The effect of extreme ionization rates during the initial collapse of a molecular cloud core (dataset)

What cosmic ray ionization rate is required such that a non-ideal magnetohydrodynamics (MHD) simulation of a collapsing molecular cloud will follow the same evolutionary path as an ideal MHD simulation or as a purely hydrodynamics simulation? To investigate this question, we perform three-dimensional smoothed particle non-ideal MHD simulations of the gravitational collapse of rotating, one solar mass, magnetized molecular cloud cores, which include Ohmic resistivity, ambipolar diffusion, and the Hall effect. We assume a uniform grain size of ag = 0.1 μm, and our free parameter is the cosmic ray ionization rate, ζcr. We evolve our models, where possible, until they have produced a first hydrostatic core. Models with ζcr ≳ 10−13 s−1 are indistinguishable from ideal MHD models, and the evolution of the model with ζcr = 10−14 s−1 matches the evolution of the ideal MHD model within 1 per cent when considering maximum density, magnetic energy, and maximum magnetic field strength as a function of time; these results are independent of ag. Models with very low ionization rates (ζcr ≲ 10−24 s−1) are required to approach hydrodynamical collapse, and even lower ionization rates may be required for larger ag. Thus, it is possible to reproduce ideal MHD and purely hydrodynamical collapses using non-ideal MHD given an appropriate cosmic ray ionization rate. However, realistic cosmic ray ionization rates approach neither limit; thus, non-ideal MHD cannot be neglected in star formation simulations.

为探究需满足何种宇宙线电离率（cosmic ray ionization rate, ζcr），方能使坍缩分子云的非理想磁流体动力学（non-ideal magnetohydrodynamics, MHD）模拟与理想磁流体动力学（ideal MHD）模拟或纯流体动力学（purely hydrodynamics）模拟遵循相同的演化路径，我们针对旋转的、1倍太阳质量（solar mass）的磁化分子云核的引力坍缩过程，开展了三维光滑粒子非理想MHD模拟。该模拟涵盖欧姆电阻率（Ohmic resistivity）、双极扩散（ambipolar diffusion）与霍尔效应（Hall effect）三类物理过程，我们设定均匀晶粒尺寸ag=0.1μm，并将ζcr作为自由可调参数。在条件允许的情况下，我们将所有模型演化至形成首个流体静力学核（first hydrostatic core）为止。当ζcr≳10⁻¹³ s⁻¹时，模拟结果与理想MHD模型几乎无法区分；而当ζcr=10⁻¹⁴ s⁻¹时，若以最大密度、磁能及最大磁场强度随时间的变化为考察指标，其演化过程与理想MHD模型的偏差不超过1%，且上述结论与ag的取值无关。若要逼近纯流体动力学坍缩的演化过程，则需极低的宇宙线电离率（ζcr≲10⁻²⁴ s⁻¹）；若分子云核的晶粒尺寸更大，则可能需要更低的电离率方能实现。综上，通过选取合适的宇宙线电离率，可利用非理想MHD模拟复现理想MHD与纯流体动力学坍缩过程。但实际宇宙线电离率并不趋近于这两类极端情形，因此在恒星形成模拟中，非理想MHD效应不容忽视。