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We investigate the rapid growth phase of supermassive black holes (BHs) within the hydrodynamical cosmological eagle simulation. This non-linear phase of BH growth occurs within $sim$$L_{*}$ galaxies, embedded between two regulatory states of the galaxy host: in sub $L_{*}$ galaxies efficient stellar feedback regulates the gas inflow onto the galaxy and significantly reduces the growth of the central BH, while in galaxies more massive than $L_{*}$ efficient AGN feedback regulates the gas inflow onto the galaxy and curbs further non-linear BH growth. We find evolving critical galaxy and halo mass scales at which rapid BH growth begins. Galaxies in the low-redshift Universe transition into the rapid BH growth phase in haloes that are approximately an order of magnitude more massive than their high-redshift counterparts (M{200} $approx 10^{12.4}$~Msol at $z approx 0$ decreasing to M{200} $approx 10^{11.2}$~Msol at $z approx 6$). Instead, BHs enter the rapid growth phase at a fixed critical halo virial temperature ($T_{mathrm{vir}} approx 10^{5.6}$~K). We additionally show that major galaxy--galaxy interactions ($mu geq frac{1}{4}$, where $mu$ is the stellar mass ratio) play a substantial role in triggering the rapid growth phase of BHs in the low-redshift Universe, whilst potentially having a lower influence at high redshift. Approximately 40% of BHs that initiate the rapid BH growth phase at $z approx 0$ do so within $pm 0.5$ dynamical times of a major galaxy--galaxy merger, a fourfold increase above what is expected from the background merger rate. We find that minor mergers ($frac{1}{10} leq mu < frac{1}{4}$) have a substantially lower influence in triggering the rapid growth phase at all epochs.
One of the main themes in extragalactic astronomy for the next decade will be the evolution of galaxies over cosmic time. Many future observatories, including JWST, ALMA, GMT, TMT and E-ELT will intensively observe starlight over a broad redshift ran
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