STAR FORMATION: STATISTICAL MEASURE OF THE CORRELATION BETWEEN THE PRESTELLAR CORE MASS FUNCTION AND THE STELLAR INITIAL MASS FUNCTION

We present a simple statistical analysis of recent numerical simulations exploring the correlation between the core mass function (CMF) obtained from the fragmentation of a molecular cloud and the stellar mass function which forms from these collapsing cores. Our analysis shows that the distributions of bound cores and sink particles obtained in the simulations are consistent with the sinks being formed predominantly from their parent core mass reservoir, with a statistical dispersion of the order of one-third of the core mass. Such a characteristic dispersion suggests that the stellar initial mass function (IMF) is relatively tightly correlated to the parent CMF, leading to two similar distributions, as observed. This in turn argues in favor of the IMF being essentially determined at the early stages of core formation and being only weakly affected by the various environmental factors beyond the initial core mass reservoir, at least in the mass range explored in the present study. Accordingly, the final IMF of a star-forming region should be determined reasonably accurately, statistically speaking, from the initial CMF, provided some uniform efficiency factor. The calculations also show that these statistical fluctuations, due to, e. g., variations among the core properties, broaden the low-mass tail of the IMF compared with the parent CMF, providing an explanation for the fact that the latter appears to underestimate the number of "pre brown dwarf" cores compared with the observationally derived brown dwarf IMF.