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Register a new userFormation of supermassive black holes in galactic nuclei II: retention and growth of seed intermediate-mass black holes
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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.
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Current theoretical models predict a mass gap with a dearth of stellar black holes (BHs) between roughly $50,M_odot$ and $100,M_odot$, while, above the range accessible through massive star evolution, intermediate-mass BHs (IMBHs) still remain elusive. Repeated mergers of binary BHs, detectable via gravitational wave emission with the current LIGO/Virgo/Kagra interferometers and future detectors such as LISA or the Einstein Telescope, can form both mass-gap BHs and IMBHs. Here we explore the possibility that mass-gap BHs and IMBHs are born as a result of successive BH mergers in dense star clusters. In particular, nuclear star clusters at the centers of galaxies have deep enough potential wells to retain most of the BH merger products after they receive significant recoil kicks due to anisotropic emission of gravitational radiation. We show that a massive stellar BH seed can easily grow to $sim 10^3 - 10^4,M_odot$ as a result of repeated mergers with other smaller BHs. We find that lowering the cluster metallicity leads to larger final BH masses. We also show that the growing BH spin tends to decrease in magnitude with the number of mergers, so that a negative correlation exists between final mass and spin of the resulting IMBHs. Assumptions about the birth spins of stellar BHs affect our results significantly, with low birth spins leading to the production of a larger population of massive BHs.
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.
We describe ongoing searches for intermediate-mass black holes with M_BH ~ 100-10^5 M_sun. We review a range of search mechanisms, both dynamical and those that rely on accretion signatures. We find that dynamical and accretion signatures alike point to a high fraction of 10^9-10^10 M_sun galaxies hosting black holes with M_BH<10^5 M_sun. In contrast, there are no solid detections of black holes in globular clusters. There are few observational constraints on black holes in any environment with M_BH ~ 100-10^4 M_sun. Considering low-mass galaxies with dynamical black hole masses and constraining limits, we find that the M_BH-sigma_* relation continues unbroken to M_BH~10^5 M_sun, albeit with large scatter. We believe the scatter is at least partially driven by a broad range in black hole mass, since the occupation fraction appears to be relatively high in these galaxies. We fold the observed scaling relations with our empirical limits on occupation fraction and the galaxy mass function to put observational bounds on the black hole mass function in galaxy nuclei. We are pessimistic that local demographic observations of galaxy nuclei alone could constrain seeding mechanisms, although either high-redshift luminosity functions or robust measurements of off-nuclear black holes could begin to discriminate models.
Intermediate-mass black holes (IMBHs) have masses of about 100 to 100,000 solar masses. They remain elusive. Observing IMBHs in present-day globular clusters (GCs) would validate a formation channel for seed black holes in the early universe and inform event predictions for gravitational wave facilities. Reaching a large number of GCs per galaxy is key, as models predict that only a few percent will have retained their gravitational-wave fostering IMBHs. Related, many galaxies will need to be examined to establish a robust sample of IMBHs in GCs. These needs can be meet by using a next-generation Very Large Array (ngVLA) to search for IMBHs in the GCs of hundreds of galaxies out to a distance of 25 Mpc. These galaxies hold tens of thousands of GCs in total. We describe how to convert an ngVLA signal from a GC to an IMBH mass according to a semi-empirical accretion model. Simulations of gas flows in GCs would help to improve the robustness of the conversion. Also, self-consistent dynamical models of GCs, with stellar and binary evolution in the presence of IMBHs, would help to improve IMBH retention predictions for present-day GCs.
Using the Next Generation Very Large Array (ngVLA), we will make a comprehensive inventory of intermediate-mass black holes (IMBHs) in hundreds of globular cluster systems out to a distance of 25 Mpc. IMBHs have masses of about 100 to 100,000 solar masses. Finding them in globular clusters would validate a formation channel for seed black holes in the early universe and inform event predictions for gravitational wave facilities. Reaching a large number of globular clusters is key, as Fragione et al. (2018) predict that only a few percent will have retained their gravitational-wave fostering IMBHs.
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