order of magnitude. 

Solar flares are among the most dramatic events in the solar system, releasing substantial magnetic energy and accelerating a large number of electrons to high energies. Notably, in certain events, the above-the-looptop region may contain a significant population of nonthermal electrons, both in number and energy. For the first time, we adopt a novel numerical method that combines magnetohydrodynamics with energetic particles incorporating feedback from nonthermal electrons to investigate electron acceleration and transport in solar flares. We find that a large fraction of energetic electrons are accelerated via the current sheet and termination shock regions. Most energetic electrons are concentrated in the above-the-looptop region, carrying a sizable amount of the released energy. We observe that greater feedback of nonthermal electrons leads to steeper energy spectra. The energy density of the nonthermal electrons oscillates due to the periodic impact of magnetic islands into the above-the-looptop region, which may help explain the observed quasiperiodic pulsations. Our simulations provide new insights into the origin of nonthermal electrons and associated emissions in the above-the-looptop region. 

Abstract In astronomical environments, the high-temperature emission of plasma mainly depends on ion charge states, requiring accurate analysis of the ionization and recombination processes. For various phenomena involving energetic particles, non-Maxwellian distributions of electrons exhibiting high-energy tails can significantly enhance the ionization process. Therefore, accurately computing ionization and recombination rates with non-Maxwellian electron distributions is essential for emission diagnostic analysis. In this work, we report two methods for fitting various non-Maxwellian distributions by using the Maxwellian decomposition strategy. For standardκ-distributions, the calculated ionization and recombination rate coefficients show comparable accuracy to other public packages. Additionally, our methods support arbitrary electron distributions and can be easily extended to updated atomic databases. We apply the above methods to two specific non-Maxwellian distribution scenarios: (i) accelerated electron distributions due to magnetic reconnection revealed in a combined MHD–particle simulation; and (ii) the high-energy truncatedκ-distribution predicted by the exospheric model of the solar wind. During the electron acceleration process, we show that the ionization rates of high-temperature iron ions increase significantly compared to their initial Maxwellian distribution, while the recombination rates may decrease due to the electron distribution changes in low-energy ranges. This can potentially lead to an overestimation of the plasma temperature when analyzing the Fe emission lines under the Maxwellian distribution assumption. For the truncatedκ-distribution in the solar wind, our results show that the ionization rates are lower than those for the standardκ-distribution, while the recombination rates remain similar. This leads to an overestimation of the plasma temperature when assuming aκ-distribution. 

Abstract Determining the relative contribution of solar flares versus coronal mass ejections in large solar energetic particle (SEP) events is a long-standing problem. Flare-accelerated particles may travel through complex magnetic fields in the eruption region and escape into interplanetary space, thereby contributing to large SEP events. The process by which flare accelerated particles are released into the heliosphere is poorly understood and yet is critical to advancing our understanding of SEPs. In this work, we address the release problem by solving the focused transport equation in the context of a 2.5D ARMS magnetohydrodynamic simulation of a breakout coronal mass ejection (CME)/flare event. We find that particles accelerated by flare reconnection can be released into interplanetary space through interchange reconnection between closed and open field lines. These particles can contribute directly to SEP events and may become an important seed population for further acceleration by CME-driven shocks. Additionally, we find that the energetic particle fluxes in the inner heliosphere remain elevated for an extended period, allowing them to contribute to SEP acceleration by subsequent CMEs. This study represents the first direct particle modeling of how flare-accelerated particles can contribute to major SEP events. 

