In the early Universe, while galaxies were still forming, black holes as massive as a billion solar masses powered quasars. Supermassive black holes are found at the centers of most galaxies today 1,2,3 , where their masses are related to the velocity dispersions of stars in their host galaxies and hence to the mass of the central bulge of the galaxy 4,5 . This suggests a link between the growth of the black holes and the host galaxies 6,7,8,9 , which has indeed been assumed for a number of years. But the origin of the observed relation between black hole mass and stellar velocity dispersion, and its connection with the evolution of galaxies have remained unclear. Here we report hydrodynamical simulations that simultaneously follow star formation and the growth of black holes during galaxy-galaxy collisions. We find that in addition to generating a burst of star formation 10 , a merger leads to strong inflows that feed gas to the supermassive black hole and thereby power the quasar. The energy released by the quasar expels enough gas to quench both star formation and further black hole growth. This determines the lifetime of the quasar phase (approaching 100 million years) and explains the relationship between the black hole mass and the stellar velocity

We describe techniques for incorporating feedback from star formation and black hole (BH) accretion into simulations of isolated and merging galaxies. At present, the details of these processes cannot be resolved in simulations on galactic scales. Our basic approach therefore involves forming coarse‐grained representations of the properties of the interstellar medium (ISM) and BH accretion starting from basic physical assumptions, so that the impact of these effects can be included on resolved scales. We illustrate our method using a multiphase description of star‐forming gas. Feedback from star formation pressurizes highly overdense gas, altering its effective equation of state (EOS). We show that this allows the construction of stable galaxy models with much larger gas fractions than possible in earlier numerical work. We extend the model by including a treatment of gas accretion onto central supermassive BHs in galaxies. Assuming thermal coupling of a small fraction of the bolometric luminosity of accreting BHs to the surrounding gas, we show how this feedback regulates the growth of BHs. In gas‐rich mergers of galaxies, we observe a complex interplay between starbursts and central active galactic nuclei (AGN) activity when the tidal interaction triggers intense nuclear inflows of gas. Once an accreting supermassive BH has grown to a critical size, feedback terminates its further growth and expels gas from the central region in a powerful quasar‐driven wind. Our simulation methodology is therefore able to address the coupled processes of gas dynamics, star formation and BH accretion during the formation of galaxies.

We examine the disc–jet connection in stellar mass and supermassive black holes by investigating the properties of their compact emission in the X‐ray and radio bands. We compile a sample of ∼100 active galactic nuclei with measured masses, 5‐GHz core emission, and 2–10 keV luminosities, together with eight galactic black holes with a total of ∼50 simultaneous observations in the radio and X‐ray bands. Using this sample, we study the correlations between the radio (LR) and the X‐ray (LX) luminosity and the black hole mass (M). We find that the radio luminosity is correlated with bothM and LX, at a highly significant level. In particular, we show that the sources define a ‘Fundamental Plane’ in the three‐dimensional (log LR, log LX, log M) space, given by log LR= (0.60+0.11−0.11) log LX+ (0.78+0.11−0.09) log M+ 7.33+4.05−4.07, with a substantial scatter of σR= 0.88. We compare our results to the theoretical relations between radio flux, black hole mass, and accretion rate derived by Heinz & Sunyaev. Such relations depend only on the assumed accretion model and on the observed radio spectral index. Therefore, we are able to show that the X‐ray emission from black holes accreting at less than a few per cent of the Eddington rate is unlikely to be produced by radiatively efficient accretion, and is marginally consistent with optically thin synchrotron emission from the jet. On the other hand, models for radiatively inefficient accretion flows seem to agree well with the data.

We discuss a numerical model for black hole growth and its associated feedback processes that for the first time allows cosmological simulations of structure formation to self‐consistently follow the build up of the cosmic population of galaxies and active galactic nuclei (AGNs). Our model assumes that seed black holes are present at early cosmic epochs at the centres of forming haloes. We then track their growth from gas accretion and mergers with other black holes in the course of cosmic time. For black holes that are active, we distinguish between two distinct modes of feedback, depending on the black hole accretion rate itself. Black holes that accrete at high rates are assumed to be in a ‘quasar regime’, where we model their feedback by thermally coupling a small fraction of their bolometric luminosity to the surrounding gas. The quasar activity requires high densities of relatively cold gas around the black hole, as it is achieved through large‐scale inflows triggered by galaxy mergers. For black holes with low accretion rates, we conjecture that most of their feedback occurs in mechanical form, where AGN‐driven bubbles are injected into a gaseous environment. This regime of activity, which is subdominant in terms of total black hole mass growth, can be identified with radio galaxies in clusters of galaxies, and can suppress cluster cooling flows without the requirement of a triggering by mergers. Using our new model, we carry out treesph cosmological simulations on the scales of individual galaxies to those of massive galaxy clusters, both for isolated systems and for cosmological boxes. We demonstrate that our model produces results for the black hole and stellar mass densities in broad agreement with observational constraints. We find that the black holes significantly influence the evolution of their host galaxies, changing their star formation history, their amount of cold gas and their colours. Furthermore, the properties of intracluster gas are affected strongly by the presence of massive black holes in the cores of galaxy clusters, leading to shallower metallicity and entropy profiles, and to a suppression of strong cooling flows. Our results support the notion that AGNs are a key ingredient in cosmological structure formation. They lead to a self‐regulated growth of black holes and bring the simulated properties of their host galaxies into much better agreement with observations.