相对论性激波有限循环输运中的本征谱曲率
Intrinsic Spectral Curvature from Finite-Cycle Transport at Relativistic Shocks
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中文总结 AI 辅助
研究相对论性激波有限循环输运，通过离散激波穿越映射和能量依赖返回概率建立框架，得出返回概率随能量降低产生本征谱曲率，其能量依赖性由相关竞争决定，结果指向预渐近有限循环极限及非幂律谱产生原因。
中文摘要 AI 辅助
幂律谱是激波加速的核心预测，通常与扩散输运下的渐近尺度不变性相关。在有限相对论性激波中，强各向异性和有限停留时间可能限制在建立多循环扩散极限之前有效激波穿越的次数。本文建立了一个简化的有限循环框架，其中粒子加速由离散的激波穿越映射描述，下游输运通过能量依赖的返回概率编码。在此框架下，局部谱由每循环平均能量增益与存活到下一个循环的概率之间的竞争控制。返回概率随能量的系统性降低会因输运限制的循环存活而产生本征谱曲率。通过磁偏转、下游平流和有限激波寿命之间的竞争估计返回概率的能量依赖性，得出由宏观源参数决定的特征陡化尺度。对于与致密耀变体发射区域相关的基准参数，陡化尺度低于最终加速截止，因此在达到终端最大能量之前可能出现曲率。这些结果指向相对论性激波输运的预渐近有限循环极限，其中非幂律谱可能源于重复激波穿越循环的有限存活。
英文摘要
Power-law spectra are a central prediction of shock acceleration and are commonly associated with asymptotic scale invariance under diffusive transport. In finite relativistic shocks, strong anisotropy and limited residence times may restrict the number of effective shock crossings before the many-cycle diffusive limit is established. This work develops a reduced finite-cycle framework in which particle energization is described by discrete shock-crossing mappings, while downstream transport is encoded through an energy-dependent return probability. In this formulation, the local spectrum is controlled by the competition between the mean energy gain per cycle and the probability of surviving to the next cycle. A systematic decrease of the return probability with energy then produces intrinsic spectral curvature as a consequence of transport-limited cycle survival. The energy dependence of the return probability is estimated from the competition between magnetic deflection, downstream advection, and finite shock lifetime, yielding a characteristic steepening scale determined by macroscopic source parameters. For fiducial parameters relevant to compact blazar emission regions, the steepening scale lies below the ultimate acceleration cutoff, so that curvature can appear before the terminal maximum energy is reached. These results point to a pre-asymptotic finite-cycle limit of relativistic shock transport in which non-power-law spectra can arise from the limited survival of repeated shock-crossing cycles.
