是否存在普遍的质量函数？
Is There a Universal Mass Function?
摘要：
根据Fritz Zwicky的旧思想，我们试图建立一个所有尺度上天体的普遍质量函数。所考虑的天体类别是：太阳系行星和小天体、系外行星、褐矮星、恒星和恒星残骸、疏散星团和球状星团、分子云、星系、星系群和星系团。为了比较，我们还包括CDM晕从数值模拟。我们发现，当适当地归一化时，单个对象类的质量函数确实可以连接起来，以建立一个令人惊讶的连续宇宙质量函数，从大约M = 10^（-20）Msun（小于公里大小的小行星）到M = 10^（16）Msun（丰富的星系团），覆盖36个数量级的质量。大多数单个质量函数大致遵循形式为φ（M）propto M^（-2）的幂律。一个值得注意的例外是行星和小天体，它们似乎服从更平坦的分布。高分辨率数值模拟的CDM晕显示了一个非常相似的关系，同样是普遍的斜率-2，从星系团一直到行星质量尺度。在恒星和星团的尺度上，这是一个显著的巧合，因为所涉及的形成过程被认为是完全不同的（DM晕的自下而上的重力聚集与气体云的自上而下的重力湍流破碎）。
英文摘要：
Following an old idea of Fritz Zwicky, we make an attempt to establish a universal mass function for astronomical objects on all scales. The object classes considered are: solar system planets and small bodies, exoplanets, brown dwarfs, stars and stellar remnants, open and globular clusters, molecular clouds, galaxies, groups and clusters of galaxies. For comparison we also include CDM halos taken from numerical simulations. We show that the mass functions of individual object classes, when properly normalized, can indeed be concatenated to build a surprisingly continuous mass function of the universe, from approximately M = 10^(-20)Msun (sub-kilometer size asteroids) up to M = 10^(16)Msun (rich clusters of galaxies), covering 36 orders of magnitude in mass. Most individual mass functions roughly follow a power law of the form phi(M) propto M^(-2). A notable exception are planets and small bodies which seem to obey a flatter distribution. CDM halos from high-resolution numerical simulations show a very similar relation, again of universal slope -2, from clusters of galaxies all the way down to the planetary mass scale. On the scale of stars and star clusters this is a remarkable coincidence, as the formation processes involved are thought to be totally different (bottom-up gravitational clustering of DM halos versus top-down gravoturbulent fragmentation of gas clouds).
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