Capture Probability of Colliding Planetesimals: Dynamical Constraints on Accretion of Planets, Satellites, and Ring Particles
Capture Probability of Colliding Planetesimals: Dynamical Constraints on Accretion of Planets, Satellites, and Ring Particles
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捕捉小行星碰撞的概率：行星、卫星和环粒子吸积的动力学约束
DOI：
10.1006/icar.1993.1168
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发表时间：
1993
期刊：
影响因子：
3.2
通讯作者：
K. Ohtsuki
中科院分区：
文献类型：
--
作者：
K. Ohtsuki
我们评估吸积率和捕获概率的小行星在开普勒运动的三体轨道积分和解析计算检查吸积的行星，卫星和环粒子的条件。不考虑碰撞体的碎裂或撞击坑，但在不假设吸积不可避免的情况下，计算了给定恢复系数的非弹性回弹引起的轨道变化。数值结果表明，在相对随机速度v/ve ≤ 0.1（ve为逃逸速度）的情况下，动能的轻微非弹性耗散足以使大多数碰撞体吸积，但当v ≥ ve时，为了捕获碰撞体，需要耗散大量的动能.在日心轨道上的微行星之间或围绕行星的卫星之间的相对高速碰撞中，捕获概率C由捕获率与碰撞率之比定义，分别用法向和切向的恢复系数en和et以及某个临界值ecr表示，如下所示：（i）如果en，et < ecr，则C = 1，（ii）C =（e2 cr-e2 n）/（e2 t-e2 n）。如果en < ecr ≤t et. (iii)如果et < ecr ≤ en，则C =（e2 cr-e2 t）/（e2 n-e2 t）。(iv)如果ecr ≤ en，则C = 0。临界值ecr是v /ve和rp（rp是碰撞体半径之和与希尔球半径之比）的函数，当v = ve和rp <$1时，ecr <$0. 7。当v /ve ≥ 0.2时，这些解析结果与轨迹积分的数值结果吻合得很好。我们发现，只要v/ve ≥ 0.2，rp ≥ 1，中心体的潮汐效应就不显著，在这种情况下，我们可以用二体近似计算俘获几率。使用这些结果，再加上冰的恢复系数的实验数据，我们估计一个临界质量的冰卫星以上，他们通过引力吸积。我们还研究了捕获概率的行星环粒子之间的碰撞，其中rp 1和潮汐效应更重要。我们发现，吸积是可能的，即使在罗氏极限和捕获概率急剧下降，为rp 23，当目标体突出的希尔球。这表明，在土星的B环引力吸积似乎是相当困难的，除非恢复系数足够小，而吸积的小粒子到大的机构可能在A环，除非物质密度的粒子是远远小于1克厘米-3。
We evaluate accretion rate and capture probability of planetesimals in Keplerian motion by three-body trajectory integration and analytic calculation to examine conditions for accretion of planets, satellites, and ring particles. Fragmentation or cratering of colliding bodies is not considered, but the changes of orbits caused by inelastic rebound with given restitution coefficient are calculated without the assumption of inevitable accretion. Numerical results show that with such low relative random velocities that v/ve ≤ 0.1 (ve is the escape velocity), slight inelastic dissipation of kinetic energy is enough to lead most colliding bodies to accretion, but substantial kinetic, energy needs to be dissipated for capture when v ≥ ve. In relatively high-velocity collisions between planetesimals in heliocentric orbits or between satellites around a planet, capture probability, C, which is defined by the ratio of the capture rate to the collision rate, is expressed in terms of the restitution coefficients in normal and tangential direction, en and et, respectively, and a certain critical value, ecr, as follows: (i) C = 1 if en, et < ecr, (ii) C = (e2cr - e2n)/(e2t - e2n.) if en < ecr ≤t et. (iii) C = (e2cr - e2t)/(e2n - e2t) if et < ecr ≤ en. (iv) C = 0 if ecr ≤ en, et. The critical value ecr is a function of v /ve and rp(rp is the ratio of the sum of radii of colliding bodies to the Hill sphere radius), and ecr ≃ 0.7 when v = ve and rp ⪡ 1. These analytic results and the numerical results obtained by trajectory integrations show quite a good agreement for v /ve ≥ 0.2. We find that tidal effects of the central body is not significant as long as v/ve ≥ 0.2 and rp⪡ 1, and we may apply the two-body approximation for capture probability in such cases. Using these results, together with experimental data for the restitution coefficient of ice, we estimate a critical mass of icy satellites above which they accrete by gravitational force. We also investigate the capture probability for collisions between planetary ring particles where rp ≃ 1 and tidal effects are more important. We find that accretion is possible even inside the Roche limit and the capture probability decreases abruptly for rp ≃23, when the target body protrudes out of the Hill sphere. This suggests that in Saturn's B ring gravitational accretion seems quite difficult unless the restitution coefficient is sufficiently small, while accretion of small particles onto large bodies may be possible in A ring unless the material density of particles is substantially smaller than 1 g cm-3.