Effect of Binarity in Star Cluster Dynamical Mass Determination

In this paper we explore the effects that the presence of a fraction of binary stars has in the determination of a star cluster mass via the virial theorem. To reach this aim in an accurate and consistent way, we run a set of simulations using the direct summation, high precision, code NBODY7. By means of this suite of simulations we are able to quantify the overestimate of open-star-cluster-like models' dynamical masses when making a straight application of the virial theorem using available position and radial velocity measurements. The mass inflation caused by the binary "heating"contribution to the measured velocity dispersion depends, of course, on the initial binary fraction, f b0 and its following dynamical evolution. For an f b (evolved up to 1.5 Gyr) in the range 8%-42% the overestimate of the mass done using experimentally sounding estimates for the velocity dispersion can be up to a factor of 45. We provide a useful fitting formula to correct the dynamical mass determination for the presence of binaries, and underline how neglecting the role of binaries in stellar systems might lead to erroneous conclusions about their total mass budget. If this trend remains valid for larger systems like dwarf spheroidal galaxies, which are still far out of reach for high-precision dynamical simulations taking their binaries into account, it would imply an incorrect overestimation of their dark matter content, as inferred by means of available velocity dispersion measurements.