The influence of binary stars on the kinematics of low-mass galaxies

In this paper, the influence of binary stars on the measured kinematics of dwarf galaxies is investigated. Using realistic distributions of the orbital parameters (semi-major axis, eccentricity, etc.). analytical expressions are derived for the changes induced by the presence of binary stars in the measured velocity moments of low-mass galaxies (such as the projected velocity dispersion and the fourth-order Gauss-Hermite coefficient h(4)). It is shown that there is a noticeable change in the observed velocity dispersion if the intrinsic velocity dispersion of a galaxy is of the same order as the binary velocity dispersion. The kurtosis of the line-of-sight velocity distribution (LOSVD) is affected even at higher values of the intrinsic velocity dispersion. Moreover, the LOSVD of the binary stars (i.e. the probability of finding a star in a binary system with a particular projected velocity) is given in closed form, approximating the constituent stars of all binaries to revolve on circular orbits around each other. With this binary LOSVD, we calculate the observed LOSVD, the latter quantifying the movement of stars along the line of sight caused both by the orbits of the stars through the galaxy and by the motion of the stars in binary systems. As suggested by the changes induced in the moments, the observed LOSVD becomes more peaked around zero velocity and develops broader high-velocity wings. These results are important in interpreting kinematics derived from integrated-light spectra of low-mass galaxies and many of the intermediate results are useful for comparison with Monte Carlo simulations.