Red giant stellar collisions in the Galactic Centre

We show that collisions with stellar-mass black holes can partially explain the absence of bright giant stars in the Galactic Centre, first noted by Genzel et al. We show that the missing objects are low-mass giants and asymptotic giant branch stars in the range 1-3 M-circle dot. Using detailed stellar evolution calculations, we find that to prevent these objects from evolving to become visible in the depleted K bands, we require that they suffer collisions on the red giant branch, and we calculate the fractional envelope mass losses required. Using a combination of smoothed particle hydrodynamic calculations, restricted three-body analysis and Monte Carlo simulations, we compute the expected collision rates between giants and black holes, and between giants and main-sequence stars in the Galactic Centre. We show that collisions can plausibly explain the missing giants in the 10.5 < K < 12 band. However, depleting the brighter (K < 10.5) objects out to the required radius would require a large population of black hole impactors which would in turn deplete the 10.5 < K < 12 giants in a region much larger than is observed. We conclude that collisions with stellar-mass black holes cannot account for the depletion of the very brightest giants, and we use our results to place limits on the population of stellar-mass black holes in the Galactic Centre.