On the mass function of star clusters

Clusters that form in total 10^3 < N < 10^5 stars (type II clusters) lose their gas within a dynamical time as a result of the photo-ionising flux from O stars. Sparser (type I) clusters get rid of their residual gas on a timescale longer or comparable to the nominal crossing time and thus evolve approximately adiabatically. This is also true for massive embedded clusters (type III) for which the velocity dispersion is larger than the sound speed of the ionised gas. On expelling their residual gas, type I and III clusters are therefore expected to lose a smaller fraction of their stellar component than type II clusters. We outline the effect this has on the transformation of the mass function of embedded clusters (ECMF), which is directly related to the mass function of star-cluster-forming molecular cloud cores, to the ``initial'' MF of bound gas-free star clusters (ICMF). The resulting ICMF has, for a featureless power-law ECMF, a turnover near 10^{4.5} Msun and a peak near 10^3 Msun. The peak lies around the initial masses of the Hyades, Praesepe and Pleiades clusters. We also find that the entire Galactic population II stellar spheroid can be generated if star formation proceeded via embedded clusters distributed like a power-law MF with exponent 0.9 < beta < 2.6.Comment: 10 pages, 4 figures, accepted by MNRAS, small adjustments for consistency with published versio

Evidence for a fundamental stellar upper mass limit from clustered star formation

The observed masses of the most massive stars do not surpass about 150Msun. This may either be a fundamental upper mass limit which is defined by the physics of massive stars and/or their formation, or it may simply reflect the increasing sparsity of such very massive stars so that observing even higher-mass stars becomes unlikely in the Galaxy and the Magellanic Clouds. It is shown here that if the stellar initial mass function (IMF) is a power-law with a Salpeter exponent (alpha=2.35) for massive stars then the richest very young cluster R136 seen in the Large Magellanic Cloud (LMC) should contain stars with masses larger than 750Msun. If, however, the IMF is formulated by consistently incorporating a fundamental upper mass limit then the observed upper mass limit is arrived at readily even if the IMF is invariant. An explicit turn-down or cutoff of the IMF near 150Msun is not required; our formulation of the problem contains this implicitly. We are therefore led to conclude that a fundamental maximum stellar mass near 150Msun exists, unless the true IMF has alpha>2.8.Comment: MNRAS, accepted, 6 page

On the origin of the distribution of binary-star periods

Pre-main sequence and main-sequence binary systems are observed to have periods, P, ranging from one day to 10^(10) days and eccentricities, e, ranging from 0 to 1. We pose the problem if stellar-dynamical interactions in very young and compact star clusters may broaden an initially narrow period distribution to the observed width. N-body computations of extremely compact clusters containing 100 and 1000 stars initially in equilibrium and in cold collapse are preformed. In all cases the assumed initial period distribution is uniform in the narrow range 4.5 < log10(P) < 5.5 (P in days) which straddles the maximum in the observed period distribution of late-type Galactic-field dwarf systems. None of the models lead to the necessary broadening of the period distribution, despite our adopted extreme conditions that favour binary--binary interactions. Stellar-dynamical interactions in embedded clusters thus cannot, under any circumstances, widen the period distribution sufficiently. The wide range of orbital periods of very young and old binary systems is therefore a result of cloud fragmentation and immediate subsequent magneto-hydrodynamical processes operating within the multiple proto-stellar system.Comment: 11 pages, 4 figures, ApJ, in pres

The mean surface density of companions in a stellar-dynamical context

Applying the mean surface density of companions, Sigma(r), to the dynamical evolution of star clusters is an interesting approach to quantifying structural changes in a cluster. It has the advantage that the entire density structure, ranging from the closest binary separations, over the core-halo structure through to the density distribution in moving groups that originate from clusters, can be analysed coherently as one function of the stellar separations r. This contribution assesses the evolution of Sigma(r) for clusters with different initial densities and binary populations. The changes in the binary, cluster and halo branches as the clusters evolve are documented using direct N-body calculations, and are correlated with the cluster core and half-mass radius. The location of breaks in the slope of Sigma(r) and the possible occurrence of a binary gap can be used to infer dynamical cluster properties.Comment: 12 pages including 7 figures, accepted for publication in A&

Limits on the primordial stellar multiplicity

Most stars - especially young stars - are observed to be in multiple systems. Dynamical evolution is unable to pair stars efficiently, which leads to the conclusion that star-forming cores must usually fragment into \geq 2 stars. However, the dynamical decay of systems with \geq 3 or 4 stars would result in a large single-star population that is not seen in the young stellar population. Additionally, ejections would produce a significant population of hard binaries that are not observed. This leads to a strong constraint on star formation theories that cores must typically produce only 2 or 3 stars. This conclusion is in sharp disagreement with the results of currently available numerical simulations that follow the fragmentation of molecular cores and typically predict the formation of 5--10 seeds per core. In addition, open cluster remnants may account for the majority of observed highly hierarchical higher-order multiple systems in the field.Comment: A&A in press, 5 pages (no figures