Numerical Calculations of the Linear Response of a Gaseous Disk to a Protoplanet
Numerical Calculations of the Linear Response of a Gaseous Disk to a Protoplanet
复制标题
气态盘对原行星线性响应的数值计算
DOI：
10.1006/icar.1993.1039
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发表时间：
1993
期刊：
影响因子：
3.2
通讯作者：
James B. Pollack
中科院分区：
文献类型：
--
作者：
D. Korycansky;James B. Pollack
摘要在本文中，我们提出了一个扁平的气体盘的线性响应的存在嵌入的原行星的计算。计算是数值的，并考虑到被分析理论忽略的条款，还研究了磁盘中的表面密度和声速梯度的影响。我们还发展了一种快速计算软化势（或非零高度圆盘）的拉普拉斯系数的方法。在一般情况下，经典的分析理论得到证实。然而，由于共转共振的计算扭矩的大小不同意与以前推导的分析结果。计算得到的共转力矩小于解析值，对共转时扰动势的值不太敏感，并且福尔斯作为方位波数m的函数下降得更快。这可能是由于在共转附近扰动势的快速变化造成的。我们发现，压力梯度的主要影响是增加净扭矩，由于向内位移的Lindblad共振。一般来说，这种效应抵消了圆盘表面密度梯度的相反效应。我们已经计算了各种模型星云的地球和外行星的推断轨道演化时标。一般来说，地球的轨道演变时间尺度为10 - 6年。外行星的时间尺度要短得多：一般为10 3 - 10 4年。虽然在我们的计算中忽略了太阳星云对扭矩的反应的影响，但结果表明了原行星对星云演化后期的重要性。
Abstract In this paper we present calculations of the linear response of a flat gaseous disk to the presence of an embedded protoplanet. The calculations are numerical and take into account terms neglected by analytic theory and also examine the effects of gradients in surface density and sound speed in the disk. We have also developed a means of rapid calculation of Laplace coefficients for a softened potential (or for a disk of nonzero height). In general, the classical analytic theory is confirmed. However, the magnitude of calculated torque due to the corotation resonance disagrees with previously derived analytical results. The calculated corotation torque is smaller than the analytic value, is much less sensitive to the value of the perturbing potential at corotation, and falls off more rapidly as a function of the azimuthal wavenumber m . It is possible that the rapid variation of the perturbing potential near corotation is responsible for this behavior. We find that the dominant effect of a pressure gradient is to increase the net torque, due to the inward displacement of the Lindblad resonances. The effect countervails the opposing effect of a gradient in disk surface density, in general. We have calculated the inferred orbital evolution timescales for the Earth and outer planets for a variety of model nebulae. In general the orbital evolution timescale for the Earth is on the order of 10 6 years. Timescales for the outer planets are much shorter: 10 3 -10 4 years in general. Although the effects of the reaction of the solar nebula to the torques have been neglected in our calculations, the results indicate the importance of the protoplanets for the later stages of nebular evolution.