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The impact of binary stars on the colors of high-redshift galaxies

Evolutionary population synthesis (EPS) models play an important role in many studies on the formation and evolution of galaxies. Most EPS models are still poorly calibrated for certain stellar evolution stages, especially for the treatment of binary stars, which are very different from single stars. We aim to present color-magnitude (C-M) and color-color (C-C) relations for passive model galaxies in the redshift z$\sim0.0-3.0$ and to study the effect of binary interactions on these relations for high-redshift passive galaxies. Assuming exponentially declining star formation rate, we used a set of theoretical galaxy templates obtained from Yunnan EPS models (with and without binary interactions) to present the C-M and C-C relations for passive galaxies via Monte Carlo simulation. In Yunnan EPS models with binary interactions, various processes are included, such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks, tidal evolution, and all angular momentum loss mechanisms. In these models, approximately 50 per cent of the stellar systems are binary systems with orbital periods less than 100\,yr. This fraction is a typical value for the Milky Way. We find that the inclusion of binary interactions in the model galaxies' spectra can dramatically alter the predicted C-M and C-C relations and their evolution with redshift. For $z\sim 0.0$ and $1.0$, the binary interactions have a minor effect on the C-M and C-C relations, but at $z\sim 2.0$ and $3.0$ the binary interactions have a major effect on the C-M and C-C relations. Especially for the redshift $z\sim 2.0$, the $g-$band magnitude becomes smaller by $1.5$\,mag, the $g-r$ color becomes bluer by $1.0$\,mag, and the $u-g$ color becomes redder by $1.0$\,mag when binary interactions are included.