标题： 关于热恒星系统的质量-半径关系 显示英文标题

标题： On the mass-radius relation of hot stellar systems

摘要： 大多数球状星团的半质量半径为几秒差距，与其质量之间没有明显的相关性。 这与椭圆星系不同，法伯-杰克逊关系表明质量与半径之间存在强烈的正相关性。 介于球状星团和低质量星系之间的天体，例如超致密矮星系，其质量-半径关系与明亮椭圆星系关系的延伸一致。 在这里我们表明，在10 Gyr的年龄时，在约10^6 Msun处出现质量-半径关系的转折，因为低于该质量的天体，即球状星团，由于恒星演化和硬双星而经历了膨胀。 从数值模拟中我们发现，这两个效应在核心中的联合能量产生与通过弛豫在半质量半径上传导的能量通量达到平衡。 这种“平衡”演化的关键特性是，星团的半质量半径与其初始值无关，仅取决于束缚恒星的数量和年龄。 因此无法推断球状星团的初始质量-半径关系，我们只能得出结论，目前的性质与所有热恒星系统最初具有相同质量-半径关系的假设是一致的，并且球状星团由于哈勃时间的恒星和动力学演化而偏离了这一关系。 显示英文摘要

摘要： Most globular clusters have half-mass radii of a few pc with no apparent correlation with their masses. This is different from elliptical galaxies, for which the Faber-Jackson relation suggests a strong positive correlation between mass and radius. Objects that are somewhat in between globular clusters and low-mass galaxies, such as ultra-compact dwarf galaxies, have a mass-radius relation consistent with the extension of the relation for bright ellipticals. Here we show that at an age of 10 Gyr a break in the mass-radius relation at ~10^6 Msun is established because objects below this mass, i.e. globular clusters, have undergone expansion driven by stellar evolution and hard binaries. From numerical simulations we find that the combined energy production of these two effects in the core comes into balance with the flux of energy that is conducted across the half-mass radius by relaxation. An important property of this `balanced' evolution is that the cluster half-mass radius is independent of its initial value and is a function of the number of bound stars and the age only. It is therefore not possible to infer the initial mass-radius relation of globular clusters and we can only conclude that the present day properties are consistent with the hypothesis that all hot stellar systems formed with the same mass-radius relation and that globular clusters have moved away from this relation because of a Hubble time of stellar and dynamical evolution.