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

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

The Age Distribution of Massive Star Clusters in the Antennae Galaxies

We determine the age distribution of star clusters in the Antennae galaxies (NGC 4038/9) for two mass-limited samples (M > 3 x 10^4 M_{\odot} and M > 2 x 10^5 M_{\odot}). This is based on integrated broadband UBVI and narrowband H-alpha photometry from deep images taken with the Hubble Space Telescope. We find that the age distribution of the clusters declines steeply, approximately as dN/d\tau \propto \tau^{-1}. The median age of the clusters is ~10^7 yr, which we interpret as evidence for rapid disruption ("infant mortality"). It is very likely that most of the young clusters are not gravitationally bound and were disrupted near the times they formed by the energy and momentum input from young stars to the interstellar matter of the protoclusters. At least 20% and possibly all stars form in clusters and/or associations, including those that are unbound and short-lived.Comment: 11 pages, 2 figures. To appear in the ApJ Letters; Submitted 2004 July 29; accepted 2005 August

System locates randomly placed remote objects

System to locate objects submerged underwater uses active/passive sonar techniques in which a transmitter is attached to the object to be recovered and a receiver is used for search. The system is rugged, has a long term operating life, and furnishes a precise bearing on the object

Modeling Heterogeneity in Indirect Effects: Multilevel Structural Equation Modeling Strategies

The heterogeneity implicit in much of social science research can be accommodated by using complex modeling procedures such as SEM or MLM. Ignoring heterogeneity, particularly with regard to nested data structures, can have serious consequences for model estimation and lead to incorrect conclusions about tested hypotheses. In mediation models, the consequences of ignoring nesting can have a substantial impact on the indirect effect. Inflated standard errors and bias in the parameter estimates lead to inaccurate estimates of the indirect effect, as well as reduced power to detect the effect. Using multilevel structural equation modeling (MSEM), data were generated based on a cross-lagged panel model for mediation. By fitting a single-level model to the data, the consequences for the estimation and detection of the indirect effect when heterogeneity is ignored is examined through measures of relative bias, power, and model fit

New Constraints on Mass-Dependent Disruption of Star Clusters in M51

We use UBVI,Ha images of the Whirlpool galaxy, M51, taken with the ACS and WFPC2 cameras on the Hubble Space Telescope (HST) to select star clusters, and to estimate their masses and ages by comparing their observed colors with predictions from population synthesis models. We construct the mass function of intermediate age (1-4x10^8 yr) clusters, and find that it is well described by a power law, psi(M) propto M^beta, with beta=-2.1 +/- 0.2, for clusters more massive than approximately 6x10^3 Msun. This extends the mass function of intermediate age clusters in M51 to masses lower by nearly a factor of five over previous determinations. The mass function does not show evidence for curvature at either the high or low mass end. This shape indicates that there is no evidence for the earlier disruption of lower mass clusters compared with their higher mass counterparts (i.e., no mass-dependent disruption) over the observed range of masses and ages, or for a physical upper mass limit Mc with which clusters in M51 can form. These conclusions differ from previous suggestions based on poorer-quality HST observations. We discuss their implications for the formation and disruption of the clusters. Ages of clusters in two "feathers," stellar features extending from the outer portion of a spiral arm, show that the feather with a larger pitch angle formed earlier, and over a longer period, than the other.Comment: 24 pages, 7 figures; to be published in ApJ, 727, 8

Applications of Exploratory Q-Matrix Discovery Procedures in Diagnostic Classification Models

Diagnostic Classification Models (DCM) use a Q-matrix to determine which skills are required to correctly answer items on large-scale assessments. DCMs are fit under the assumption that the Q-matrix is correctly specified. Misspecification of the Q-matrix is problematic for several reasons; problems with model convergence, poor model fit, and inflated model parameters. The current study examines the use of probabilistic estimation of the Q-matrix for cognitive diagnosis modeling in order to allow for uncertainty to help shape the construction of the Q-matrix. Two DCMs, the DINA and the DINO, were estimated for common reading comprehension tests using an EM algorithm and the goodness of fit was checked. Models using a probabilistic Q-matrix showed better fit and lower slip and guess parameters, suggesting that the probabilistic model provided more accurate Q-matrix specification and more accurate prediction of examinee skills

High-Redshift Galaxies: Their Predicted Size and Surface Brightness Distributions and Their Gravitational Lensing Probability

Direct observations of the first generation of luminous objects will likely become feasible over the next decade. The advent of the Next Generation Space Telescope (NGST) will allow imaging of numerous galaxies and mini-quasars at redshifts z>5. We apply semi-analytic models of structure formation to estimate the rate of multiple imaging of these sources by intervening gravitational lenses. Popular CDM models for galaxy formation yield a lensing optical depth of about 1% for sources at redshift 10. The expected slope of the luminosity function of the early sources implies an additional magnification bias of about 5, bringing the fraction of lensed sources at z=10 to about 5%. We estimate the angular size distribution of high-redshift disk galaxies and find that most of them are more extended than the resolution limit of NGST, roughly 0.06 arcseconds. We also show that there is only a modest redshift evolution in the mean surface brightness of galaxies at z>2. The expected increase by 1-2 orders of magnitude in the number of resolved sources on the sky, due to observations with NGST, will dramatically improve upon the statistical significance of existing weak lensing measurements. We show that, despite this increase in the density of sources, confusion noise from z>2 galaxies is expected to be small for NGST observations.Comment: 27 pages, 8 PostScript figures (of which two are new), revised version accepted for Ap

New Tests for Disruption Mechanisms of Star Clusters: Methods and Application to the Antennae Galaxies

We present new tests for disruption mechanisms of star clusters based on the bivariate mass-age distribution g(M,\tau). In particular, we derive formulae for g(M,\tau) for two idealized models in which the rate of disruption depends on the masses of the clusters and one in which it does not. We then compare these models with our Hubble Space Telescope observations of star clusters in the Antennae galaxies over the mass-age domain in which we can readily distinguish clusters from individual stars: \tau\la10^7(M/10^4 M_{\odot})^{1.3} yr. We find that the models with mass-dependent disruption are poor fits to the data, even with complete freedom to adjust several parameters, while the model with mass-independent disruption is a good fit. The successful model has the simple form g(M,\tau) \propto M^{-2} \tau^{-1}, with power-law mass and age distributions, dN/dM propto M^{-2} and dN/d\tau\propto\tau^{-1}. The predicted luminosity function is also a power law, dN/dL \propto L^{-2}, in good agreement with our observations of the Antennae clusters. The similarity of the mass functions of star clusters and molecular clouds indicates that the efficiency of star formation in the clouds is roughly independent of their masses. The age distribution of the massive young clusters is plausibly explained by the following combination of disruption mechanisms: (1) removal of interstellar material by stellar feedback, \tau \la 10^7$ yr; (2) continued stellar mass loss, 10^7 yr \la \tau \la 10^8 yr; (3), tidal disturbances by passing molecular clouds, \tau \ga 10^8 yr. None of these processes is expected to have a strong dependence on mass, consistent with our observations of the Antennae clusters. We speculate that this simple picture also applies--at least approximately--to the clusters in many other galaxies.Comment: 30 pages, 15 figures; Published in the Asrophysical Journal, volume 704, pages 453-46