Unresolved Binaries and the Initial Mass Function

In the area of binary stars the important contribution of GAIA will be towards statistical studies of the binary star distribution functions. On the other hand, from the GAIA observations, more than 10 000 masses accurate to 1% can be expected. This improves accuracy of the stellar initial mass function (IMF) still poorly known, particularly for the low-mass stars. A goal of the present study is to simulate a solar vicinity model with 100% binaries for predicting observational distributions. Under the assumption that star formation rate is constant, a random pairing of objects drawn from a pre-assumed single star power-law IMF is generated. Stellar evolution and selection effects are taken into account. Orbital parameters are assumed to be spread according to the common distributions. It is shown that under given assumptions the power-law IMF does lead to quasi-lognormal turnovers for the resulting observational mass function. The described model can be used to estimate, under reasonable assumptions on the IMF shape, the number of binaries of the different types that can be observed with GAIA.