An analytical description of the disruption of star clusters in tidal fields with an application to Galactic open clusters

By H. Lamers, M. Gieles, N. Bastian, H. Baumgardt, N. Kharchenko, S. P. Portegies Zwart. 2005

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We present a simple analytical description of the disruption of star clusters in a tidal field. The cluster disruption time, defined as tdis = {dln M/dt} −1 , depends on the mass M of the cluster as tdis = t0(M/M� ) γ with γ = 0.62 for clusters in a tidal field, as shown by empirical studies of cluster samples in different galaxies and by N-body simulations. Using this simple description we derive an analytic expression for the way in which the mass of a cluster decreases with time due to stellar evolution and disruption. The result agrees very well with those of detailed N-body simulations for clusters in the tidal field of our galaxy. The analytic expression can be used to predict the mass and age histograms of surviving clusters for any cluster initial mass function and any cluster formation history. The method is applied to explain the age distribution of the open clusters in the solar neighbourhood within 600 pc, based on a new cluster sample that appears to be unbiased within a distance of about 1 kpc. From a comparison between the observed and predicted age distributions in the age range between 10 Myr to 3 Gyr we find the following results: (1) The disruption time of a 10 4 Mcluster in the solar neighbourhood is about 1.3 ± 0.5 Gyr. This is a factor of 5 shorter than that derived from N-body simulations of clusters in the tidal field of the galaxy. Possible reasons for this discrepancy are discussed. (2) The present star formation rate in bound clusters within 600 pc of the Sun is 5.9 ± 0.8 × 10 2 MMyr −1 , which corresponds to a surface star formation rate of bound clusters of 5.2 ± 0.7 × 10 −10 Myr −1 pc −2 . (3) The age distribution of open clusters shows a bump between 0.26 and 0.6 Gyr when the cluster formation rate was 2.5 times higher than before and after. (4) The present star formation rate in bound clusters is about half that derived from the study of embedded clusters. The difference suggests that about half of the clusters in the solar neighbourhood become unbound within about 10 Myr. (5) The most massive clusters within 600 pc had an initial mass of about 3 × 10 4 M� . This is in agreement with the statistically expected value based on a cluster initial mass function with a slope of −2, even if the physical upper mass limit for cluster formation is as high as 10 6 M� .

Subfields: Astronomy and Astrophysics

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Citations in the corpus

On the star formation rate – brightest cluster relation: estimating the peak star formation rate in post-merger galaxies (2008, background): “…cluster in the galaxy, given here as an example of the uncertainties in the method. to correct for mass loss due to tidal/dynamical effects, which are expected to be relatively small since the mass loss is inversely related to cluster mass (e.g. Baumgardt & Makino 2003; Lamers et al. 2005).”
The mass function of young star clusters in spiral galaxies (2008, background): “About a dozen star clusters with ages ∼10 Myr and masses in the range 104 M −105 M have now been found within several kpc from the Sun (Figer 2008).”
Revisiting the population of Galactic open clusters (2005, background): “The rather low input of open clusters to the stellar population of the Galactic disk can be explained by their high infant mortality, reducing generations of newly born clusters by a half (Lamers et al. 2005).”
Star cluster disruption by giant molecular clouds (2006, background): “In the solar neighbourhood, the observed t4 for open clusters (t4 = 1.3Gyr, see Lamers et al. 2005) is a factor of 5 lower than expected from the disruption time due to the galactic tidal field, combined with a realistic stellar mass function and with stellar evolution (t4 = 6.9Gyr, see Baumgardt &…”
Building the terrestrial planets: Constrained accretion in the inner Solar System (2009, background): “These two constraints are not at odds if the giant plan- ets evolved on long timescales, because the galactic environment can change on a 10-100 Myr timescale (e.g., Lamers et al. 2005).”
THE ANTENNAE GALAXIES (NGC 4038/4039) REVISITED: ADVANCED CAMERA FOR SURVEYS AND NICMOS OBSERVATIONS OF A PROTOTYPICAL MERGER (2010, background): “…for several galaxies, including the Antennae, that there is a cutoff to the upper mass with which clusters can form (e.g., Gieles et al. 2006; Bastian 2008; Larsen 2009), and that there are bends in the age distributions of some galaxies (e.g., Boutloukos & Lamers 2003, and Lamers et al. 2005).”
The formation and assembly history of the Milky Way revealed by its globular cluster population (2018, methodology): “Thirdly, we include mass loss by two-body interactions between the stars in a cluster (Kruijssen et al. 2011, see also Lamers et al. 2005).”
Star Cluster Demographics. I. A General Framework and Application to the Antennae Galaxies (2006, background): “The fourth cluster disruption law is described in detail in BL03 (also see Lamers et al. 2005a).”