There have been reports of possible detections of intermediate-mass black holes ( IMBHs ) in globular clusters ( GCs ) .
Empirically , there exists a tight correlation between the central supermassive black hole ( SMBH ) mass and the mean velocity dispersion of elliptical galaxies , “ pseudobulges ” and classical bulges of spiral galaxies .
We explore such a possible correlation for IMBHs in spherical GCs .
In our model of self-similar general polytropic quasi-static dynamic evolution of GCs , a criterion of forming an IMBH is proposed .
The key result is M _ { BH } = \mathcal { L } \sigma ^ { 1 / ( 1 - n ) } where M _ { BH } is the IMBH mass , \sigma is the GC mean stellar velocity , \mathcal { L } is a coefficient , and 2 / 3 < n < 1 .