The emergence and development of a power-law tail (PLT) at the high-density end of the observed column-density distribution are thought to be indicative for advanced evolution of star-forming molecular clouds. As shown from many numerical simulations, it corresponds to a morphologically analogous evolution of the mass-density distribution (ρ-PDF). The latter may display also a second, shallower PLT at the stage of collapse of the first formed protostellar cores. It is difficult to estimate the parameters of a possible second PLT due to resolution constraints. To address the issue, we extend the method for the extraction of single PLTs from arbitrary density distributions suggested by Veltchev et al. (MNRAS, 489, 788, 2019) to detect a second PLT. The technique is elaborated through tests on an analytic ρ-PDF and applied to a set of hydrodynamical high-resolution simulations of isothermal self-gravitating clouds. In all but one case two PLTs were detected—the first slope is always steeper and the second one is typically . These results are in a good agreement with numerical and theoretical works and do suggest that the technique extracts correctly double PLTs from smooth PDFs.

中文翻译：

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提取模拟云中密度分布的二次幂律尾

在观测到的柱密度分布的高密度端出现和发展幂律尾 (PLT) 被认为是恒星形成分子云高级演化的指示。正如许多数值模拟所示，它对应于质量密度分布 ( ρ -PDF)的形态学类似演变。后者也可能在最初形成的原恒星核心坍缩阶段显示出第二个更浅的 PLT。由于分辨率限制，很难估计可能的第二个 PLT 的参数。为了解决这个问题，我们扩展了从 Veltchev 等人建议的任意密度分布中提取单个 PLT 的方法。( MNRAS, 489, 788, 2019) 来检测第二个 PLT。该技术通过对解析ρ -PDF 的测试进行了阐述，并应用于一组等温自引力云的流体动力学高分辨率模拟。除了一种情况外，在所有情况下都检测到两个 PLT——第一个斜率总是更陡，而第二个斜率通常是。这些结果与数值和理论工作非常一致，并且确实表明该技术从平滑 PDF 中正确提取了双 PLT。