Stelle iperveloci come sonde della Dinamica Newtoniana Modificata

A great amount of astronomical data suggests the presence of mass discrepancies in the Universe. Based on the visible stars and gas, the motion of numerous objects cannot be explained. Possible interpretations are (i) the existence of a large amount of unseen mass (dark matter), (ii) an incomplete understanding of the laws ruling the dynamics in the Universe, or (iii) both. Modified Newtonian Dynamics (MOND) has been successful in predicting a number of observed relations, even though originally defined to solve the asymptotic flat rotation curve dilemma only. Because no dark matter is needed in MOND, there is no necessity for new particle physics; however, MOND has major problems on the scale of galaxy clusters. It is possible to test MOND by studying our own Galaxy. In this respect, a peculiar group of B-type stars called Hypervelocity stars (HVSs) has been deeply investigated since the discovery of the first HVS by Brown et al. (2005). HVSs are unbound stars that cross the Galaxy, as so they can be used as probes of the Galactic gravitational potential. In this Thesis, I investigated the HVS phase-space distribution expected in a MONDian Galactic gravitational potential. To this purpose, I adopted the MW mass distribution parametric model described by McGaugh (2008). Then, I computed the gravitational potential numerically by solving Poisson's equations in cylindrical symmetry, as prescribed in QUMOND (a particular formulation of MOND). I performed my simulations by means of a C++ code in which the equations are solved by applying a Successive Over Relaxation method on non-uniform grids. I constrained the physical parameters of the model (i.e. the disc scale length, Rd, and the bulge scale length, bm) by fitting the simulated MW rotation curve (RC) to the observational RC derived by Bhattacharjee et al. (2014) and by Crosta et al. (2020). I chose to model the observational data by using two different optimisation algorithms: Biteopt and GSL-GNU Scientific Library. Next, I studied a population of synthetic HVS generated through numerical simulations of the Hills' ejection mechanism. I implemented the Position Verlet algorithm in a C++ code to trace the time evolution of the phase-space distribution of the stars with time within the computed gravitational potential. Finally, I compared the simulated HVS phase-space distribution in MOND with the distribution obtained in three different models of Newtonian gravitational potentials. These three models include the same distribution of baryonic matter and a dark matter halo with spherical, oblate, and prolate shape, respectively. I computed the Cumulative Distribution Functions (CDFs) for the most relevant physical quantities in the Galactocentric Reference Frame, as the distance of the HVS from the Galactic Center, R, the Cartesian velocity components, vx, vy, vz, and the radial and tangential velocity components vr and vϑ. I adopted the Kolmogorov- Smirnov test to check the compatibility between CDFs in MOND and in Newtonian gravity. The distribution of the tangential velocity, vϑ, proved to be the observable which is most sensitive to the adopted gravitational model. Therefore, the distribution of vϑ of a sample of HVSs is a useful means to discriminate between different gravitational models, but further investigations are needed to clearly distinguish between MOND and Newtonian gravity.