Dynamics of stars and planets in the super dense Central Galactic Region

There is observational evidence that a compact massive object (CMO) of about four million solar masses cloaks at the heart of the Milky Way (MW), known as Sgr A*. The gravitational tidal field of this CMO (probably a Supermassive black hole, SMBH) is extremely strong so that binary star passing in its vicinity are likely stripped apart. One component of the binary can be hurled swiftly out of the Galactic Centre, or even the MW, as Hypervelocity Star (HVS) and its twin could be seized on an eccentric orbit revolving around the central massive object, similar to the observed S-stars (Hills mechanism). Given that many binary star systems are acknowledged to host planets, we intend in this thesis deepening the study of the violent dynamics of binary stars and their planetary systems with the Sgr A* massive object, highlighting the resulting fraction of HVS hosting planet. In the first part of this thesis, we focus on tight binary stars with one planet for each component of the binary, and investigate the fate of the four-body system after the interaction with the SMBH. Results are achieved by means of a high precision, regularized, numerical integrator suitable for those large mass ratios which are involved in the interaction of SMBH and stars/planets. Furthermore, in order to develop the investigation of dynamics in the proximity of Sgr A*, we model the environment of the Galactic Centre (GC) by applying the local distribution of stars in the form of a regular external potential which also generates dynamical friction on the approaching objects. The Galaxy density profile, is represented in spherical symmetry as the sum of a Dehnen and a Plummer distribution for the galactic background and the nuclear star cluster (NSC) around the GC, respectively. After setting proper initial conditions for our chosen set of binary stars hosting one planet each, we carried out integrations taking into account the gravity field of the massive object in the post-Newtonian approximation up to 2.5 order. This allows us to evaluate the likelihood of ejection and capture of the four-body system in its interaction with Sgr A* emphasizing mainly on the fate of the planets initially bound to the binary star. Our simulations show that after the interplay between four-body system and the SMBH, the result is that of giving rise to lonely hypervelocity stars (HVSs) or S-stars and, also, to HVSs or S-stars that would keep their planets. Furthermore, it is possible to spectate rogue hypervelocity planets (HVP) thrown out of the Galaxy or starless planets (S-planets) revolving around the SMBH in independent eccentric orbits similar to those of S-stars. Stars and/or planets can be, also, devoured by the SMBH. Here, "devoured" means that a star or planet enters inside $3 R_s$ i.e. within the innermost stable circular orbit (ISCO) of the non-rotating SMBH. We show that both starless S-planets and S-stars with planets can exist around the SMBH on high eccentric ($e sim 0.97$) orbits similar to the G2 cloud orbital eccentricity. Eventually, in this thesis we focus on the dynamical evolution and stability of populous planetary systems in the vicinity of Sgr A*. The S-star cluster, which is a dynamically relaxed dense cluster of stars and consists of roughly 40 stars, inhabits in the centre of the Galaxy. Spectroscopic analysis of the S-stars reveals the existence of both a population of early- and late-type stars on tightly eccentric orbits, with different orientations and semi-major axes. These stars are believed to be the captured companions of the HVSs in the binary-SMBH disruption. Accordingly, they might have formed elsewhere and migrated to the GC, probably hosting planetary systems. The existence of planets or planetary systems in the vicinity of Sgr A* is still an open argument. Our aim is to investigate the destiny of their putative planetary systems after close interaction with the central black hole of our Galaxy. We run simulations for the 40 stars of this cluster for which the orbital parameters are known from the literature. For the sake of simplicity, the planetary systems assigned to each of the stars of this cluster are similar to our Solar planetary system in mass, eccentricity and semi-major axis. Our simulations show that the innermost planets are more likely to remain bound to their host stars until the end of the simulation. However, we show that starless Jupiter-like planets can be found in orbits similar to the G1 cloud as semi-major axis and eccentricity. In addition, a small fraction of starless Uranus-like planets can revolve Sgr A* in a way consistent with the G1 cloud as semi-major axis and inclination.