碎裂级联中的非幂律行为
Non-Power Law Behavior in Fragmentation Cascades
摘要：
碰撞造成的碎裂对形成小行星带、柯伊伯带和碎片盘中的小天体的质量谱很重要。碎裂级联模型通常发现，在稳定状态下，粒子质量分布的解是质量的幂律。然而，以前的研究通常假设，在碰撞中产生的最大碎片的质量与目标质量成正比，碰撞的能量刚好足以粉碎目标并将其一半质量分散到无穷大。我们表明，如果这个假设是不满足的，那么幂律解的稳态粒子质量分布修改的乘法因子，这是一个缓慢变化的函数的质量。我们推导出这个校正因子的解析解，并在数值上证实了我们的结果。我们发现，这个校正因子证明是重要的外推时，在许多数量级的质量，如推断系统中的大型物体的红外观测的基础上的数量。在我们的工作过程中，我们还发现了一种不相关的非幂律行为：即使在没有质量分布的上限或下限或强度定律的突破的情况下，波也可以在物体的质量分布中持续存在。
英文摘要：
Collisions resulting in fragmentation are important in shaping the mass spectrum of minor bodies in the asteroid belt, the Kuiper belt, and debris disks. Models of fragmentation cascades typically find that in steady-state, the solution for the particle mass distribution is a power law in the mass. However, previous studies have typically assumed that the mass of the largest fragment produced in a collision with just enough energy to shatter the target and disperse half its mass to infinity is directly proportional to the target mass. We show that if this assumption is not satisfied, then the power law solution for the steady-state particle mass distribution is modified by a multiplicative factor, which is a slowly varying function of the mass. We derive analytic solutions for this correction factor and confirm our results numerically. We find that this correction factor proves important when extrapolating over many orders of magnitude in mass, such as when inferring the number of large objects in a system based on infrared observations. In the course of our work, we have also discovered an unrelated type of non-power law behavior: waves can persist in the mass distribution of objects even in the absence of upper or lower cutoffs to the mass distribution or breaks in the strength law.
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