Abstract Relativistic magnetic turbulence has been proposed as a process for producing nonthermal particles in high-energy astrophysics. The particle energization may be contributed by both magnetic reconnection and turbulent fluctuations, but their interplay is poorly understood. It has been suggested that during magnetic reconnection the parallel electric field dominates the particle acceleration up to the lower bound of the power-law particle spectrum, but recent studies show that electric fields perpendicular to the magnetic field can play an important, if not dominant role. In this study, we carry out two-dimensional fully kinetic particle-in-cell simulations of magnetically dominated decaying turbulence in a relativistic pair plasma. For a fixed magnetization parameterσ₀ = 20, we find that the injection energyε_injconverges with increasing domain size toε_inj ≃ 10m_ec². In contrast, the power-law index, the cut-off energy, and the power-law extent increase steadily with domain size. We trace a large number of particles and evaluate the contributions of the work done by the parallel (W_∥) and perpendicular (W_⊥) electric fields during both the injection phase and the postinjection phase. We find that during the injection phase, theW_⊥contribution increases with domain size, suggesting that it may eventually dominate injection for a sufficiently large domain. In contrast, on average, both components contribute equally during the postinjection phase, insensitive to the domain size. For high energy (ε ≫ ε_inj) particles,W_⊥dominates the subsequent energization. These findings may improve our understanding of nonthermal particles and their emissions in astrophysical plasmas. 

Abstract Magnetic reconnection regions in space and astrophysics are known as active particle acceleration sites. There is ample evidence showing that energetic particles can take a substantial amount of converted energy during magnetic reconnection. However, there has been a lack of studies understanding the backreaction of energetic particles at magnetohydrodynamical scales in magnetic reconnection. To address this, we have developed a new computational method to explore the feedback by nonthermal energetic particles. This approach considers the backreaction from these energetic particles by incorporating their pressure into magnetohydrodynamics (MHD) equations. The pressure of the energetic particles is evaluated from their distribution evolved through Parker’s transport equation, solved using stochastic differential equations (SDEs), so we coin the name MHD-SDE. Applying this method to low-βmagnetic reconnection simulations, we find that reconnection is capable of accelerating a large fraction of energetic particles that contain a substantial amount of energy. When the feedback from these particles is included, their pressure suppresses the compression structures generated by magnetic reconnection, thereby mediating particle energization. Consequently, the feedback from energetic particles results in a steeper power-law energy spectrum. These findings suggest that feedback from nonthermal energetic particles plays a crucial role in magnetic reconnection and particle acceleration. 

Abstract “Electron-only” reconnection, which is both uncoupled from the surrounding ions and much faster than standard reconnection, is arguably ubiquitous in turbulence. One critical step to understanding the rate in this novel regime is to model the outflow speed that limits the transport of the magnetic flux, which is super ion Alfvénic but significantly lower than the electron Alfvén speed based on the asymptotic reconnecting field. Here we develop a simple model to determine this limiting speed by taking into account the multiscale nature of reconnection, the Hall-mediated electron outflow speed, and the pressure buildup within the small system. The predicted scalings of rates and various key quantities compare well with fully kinetic simulations and can be useful for interpreting the observations of NASA’s Magnetospheric-Multiscale (MMS) mission and other ongoing missions. 

Abstract Recent observations and simulations indicate that solar flares undergo extremely complex 3D evolution, making 3D particle transport models essential for understanding electron acceleration and interpreting flare emissions. In this study, we investigate this problem by solving Parker’s transport equation with 3D MHD simulations of solar flares. By examining energy conversion in the 3D system, we evaluate the roles of different acceleration mechanisms, including reconnection current sheet (CS), termination shock (TS), and supra-arcade downflows (SADs). We find that large-amplitude turbulent fluctuations are generated and sustained in the 3D system. The model results demonstrate that a significant number of electrons are accelerated to hundreds of keV and even a few MeV, forming power-law energy spectra. These energetic particles are widely distributed, with concentrations at the TS and in the flare looptop region, consistent with results derived from recent hard X-ray (HXR) and microwave (MW) observations. By selectively turning particle acceleration on or off in specific regions, we find that the CS and SADs effectively accelerate electrons to several hundred keV, while the TS enables further acceleration to MeV. However, no single mechanism can independently account for the significant number of energetic electrons observed. Instead, the mechanisms work synergistically to produce a large population of accelerated electrons. Our model provides spatially and temporally resolved electron distributions in the whole flare region and at the flare footpoints, enabling synthetic HXR and MW emission modeling for comparison with observations. These results offer important insights into electron acceleration and transport in 3D solar flare regions.