Are black holes big enough to quench cooling in cluster cool cores?
  Total energy arguments (e.g., Fabian et al. 2002) suggest that black holes
need to have masses significantly in excess of the prediction from the classic
black hole mass - velocity dispersion relation (M-sigma) in order to offset the
cooling losses in massive cool core clusters. This suggests that the black
holes may be too small to power such clusters. However, Lauer et al. (2007)
argue that the black hole mass - bulge luminosity relationship is a better
predictor of black hole masses in high luminosity galaxies and that this
relationship predicts significantly higher masses in BCGs. They find slow
increase in the velocity dispersion with luminosity and a more rapid increase
in effective radii with luminosity seen in BCGs as opposed to less luminous
galaxies. Motivated by these results and the theoretical work of Boylan-Kolchin
et al. (2006) on isolated mergers, we perform high-resolution cosmological
simulations of dry mergers in a massive galaxy cluster identified in the
Millennium Run including both the dark matter halos and stellar bulges of
merging galaxies. We demonstrate that the BCG clearly evolves away from the
size-luminosity relation as defined by the smaller galaxies (i.e., the relation
bends) and we also see a bending in the luminosity-sigma relation. As black
hole mass is expected to be proportional to the mass and luminosity of the
stellar bulge of the BCGs (if they were formed in predominantly dissipationless
mergers), our findings are consistent with those of Lauer et al. (2007) on a
qualitative level and suggest that the black holes in BCGs may indeed be more
massive than predicted from the standard M-sigma relation.
