Widespread presence of shallow cusps in the surface-brightness profile
  of globular clusters
  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 <v> <~ -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.
