Supermassive Black Holes in Galactic Nuclei and their Models of Formation Clemence Yun Chan Lee Abstract Supermassive black holes (SMBHs) are black holes with masses larger than 10 5 solar mass, and they are distinctive in terms of their formation and structural properties from their lower mass counterparts, which are typically thought to be produced at the end of stellar life cycles. In particular, the mechanism of their formation has been a largely contested field. So far, numerous models of its formation has been suggested, three of which are formation from seed black holes formed by the collapse of primordial population III stars; from collapse of large masses of gas in proto-galaxies; and from direct formation from merging of proto-galaxies. Each model has its own merits and problems, and for further study, development of a novel method for detecting & studying supermassive black holes in inactive galactic nuclei or far away from us is required.
Background Black Holes Black holes are, by definition, physical entities that forbid escape of all particles including photons inside a finite sphere of influence surrounding the entities. Such broad definition encompasses objects with a wide Figure 1 A rendering of Eddington- Finklestein Diagram. Light inside the Schwarzschild radius cannot escape. From casa.coloardo.edu/~ajsh/schwp.html range of mass, varying in orders of magnitude. Even when only the astrophysical black holes are considered, their mass varies from masses of ~3M to billions of M. Within this broad sub-realm of astrophysical black holes, these objects can be further categorized into three types depending on their respective masses; stellar black holes, which originate from collapse of massive stars, with masses within a single order of magnitude (~3 25 M ); intermediate mass black holes, which have been suggested to exist in the centers of ultraluminous X-ray sources, with mass of 10 2 10 5 M ; and finally, SMBHs with masses larger than 10 6 M.
Unlike stellar black holes, whose sources and mechanisms of formation are fairly well established, such is not the case for intermediate-mass and supermassive black holes. In particular, three contending models of formation have been proposed for SMBHs, each with its merits and problems. Supermassive Black Holes SMBHs have been source of interest in understanding the universe, due to their place in theories of galactic structures, in which they are thought to play a crucial role as galactic nuclei. Various factors have led to the conclusion that both inactive galactic centers and active galactic nuclei (AGNs) contain SMBHs at their centers (Ferrarese and Ford 2005). The Keplerian motion of surrounding masses of gas and stars in observable Figure 2 Mass of SMBH vs Bulge Luminosity (Left) and Velocity dispersion of Stellar Objects within the effective radius (Karl and et al. 2000)
galactic centers, and the consistent accretion and luminescence of AGNs and their theoretical masses, both lead to the prediction of a massive, compact central object (Rees 1984). Although it must be noted that this does not imply that the structural integrity of galaxies are solely maintained by the gravitational pull of the central SMBHs, observations of these objects and their host galaxies have shown a strong correlation between the properties of host galaxies and the mass of the SMBHs, as seen on figure 2. (Ferrarese and Merritt 2000; Karl and et al. 2000). In particular the stark correlation between velocity dispersion and black hole mass despite the weak interaction between the SMBH core and the peripheral stellar objects requires further explanation than as observed in the current state. This suggests that evolution of galaxies and their central SMBHs are in a symbiotic relationship, forming through a single mechanism. It is therefore irrefutable that the understanding of these objects and the mechanism of their formation concurrently provide valuable addition to our understanding of galactic structures and their formation, as well as deepen our understanding with black holes in general. Before proceeding with the rest of the paper, a point of concern in studying these SMBHs must be noted. By the very definition of black holes, these supermassive black holes do not allow escape of photons and therefore direct detection by
electromagnetic waves is not possible, which means the only possible method of optical detection is through gravitational lensing effect, through observing the motions of adjacent objects, or through radiation bursts as seen in AGNs. This limits the scope of SMBH detection, as the objects of interest are embedded inside the bright cores of galaxies, which means the gravitational lensing effect cannot be used, and the latter two limitations mean the only observable SMBHs are those in AGNs and in nearby galaxies, where optical observation of stellar objects is possible. In this paper, examples of contesting models of formation will be introduced and summarized, noting the problems that each model faces. A suggestion for solving the detection problem through gravitational wave detection will be introduced. Paper will conclude with a summary. Models of Formation As mentioned previously, the field has yet to reach a conclusion on a unified theory of SMBH formation. In this paper, three models have been considered; formation from collapse of primordial population III stars; direct formation from primordial gas collapse; direct formation through galaxy mergers.
