arXiv 0907.29072009-07-16astro-ph.GAastro-ph.SR

星际介质中的激波涡和恒星初始质量函数的起源

Shock generated vorticity in the interstellar medium and the origin of the stellar initial mass function

N. Kevlahan, Ralph E. Pudritz

备注：: 26 pages, 5 figures, accepted for publication in the Astrophysical Journal
DOI：: 10.1088/0004-637X/702/1/39

摘要：

星际介质和分子云中湍流的主要观测证据是速度涨落的幂律能谱E（k）\propto k ^α。柯尔莫哥洛夫标度指数α =-5/3是典型的。同时，在ISM和分子云中观测到的气体密度的概率分布函数（PDF）都是对数正态分布，这与描述恒星质量分布的初始质量函数（IMF）相似。本文研究了在运动学极限下弯曲激波穿越星际气体时的密度和速度结构。我们从数学上证明，只有几个通道的弯曲冲击波一般产生对数正态密度PDF。这解释了对数正态PDF在许多不同数值模拟中的普遍性。我们还表明，随后的相互作用与球形爆炸波产生的幂律密度分布在高密度，定性类似的萨尔彼得幂律的IMF。最后，我们表明，一个聚焦激波产生的下游流的能谱指数α =-2。随后的激波通道减小了这个斜率，在几个通道后达到α \approx-5/3。随后在小尺度上堆积的能量的耗散将起作用，以保持光谱非常接近Kolomogorov值。因此，可能不需要充分发展的湍流来解释观测到的能谱和密度PDF。我们认为，自相似的球形冲击波所产生的HII区域或恒星风从大质量的恒星可能最终负责创建高质量，幂律，在IMF的尾巴。

英文摘要：

The main observational evidence for turbulence in the interstellar medium (ISM) and molecular clouds is the power-law energy spectrum for velocity fluctuations, E(k) \propto k^α. The Kolmogorov scaling exponent, α=-5/3, is typical. At the same time, the observed probability distribution function (PDF) of gas densities in both the ISM as well as in molecular clouds is a log-normal distribution, which is similar to the initial mass function (IMF) that describes the distribution of stellar masses. We examine the density and velocity structure of interstellar gas traversed by curved shock waves in the kinematic limit. We demonstrate mathematically that just a few passages of curved shock waves generically produces a log-normal density PDF. This explains the ubiquity of the log-normal PDF in many different numerical simulations. We also show that subsequent interaction with a spherical blast wave generates a power-law density distribution at high densities, qualitatively similar to the Salpeter power-law for the IMF. Finally, we show that a focused shock produces a downstream flow with energy spectrum exponent α=-2. Subsequent shock passages reduce this slope, achieving α\approx -5/3 after a few passages. Subsequent dissipation of energy piled up at the small scales will act to maintain the spectrum very near to the Kolomogorov value. Therefore, fully-developed turbulence may not be required to explain the observed energy spectrum and density PDF. We argue that the self-similar spherical blast wave arising from expanding HII regions or stellar winds from massive stars may ultimately be responsible for creating the high mass, power-law, tail in the IMF.

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