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Register a new userBinaries and the dynamical mass of star clusters
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Added by
M. B. N. Kouwenhoven
Publication date
2007
fields
Physics
and research's language is
English
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The total mass of a distant star cluster is often derived from the virial theorem, using line-of-sight velocity dispersion measurements and half-light radii, under the implicit assumption that all stars are single (although it is known that most stars form part of binary systems). The components of binary stars exhibit orbital motion, which increases the measured velocity dispersion, resulting in a dynamical mass overestimation. In this article we quantify the effect of neglecting the binary population on the derivation of the dynamical mass of a star cluster. We find that the presence of binaries plays an important role for clusters with total mass M < 10^5 Msun; the dynamical mass can be significantly overestimated (by a factor of two or more). For the more massive clusters, with Mcl > 10^5 Msun, binaries do not affect the dynamical mass estimation significantly, provided that the cluster is significantly compact (half-mass radius < 5 pc).
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The total mass of distant star clusters is often derived from the virial theorem, using line-of-sight velocity dispersion measurements and half-light radii. Although most stars form in binary systems, this is mostly ignored when interpreting the observations. The components of binary stars exhibit orbital motion, which may increase the measured velocity dispersion, and may therefore result in a dynamical mass overestimation. In this paper we quantify the effect of neglecting the binary population on the derivation of the dynamical mass of a star cluster. We simulate star clusters numerically, and study the dependence of the derived dynamical mass on the properties of the binary population. We find that the presence of binaries plays a crucial role for very sparse clusters with a stellar density comparable to that of the field star population (~0.1 stars/pc3), as the velocity dispersion is fully dominated by the binary orbital motion. For such clusters, the dynamical mass may overestimate the true mass by up to an order of magnitude. For very dense clusters (>10^7 stars/pc3), binaries do not affect the dynamical mass estimation significantly. For clusters of intermediate density (0.1-10^7 stars/pc3), the dynamical mass can be overestimated by 10-100%, depending on the properties of the binary population.
Observations of young star-forming regions suggest that star clusters are born completely mass segregated. These initial conditions are, however, gradually lost as the star cluster evolves dynamically. For star clusters with single stars only and a canonical initial mass function, it has been suggested that traces of these initial conditions vanish at a time $tau_mathrm{v}$ between 3 and $3.5,t_mathrm{rh}$ (initial half-mass relaxation times). Since a significant fraction of stars are observed in binary systems and it is widely accepted that most stars are born in binary systems, we aim to investigate what role a primordial binary population (even up to $100,%$ binaries) plays in the loss of primordial mass segregation of young star clusters. We used numerical $N$-body models similar in size to the Orion Nebula Cluster (ONC) -- a representative of young open clusters -- integrated over several relaxation times to draw conclusions on the evolution of its mass segregation. We also compared our models to the observed ONC. We found that $tau_mathrm{v}$ depends on the binary star fraction and the distribution of initial binary parameters that include a semi-major axis, eccentricity, and mass ratio. For instance, in the models with $50,%$ binaries, we find $tau_mathrm{v} = (2.7 pm 0.8),t_mathrm{rh}$, while for $100,%$ binary fraction, we find a lower value $tau_mathrm{v} = (2.1 pm 0.6),t_mathrm{rh}$. We also conclude that the initially completely mass segregated clusters, even with binaries, are more compatible with the present-day ONC than the non-segregated ones.
The dynamical mass of a star cluster can be derived from the virial theorem, using the measured half-mass radius and line-of-sight velocity dispersion of the cluster. However, this dynamical mass may be a significant overestimation of the cluster mass if the contribution of the binary orbital motion is not taken into account. In these proceedings we describe the mass overestimation as a function of cluster properties and binary population properties, and briefly touch the issue of selection effects. We find that for clusters with a measured velocity dispersion of sigma > 10 km/s the presence of binaries does not affect the dynamical mass significantly. For clusters with sigma < 1 km/s (i.e., low-density clusters), the contribution of binaries to sigma is significant, and may result in a major dynamical mass overestimation. The presence of binaries may introduce a downward shift of Delta log(L/Mdyn) = 0.05-0.4 in the log(L/Mdyn) vs. age diagram.
We summarize and discuss recent work (Fregeau 2007) that presents the confluence of three results suggesting that most Galactic globular clusters are still in the process of core contraction, and have not yet reached the thermal equilibrium phase driven by binary scattering interactions: that 1) the three clusters that appear to be overabundant in X-ray binaries per unit encounter frequency are observationally classified as core-collapsed, 2) recent numerical simulations of cluster evolution with primordial binaries show that structural parameters of clusters in the binary-burning phase agree only with core-collapsed clusters, and 3) a cluster in the binary-burning phase for the last few Gyr should have about 5 times more dynamically formed X-ray sources than if it were in the core contraction phase for the same time.
We highlight the impact of cluster-mass-dependent evolutionary rates upon the evolution of the cluster mass function during violent relaxation, that is, while clusters dynamically respond to the expulsion of their residual star-forming gas. Mass-dependent evolutionary rates arise when the mean volume density of cluster-forming regions is mass-dependent. In that case, even if the initial conditions are such that the cluster mass function at the end of violent relaxation has the same shape as the embedded-cluster mass function (i.e. infant weight-loss is mass-independent), the shape of the cluster mass function does change transiently {it during} violent relaxation. In contrast, for cluster-forming regions of constant mean volume density, the cluster mass function shape is preserved all through violent relaxation since all clusters then evolve at the same mass-independent rate. On the scale of individual clusters, we model the evolution of the ratio between the dynamical mass and luminous mass of a cluster after gas expulsion. Specifically, we map the radial dependence of the time-scale for a star cluster to return to equilibrium. We stress that fields-of-view a few pc in size only, typical of compact clusters with rapid evolutionary rates, are likely to reveal cluster regions which have returned to equilibrium even if the cluster experienced a major gas expulsion episode a few Myr earlier. We provide models with the aperture and time expressed in units of the initial half-mass radius and initial crossing-time, respectively, so that our results can be applied to clusters with initial densities, sizes, and apertures different from ours.
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