初始质量函数的解析理论：CO团块和星前核
Analytical theory for the initial mass function: CO clumps and prestellar cores
摘要：
我们推导出一个分析理论的星前核心的初始质量函数的基础上扩展的新闻-Schechter统计形式主义。用同样的方法，我们还得到了超音速流中非自引力团簇的质谱。自引力核的质谱很好地再现了观测到的初始质量函数，并确定了对其行为负责的不同机制。该理论预测IMF的形状来自两个相互竞争的贡献，即大尺度下的幂律和以引力坍缩的特征质量为中心的指数截止（对数正态形式）。在纯热坍缩的情况下，只要下面的密度场具有对数正态分布，截止点就已经存在。而纯粹的热塌缩产生的幂律尾部比萨尔彼得值dN/dlog M \propto M^{-x}更陡，x=1.35，后者是完全恢复的速度功率谱的谱指数的（3D）值，n \simeq 3.8，发现在观测和等温超音速湍流的数值模拟。实际上，该理论预测，对于自引力结构，x=（n+1）/（2n-4），对于非自引力结构，x=2-n '/3，其中n'是log（rho）的功率谱指数。我们发现，虽然超音速湍流促进了大质量恒星和褐矮星的形成，但它对恒星形成有整体负面影响，降低了恒星形成效率。这一理论为理解货币基金组织的起源和推断其在不同环境中的行为提供了一个新的理论基础。它还为探索恒星形成的数值模拟提供了一种补充方法和有用的指导，同时做出了可测试的预测。
英文摘要：
We derive an analytical theory of the prestellar core initial mass function based on an extension of the Press-Schechter statistical formalism. With the same formalism, we also obtain the mass spectrum for the non self-gravitating clumps produced in supersonic flows. The mass spectrum of the self-gravitating cores reproduces very well the observed initial mass function and identifies the different mechanisms responsible for its behaviour. The theory predicts that the shape of the IMF results from two competing contributions, namely a power-law at large scales and an exponential cut-off (lognormal form) centered around the characteristic mass for gravitational collapse. The cut-off exists already in the case of pure thermal collapse, provided that the underlying density field has a lognormal distribution. Whereas pure thermal collapse produces a power-law tail steeper than the Salpeter value, dN/dlog M\propto M^{-x}, with x=1.35, this latter is recovered exactly for the (3D) value of the spectral index of the velocity power spectrum, n\simeq 3.8, found in observations and in numerical simulations of isothermal supersonic turbulence. Indeed, the theory predicts that x=(n+1)/(2n-4) for self-gravitating structures and x=2-n'/3 for non self-gravitating structures, where n' is the power spectrum index of log(rho). We show that, whereas supersonic turbulence promotes the formation of both massive stars and brown dwarfs, it has an overall negative impact on star formation, decreasing the star formation efficiency. This theory provides a novel theoretical foundation to understand the origin of the IMF and to infer its behaviour in different environments. It also provides a complementary approach and useful guidance to numerical simulations exploring star formation, while making testable predictions.
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