Surface brightness profiles of globular clusters with shallow central cusps ( \Sigma \sim R ^ { \nu } with -0.3 \hbox { \hbox to 0.0 pt { \raise 1.8275 pt \hbox { $ < $ } } \lower 2.795 pt \hbox { $ \sim$% } } \nu \hbox { \hbox to 0.0 pt { \raise 1.8275 pt \hbox { $ < $ } } \lower 2.795 pt \hbox { $% \sim$ } } -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 \nu \hbox { \hbox to 0.0 pt { \raise 1.8275 pt \hbox { $ > $ } } \lower 2.795 pt \hbox { $ \sim$ } % } -0.3 in the pre-core-collapse and core-collapse phases .
Post-core-collapse clusters without an IMBH transition to steeper cusps , -0.7 \hbox { \hbox to 0.0 pt { \raise 1.8275 pt \hbox { $ < $ } } \lower 2.795 pt \hbox { $ \sim$% } } \nu \hbox { \hbox to 0.0 pt { \raise 1.8275 pt \hbox { $ < $ } } \lower 2.795 pt \hbox { $% \sim$ } } -0.4 , only if the primordial binary fraction is very small , f _ { bin } < 3 \% , and if there are few stellar-mass black holes remaining .
Otherwise \nu values overlap the range usually ascribed to the presence of an IMBH throughout the entire duration of the simulations .
In addition , measuring \nu is intrinsically prone to significant uncertainty , therefore typical measurement errors may lead to \nu \geq - 0.3 even when \langle \nu \rangle \lesssim - 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 \nu in the context of the hunt for IMBHs in globular clusters .