The masses of supermassive black holes correlate almost perfectly with the velocity dispersions of their host bulges , M _ { \bullet } \propto \sigma ^ { \alpha } , where \alpha = 4.8 \pm 0.5 .
The relation is much tighter than the relation between M _ { \bullet } and bulge luminosity , with a scatter no larger than expected on the basis of measurement error alone .
Black hole masses estimated by Magorrian et al .
( 1998 ) lie systematically above the M _ { \bullet } - \sigma relation defined by more accurate mass estimates , some by as much as two orders of magnitude .
The tightness of the M _ { \bullet } - \sigma relation implies a strong link between black hole formation and the properties of the stellar bulge .