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The spin angular momentum S of a supermassive black hole (SBH) precesses due to torques from orbiting stars, and the stellar orbits precess due to dragging of inertial frames by the spinning hole. We solve the coupled post-Newtonian equations describing the joint evolution of S and the stellar angular momenta Lj, j = 1...N in spherical, rotating nuclear star clusters. In the absence of gravitational interactions between the stars, two evolutionary modes are found: (1) nearly uniform precession of S about the total angular momentum vector of the system; (2) damped precession, leading, in less than one precessional period, to alignment of S with the angular momentum of the rotating cluster. Beyond a certain distance from the SBH, the time scale for angular momentum changes due to gravitational encounters between the stars is shorter than spin-orbit precession times. We present a model, based on the Ornstein-Uhlenbeck equation, for the stochastic evolution of star clusters due to gravitational encounters and use it to evaluate the evolution of S in nuclei where changes in the Lj are due to frame dragging close to the SBH and to encounters farther out. Long-term evolution in this case is well described as uniform precession of the SBH about the clusters rotational axis, with an increasingly important stochastic contribution when SBH masses are small. Spin precessional periods are predicted to be strongly dependent on nuclear properties, but typical values are 10-100 Myr for low-mass SBHs in dense nuclei, 100 Myr - 10 Gyr for intermediate mass SBHs, and > 10 Gyr for the most massive SBHs. We compare the evolution of SBH spins in stellar nuclei to the case of torquing by an inclined, gaseous accretion disk.
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Interaction of a binary supermassive black hole with stars in a galactic nucleus can result in changes to all the elements of the binarys orbit, including the angles that define its orientation. If the nucleus is rotating, the orientation changes can be large, causing large changes in the binarys orbital eccentricity as well. We present a general treatment of this problem based on the Fokker-Planck equation for f, defined as the probability distribution for the binarys orbital elements. First- and second-order diffusion coefficients are derived for the orbital elements of the binary using numerical scattering experiments, and analytic approximations are presented for some of these coefficients. Solutions of the Fokker-Planck equation are then derived under various assumptions about the initial rotational state of the nucleus and the binary hardening rate. We find that the evolution of the orbital elements can become qualitatively different when we introduce nuclear rotation: 1) the orientation of the binarys orbit evolves toward alignment with the plane of rotation of the nucleus; 2) binary orbital eccentricity decreases for aligned binaries and increases for counter-aligned ones. We find that the diffusive (random-walk) component of a binarys evolution is small in nuclei with non-negligible rotation, and we derive the time-evolution equations for the semimajor axis, eccentricity and inclination in that approximation. The aforementioned effects could influence gravitational wave production as well as the relative orientation of host galaxies and radio jets.
In many galactic nuclei, a nuclear stellar cluster (NSC) co-exists with a supermassive black hole (SMBH). In this work, we explore the idea that the NSC forms before the SMBH through the merger of several stellar clusters that may contain intermediate-mass black holes (IMBHs). These IMBHs can subsequently grow by mergers and accretion to form an SMBH. To check the observable consequences of this proposed SMBH seeding mechanism, we created an observationally motivated mock population of galaxies, in which NSCs are constructed by aggregating stellar clusters that may or may not contain IMBHs. We model the growth of IMBHs in the NSCs through gravitational wave (GW) mergers with other IMBHs and gas accretion. In the case of GW mergers, the merged BH can either be retained or ejected depending on the GW recoil kick it receives. The likelihood of retaining the merged BH increases if we consider growth of IMBHs in the NSC through gas accretion. We find that nucleated lower-mass galaxies ($rm M_{star} lesssim 10^{9} M_{odot}$; e.g. M33) have an SMBH seed occupation fraction of about 0.3 to 0.5. This occupation fraction increases with galaxy stellar mass and for more massive galaxies ($rm 10^{9} M_{odot} lesssim rm M_{star} lesssim 10^{11} M_{odot}$), it is between 0.5 and 0.8, depending on how BH growth is modelled. These occupation fractions are consistent with observational constraints. Furthermore, allowing for BH growth also allows us to reproduce the observed diversity in the mass range of SMBHs in the $rm M_{rm NSC} - M_{rm BH}$ plane.
