Red giant collisions in the Galactic Centre

We simulate collisions involving red giant stars in the centre of our Galaxy. Such encounters may explain the observed paucity of highly luminous red giants within similar to 0.2 pc of Sgr A*. The masses of the missing stars are likely to be in the range similar to 2-8 M.. Recent models of the density distribution and velocity dispersion of the Galactic Centre cluster are used to calculate two-body collision rates. In particular, we use stellar-evolution models to calculate the number of collisions a star will have during different evolutionary phases. We find that the number of two-body collisions per star is less than or similar to 1 in the central 0.1-0.2pc, depending strongly on the Galactocentric radius, with some uncertainty from the assumed cluster models and stellar-evolution models. Using a 3D numerical hydrodynamics code (SPH), we simulate encounters involving cluster stars of various masses with a 2-M. red giant and an 8-M. red giant. The instantaneous mass loss in such collisions is rarely enough to destroy either giant. A fraction of the collisions do, however, lead to the formation of common-envelope systems where the impactor and core of the giant are enshrouded by the envelope of the giant. Such systems may evolve to expel the envelope, leaving a tight binary; the original giant is destroyed. The fraction of collisions that produce common-envelope systems is sensitive to the local velocity dispersion and hence Galactocentric radius. Whereas most of our collisions lead to common-envelope formation at a few parsecs from Sgr A*, very few collisions do so within the central 0.2pc. Using our collision-rate calculations, we then compute the time-scales for a giant star to suffer such a collision within the Galactic Centre. These time-scales are greater than or similar to 10(9-10) yr, and so are longer than the lifetimes of stars more massive than similar to 2 M.. Thus the observed paucity of luminous giants is unlikely to be caused by the formation of common-envelope systems as a result of two-body encounters involving giant stars.