Determination method for binary fractions using the integrated spectrum

Abstract

ABSTRACT We need to resolve the individual stars for binary-fraction determinations of stellar systems. Therefore, it is not possible to obtain the binary fractions for dense or distant stellar systems. We propose a method to determine the binary fraction of a dense or distant stellar system: this method is first to determine the binary-fraction variation for any two adjacent regions and then to add up those binary-fraction variations along the radial direction to obtain the binary fraction for a stellar system. The binary-fraction variation is derived using 10 binary-fraction-sensitive spectral absorption feature indices (SAFIs) and the binary-fraction variation calibrations in terms of these SAFIs. Using this method, we first present the binary-fraction variations for 21 Galactic globular clusters (GCs). By comparison, we find that they agree well with the binary fractions based on the main-sequence fiducial line method from previous studies. This verifies that the above-mentioned method is feasible. Next, we present the binary-fraction variations of 13 Galactic GCs. We give the relationships between the binary fraction and various parameters, and find that the binary fraction is negatively correlated with NHB and NRR, the binary fraction of some studies is not strongly correlated with NBS, and the number of GCs with large binary fraction is greater for the extreme blue horizontal branch population ratio. Finally, if we want to obtain a more accurate binary fraction, we suggest that spectroscopic and photometric observations are conducted at an appropriate area interval for a stellar system.