具有非零初速度的奇异等温球形分子云核的非相似坍缩
Non-similar collapse of singular isothermal spherical molecular cloud cores with nonzero initial velocities
摘要：
从理论上讲，恒星是由分子云的核心坍缩形成的。历史上，核被假定为一个奇异的等温球（SIS），并通过自相似的方式研究了崩溃。这是因为旋转和磁场导致非对称塌陷，从而可能出现球体形状。这里，假设离心力和磁场梯度的合力在旋转轴的法线方向上，并且假设其分量是局部重力的分数$β$。在这项研究中，一个崩溃的SIS核心被认为是发现的重要性，参数$β$的扁率的质量壳的头部以上的膨胀波。我们应用Adomian分解方法求解非线性偏微分方程组，因为坍缩不会发生在具有自相似行为的球对称中。这样，我们得到了壳在包线处的质量下落率$\dot{M}$的半解析关系式。在旋转轴附近，$\dot{M}$随无量纲半径$ξ$的增大而减小，而在赤道区，$\dot{M}$与$ξ$之间存在正相关关系。此外，极区中的$\dot{M}$值大于赤道区的值，并且这种差异更经常出现在较小的$ξ$值处。结果表明，在到达膨胀波头部之前，分子云核的可见形状可以演化为扁球体。扁圆核的长短轴比随参数$β$的增大而增大，其值可接近于金牛座和英仙座等分子云图中明显观察到的细长核形状。
英文摘要：
Theoretically, stars have been formed from the collapse of cores in the molecular clouds. Historically, the core had been assumed as an singular isothermal sphere (SIS), and the collapse had been investigated by a self-similar manner. This is while the rotation and magnetic field lead to non-symmetric collapse so that a spheroid shape may be occurred. Here, the resultant of the centrifugal force and magnetic field gradient is assumed to be in the normal direction of the rotational axis, and its components are supposed to be a fraction $β$ of the local gravitational force. In this research, a collapsing SIS core is considered to find the importance of the parameter $β$ for oblateness of the mass shells which are above the head of the expansion wave. We apply the Adomian decomposition method to solve the system of nonlinear partial differential equations because the collapse does not occur in a spherical symmetry with self-similar behavior. In this way, we obtain a semi-analytical relation for the mass infall rate $\dot{M}$ of the shells at the envelope. Near the rotational axis, the $\dot{M}$ decreases with increasing of the non-dimensional radius $ξ$, while a direct relation is observed between $\dot{M}$ and $ξ$ in the equatorial regions. Also, the values of $\dot{M}$ in the polar regions are greater than the equatorial values, and this difference is more often at smaller values of $ξ$. Overall, the results show that before reaching the head of expansion wave, the visible shape of the molecular cloud cores can evolve to oblate spheroids. The ratio of major to minor axes of oblate cores increases with increasing the parameter $β$, and its value can approach to the apparently observed elongated shapes of cores in the maps of molecular clouds such as Taurus and Perseus.
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