The masses of open star clusters and their tidal tails and the stellar initial mass function

Context. Unresolved binaries have a strong influence on the observed parameters of stellar clusters (SCs). Aims. We quantify this influence and compute the resulting mass underestimates and stellar mass function (MF). Methods. N-body simulations of realistic SCs were used to investigate the evolution of the binary population in a SC and its tidal tails. Together with an empirically gauged stellar mass-luminosity relation, the results were then used to determine how the presence of binaries changes the photometric mass and MF of the SC and its tails as deduced from observations. Results. Tail 1 (T1), which is the tidal tail caused by gas expulsion, contains a larger fraction of binaries than both the SC and Tail 2 (T2), which forms after gas expulsion. Additionally, T1 has a larger velocity dispersion. Using the luminosity of an unresolved binary, an observer would underestimate its mass. This bias sensitively depends on the companion masses due to the structure of the stellar mass-luminosity relation. Combining the effect of all binaries in the simulation, the total photometric mass of the SC is underestimated by 15%. Dark objects (black holes and neutron stars) increase the difference between the real and observed mass of the SC further. For both the SC and the tails, the observed power-law index of the MF between a stellar mass of 0.3 and 0.7 M⊙ is smaller by up to 0.2 than the real one, the real initial mass function (IMF) being steeper by this amount. This difference is larger for stars with a larger velocity dispersion or binary fraction. Conclusions. Since the stars formed in SCs are the progenitors of the Galactic field stars, this work suggests that the binary fractions of different populations of stars in the Galactic disc will differ as a function of the velocity dispersion. However, the direction of this correlation is currently unclear, and a complete population synthesis will be needed to investigate this effect. Variations in the binary fractions of different clusters can lead to perceived variations of the deduced stellar MFs.