Formation from massive population III stars One of the most popular theories on formation of SMBHs is formation from the collapse of primordial massive stars termed population III stars. Population III (PopIII) stars are the first generation of stars, which have very low metallicity and high mass. These PopIII stars that form from predominantly metal-free primordial gas have been predicted to be able to contain a large mass, with their stellar mass > 100 M. These stars have a relatively short life-time, in order of ~10 6 years, after which they undergo similar collapse as current (population II) stars. The fates of PopIII stars depend on their mass, as seen in figure 2. At low metallicty, direct formation of black holes from collapse of massive stars occur at regions 25M 140M and >260M. Black holes formed at the lower mass region form black holes of approximately 10M 40M in their size. It is likely that these black holes are too light to become seeds for supermassive black holes, and instead interact with the peripheral gas masses within the larger gas clusters or galaxies. However, the larger black holes, formed from PopIII stars with masses >260M, have masses in the intermediate-mass black hole range, and have been theorized to settle at the core of the gas clusters. It has been suggested that, occurrence of numerous PopIII stars within the primordial gas clusters will result in formation of a multiple of these
intermediate-mass black holes, which will cluster at the core of the galactic halo, providing seeds for formation of a single supermassive black hole. Figure 3. Fate of massive stars after collapse, depending on its initial mass and metallicity. The white region at the bottom left indicates a pair-energy supernovae region where no remnant is seen. (Heger and et al. 2003) However, several questions have been raised on the feasibility of this model. Whereas existence of PopIII stars with mass >260M is crucial for seed black hole formation, several simulation studies indicate that PopIII stars are unlikely to reach such a large mass, either due to fragmentation of proto-star to multiple smaller stars during PopIII formation, or due to factors opposing the accretion process to form these massive stars (Stacy, Greif et al. 2010).
Furthermore, observational evidence from distance quasars at z ~ 6 indicate that supermassive black holes were in existence less than 10 9 years after big bang. However, recent studies have shown that the seed black holes of ~100M cannot maintain the accretion rate required for the formation of supermassive black holes in time. Gas surrounding the seed black holes have low densities, and along with the radiation pressure generated during the accretion process, can result in inefficient accretion of gas particles. Direct formation from gas collapse An alternative model of SMBH formation proposes that they form from direct collapse of gas. In this model, self-gravitating gas in proto-galaxies loses its support and collapse to form black holes of ~ 20M and quickly accrete mass at super-eddington rate (Begelman, Volonteri et al. 2006). In proto-galaxies with near-zero metallicity, large masses of gas held together through self-gravitation are supported by its rotation and hence its angular momentum, caused by the tidal forces from interaction with other nearby masses of gas (halos). It has been proposed that these rotating gases quickly lose their angular momentum through larger gas dynamics, and hence lose the rotational support and collapse,
accreting surrounding gas particles whilst decreasing in radius. As the structure collapses, whilst rotational support continues to decrease and become negligible in supporting the structure, the increased density of the inner sphere and hence the gas pressure that arises counter-acts the gravitational collapse. A quasi-star forms where the luminosity of the released gravitational binding energy exceeds the Eddington limit, with mass in order of million solar masses. At this stage, the change in radius of this quasi-star halts, whilst mass continues to be accreted. With mass being continually added, the core of this quasi-star increases in temperature, until at 10 9 K, undergoes rapid cooling through thermal neutrino emissions (Urca process), a process which is 300 times faster than photodisintegration. The core collapses to form a black hole of ~20 M, immediately accreting mass inside the quasi-star. This initial black hole rapidly accretes the surrounding mass, which is in abundance due to the previous quasi-star formation. It has been theorized that the rate of growth is extremely fast, i.e. at super-eddington rate, so long as the mass of the quasi-star exceeds that of the core black hole, and provided that the mass of the quasi-star continues to increase at a constant rate, evolving at a rate given by : ( ) ( ) ( ),
until the mass of the black hole reaches that of the quasi-star, ~ 10 6 M, from then on which the black hole can continue to grow, accreting mass at a Eddington-limited rate. This model provides explanation for the existence of SMBHs at z ~ 6, or less than a billion years after the big bang. Furthermore, it provides an alternative to requiring a very high mass PopIII star formation as a prerequisite for SMBH formation. However, this model is not without its faults. As with the PopIII model, the current model requires a metal-free environment in order to prevent early cooling in the quasi-star formation stage, and hence prevent star formation prior to the singular collapse of the halo. The current model also proposes that a strong cosmic background UV radiation prevents or dissociates molecular gas interactions which lead to star formation. However, recent studies have suggested that, in fact, this is not the case. Proto-galactic gas mass, which has been previously presumed to be metal-free have been found to undergo fragmentation, even under strong UV radiation, and proceed to stellar formation when its metallicity is above a very low threshold (Omukai and et al. 2008). Another study suggests that only 5% of these protogalactic gas mass that undergo collapse end up as large mass intermediate-mass black holes (Lodato and Natarajan 2006) proposed by this model, further questioning the feasibility of formation through this pathway.
