Close stellar encounters at the Galactic Centre I: The effect on the observed stellar populations

We model the effects of stellar collisions and close encounters on the stellar populations observed in the Milky Way nuclear stellar cluster. Our analysis is based on $N$-body simulations in which the nuclear stellar cluster forms by accretion of massive stellar clusters in the presence of a supermassive black hole. We attach stellar populations to our $N$-body particles and follow the evolution of their stars and the rate of collisions and close encounters between different types of stars. We find that the most common encounters are collisions between pairs of main-sequence stars, which lead to merger; destructive collisions of stars with compact objects are relatively rare. We find that the effects of collisions on the stellar populations are small for three reasons. First, the core-like density profile in our $N$-body models limits the stellar density. Secondly, the velocity dispersion in the nuclear stellar cluster is similar to the surface escape velocities of the stars, which minimises the collision rate. Finally, whilst collisions between main-sequence stars can destroy bright giants by accelerating the evolution of their progenitors, they can also create them by accelerating the evolution of lower-mass stars. To a good approximation these two effects cancel out. We also investigate whether the G2 cloud that made a close pass by Sgr A* in 2014 could be a fuzzball: a compact stellar core which has accreted a tenuous envelope in a close encounter with a red giant. We conclude that fuzzballs with cores below about $2\,\msun$ have thermal times-scales that are too short to be compatible with observations of G2. A fuzzball with a black-hole core could reproduce the surface properties of G2 but the production rate of such objects in our model is low.