STAR CLUSTER EVOLUTION, DYNAMICAL AGE ESTIMATION AND THE KINEMATICAL SIGNATURE OF STAR-FORMATION

We distribute 400 model stars in N-bin = 200 binary systems in cluster s with initial half-mass radii 0.077 less than or equal to R(0.5) less than or equal to 2.53 pc and follow the subsequent evolution of the s tellar systems by direct N-body integration. The stellar masses are in itially paired at random from the KTG(1.3) initial stellar mass functi on. The initial period distribution is flat ranging from 10(3) to 10(7 .5) d, but We also perform simulations with a realistic distribution o f periods which rises with increasing P (> 3 d) and which is consisten t with pre-main-sequence observational constraints. For comparison we simulate the evolution of single-star clusters. After an initial relax ation phase, all clusters evolve according to the same n(t)(proportion al to)exp(-t/tau(e)) curve, where n(t) is the number density of stars in the central 2-pc sphere at time t and tau(e) approximate to 230 Myr . All clusters have the same lifetime tau. n(t) and tau are thus indep endent of (i) the initial proportion of binaries and (ii) the initial R(0.5). Mass segregation measures the dynamical age of the cluster: it is found that the mean stellar mass inside the central region increas es approximately linearly with age. The proportion of binaries in the central cluster region is a sensitive indicator of the initial cluster concentration: it declines within approximately the first 10-20 initi al relaxation times and rises only slowly with age, but for initial R( 0.5) < 0.8 pc, it is always significantly larger than the binary propo rtion outside the central region. If most stars form in binaries in em bedded clusters that are dynamically equivalent to a cluster specified initially by (N-bin, R(0.5)) = (200, 0.85 pc), which is located at th e edge of a 1.5 x 10(5) M(circle dot) molecular cloud with a diameter of 40 pc, then we estimate that at most about 10 per cent of all pre-m ain-sequence stars achieve near escape velocities from the molecular c loud. The large ejection velocities resulting from close encounters be tween binary systems imply a distribution of young stars over large ar eas surrounding star-forming sites. This 'halo' population of a molecu lar cloud complex is expected to have a significantly reduced binary p roportion (about 15 per cent or less) and a significantly increased pr oportion of stars with depleted or completely removed circumstellar di scs. In this scenario, the distributed population is expected to have a similar proportion of binaries to the Galactic field (about 50 per c ent). If a distributed population shows orbital parameter distribution s not affected by stimulated evolution (e.g. as in Taurus-Auriga) then it probably originated in a star formation mode in which the binaries formed in relative isolation rather than in embedded clusters. The Hy ades cluster luminosity function suggests an advanced dynamical age. T he Pleiades luminosity function data suggest a distance modulus m - M = 6, rather than 5.5. The total proportion of binaries in the central region of the Hyades and Pleiades clusters is probably 0.6-0.7. Any ob servational luminosity function of a Galactic cluster must be correcte d for unresolved binaries when studying the stellar mass function. App lying our parametrization for open cluster evolution we estimate the b irth masses of both clusters. We find no evidence for different dynami cal properties of stellar systems at birth in the Hyades, Pleiades and Galactic field stellar samples. Parametrizing the depletion of low-ma ss stars in the central cluster region by the ratio, xi(t), of the ste llar luminosity function at the 'H-2-convection peak' (M(v) approximat e to 12) and 'H- plateau' (M(v) approximate to 7), we find good agreem ent with the Pleiades and Hyades xi(t) values. The observed proportion of binary stars in the very young Trapezium cluster is consistent wit h the early dynamical evolution of a cluster with a very high initial stellar number density.