A Semianalytic Model for Supercritical Core Collapse: Self-Similar Evolution and the Approach to Protostar Formation
A Semianalytic Model for Supercritical Core Collapse: Self-Similar Evolution and the Approach to Protostar Formation
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超临界核心塌陷的半解析模型：自相似演化和原恒星形成方法
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发表时间：
1997
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通讯作者：
S. Basu
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作者：
S. Basu
我们使用半分析模型来研究超临界堆芯的坍塌（即，具有超过临界值的质量-通量比的芯）。最近对超临界核的形成和收缩的数值模拟表明，内解趋向于自相似演化。我们使用这个功能来开发的数量，如密度，角速度和磁场的解析表达式。所有的力（重力、磁力、热力和离心力）都可以在薄圆盘几何中解析计算。分析了收缩过程中各力的作用。我们确定了双极扩散的关键作用，在生产偏离一个确切的相似性解决方案。在超临界阶段期间磁通量的缓慢泄漏足以显著加速否则接近准静态的收缩。这导致在原恒星形成时，核心最内部区域以超音速的速度坍缩。我们发现一个依赖于时间的半解析解的后期超临界阶段，并获得渐近形式的重要配置文件的时刻，一个中央原恒星形成。我们得到的旋转速度，下落速度，质量吸积率在这一刻的估计。质量吸积率是显着大于典型的C3/G（其中C是等温声速和G是普遍的引力常数）在原恒星形成的时刻，虽然我们认为，它是随时间而定，并最终会减少。与现有的球形相似性解决方案的预测进行比较。
We use a semianalytic model to examine the collapse of supercritical cores (i.e., cores with a mass-to-flux ratio exceeding a critical value). Recent numerical simulations of the formation and contraction of supercritical cores show that the inner solution tends toward self-similar evolution. We use this feature to develop analytic expressions for quantities such as the density, angular velocity, and magnetic field. All forces involved in the problem (gravitational, magnetic, thermal, and centrifugal) can be calculated analytically in the thin-disk geometry of the problem. The role of each force during the contraction is analyzed. We identify the key role of ambipolar diffusion in producing a departure from an exact similarity solution. The slow leakage of magnetic flux during the supercritical phase is enough to significantly accelerate an otherwise near-quasi-static contraction. This leads to dynamic collapse with supersonic infall speeds in the innermost region of the core by the time of protostar formation. We find a time-dependent semianalytic solution for the late supercritical phase, and asymptotic forms are obtained for important profiles at the moment that a central protostar is formed. We obtain estimates for the rotational velocity, infall velocity, and mass accretion rate at this moment. The mass accretion rate is significantly greater than the canonical C3/G (where C is the isothermal sound speed and G is the universal gravitational constant) at the moment of protostar formation, although we argue that it is time-dependent and will eventually decrease. Comparisons are made with the predictions of existing spherical similarity solutions.