Universality of the subsolar mass distribution from critical gravitational collapse

Abstract

Self-similarity induced by critical gravitational collapse is used as a paradigm to probe the mass distribution of subsolar objects. At large mass (solar mass and above) there is widespread agreement as to both the form and parameter values arising in the mass distribution of stellar objects. At subsolar mass there is still considerable disagreement as to the qualitative form of the mass distribution, let alone the specific parameter values characterizing that distribution. For the first time, the paradigm of critical gravitational collapse is applied to several concrete astrophysical scenarios to derive robust qualitative features of the subsolar mass distribution. We further contrast these theoretically derived ideas with the observational situation. In particular, we demonstrate that at very low mass the distribution is given by a power law, with an exponent opposite in sign to that observed in the high-mass regime. The value of this low-mass exponent is in principle calculable via dynamical systems theory applied to gravitational collapse. Qualitative agreement between theory, numerical experiments, and observational data is good, though quantitative issues remain troublesome.