It is well established that the properties of supermassive black holes and their host galaxies are correlated through scaling relations. While hydrodynamical cosmological simulations have begun to account for the co-evolution of BHs and galaxies, they typically have neglected the BH spin, even though it may play an important role in modulating the growth and feedback of BHs. Here we introduce a new sub-grid model for the BH spin evolution in the moving-mesh code {small AREPO} in order to improve the physical faithfulness of the BH modelling in galaxy formation simulations. We account for several different channels of spin evolution, in particular gas accretion through a Shakura-Sunyaev $alpha$-disc, chaotic accretion, and BH mergers. For BH feedback, we extend the IllustrisTNG model, which considers two different BH feedback modes, a thermal quasar mode for high accretion states and a kinetic mode for low Eddington ratios, with a self-consistent accounting of spin-dependent radiative efficiencies and thus feedback strength. We find that BHs with mass $M_{rm{bh}}lesssim 10^{8}, {rm M}_odot$ reach high spin values as they typically evolve in the coherent gas accretion regime. On the other hand, BHs with mass $M_{rm{bh}}gtrsim 10^{8}, {rm M}_odot$ have lower spins as BH mergers become more frequent, and their accretion discs fragment due to self-gravity, inducing chaotic accretion. We also explore the hypothesis that the transition between the quasar and kinetic feedback modes is mediated by the accretion mode of the BH disc itself, i.e.~the kinetic feedback mode is activated when the disc enters the self-gravity regime. We find excellent agreement between the galaxy and BH populations for this approach and the fiducial TNG model with no spin evolution. Furthermore, our new approach alleviates a tension in the galaxy morphology -- colour relation of the original TNG model.
Changing-look active galactic nuclei (CL-AGNs) as a new subpopulation challenge some fundamental physics of AGNs because the timescales of the phenomenon can hardly be reconciled with accretion disk models. In this Letter{textit{}}, we demonstrate the extreme case: close binaries of supermassive black holes (CB-SMBHs) with high eccentricities are able to trigger the CL transition through one orbit. In this scenario, binary black holes build up their own mini-disks by peeling gas off the inner edges of the circumbinary disk during the apastron phase, after which they tidally interact with the disks during the periastron phase to efficiently exchange angular momentum within one orbital period. For mini-disks rotating retrograde to the orbit, the tidal torque rapidly squeezes the tidal parts of the mini-disks into a much smaller radius, which rapidly results in higher accretion and short flares before the disks decline into type-2 AGNs. Prograde-rotation mini-disks gain angular momentum from the binary and rotate outward, which causes a rapid turn-off from type-1 to type-2. Turn-on occurs around the apastron phase. CB-SMBHs control cycle transitions between type-1 and type-2 with orbital periods but allow diverse properties in CL-AGN light curves.
We summarize a study where we test the hypothesis that local black holes (BH) are relics of AGN activity. We compare the mass function of BHs in the local universe with that expected from AGN relics, which are BHs grown entirely with mass accretion during AGN phases. The local BH mass function (BHMF) is estimated by applying the well-known correlations between BH mass, bulge luminosity and stellar velocity dispersion to galaxy luminosity and velocity functions. The density of BHs in the local universe is 4.6 (-1.4;+1.9) 10^5 Msun Mpc-3. The relic BHMF is derived from the continuity equation with the only assumption that AGN activity is due to accretion onto massive BHs and that merging is not important. We find that the relic BHMF at z=0 is generated mainly at z<3. Moreover, the BH growth is anti-hierarchical in the sense that smaller BHs (MBH<10^7 Msun) grow at lower redshifts (z<1) with respect to more massive ones (z~1-3). Unlike previous work, we find that the BHMF of AGN relics is perfectly consistent with the local BHMF indicating the local BHs were mainly grown during AGN activity. This agreement is obtained while satisfying, at the same time, the constraints imposed by the X-ray background. The comparison with the local BHMF also suggests that the merging process is not important in shaping the relic BHMF, at least at low redshifts (z<3). Our analysis thus suggests the following scenario: local BHs grew during AGN phases in which accreting matter was converted into radiation with efficiencies eff=0.04-0.16 and emitted at a fraction lambda=0.1-1.7 of the Eddington luminosity. The average total lifetime of these active phases ranges from ~4.5 10^8 yr for MBH<10^7 Msun to ~1.5 10^8 yr for MBH>10^9 Msun.
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