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The Probability Distribution Function of Column Density in Molecular Clouds

机译:分子云中列密度的概率分布函数

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We discuss the probability distribution function (PDF) of column density resulting from density fields with lognormal PDFs, applicable to isothermal gas (e.g., probably molecular clouds). For magnetic and nonmagnetic numerical simulations of compressible, isothermal turbulence forced at intermediate scales ( of the box size), we find that the autocorrelation function (ACF) of the density field decays over relatively short distances compared to the simulation size. We suggest that a "decorrelation length" can be defined as the distance over which the density ACF has decayed to, for example, 10% of its zero-lag value, so that the density "events" along a line of sight can be assumed to be independent over distances larger than this, and the central limit theorem should be applicable. However, using random realizations of lognormal fields, we show that the convergence to a Gaussian is extremely slow in the high-density tail. As a consequence, the column density PDF is not expected to exhibit a unique functional shape, but to transit instead from a lognormal to a Gaussian form as the ratio η of the column length to the decorrelation length (i.e., the number of independent events in the cloud) increases. Simultaneously, the variance of the PDF decreases. For intermediate values of η, the column density PDF assumes a nearly exponential decay. For cases with a density contrast of 104, as found in intermediate-resolution simulations, and expected from giant molecular clouds (GMCs) to dense molecular cores, the required value of η for convergence to a Gaussian is at least a few hundred, or, for 106, several thousand. We then discuss the density power spectrum and the expected value of η in actual molecular clouds, concluding that they are uncertain since they may depend on several physical parameters. Observationally, our results suggest that η may be inferred from the shape and width of the column density PDF in optically thin line or extinction studies. Our results should also hold for gas with finite-extent power-law underlying density PDFs, which should be characteristic of the diffuse, nonisothermal neutral medium (with temperatures ranging from a few hundred to a few thousand degrees). Finally, we note that for η 100, the dynamic range in column density is small (less than a factor of 10), but this is only an averaging effect, with no implication on the dynamic range of the underlying density distribution.
机译:我们讨论了适用于等温气体(例如,可能是分子云)的具有对数正态PDF的密度场所导致的列密度的概率分布函数(PDF)。对于在中间尺度(箱尺寸)下受迫的可压缩等温湍流的磁性和非磁性数值模拟,我们发现密度场的自相关函数(ACF)与模拟尺寸相比在相对较短的距离上衰减。我们建议将“去相关长度”定义为密度ACF衰减至例如其零延迟值的10%的距离,以便可以假定沿视线的密度“事件”在大于此距离的距离上是独立的,并且中心极限定理应该适用。但是,使用对数正态场的随机实现,我们表明在高密度尾部,收敛到高斯的速度非常慢。结果,列密度PDF不会表现出独特的功能形状,而是会从对数正态转换为高斯形式,因为列长度与去相关长度的比值η(即,独立事件的数量云)增加。同时,PDF的方差减小。对于η的中间值,列密度PDF假设接近指数衰减。对于中等分辨率模拟中发现的密度对比为104的情况,并且预期从巨分子云(GMC)到致密分子核,收敛到高斯所需的η值至少为几百,或者,为106,几千。然后,我们讨论了实际分子云中的密度功率谱和η的期望值,认为它们不确定,因为它们可能取决于几个物理参数。观察到的结果表明,在光学细线或消光研究中,η可以从柱密度PDF的形状和宽度推断得出。对于具有有限范围幂律下标密度PDF的气体,我们的结果也应成立,这应该是弥散的非等温中性介质(温度范围从几百到几千度)的特征。最后,我们注意到对于η100,色谱柱密度的动态范围很小(小于10倍),但这只是平均效应,对基础密度分布的动态范围没有影响。

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