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arXiv 1208.3170astro-ph.EP
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近无粘性盘中的低质量行星:数值处理

Low-mass planets in nearly inviscid disks: Numerical treatment

Wilhelm Kley, Tobias W. A. Mueller, Stefan M. Kolb, Pablo Benitez-Llambay, Frederic Masset

摘要:

嵌入行星扰动了周围盘的密度结构,引力反作用可能引起行星轨道根数的变化。精确测定作用在行星上的力需要仔细的数值分析。最近,经常使用的快速轨道平流算法(FARGO)的有效性已被质疑,并提出了特殊的数值分辨率和稳定性要求。本文研究了几个地球质量的小质量行星的行星-盘相互作用过程,并重新分析了数值要求,以获得收敛和稳定的结果。一个焦点在于FARGO算法的适用性。此外,我们研究了二维和三维模拟的差异,比较全球与本地设置,以及等温和绝热条件。我们通过二维和三维流体动力学模拟研究行星对盘的影响。为了加强我们的结论,我们进行了详细的数值比较,几个逆风和黎曼求解器为基础的代码使用和不使用FARGO算法。关于尾流结构和作用在行星上的扭矩密度,我们证明了FARGO算法产生正确的结果,并且在常规CPU时间的一小部分。我们发现,在unshocked区域实现收敛的结果的分辨率要求是相当温和的,并依赖于磁盘的压力标度高度。通过比较2D和3D模拟的扭矩密度,我们表明,一个合适的垂直平均力的程序给出了一个很好的协议两者之间。我们表明,等温和绝热运行可以有很大的不同,即使绝热指数非常接近统一。

英文摘要:

Embedded planets disturb the density structure of the ambient disk and gravitational back-reaction will induce possibly a change in the planet's orbital elements. The accurate determination of the forces acting on the planet requires careful numerical analysis. Recently, the validity of the often used fast orbital advection algorithm (FARGO) has been put into question, and special numerical resolution and stability requirements have been suggested. In this paper we study the process of planet-disk interaction for small mass planets of a few Earth masses, and reanalyze the numerical requirements to obtain converged and stable results. One focus lies on the applicability of the FARGO-algorithm. Additionally, we study the difference of two and three-dimensional simulations, compare global with local setups, as well as isothermal and adiabatic conditions. We study the influence of the planet on the disk through two- and three-dimensional hydrodynamical simulations. To strengthen our conclusions we perform a detailed numerical comparison where several upwind and Riemann-solver based codes are used with and without the FARGO-algorithm. With respect to the wake structure and the torque density acting on the planet we demonstrate that the FARGO-algorithm yields correct results, and that at a fraction of the regular cpu-time. We find that the resolution requirements for achieving convergent results in unshocked regions are rather modest and depend on the pressure scale height of the disk. By comparing the torque densities of 2D and 3D simulations we show that a suitable vertical averaging procedure for the force gives an excellent agreement between the two. We show that isothermal and adiabatic runs can differ considerably, even for adiabatic indices very close to unity.

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