THE L∝σ8 CORRELATION FOR ELLIPTICAL GALAXIES WITH CORES: RELATION WITH BLACK HOLE MASS

We construct the Faber-Jackson correlation between velocity dispersion σ and total galaxy luminosity LV separately for elliptical galaxies with and without cores. The coreless ellipticals show the well-known, steep relationship dlog σ/dlog LV = 0.268 or LV ∝σ3.74. This corresponds to dlog σ/dlog M = 0.203, where M is the stellar mass and we use M/L∝L 0.32. In contrast, the velocity dispersions of core ellipticals increase much more slowly with LV and M: dlog σ/dlog LV = 0.120, LV ∝σ8.33, and dlog σ/dlog M = 0.091. Dissipationless major galaxy mergers are expected to preserve σ according to the simplest virial-theorem arguments. However, numerical simulations show that σ increases slowly in dry major mergers, with dlog σ/dlog M ≅ +0.15. In contrast, minor mergers cause σ to decrease, with dlog σ/dlog M ≅ –0.05. Thus, the observed relation argues for dry major mergers as the dominant growth mode of the most massive ellipticals. This is consistent with what we know about the formation of cores. We know no viable way to explain galaxy cores except through dissipationless mergers of approximately equal-mass galaxies followed by core scouring by binary supermassive black holes. The observed, shallow σ∝LV+0.12 relation for core ellipticals provides further evidence that they formed in dissipationless and predominantly major mergers. Also, it explains the observation that the correlation of supermassive black hole mass with velocity dispersion, M.∝σ4, ''saturates'' at high M. such that M. becomes almost independent of σ.