Relations Between the Luminosity, Mass, and Age Distributions of Young Star Clusters

We derive and interpret some relations between the luminosity, mass, and age distributions of star clusters, denoted here by phi(L), psi(M), and chi(tau), respectively. Of these, phi(L) is the easiest to determine observationally, whereas psi(M) and chi(tau) are more informative about formation and disruption processes. For populations of young clusters, with a relatively wide range of ages, phi(L) depends on both psi(M) and chi(tau) and thus cannot serve as a proxy for psi(M) in general. We demonstrate this explicitly by four illustrative examples with specific forms for either psi(M) or chi(tau). In the special case in which psi(M) is a power law and is independent of chi(tau), however, phi(L) is also a power law with the same exponent as psi(M). We conclude that this accounts for the observed similarity between phi(L) and psi(M) for the young clusters in the Antennae galaxies. This result reinforces our picture in which clusters form with psi(M) propto M^{-2} and are then disrupted rapidly at a rate roughly independent of their masses. The most likely disruptive process in this first stage is the removal of interstellar matter by the energy and momentum input from young stars (by photoionization, winds, jets, and supernovae). The few clusters that avoid this "infant mortality" are eventually disrupted in a second stage by the evaporation of stars driven by two-body relaxation, a process with a strong dependence on mass. We suspect this picture may apply to many, if not all, populations of star clusters, but this needs to be verified observationally by determinations of psi(M) and chi(tau) in more galaxies.Comment: Ten pages. Astrophysical Journal. Submitted 2005 October 20. Accepted 2006 August 15. V2--Minor improvements for consistency with published articl

The Dust Depletion and Extinction of the GRB 020813 Afterglow

The Keck optical spectrum of the GRB 020813 afterglow is the best ever obtained for GRBs. Its large spectral range and very high S/N ratio allowed for the first time the detection of a vast variety of absorption lines, associated with the circumburst medium or interstellar medium of the host. The remarkable similarity of the relative abundances of 8 elements with the dust depletion pattern seen in the Galactic ISM suggests the presence of dust. The derived visual dust extinction A_V=0.40+/-0.06 contradicts the featureless UV spectrum of the afterglow, very well described by a unreddened power law. The forthcoming Swift era will open exciting opportunities to explain similar phenomena in other GRB afterglows.Comment: To be published in "Il Nuovo Cimento", Proceedings of the 4th Rome Workshop on Gamma-Ray Bursts in the Afterglow Era, eds. L. Piro, L. Amati, S. Covino, B. Gendr

A Comparison of Methods for Determining the Age Distribution of Star Clusters: Application to the Large Magellanic Cloud

The age distribution of star clusters in nearby galaxies plays a crucial role in evaluating the lifetimes and disruption mechanisms of the clusters. Two very different results have been found recently for the age distribution chi(t) of clusters in the Large Magellanic Cloud (LMC). We found that chi(t) can be described approximately by a power law chi(t) propto t^{gamma}, with gamma -0.8, by counting clusters in the mass-age plane, i.e., by constructing chi(t) directly from mass-limited samples. Gieles & Bastian inferred a value of gamma~, based on the slope of the relation between the maximum mass of clusters in equal intervals of log t, hereafter the M_max method, an indirect technique that requires additional assumptions about the upper end of the mass function. However, our own analysis shows that the M_max method gives a result consistent with our direct counting method for clusters in the LMC, namely chi(t) propto t^-0.8 for t<10^9 yr. The reason for the apparent discrepancy is that our analysis includes many massive (M>1.5x10^3 M_sol), recently formed (t<10^7 yr) clusters, which are known to exist in the LMC, whereas Gieles & Bastian are missing such clusters. We compile recent results from the literature showing that the age distribution of young star clusters in more than a dozen galaxies, including dwarf and giant galaxies, isolated and interacting galaxies, irregular and spiral galaxies, has a similar declining shape. We interpret this approximately "universal" shape as due primarily to the progressive disruption of star clusters over their first ~few x 10^8 yr, starting soon after formation, and discuss some observational and physical implications of this early disruption for stellar populations in galaxies.Comment: 21 pages, 5 figures, published in the Astrophysical Journal, volume 713, page 134

Similarities in Populations of Star Clusters

We compare the observed mass functions and age distributions of star clusters in six well-studied galaxies: the Milky Way, Magellanic Clouds, M83, M51, and Antennae. In combination, these distributions span wide ranges of mass and age: 10^2\lea M/M_{\odot}\lea10^6 and 10^6\lea\tau/yr \lea10^9. We confirm that the distributions are well represented by power laws: $dN/dM\propto M^{\beta}$ with $\beta \approx-1.9$ and $dN/d\tau\propto\tau^{\gamma}$ with $\gamma\approx -0.8$. The mass and age distributions are approximately independent of each other, ruling out simple models of mass-dependent disruption. As expected, there are minor differences among the exponents, at a level close to the true uncertainties, $\epsilon_{\beta}\sim\epsilon_{\gamma}\sim$~0.1--0.2. However, the overwhelming impression is the similarity of the mass functions and age distributions of clusters in these different galaxies, including giant and dwarf, quiescent and interacting galaxies. This is an important empirical result, justifying terms such as "universal" or "quasi-universal." We provide a partial theoretical explanation for these observations in terms of physical processes operating during the formation and disruption of the clusters, including star formation and feedback, subsequent stellar mass loss, and tidal interactions with passing molecular clouds. A full explanation will require additional information about the molecular clumps and star clusters in galaxies beyond the Milky Way.Comment: 20 pages, 4 figures, 2 tables; published in the Astrophysical Journal, 752:96 (2012 June 20

New Tests for Disruption Mechanisms of Star Clusters: The Large and Small Magellanic Clouds

We compare the observed bivariate distribution of masses(M) and ages(t) of star clusters in the LMC with the predicted distributions g(M,t) from 3 idealized models for the disruption of star clusters: (1)sudden mass-dependent disruption;(2)gradual mass-dependent disruption; and (3)gradual mass-independent disruption. The model with mass-{\em in}dependent disruption provides a good, first-order description of these cluster populations, with g(M,t) propto M^{beta} t^{gamma}, beta=-1.8+/-0.2 and gamma=-0.8+/-0.2, at least for clusters with ages t<10^9 yr and masses M<10^3 M_sol (more specifically, t<10^7(M/10^2 M_sol)^{1.3} yr). This model predicts that the clusters should have a power-law luminosity function, dN/dL propto L^-1.8, in agreement with observations. The first two models, on the other hand, fare poorly when describing the observations, refuting previous claims that mass-dependent disruption of star clusters is observed in the LMC over the studied M-t domain. Clusters in the SMC can be described by the same g(M,t) distribution as for the LMC, but with smaller samples and hence larger uncertainties. The successful g(M,t) model for clusters in the Magellanic Clouds is virtually the same as the one for clusters in the merging Antennae galaxies, but extends the domain of validity to lower masses and to older ages. This indicates that the dominant disruption processes are similar in these very different galaxies over at least t<10^8 yr and possibly t<10^9 yr. The mass functions for young clusters in the LMC are power-laws, while that for ancient globular clusters is peaked. We show that the observed shapes of these mass functions are consistent with expectations from the simple evaporation model presented by McLaughlin & Fall.Comment: 46 pages, 17 figures, published ApJ, vol 711, page 126