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.
