巨分子云（GMC）的柱密度概率分布函数（N-PDF）已被用作恒星形成的诊断工具。模拟与解析预言表明，N-PDF 由低密度的对数正态分量与高密度的幂律分量组成，分别追踪湍流与引力坍缩。本文研究真实二维柱密度分布的各种性质如何塑造 PDF 的形状，即其“结构”。我们同时利用基于 Herschel 尘埃辐射观测的真实 PDF，以及采用 ENZO 程序的模拟来检验这些思想与解析方法。通过树状图（dendrogram）分析，我们考察 N-PDF 的三个主要组成部分：对数正态分量、幂律分量，以及两者之间的过渡点。我们发现，N-PDF 的幂律分量是由树状图算法所识别的各幂律子结构的 N-PDF 之和。我们还发现，Burkhart、Stalpes 与 Collins（2017）提出的对数正态分量与幂律分量之间过渡点的解析解，在观测与模拟的不确定度范围内是适用的。我们进一步确认并拓展了 Lombardi、Alves 与 Lada（2015）的结论：由于地图范围的人为选择，N-PDF 的对数正态分量难以约束。基于所得到的 N-PDF 结构分析，我们建议不要仅凭对对数正态分量的拟合来分析恒星形成区的柱密度结构，并建议将 N-PDF 分析与树状图算法结合使用，以更全面地了解全局与局域环境及其对密度结构的影响。
主题词： ISM： 云，星系：恒星形成，磁流体动力学： MHD:主题词： ISM： 云，星系：恒星形成，磁流体动力学： MHD
恒星形成发生于分子环境中致密的丝状结构内，这些结构受引力、磁场与湍流复杂相互作用的支配（McKee & Ostriker 2007）。在秒差距尺度上，气体密度的初始分布受平均密度、湍流强度与磁场强度的影响，可能决定恒星形成在天文单位尺度上的性质，如初始质量函数（IMF）与整体恒星形成率（Krumholz & McKee 2005；Hennebelle & Chabrier 2011；Padoan & Nordlund 2011a,b；Federrath & Klessen 2012；Mocz et al. 2017）。
柱密度概率分布函数（N-PDF）是量化气体分布的常用工具。模拟与观测均表明，N-PDF 是诊断局域恒星形成云中湍流与恒星形成效率的重要手段（Federrath & Klessen 2012；Collins et al. 2010；Burkhart et al. 2015a；Myers 2015）。这是因为 N-PDF 能约束分子云中致密气体的比例，并提供与解析模型以及数值模拟（经由合成观测）比较的途径。
就观测而言，N-PDF 已被广泛用于星际介质的多种示踪物，包括如 CO 的分子谱线示踪物（Lee et al.
2012；Burkhart et al. 2013b），以及如尘埃的柱密度示踪物（Kainulainen et al. 2009；Froebrich & Rowles 2010；Schneider et al. 2013, 2014, 2015b；Lombardi et al. 2015）。利用尘埃辐射与吸收来示踪 N-PDF 可提供最大的密度动态范围，这与 CO 等分子谱线示踪物形成对比——后者因耗损与不透明效应而无法示踪真实的柱密度分布（Goodman et al. 2009a；Burkhart et al. 2013a,b）。
真实的三维密度（体密度）PDF 与 N-PDF 都被用于理解银河系气体动力学的性质，从弥漫的电离介质到致密的恒星形成云（Hill et al. 2008；Burkhart et al. 2010；Maier et al. 2017）。这是因为密度／柱密度 PDF 的形状预期与云的基础物理相关，并与气体的运动学和化学相联系（Vazquez-Semadeni 1994；Padoan et al. 1997；Kritsuk et al. 2007；Burkhart et al. 2013b, 2015a）。
分子云中的低柱密度气体，以及弥漫的中性与电离星际介质，呈现对数正态形式（Vazquez-Semadeni 1994；Hill et al. 2008；Kainulainen & Tan 2013）。这主要归因于中心极限定理应用于由乘积过程（如激波）所产生的层级（如湍流）密度场。若能测量 N-PDF 对数正态部分的宽度，则其可能与近等温云中气体的声速马赫数相关（Federrath et al. 2008；Burkhart et al. 2009；Kainulainen & Tan 2013；Burkhart & Lazarian 2012；Burkhart et al. 2015a）。
然而，对该分布进行约束存在已知的注意事项，
The column density probability distribution function (N-PDF) of GMCs has been used as a diagnostic of star formation. Simulations and analytic predictions have suggested the N-PDF is composed of a low density lognormal component and a high density power-law component, tracing turbulence and gravitational collapse, respectively. In this paper, we study how various properties of the true 2D column density distribution create the shape, or "anatomy" of the PDF. We test our ideas and analytic approaches using both a real, observed, PDF based on Herschel observations of dust emission as well as a simulation that uses the ENZO code. Using a dendrogram analysis, we examine the three main components of the N-PDF: the lognormal component, the power-law component, and the transition point between these two components. We find that the power-law component of an N-PDF is the summation of N-PDFs of power-law substructures identified by the dendrogram algorithm. We also find that the analytic solution to the transition point between lognormal and power-law components proposed by Burkhart, Stalpes, & Collins (2017) is applicable when tested on observations and simulations, within the uncertainties. We reconfirm and extend the results of Lombardi, Alves, & Lada (2015), which stated that the lognormal component of the N-PDF is difficult to constrain due to the artificial choice of the map area. Based on the resulting anatomy of the N-PDF, we suggest avoiding analyzing the column density structures of a star forming region based solely on fits to the lognormal component of an N-PDF. We also suggest applying the N-PDF analysis in combination with the dendrogram algorithm, to obtain a more complete picture of the global and local environments and their effects on the density structures.
