Studies of relativistic effects at the Galactic Center by using stellar-orbit observation simulations of the Gravity instrument

Decades of studies have demonstrated the presence of a compact object of several million solar masses at the center of the Galaxy. Nowadays, the assumption is that this compact object is probably a supermassive black hole described by general relativity. The second generation instrument at the Very Large Telescope Interferometer, Gravity, is expected to better constrain the nature of this central object. By using its astrometric accuracy of about 10 micro-arc-seconds, it will probe spacetime in strong gravitational fields by observing stars and gas located near the compact object. During my PhD I have developed a stellar-orbit model in order to interpret the future Gravity observations. By using this model it will be possible to extract the central black hole candidate parameters and relativistic effects. To implement the model, I used the ray-tracing code GYOTO developed at Observatoire de Paris. This code allows computing star and photon trajectories obtained in the vicinity of a compact object. It is thus possible to simulate apparent positions of stars orbiting the Galactic Center by computing relativistic images. My work started by validating the photon trajectories computed in GYOTO. By doing tests in both weak- and strong-deflection limits, I have shown that the GYOTO code is highly qualified to simulate Gravity observations. Indeed, the error made on the photon trajectories is inferior to 10^-2 micro-arc-second, even when integrating over large distances. Then, I was interested in studying a star called S2 that contributed to importantly constrain the mass of the central object. This star is the closest star to the Galactic Center and has an orbital period of about 16 years. Nowadays, we do not know whether closer-in stars will be discovered by Gravity. It is thus important to extract as much information as possible from this star. In particular, I have estimated the minimal observation times needed to detect relativistic effects by using astrometric and spectroscopic measurements of S2. To do so, I have developed different stellar-orbit models taking into account a certain number of relativistic effects. The more accurate model is obtained by using the ray-tracing code GYOTO and considering all relativistic effects. However, as the S2 star is sufficiently far from the compact object, this model neglects certain gravitational lensing effects such as the secondary images and the primary images amplification. Besides, I was also interested in the possibility of constraining the angular momentum of the central black hole candidate with the S2 star. In particular, I have shown that with a model which does not use ray-tracing, the norm and the direction of the angular momentum can be constrained with an uncertainty of about 0.1 and 20 degrees, respectively, by using observations obtained during three periods of S2 and with accuracies reaching 10 micro-arc-seconds and 10 km/s. Since closer-in stars could be detected by Gravity, I have developed a more accurate stellar-orbit model taking into account the lensing effects neglected in the previous model. However, in order to minimize the computing time required by this model, I determined a volume in which it is possible to neglect both the secondary images and the primary images amplification. Finally, I studied the impact of different components of the Solar System on astrometric positions measured by Gravity. This study has shown that those measurements are deviated by an amount of a few micro-arc-seconds by the gravitational perturbation generated by the Sun. However, those apparent positions are shifted by several hundred micro-arc-seconds by the aberration effect due to the movement of the Earth with respect to the Galactic Center. It is thus necessary to take into account this effect in future interpretations of Gravity observations. (author)