Determining Metallicities of Globular Clusters using Simulated Integrated Spectra and Bayesian Statistics

Abstract

Using Monte Carlo simulations of globular clusters we developed a method separating metallicity effects from age effects on observed integrated ugriz colors. We demonstrate that these colors do not evolve with time significantly after an age of 4 Gyr and use Bayesian statistics to calculate a probability distribution function of the metallicity. We tested the method using the M31 globular cluster system and then applied to explain the observed color bimodality in globular cluster sets and tidal effects on it. We show that the color bimodality is an effect of a nonlinearity in the color-metallicity relation caused by stellar dynamics on the Giant Branch, that colors including only the UV show a weaker bimodality than those subtracting from visual bands and that cluster sets with a distinct bimodality are in principle older than those with only a weak bimodal distribution. Furthermore a bimodal color distribution of coeval clusters implies a bimodal metallicity distribution, but a unimodal color distribution does not imply a unimodal metallicity distribution. The tidal field can finally shift the modes of the color distribution and therefore cause a bimodal color distribution. This work presents results obtained between 2011 and 2012 in the Astronomisches Rechen-Institut, Zentrum f\"{u}r Astronomie der Universit\"{a}t Heidelberg, M\"{o}nchhofstra{\ss}e 12-14, 69120 Heidelberg, Germany.