# 2.2.3 Simulation of binary and multiple objects

Author(s): Frédéric Arenou

As indicated above, single stars and primaries are chosen so as to follow the luminosity function (LF) of primaries in the solar neighbourhood. Stellar systems may subsequently be generated by accompanying these primaries with a secondary or higher multiple order companions with characteristics described below (for more details, see Arenou 2011), in accordance with the available observations.

An initially single star given as input can randomly be transformed into a binary, based on a binary fraction set as an increasing function of the primary mass. For giants and white dwarfs, this “primary-constrained pairing” process is applied using the progenitor mass. The binary may then randomly be transformed into a ternary system, the frequency being strongly related to the inner period. Higher multiplicity may also be generated with an exponentially decreasing probability.

The mass ratio is drawn using several probability density functions linear by segment, depending on the primary mass and period. The mass of the secondary being known, and the age of the primary too, the physical parameters of the secondary are obtained using the Hess diagram distribution in the Besançon model, and the secondary can with some probability be main sequence, giant or white dwarf. Then the semi-major axis between the components is drawn from a Gaussian in log of separation, with parameters depending whether the primary is solar-type, M-type or very low mass. The period of the orbit then follows from the semi-major axes and the masses. The orbital eccentricity is known from long to depend on period, and it is generated with parameters depending on the spectral type of the primary. The other orbital parameters are finally generated uniformly or uniform in cosine for the inclination.

Simulated samples have been compared to available observations, in particular the fraction of systems of various spectral types available in the literature, and are statistically consistent.

Beyond the generation of these multiple systems, the orbital motion is taken into account so as to give a realistic snapshot of the various astrometric, spectroscopic (radial velocity) and photometric (eclipses) effects when a simulated catalogue is generated. In the course of the simulations of Gaia transits, the orbits are thus computed, the positions of the system components their photometry and velocimetry are modified accordingly. For possibly interacting very close pairs, the more complicated physics relies on the simulator developed for the Gaia non-single star data processing (Siopis and Sadowski 2012).