Subject headings: ISM: clouds, galaxies: star formation, magnetohydrodynamics: MHD
Star formation occurs in dense filamentary structures within molecular environments that are governed by the complex interaction of gravity, magnetic fields, and turbulence (McKee & Ostriker 2007). The initial distribution of the gas density at parsec scales, which is affected by the average density, level of turbulence and magnetic field strength, may determine the AU scale properties of star formation such as the initial mass function (IMF) and the overall star formation rate (Krumholz & McKee 2005; Hennebelle & Chabrier 2011; Padoan & Nordlund 2011a,b; Federrath & Klessen 2012; Mocz et al. 2017).
The column density probability distribution function (N-PDF) is a commonly used tool for quantifying the distribution of gas. Simulations and observations have shown N-PDFs to be an important diagnostic of turbulence and star formation efficiency in local star forming clouds (Federrath & Klessen 2012; Collins et al. 2010; Burkhart et al. 2015a; Myers 2015). This is because N-PDFs can constrain the fraction of dense gas within molecular clouds and provide a means of comparison with analytic models as well as numerical simulations (via synthetic observations) of star formation.
N-PDFs, as available from observations, have been utilized extensively for many different tracers of the ISM. This includes molecular line tracers such as CO (Lee et al.
2012; Burkhart et al. 2013b) and column density tracers such as dust (Kainulainen et al. 2009; Froebrich & Rowles 2010; Schneider et al. 2013, 2014, 2015b; Lombardi et al. 2015). Tracing the N-PDF using dust emission and absorption provides the largest dynamic range of densities, in contrast to molecular line tracers such as CO, which do not trace the true column density distribution due to depletion and opacity effects (Goodman et al. 2009a; Burkhart et al. 2013a,b).
Both the true 3D density (volume density) PDF and N-PDFs have been used to understand the properties of galactic gas dynamics, from the diffuse ionized medium to dense star-forming clouds (Hill et al. 2008; Burkhart et al. 2010; Maier et al. 2017). This is because the shape of the density/column density PDF is expected to be related to the underlying physics of the cloud and linked to the kinematics and the chemistry of the gas (Vazquez-Semadeni 1994; Padoan et al. 1997; Kritsuk et al. 2007; Burkhart et al. 2013b, 2015a).
The low column density gas in molecular clouds, as well as in the diffuse neutral and ionized ISM, takes on the form of a lognormal (Vazquez-Semadeni 1994; Hill et al. 2008; Kainulainen & Tan 2013). This is primarily attributed to the application of the central limit theorem to a hierarchical (e.g. turbulent) density field generated by a multiplicative process, such as shocks. If the width of the lognormal portion of the N-PDF can be measured, it may be related to the sonic Mach number of the gas in a nearly isothermal cloud (Federrath et al. 2008; Burkhart et al. 2009; Kainulainen & Tan 2013; Burkhart & Lazarian 2012; Burkhart et al. 2015a).
However, there are known caveats to constraining the
The same paper, in two languages. Every column, equation, and footnote exactly where the author set it.
Figures carry over too: axes, labels, and captions, down to the dendrogram’s smallest leaves.