Inverse dynamical population synthesis and star formation

Recent observations of pre-main-sequence stars suggest that all stars may form in multiple systems. However, in the Galactic field only about 50 per cent of all systems are binary stars. We investigate the hypothesis that stars form in aggregates of binary systems and that the dynamical evolution of these aggregates leads to the observed properties of binary stars in the Galactic field. A thorough analysis of star count data implies that the initial stellar mass function rises monotonically with decreasing mass and that it can be approximated by three power-law segments. Together with our assumption that the birth mass-ratio distribution is not correlated, this leads to a contradiction with the distribution of secondary masses in Galactic field binaries with G dwarf primaries which have too few low-mass companions. For the inverse dynamical population synthesis we assume that the initial distribution of periods is flat in log(10)P, where P is the orbital period in days, and 3 less than or equal to log(10)P less than or equal to 17.5. This is consistent with pre-main-sequence data. We distribute N-bin = 200 binaries in aggregates with half-mass radii 0.077 less than or equal to R(0.5)less than or equal to 2.53 pc, corresponding to the range from tightly clustered to isolated star formation, and follow the subsequent evolution of the stellar systems by direct N-body integration. We find that hardening and softening of binary systems do not significantly increase the numbers of orbits with log(10)P<3 and log(10)P>7.5, respectively. After the cluster with R(0.5) approximate to 0.8 pc disintegrates we obtain a population which consists of about 60 per cent binary systems with a period distribution for log(10)P>4, as is observed, and in which the G dwarf binaries have a mass-ratio distribution which agrees with the observed distribution. This result indicates that the majority of Galactic field stars may originate from a clustered star-formation mode, characterized by the dominant-mode cluster which has initially (N-bin, R(0.5)) approximate to (200, 0.8 pc). We invert the orbit depletion function and obtain an approximation to the initial binary star period distribution for star formation in the dominant-mode cluster. Comparison with the measured distribution of orbits for pre-main-sequence stars formed in the distributed mode of star formation suggests that the initial distribution of binary star orbits may not depend on the star-formation environment. If a different stellar mass function to the one we adopted is assumed then inverse dynamical population synthesis cannot solve for an aggregate in which the initial binary star population evolves to the observed population in the Galactic field. This implies that the Galactic field stellar mass function may be related to the stellar density at birth in the most common, or dominant, mode of star formation.