Scaling Relations Between Low-mass Black Holes and Their Host Galaxies

Abstract: It is well established that supermassive black holes in nearby elliptical galaxies correlate tightly with the kinematic property ($\mbhsigma$ correlation) and stellar mass ($\mbhhost$ correlation) of their host spheroids. However, it is not clear what the relations would be at the low-mass end, and how they evolve. Here, we investigate these relations in low-mass systems ($\MBH \sim \rm{10^{6}- 10^{8}}\, \Msun$) using the Aquila Simulation, a high-resolution cosmological hydrodynamic simulation which follows the formation and evolution of stars and black holes in a Milky Way-size galaxy and its substructures. We find a number of interesting results on the origin and evolution of the scaling relations in these systems: (1) there is a strong redshift evolution in the $\mbhsigma$ relation, but a much weaker one in the $\mbhhost$ relation; (2) there is a close link between the $\mbhsigma$ relation and the dynamical state of the system -- the galaxies that fall on the observed correlation appear to have reached virial equilibrium. (3) the star formation and black hole growth are self-regulated in galaxies -- the ratio between black hole accretion rate and star formation rate remains nearly constant in a wide redshift span $z = 0-6$. These findings suggest that the observed correlations have different origins: the $\mbhsigma$ relation may be the result of virial equilibrium, while the $\mbhhost$ relation may the result of self-regulated star formation and black hole growth in galaxies.