Ranges of the relative velocity between stars and stellar density for destructive (magenta-shaded) and non-destructive (gray-shaded) collisions, separated by the surface escape velocity of a 1 M_⊙ main-sequence star. The velocity v and distance R from the black hole are related by $v/c=\sqrt{r_{\mathrm{g}}/R}$, with the black-shaded region (“Inside black hole”) indicating v/c>1. Here, r_g is the gravitational radius. Black diagonal lines indicate nuclear clusters with the same mass as the black hole, assuming a Bahcall & Wolf (1976) profile extending inward (arrow) from the influence radius until 2 M_⊙ is enclosed or the event horizon is reached. The red and blue crosses indicate the observationally constrained density at 0.25 pc from the Galactic center (Genzel et al. 2010) and the semimajor axis of the S2 star (Gillessen et al. 2009), respectively.