8.1. Feedback from supermassive black holes
In order to solve the "overcooling" problem in massive galaxies (given the high rate at which gas can cool within galaxies, they should be, at the present epoch, much more massive and luminous than observed) some source of heating of the cold gas is needed. While the evolution of low mass galaxies is mainly driven by feedback from SNe explosions, this type of feedback has little impact on the formation of massive galaxies. An energy budget analysis suggests that a possible source of feedback in such massive galaxies is AGN feedback from supermassive black holes (SMBHs), which release an amount of energy up to a factor 20-50 higher than from SNe.
Feedback from AGN will naturally result in a connection between the properties of a SMBH and its host galaxy. Therefore, this process will also explain the observed correlation between the SMBH mass and galaxy mass or velocity dispersion, fig. 22. Indeed, coupling the energy released by the formation of the SMBH to the surrounding gas content of the forming galaxy will inevitably lead to a relationship like the observed MBH - σ relation. If the BH is massive enough, outflows from its center will result in residual gas ejection, regulating star formation. This condition requires the Eddington luminosity of the BH to be LEdd / c = GMBH Mgas / r2. The MW is in the lower left corner of fig. 22, and represents a typical example of a late-type galaxy whose central BH is less massive than those typically observed in early-type galaxies.
Figure 22. Black hole mass vs spheroid velocity dispersion, figure from .
The slope of MBH - σ depends on whether the quasar feedback is predominantly energy-conserving MBH ∝ σ5  or momentum-conserving MBH ∝ σ4 [110, 111]: both data  and 3-d simulations  favor the steeper slope.
AGN feedback can explain the exponential break in the galaxy luminosity function (fig. 10) and, by quenching star formation, can reproduce the bimodal distribution of galaxy colors: massive, early-type galaxies will be "red and dead", with star formation quenched by the SMBH feedback. Reference  found observational evidence for AGN feedback in early-type galaxies, with star-forming early types inhabiting the blue cloud, while early types with AGN being located considerably closer to the red sequence.
Fig. 23 shows how star-forming objects have a starburst age around 150-300 Myr, while the most common starburst age ty for the transition region objects is around 300 to 500 Myr. The peak AGN phase occurs roughly half a Gyr after the starburst. The most likely interpretation is that star formation is suppressed by nuclear activity in these objects.
Figure 23. Top panel, normalised probability distribution functions for the time elapsed since the start of the starburst ty. Bottom panel, 50% of such probability as a function of ty. Figure from .
8.2. Modes of AGN feedback
There are two modes of AGN feedback: the quasar mode, occurring when large amounts of gas flow inwards, during the dominant accretion of BH mass, and the radio mode, during which the BH accretes at a lower rate. During the radio mode, the AGN drives powerful jets and cocoons that heat the circumgalactic and halo gas, effectively shutting down cooling in massive haloes and resulting in agreement with the bright end of the observed luminosity function.
AGN activity is important in the cosmological feedback cycles of galaxy formation. Reference  studied the internal circulation within the cocoon arising from such a relativistic jet emanating from an AGN, performing 2D simulations, and found that backflows could feed the AGN and provide a self-regulatory mechanism of its activity. The study  used 3D grid-based hydrodynamical simulations to show that ultra-fast outflows (UFO) from AGN result in considerable feedback of energy and momentum into the interstellar medium of the host galaxy. They performed simulations of the UFO interacting with a two-phase ISM in which the clouds are distributed spherically or in a disc. Differences are show in fig. 24. Within 10 kyr after the start of the UFO, the evolution starts to differ between the cases of bulge-like and disc-like cloud distributions. In the former case, the UFO streams continue to channel and branch out quasi-isotropically and inflate a quasi-spherical energy bubble.
Figure 24. Top panel, midplane density slices of the evolution of a 1044ergs-1 ultra-fast outflow for a two-phase ISM with spherically distributed clouds. Lower panel, same as top but for a ISM with disc-distributed clouds. Figure from .
8.3. Positive feedback from AGN
We have seen that negative feedback from AGN helps account for the BH mass-σ correlation and for the luminosity function of massive galaxies. At the same time, AGN activity could result in positive feedback on the star formation rate [117, 118]. A phase of positive feedback is motivated by evidence for AGN triggering of star formation [119, 120], discussed further below.
AGN outflows can trigger star formation by compressing dense clouds. Propagation of jets into a clumpy interstellar medium will lead to the formation of an expanding, over-pressurized cocoon at vco, which is much larger than the velocity field associated with the gravitational potential well. Therefore, protogalactic clouds that are above the Jeans, or the more appropriate Bonnor-Ebert, mass may be induced to collapse.
The region where AGN feedback can be positive is determined by the condition that the AGN-induced pressure exceeds the dynamical pressure that controls the ambient interstellar medium. A key ingredient in star formation is molecular hydrogen. The molecular hydrogen fraction correlates with interstellar pressure in nearby star-forming galaxies . Enhanced pressure from AGN is likely to accelerate molecular cloud formation and thereby star formation.
If one replaces the gas pressure, ρg, by the AGN-driven pressure, ρAGN, then the AGN-driven-star-formation-enhancement factor is (ρAGN / ρg)1/2 ≈ (vco / σ) τ1/2 where τ is the optical depth. Since єSN ~ σ the fraction of stars formed per dynamical time is boosted for spheroids relative to disks. Numerical simulations  of the interaction of a powerful AGN jet with the massive gaseous disc of a high-redshift galaxy demonstrate that such enhanced AGN-driven pressure from jets is effectively able to compress the disk gas and to enhance star formation, as shown in fig. 25.
Figure 25. The gaseous disc gets compressed by the expanding over-pressurized cocoon driven by AGN outflows. Left panel, initial state;right panel, final stage of evolution. The figures are color-coded according to increasing pressure, from blue to yellow. Simulation from .
8.4. SMBH formation
The epoch of first quasars, first galaxies and first stars is at about z = 6-10. But how does a SMBH form? Before supermassive black holes can grow via accretion or merging, there must be some pre-existing seed black holes. There are two models for the creation of SMBH seed: via remnants of PopIII stars  or by direct halo gas collapse . In the first scenario, the seed is created at high redshift by the remnants of the earliest generation of Population III stars, which have reached the end of their stellar lifetimes. Gas collapse in a 106 M halo leads to an BH seed that will grow into an AGN by gas accretion. In the second scenario, the halo gas collapse directly to form a massive IMBH seed. Since the halo virial temperature is:
at 108 M, the Lyman-alpha cooling operates at 104 K, so direct collapse via atomic cooling is possible. In this latter case, there are two dynamical problems: the angular momentum barrier prohibits the gas from collapsing and the fragmentation depletes the accreting gas. However, while the gas collapses and becomes turbulent, the fragmentation is suppressed and, once a gaseous bar is formed, it redistributes J, overcoming the angular momentum barrier by a sequence of bar formation and dissolution to progressively smaller scales .