Relation between spectral indices and binary fractions in GCs

Context. We study the relation between the known binary fraction and spectral absorption feature index to judge whether (and potentially which) spectral absorption feature indices are suitable for determining the binary fraction. Aims. The determination of the binary fraction is important in studies of binary star formation, evolutionary population synthesis models, and other works. The number of binary stars is difficult to determine for nearly all stellar systems because the individual stars are need to be resolved photometrically or spectroscopically. By comparison, their integrated spectra or spectral absorption feature indices are relatively easy to obtain. Results. We find that the low-resolution (15\,\AA) spectrum is not suitable for this study and the binary fraction type would affect the results: $f$($q$>0.5) and $f$(tot)$^{\rm mc}$ exhibit better correlations with the spectral absorption feature index than $f$(tot)$^{\rm mf}$ and the difference in metallicity would significantly affect the above relationship. % Finally, to eliminate the effects of metallicity, age, and dynamical evolution, we only used those GCs with multiple spectra observed among different regions. % We find that OIII-1, OIII-2, H$_{\rm \gamma F}$, H$_{\rm \delta F}$, H$_{\rm \gamma A}$, H$_{\rm \delta A}$, H$_{\rm \beta}$, Ca4455, C$_2$4668, and TiO$_1$ indices have strong correlations with binary fraction. % The two OIII indices are the most sensitive to the binary fraction, followed by four Balmer indices -- the two narrower central bandpass Balmer indices ($\sim$20\AA, F-definition) are more sensitive than the wider two ($\sim$40\AA, A-definition) and, lastly, the Ca4455, C$_2$4668, and TiO$_1$ indices.