Widespread presence of shallow cusps in the surface-brightness profile of globular clusters

Abstract

Surface brightness profiles of globular clusters with shallow central cusps (Sigma ~ R^v with -0.3<~ v <~ -0.05) have been associated by several recent studies with the presence of a central intermediate mass black hole (IMBH). Such shallow slopes are observed in several globular clusters thanks to the high angular resolution of Hubble Space Telescope imaging. In this Letter we evaluate whether shallow cusps are a unique signature of a central IMBH by analyzing a sample of direct N-body simulations of star clusters with and without a central IMBH. We ``observe'' the simulations as if they were HST images. Shallow cusps are common in our simulation sample: star clusters without an IMBH have v >~ -0.3 in the pre-core-collapse and core-collapse phases. Post-core-collapse clusters without an IMBH transition to steeper cusps, -0.7<~ v <~ -0.4, only if the primordial binary fraction is very small, f_{bin}< 3 per cent, and if there are few stellar-mass black holes remaining. Otherwise v values overlap the range usually ascribed to the presence of an IMBH throughout the entire duration of the simulations. In addition, measuring v is intrinsically prone to significant uncertainty, therefore typical measurement errors may lead to v > -0.3 even when <~ -0.4. Overall our analysis shows that a shallow cusp is not an unequivocal signature of a central IMBH and casts serious doubts on the usefulness of measuring v in the context of the hunt for IMBHs in globular clusters.