On the Fraction of Star Clusters Surviving the Embedded Phase

In this paper we derive ages and masses for 276 clusters in the merger galaxy NGC 3256. This was achieved by taking accurate photometry in four wavebands from archival HST images. Photometric measurements are compared to synthetic stellar population (SSP) models to find the most probable age, mass and extinction. The cluster population of NGC 3256 reveals an increase in the star formation rate over the last 100 million years and the initial cluster mass function (ICMF) is best described by a power law relation with slope $\alpha = 1.85 \pm 0.12$. Using the observed cluster population for NGC 3256 we calculate the implied mass of clusters younger than 10 million years old, and convert this to a cluster formation rate over the last 10 million years. Comparison of this value with the star formation rate (SFR) indicates the fraction of stars found within bound clusters after the embedded phase of cluster formation, $\Gamma$, is $22.9% \pm^{7.3}_{9.8} $ for NGC 3256. We carried out an in-depth analysis into the errors associated with such calculations showing that errors introduced by the SSP fitting must be taken into account and an unconstrained metallicity adds to these uncertainties. Observational biases should also be considered. Using published cluster population data sets we calculate $\Gamma$ for six other galaxies and examine how $\Gamma$ varies with environment. We show that $\Gamma$ increases with the star formation rate density and can be described as a power law type relation of the form $\Gamma(%) = (29.0\pm{6.0}) \Sigma_{SFR}^{0.24\pm0.04} (\msol yr^{-1} kpc^{-2})$.