Invoking the virial theorem to understand the impact of (dry) mergers on the M_bh- relation

While dry mergers can produce considerable scatter in the (black hole mass, M-bh)-(spheroid stellar mass, M-*,M- sph) and M-bh-(spheroid half-light radius, R-e,R- sph) diagrams, the virial theorem is used here to explain why the scatter about the M-bh-(velocity dispersion, sigma) relation remains low in the face of such mergers. Its small scatter has been claimed as evidence of feedback from active galactic nuclei (AGNs). However, it is shown that galaxy mergers also play a significant role. The collision of two lenticular (S0) galaxies is expected to yield three types of merger product (a core-Sersic S0, an ellicular ES,e or an elliptical E galaxy), depending on the remnant's orbital angular momentum. It is shown that the major merger of two S0 galaxies with M-*,M- sph & SIM; 10(11) M-& ODOT; advances the system along a slope of & SIM;5 in the M-bh-sigma diagram, while a major E+E galaxy merger moves a system slightly along a trajectory with a slope of & SIM;9. Mergers of lower-mass S0 galaxies with M-*,M- sph & SIM; 10(10) M-& ODOT; move slightly along a trajectory with a slope of & SIM;3, thereby further contributing to the steeper distribution for the E (and Es,e) galaxies in the M-bh-sigma diagram, reported here to have a slope of 7.27 & PLUSMN; 0.91, compared to the S0 galaxies that have a slope of 5.68 & PLUSMN; 0.60. This result forms an important complement to the AGN feedback models like that from Silk & Rees, providing a more complete picture of galaxy/(black hole) co-evolution. It also has important implications for nanohertz gravitational-wave research.