2013ApJ...768..158J

Binary stars are thought to be a controlling factor in globular cluster evolution, since they can heat the environmental stars by converting their binding energy to kinetic energy during dynamical interactions. Through such interaction, the binaries determine the time until core collapse. To test predictions of this model, we have determined binary fractions for 35 clusters. Here we present our methodology with a representative globular cluster NGC 4590. We use Hubble Space Telescope archival Advanced Camera for Surveys data in the F606W and F814W bands and apply point-spread-function-fitting photometry to obtain high quality color-magnitude diagrams. We formulate the star superposition effect as a Poisson probability distribution function, with parameters optimized through Monte Carlo simulations. A model-independent binary fraction of (6.2 ±0.3)% is obtained by counting stars that extend to the red side of the residual color distribution after accounting for the photometric errors and the star superposition effect. A model-dependent binary fraction is obtained by constructing models with a known binary fraction and an assumed binary mass-ratio distribution function. This leads to a binary fraction range of 6.8%-10.8%, depending on the assumed shape to the binary mass-ratio distribution, with the best fit occurring for a binary distribution that favors low mass ratios (and higher binary fractions). We also represent the method for radial analysis of the binary fraction in the representative case of NGC 6981, which shows a decreasing trend for the binary fraction toward the outside, consistent with theoretical predictions for the dynamical effect on the binary fraction.