  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 HST archival ACS data in the F606W and F814W bands and apply
PSF-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% to 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 towards the outside, consistent with theoretical predictions for the
dynamical effect on the binary fraction.
