Towards an understanding of the evolution of the scaling relations for supermassive black holes

The growth of the supermassive black holes (BHs) that reside at the centres of most galaxies is intertwined with the physical processes that drive the formation of the galaxies themselves. The evolution of the relations between the mass of the BH, m_BH, and the properties of its host therefore represents crucial aspects of the galaxy formation process. We use a cosmological simulation, as well as an analytical model, to investigate how and why the scaling relations for BHs evolve with cosmic time. We find that a simulation that reproduces the observed redshift 0 relations between m_BH and the properties of its host galaxy, as well as the thermodynamic profiles of the intragroup medium, also reproduces the observed evolution in the ratio m_BH/m_* for massive galaxies, although the evolution of the m_BH/σ relation is in apparent conflict with observations. The simulation predicts that the relations between m_BH and the binding energies of both the galaxy and its dark matter halo do not evolve, while the ratio m_BH/m_halo increases with redshift. The simple, analytic model of Booth and Schaye, in which the mass of the BH is controlled by the gravitational binding energy of its host halo, quantitatively reproduces the latter two results. Finally, we can explain the evolution in the relations between m_BH and the mass and binding energy of the stellar component of its host galaxy for massive galaxies (m_*∼ 10¹¹ M_⊙) at low redshift (z < 1) if these galaxies grow primarily through dry mergers.