Star cluster evolution, dynamical age estimation and the kinematical signature of star formation

We distribute 400 model stars in Nbin = 200 binary systems in clusters with initial half-mass radii 0. 077 ≤ R0. 5≤ 2. 53 pc and follow the subsequent evolution of the stellar systems by direct N-body integration. The stellar masses are initially paired at random from the KTG (1. 3) initial stellar mass function. The initial period distribution is flat ranging from 103 to 107. 5 d, but we also perform simulations with a realistic distribution of periods which rises with increasing P (> 3 d) and which is consistent with pre-main-sequence observational constraints. For comparison we simulate the evolution of single-star clusters. After an initial relaxation phase, all clusters evolve according to the same |n (t) exp (-t/_ e) | curve, where n (t) is the number density of stars in the central 2-pc sphere at time t and τe ≈ 230 Myr. All clusters have the same lifetime τ. n (t) and τ are thus independent of (i) the initial proportion of binaries and (ii) the initial R0. 5. Mass segregation measures the dynamical age of the cluster: it is found that the mean stellar mass inside the central region increases 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 initial relaxation times and rises only slowly with age, but for initial R0. 5 < 0. 8 pc, it is always significantly larger than the binary proportion outside the central region. If most stars form in binaries in embedded clusters that are dynamically equivalent to a cluster specified initially by (Nbin, R0. 5) = (200, 0. 85 pc), which is located at the edge of a 1. 5 × 105 M⊙ molecular cloud with a diameter of 40 pc, then we estimate that at most about 10 per cent of all pre-main-sequence stars achieve near escape velocities from the molecular cloud. The large ejection velocities resulting from close encounters between binary systems imply a distribution of young stars over large areas surrounding star-forming sites. This ‘halo’ population of a molecular cloud complex is expected to have a significantly reduced binary proportion (about 15 per cent or less) and a significantly increased proportion of stars with depleted or completely removed circumstellar discs. In this scenario, the distributed population is expected to have a similar proportion of binaries to the Galactic field (about 50 per cent). If a distributed population shows orbital parameter distributions 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 Hyades cluster luminosity function suggests an advanced dynamical age. The 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 observational luminosity function of a Galactic cluster must be corrected for unresolved binaries when studying the stellar mass function. Applying our parametrization for open cluster evolution we estimate the birth masses of both clusters. We find no evidence for different dynamical properties of stellar systems at birth in the Hyades, Pleiades and Galactic field stellar samples. Parametrizing the depletion of low-mass stars in the central cluster region by the ratio, ζ (t), of the stellar luminosity function at the ‘H2-convection peak’ (MV≈12) and ‘H– plateau’ (MV≈7), we find good agreement with the Pleiades and Hyades ζ (t) values. The observed proportion of binary stars in the very young Trapezium cluster is consistent with the early dynamical evolution of a cluster with a very high initial stellar number density.