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

It is well established that supermassive black holes in nearby elliptical galaxies correlate tightly with the kinematic property ($\text{mbhsigma}$ correlation) and stellar mass ($\text{mbhhost}$ 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 ($\text{MBH}\sim {10}^6-{10}^8\text{Msun}$) 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 $\text{mbhsigma}$ relation, but a much weaker one in the $\text{mbhhost}$ relation; (2) there is a close link between the $\text{mbhsigma}$ 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 $\text{mbhsigma}$ relation may be the result of virial equilibrium, while the $\text{mbhhost}$ relation may the result of self-regulated star formation and black hole growth in galaxies.