Abstract Tidally enhanced stellar wind may affect horizontal branch (HB) morphology in globular clusters (GCs) by enhancing the mass loss of primary star during binary evolution. Lei et al. (2013a, A&A, 549, 145; 2013b, A&A, 554, 130) studied the effect of this kind of wind on HB morphology in detail, and their results indicated that a binary is a possible second-parameter (2P) candidate in GCs. Binary fraction is a very important fact in the tidally-enhanced-stellar-wind model. In this paper, we studied the effect of binary fraction on HB morphology by removing the effects of metallicity and age. Five different binary fractions (i.e., 10%, 15%, 20%, 30%, and 50%) are adopted in our model calculations. The synthetic HB morphologies with different binary fractions are obtained at different metallicities and ages. We found that, due to the great influence of metallicity and age, the effect of binary fraction on HB morphology may be masked by these two parameters. However, when the effects of metallicity and age are removed, the tendency of HB morphologies becoming bluer with increasing binary fractions is clearly presented. Furthermore, we compared our results with the observation by Milone et al. (2012, A&A, 540, 16). Our results are consistent with the observation at metal-rich and metal-poor GCs. For the GCs with intermediate metallicity, when the effect of age on HB morphology is removed, a weak tendency of HB morphologies becoming bluer with increasing binary fractions is presented in all regions of GCs, which is consistent with our results obtained in this metallicity range.
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