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Supermassive black hole (BH) masses (MBH) are strongly correlated with galaxystellar bulge masses (Mbulge) and there are several ideas to explain the originof this relationship. This study isolates the role of galaxy mergers fromconsiderations of other detailed physics to more clearly show how a linearBH-galaxy mass relation (MBH-Mgal) can naturally emerge regardless of howprimordial BHs were seeded inside galaxies, if the galaxy mass functiondeclines with increasing mass. Under this circumstance, the MBH-Mgal relationis a passive attractor that eventually converges to a tight linear relationbecause of two basic statistical effects: a central limit-like tendency forgalaxy mergers which is much stronger for major mergers than minor mergers, anda convergence toward a linear relation that is due mainly to minor mergers. Acurious consequence of this thought experiment is that, if galaxy bulges areformed by major mergers, then merging statistics naturally show that MBH wouldcorrelate more strongly with bulge dominated galaxies, because of strongercentral-seeking tendencies, than with disk dominated galaxies. Even if someother physics is ultimately responsible for causing a linear MBH-Mbulgerelationship, this thought experiment shows that, counter to intuition, randommerging of galaxies that harbor random BH masses tends to strengthen ratherthan weaken a pre-existing, linear, correlation. This idea may be generalizedto other gravitationally bound systems (dark matter halo, compact nuclearobjects) that retain their physical identities after experiencing mergers.

How Mergers May Affect The Mass Scaling Relations Between Black Holes, Galaxies, and Other Gravitationally Bound Systems