幂律势和对数势中的椭圆对称螺旋吸积
Cylindrically Symmetric Spiraling Accretion in Power-law and Logarithmic Potentials
摘要：
本文研究了幂律势和对数势中多方测试物质在对称轴上螺旋运动的圆柱对称稳态吸积。该模型允许一个定性地了解吸积过程中的对称性不同于经典的邦迪吸积。我们研究了积分曲线作为某些哈密顿量的能级线，并将这种方法应用于Bondi吸积。幂律势（以及任何与半径有关的势）中的等温解可以用Lambert W函数的精确形式表示，而在对数势的情况下，可以找到任何多变指数的精确解。
英文摘要：
We study cylindrically symmetric steady-state accretion of polytropic test matter spiraling onto the symmetry axis in power-law and logarithmic potentials. The model allows one to qualitatively understand the accretion process in a symmetry different from that of the classical Bondi accretion. We study the integral curves as level lines of some Hamiltonian and also apply this method to Bondi accretion. The isothermal solutions in power-law potentials (as well as in any radius-dependent potential) can be expressed in exact form in terms of the Lambert W function, while in the case of logarithmic potential, exact solutions can be found for any polytropic exponent.
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