Direct formation through galactic mergers In an attempt to resolve for these issues, a new model for SMBH formation has emerged based on a recent simulation study of early galactic mergers. Whereas in the direct formation from gas collapse model the gas inflow into the initial black hole comes from a single entity, the halo and the quasi-star that the black hole formed from, the new model proposes that the mergers between Figure 4 Simulation results from galactic merger study. Courtesy of Ohio State University proto-galaxies create a gas inflow with sufficiently high rate to create the conditions required for the SMBH formation (figure 4.), despite the counter-acting, concurrent stellar formation. Based on the premise that in the early universe protogalaxies did indeed grow primarily through mutual interactions, the simulation models the impact of two identical dark-matter halos of 10 12 M. The study found that an 80 pc, 2 x 10 9 M, highly unstable rotating disc forms, within which mass is
transferred inwards through spiral motion whilst losing angular momentum, with the inflow rate peaking at 10 4 M yr -1, an extremely high rate compared to the inflow rates observed in previous models. The simulation stops with the formation of a supermassive cloud at the center with mass ~ 2.6 x 10 8 M, from which the study postulates that the gas cloud will continue to collapse to a quasi-star and follow similar mechanism to the previous model to form SMBH. This is further supported by the increase in mass density at the very core of the gas nucleus, supporting the collapse and formation of a dense object (figure 5.) Figure 5 Evolution of the mass distribution of the nuclear region, in the large scale (left), showing the flattening of the periphery corresponding to the sharp increase in density at the very core in the smaller scale, until at 10 5 years, there is a sudden flattening of the inner core density, which corresponds to a separate supermassive gas cloud formation, which absorbs the gas mass in the core. (Mayer, Kazantzidis et al. 2010)
The model predicts that the formation of this cloud occurs in order of 10 5 years, orders of magnitude faster than the typical 10 8 years that is required for stellar formation. The model also predicts that, with the sustained high rate of gas inflow that overcomes the stellar formation rate, the resulting seed black hole of 10 5 M will grow to SMBH scale ~ 3.6 x 10 8 years, which places its timescale under a billion years as seen from observations of distant quasars. The third model presented in this paper overcomes the issue of an idealized, low metallicity condition required in previous models. It also accounts for the existence of early SMBHs that formed within a billion years after the big bang. However, the simulation model disintegrates at galactic mergers between protogalaxies of masses less than 10 11 M, where the gas inflow to the central region is not strong enough to induce gravitational collapse. Furthermore, observations have shown that in low mass galaxies the supernovae-driven gas outflows are larger than the gas inflows from galactic mergers, supporting simulation results that low mass galaxies are unable to form massive black holes. Such results are countered by recent observations of the Heinz2-10 dwarf galaxy, where an SMBH, albeit a smaller one at 10 6 M, exists in its active nucleus (Reines, Sivakoff et al. 2011). The model fails to explain such formation, and an alternative is
required to account for the SMBH formation in dwarf galaxies, which, though rare, does exist. Future Directions It is important to note that in all of these models, a set of idealized conditions is a prerequisite for the success of the model. More importantly, until recently, lack of an effective methodology to acquire the relevant observational evidence to both confirm and develop these models has made all of these models hard to prove. It is also very likely that multiple mechanisms co-exist, and subsequent mergers between SMBHs formed via different mechanisms can further complicate the search for the evidence. For this reason, only a small portion of the massive black holes have been studied through electromagnetic detection, which limited the scope of detection to those residing in active galactic nuclei or those in relative proximity to us. In a recent paper, a possible direction for a solution has been suggested, in which the researchers incorporate the use of space based gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA) (Sesana, Gair et al. 2011), a project waiting for budget and program approval. The paper developed a method by which survey data on the massive black hole binary merger observations, which can be obtained from gravitational wave
measurements, can be used to deduce certain aspects and conditions in SMBH formation and hence develop constraints by which models can be tested. Conclusion In this paper, 3 models of SMBH formation have been introduced. Formation via metal-free PopIII stars require very massive stars of >260 M. Direct formation from singular gas halos could be hindered by stellar formation during the accretion of matter which could prevent the efficient growth of seed black hole, and still require metal free environment. Direct formation through galaxy mergers is more flexible in terms of metallicity, but is constrained by the starting mass of merger galaxies, and does not account for massive black holes in dwarf galaxies. This is by no means the entire scope of the currently existing theories. Perhaps one of the reasons for such proliferation of models is due to lack of available observed constraints by which researchers can work with to develop models. It seems that this field of research is still largely developing, and requires further research, especially in observational aspect.
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