从聚集和碎裂看土星环中粒子的尺寸分布
Size distribution of particles in Saturn's rings from aggregation and fragmentation
摘要：
土星环由大量的水冰颗粒和少量的岩石物质组成。由于角动量守恒和耗散粒子间碰撞中能量的稳定损失的相互作用，它们形成了一个扁平的圆盘。对于尺寸范围从几厘米到几米的粒子，已经推断出半径的幂律分布，$\sim r^{-q}$与$q \approx 3$;对于更大的尺寸，分布具有陡峭的截止。有人建议，这种尺寸分布可能是由环形颗粒的聚集和破碎之间的平衡引起的，但无论是幂律依赖性还是上尺寸截止值都没有建立在理论基础上。在这里，我们提出了一个模型的颗粒大小分布，定量地解释的意见。根据数据，我们的模型预测指数$q$被约束到区间$2.75 \le q \le 3.5$。此外，对于较大的颗粒尺寸，自然建立指数截止，截止半径由聚集和破坏性碰撞的相对频率设定。这个截止值比土星环中典型的微观结构要小得多。
英文摘要：
Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative inter-particle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, $\sim r^{-q}$ with $q \approx 3$, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent $q$ to be constrained to the interval $2.75 \le q \le 3.5$. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff-radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of micro-structures seen in Saturn's rings.
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