We describe a novel method for determining the demographics of a population of star clusters, for example distributions of cluster mass and age, from unresolved photometry. This method has a number of desirable properties: it fully exploits all the information available in a data set without any binning, correctly accounts for both measurement error and sample incompleteness, naturally handles heterogenous data (e.g. fields that have been imaged with different sets of filters or to different depths), marginalizes over uncertain extinctions, and returns the full posterior distributions of the parameters describing star cluster demographics. We demonstrate the method using mock star cluster catalogues and show that our method is robust and accurate, and that it can recover the demographics of star cluster populations significantly better than traditional fitting methods. For realistic sample sizes, our method is sufficiently powerful that its accuracy is ultimately limited by the accuracy of the underlying physical models for stellar evolution and interstellar dust, rather than by statistical uncertainties. Our method is implemented as part of the Stochastically Lighting Up Galaxies (SLUG) stellar populations code, and is freely available.

We explore the possibility of using UV spectroscopy in combination with broad-band photometry as diagnostic tools for understanding the shape of the initial mass function (IMF) in unresolved stellar populations. Building on our previous work, we extend the Stochastically Lighting Up Galaxies (SLUG) code to include a high-resolution UV spectral synthesizer and equivalent width calculation capabilities. We first gain a qualitative understanding of how UV spectral features behave as the parameters that define a star cluster in SLUG (mass, age, extinction, and IMF slope alpha(3)) are changed. We then exploit Bayesian inference techniques to recover the alpha(3) values for clusters simulated with SLUG, using mock observations of these clusters comprised of broad-band photometry and equivalent width measurements of a selection of UV spectral features. We find some improvement when compared to attempts using broad-band photometry alone (with the interquartile range of the alpha(3) posterior PDF shrinking by similar or equal to 32%), although we still do not yet fully break the known degeneracy between the cluster mass and alpha(3). Finally, we make predictions about how effective real observations will be by quantifying our ability to constrain alpha(3) as a function of limiting equivalent width. We find that observations sensitive to a modest equivalent width of similar or equal to 9 angstrom are sufficient to improve the recovery of the IMF slope parameter by similar or equal to 32% (interquartile range of posterior PDF median residuals), moving to similar or equal to 39% when we include all the significant spectral features in the wavelength range 900 - 3000 angstrom.