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arXiv 1809.01295astro-ph.EP
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星周气尘盘中尘埃粒子轨迹计算方法分析

Analysis of Methods for Computing the Trajectories of Dust Particles in a Gas-Dust Circumstellar Disk

Olga P. Stoyanovskaya, Valeriy N. Snytnikov, Eduard I. Vorobyov

摘要:

首次对用于模拟气尘环周盘的现代天体物理程序中的固相粒子轨道计算方法进行了系统分析。考虑了尘埃颗粒的运动,其速度主要由气体阻力决定,即尘埃颗粒的停止时间或弛豫时间相对于气体颗粒的速度t_{stop}小于或等于旋转周期。的方法进行了分析,从他们的稳定性的角度来计算小机构的运动,包括尘埃颗粒小于1微米,这是强烈耦合到气体。两个测试问题都有解析解。本文提出了一种快速的一阶精度方法,它可以避免在计算任意尺寸颗粒运动时由于气体阻力而对时间步长造成的附加限制。对于星周盘的情况,当时间步长τ> t_{stop}时,用某些稳定的方法得到的速度计算误差变得不可接受。对于沿着近似开普勒轨道漂移的天体的径向迁移,一个渐近近似,有时也被称为短摩擦时间近似或漂移通量模型,给出了径向速度等于St ^2的相对误差,其中St是斯托克斯数,即天体停止时间与圆盘中旋转周期(动力学时标)的某个分数之比。

英文摘要:

A systematic analysis of methods for computing the trajectories of solid-phase particles applied in modern astrophysics codes designed for modeling gas-dust circumstellar disks has been carried out for the first time. The motion of grains whose velocities are determined mainly by the gas drag, that is, for which the stopping time or relaxation time for the velocity of the dust to the velocity of the gas t_{stop} is less than or comparable to the rotation period, are considered. The methods are analyzed from the point of view of their stability for computing the motions of small bodies, including dust grains less than 1 micron, which are strongly coupled to the gas. Two test problems are with analytical solutions. Fast first order accurate methods that make it possible to avoid additional restriction on the time step due to gas drag in computations of the motion of grains of any size are presented. For the conditions of a circumstellar disks, the error in the velocity computations obtained when using some stable methods become unacceptably large when the time step size τ>t_{stop}. For the radial migration of bodies that exhibit drifts along nearly Keplerian orbits, an asymptotic approximation, sometimes called the short friction time approximation or drift flux model, gives a relative error for the radial velocity equals to St^2 where St is the Stokes number, the ratio of the stopping time of the body to some fraction of the rotation period (dynamical time scale) in the disk.

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