Binary star formation from ring fragmentation

We present a simple model of binary star formation based on the assumption that rotating prestellar cores collapse to form rings and these rings then fragment into protostars. We assume that each ring spawns a small number (N <= 6) of protostars, and that the condensation of the protostars is sufficiently rapid that they can subsequently be treated as point masses. The first part of the model is therefore to simulate the dynamical evolution of a ring of N stars and record the properties of the single stars, binaries and higher multiples that form as a result of the dissolution of the ring. The masses of the individual stars in a ring are drawn from a log-normal distribution with dispersion sigma(logM). This part of the model is perfomed for many different realizations of the ring, to obtain good statistics. It can be formulated using dimensionless variables and immediately yields the overall multiplicity. The second part of the model is to convolve the results of these dimensionless simulations, first with the distribution of core masses, which yields the distributions of multiplicity, mass ratio and eccentricity, as a function of primary mass; and second with the distribution of core angular momenta, which yields the distributions of semi-major axis and period, again as a function of primary mass. Using the observed distribution of core masses, and a distribution of core angular momenta which is consistent with the observations, our model is able to reproduce the observed IMF, the observed high multiplicity frequency of pre-Main Sequence stars, the observed distribution of separations, and - for long-period systems - the observed distributions of eccentricity and mass-ratio, provided we invoke N = 4 or 5 and sigma(logM) = 0.6. We presume that for short-period systems the distributions of eccentricity and mass-ratio are modified by the dissipative effects of subsequent tidal interaction and competitive accretion; and that the reduced multiplicity frequency in the field, compared with young clusters, is the result of dynamical interactions between stars formed in different cores but the same cluster, following ring dissolution. Further numerical experiments are required to explore the consequences of such interactions.