Massive and Super Massive black holes (M & SMBHs) are a scaled version of each other: the former have stellar origin thus their mass is in the range 10-100 solar masses (Ms) and evolve in stellar clusters, the latter, whose origin and mechanism of formation is still under debate, are 4-5 order of magnitude more massive than BHs and lie in the innermost region of galaxies with which they co-evolve. Both M & SMBHs influence the dynamical evolution of the environment in which they live. Massive BHs which evolve in star clusters, either Globular and Open clusters (GCs & OCs), may form binary systems which may merge, because of gravitational interactions with field stars, and release gravitational waves (GW). In addition black hole binary systems play a crucial role in the evolution of star clusters acting as energy sources which are likely to prevent clusters from core collapse (CC).
On the other hand, thanks to the high resolution images provided by the Hubble Space Telescope, it is clear that the nuclei of the majority of elliptical and early-type spiral galaxies (>10^10Ms) harbor SMBHs, whose mass is between 10^6Ms and 10^9Ms. In many cases, the central SMBH is surrounded by a massive, very compact, star cluster which is commonly referred to as Nuclear Stellar Cluster (NSC), with structural properties that are reminiscent of globular clusters (GCs).
The project proposed here deals with these topics: the first part is devoted to the study of the dynamical evolution of massive black holes binary systems in low density stellar clusters in order to constrain the probability that such systems may merge in a Hubble time. The second part regards the study of the secular evolution of NSCs, with a particular focusing on the Milky Way (MW) NSC and its dynamical interaction with the central SMBH.
The recent detection of GW has shed the light on many astrophysical open questions providing the first robust confirmation of several theoretical predictions. First, the GW confirms the existence of heavy (>25 Ms) stellar-mass black holes. In particular massive BHBs may form in nature by gravitational encounters and dynamical interactions and they may merge in a detectable rate within a Hubble Time (Abbott et al. 2016). Furthermore the existence of such heavy objects open the door to new important implications on stellar theory, as for instance the BHs mass spectrum in galaxies and the stellar wind models including the dependence on metallicity. Moreover previous works suggested that massive BHBs can easily form in low-metallicity environments, where the reduced stellar winds from massive stars enable the formation of BHs with masses up to 80 Ms. Generally it is thought that the greater the BHB mass the shorter the time-scale over which it is ejected from the system, indeed massive BHBs are thought to be rapidly kicked out from their parent cluster during an early phase of the cluster lifetime. Rodriguez et al. (2016a) confirmed this mechanism, deriving that more massive and more compact clusters eject BHB with higher binding energies and smaller semi-major axes, leading a greater number of merging within 12 Gyr. However, BHB are also predicted to form in young, OCs with heavy masses. In this case, BHBs are formed mostly through dynamical exchanges in three-body encounters of single BHs with binaries containing one or two BHs. Banerjee (2017) derived that young massive clusters can host a large numbers of BHB, which in such environment are more likely to coalesce within the cluster itself.
In this framework understanding what are the better physical conditions that allow the merging of compact objects with releasing of GW is crucial. Thanks to our work we will be able to give constrains on the environment in which the merging of a massive BHB may occur on reasonable time scales with the releasing of GW.
As a first step we prepared a suit of initial conditions: the physical parameters selected for the stellar environment are based on observations, while the BHB system is modeled on the basis of the recent LIGO/VIRGO detection. In particular the stellar environment is a low density isolated OC, populated with approximately one thousand stars. It is modeled with a Kroupa IMF and a Plummer density profile. The cluster has an initial mass of about MCl~1200 Ms and a rhm~1 pc. The BHB has a total mass of 60 Ms with a unitary mass ratio. In order to span a wide range of conditions we distinguish four cases based on the BHB parameters: A) initial separation ri~10^-2 pc and initial circular orbit (ei=0.0), B) ri~10^-2 pc and ei=0.5 , C) ri~10^-4 pc and ei=0.0 and D) ri~10^-4 pc and ei=0.5. We ran 55 simulations for each cases with NBODY7 for an evolution time of ~3 Gyr. The preliminary results of these investigation show that the BHB, both in cases A and B, shrinks its semi major axis up to two-three order of magnitude (10^-4-10-5 pc) soon after few Gyr. On the contrary in cases C and D there is no evident shrinking and the BHB semi maj. axis remain in the majority of the simulations constant. This behavior is not surprisingly and it means that in a low density environment there is a limit to the shrinking of such massive BHB. These preliminary results support the idea that the gravitational collisions within a stellar cluster may led to the shrinking which occur soon after few Gyr. In order to improve the quality and the quantity of these results in our research group, we are going to run additionally set of simulations, varying the initial conditions (i.e. the OC density profile, the number of cluster stars, the orbital parameter of the BHB) in order to span a wide range of physical situations.
The work about the NSCs evolution can serve to make a fundamental progress on the study of the dynamics of such fascinating and unique systems where all physical processes proceed under extreme conditions. Nowadays, because of computational limits, there are only few studies about the evolution of NSC after their formation. For the first time we will be able to follow the dynamical secular evolution of the densest stellar system of our Galaxy in a very detailed way. In particular the novelty of our project consists on a new computational strategy that will allow to study the dynamics of a very dense and massive star clusters with a restricted number of stars and a computational reduced consumption. Indeed once we will apply this method to the MW NSC we could extend this work on various NSC in other galaxies. For the first time we will be able to study the such dense stellar systems following their secular evolution with a very high precision numerical method.