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arXiv 2003.13580gr-qcastro-ph.HE
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广义相对论辐射流体力学的双矩格式：系统描述和新应用

Two-moment scheme for general-relativistic radiation hydrodynamics: a systematic description and new applications

Lukas R. Weih, Hector Olivares, Luciano Rezzolla

备注：
22 pages, 15 figures, matches version accepted to MNRAS
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摘要：

我们提供了一个系统的描述，必要的步骤-和潜在的陷阱遇到-当实施一个两个时刻的计划内的隐式显式（IMEX）计划，包括辐射传输贡献的数值模拟的广义相对论（磁）流体动力学。我们利用的M1封闭，它提供了一个精确的解决方案，光学薄和厚的限制，以及这些限制之间的插值。特别注意的是新兴的隐式守恒方程组的有效解决方案。特别是，我们提出了一个有效的方法来解决这些方程通过反演的$4\times 4$矩阵内的IMEX计划。虽然这种方法依赖于一些近似，但它在精度和计算效率之间提供了一个很好的折衷。经过大量的狭义相对论检验，我们将新的辐射程序\texttt{FRAC}与广义相对论磁流体动力学程序\texttt{BHAC}耦合，研究了辐射Michel解，即在辐射场存在下黑洞的球形吸积问题.通过对这个问题的参数空间进行最广泛的探索，我们发现吸积的效率可以用物理量来表示，如温度、$T$、光度、$L$和黑洞质量$M$，通过表达式$\varepsilon=(L/L_{\rm Edd})/(\dot{M}/\dot{M}_{\rm Edd})= 7.41\times 10^{-7}\left(T/10^6\,\mathrm{K}\right)^{0.22} \left(L/L_\odot\right)^{0.48} \left(M/M_\odot\right)^{0.48}$，其中$L_{\mathrm{Edd}}$和$\dot{M}_{\mathrm{Edd}}$分别是爱丁顿光度和吸积率。最后，我们还考虑了远离球对称的吸积问题，发现在辐射场中的扰动下，解是稳定的。

英文摘要：

We provide a systematic description of the steps necessary -- and of the potential pitfalls to be encountered -- when implementing a two-moment scheme within an Implicit-Explicit (IMEX) scheme to include radiative-transfer contributions in numerical simulations of general-relativistic (magneto-)hydrodynamics. We make use of the M1 closure, which provides an exact solution for the optically thin and thick limit, and an interpolation between these limits. Special attention is paid to the efficient solution of the emerging set of implicit conservation equations. In particular, we present an efficient method for solving these equations via the inversion of a $4\times 4$-matrix within an IMEX scheme. While this method relies on a few approximations, it offers a very good compromise between accuracy and computational efficiency. After a large number of tests in special relativity, we couple our new radiation code, \texttt{FRAC}, with the general-relativistic magnetohydrodynamics code \texttt{BHAC} to investigate the radiative Michel solution, namely, the problem of spherical accretion onto a black hole in the presence of a radiative field. By performing the most extensive exploration of the parameter space for this problem, we find that the accretion's efficiency can be expressed in terms of physical quantities such as temperature, $T$, luminosity, $L$, and black-hole mass, $M$, via the expression $\varepsilon=(L/L_{\rm Edd})/(\dot{M}/\dot{M}_{\rm Edd})= 7.41\times 10^{-7}\left(T/10^6\,\mathrm{K}\right)^{0.22} \left(L/L_\odot\right)^{0.48} \left(M/M_\odot\right)^{0.48}$, where $L_{\mathrm{Edd}}$ and $\dot{M}_{\mathrm{Edd}}$ are the Eddington luminosity and accretion rate, respectively. Finally, we also consider the accretion problem away from spherical symmetry, finding that the solution is stable under perturbations in the radiation field.

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