Thesis title
Relativistic effects on the orbits of the closest stars to the black hole at the center of the Galaxy.
Composition of the jury
- Marie-Christine ANGONIN (LTE) : Chairwoman
- Natalie WEBB (IRAP) : rapporteur
- Christos CHARMOUSIS (IJCLab) : rapporteur
- Delphine PORQUET (LAM) : examinatrice
- Frédéric VINCENT (LIRA) : co-supervisor
- Thibaut PAUMARD (LIRA) : co-supervisor
- Guy PERRIN (LIRA) : co-supervisor
Abstract
Context : Astrometric and spectroscopic observation of stars orbiting the supermassive black hole at the center of our galaxy (Sgr A*) is an ideal way to highlight relativistic effects and test the black hole "baldness" theorem. This study can be carried out by monitoring the orbital precession induced by the black hole’s rotation rate (or spin) and quadrupole moment. Stars that are closer and more strongly affected by spin-related effects could be detected in the near future using the GRAVITY+ interferometer. Objectives. We characterize, using an analytical and numerical approach, the orbital reorientations induced by the spin of Sgr A* up to the second post-Newtonian order (2PN), and evaluate the observation conditions necessary to detect them. We also study the impact of the choice of coordinate system on the interpretation of orbital parameters, and explore strategies to improve spin constraints by combining data from multiple orbits.
Method : By applying the method to both time scales, we obtain analytical expressions of order 2PN describing the secular evolution of the orbital parameters relevant to the observer. I have extended existing dynamic models—from Keplerian and Schwarzschild to 2PN—to include spin terms at 1.5PN and 2.5PN, quadrupole moment effects at 2PN, Schwarzschild precession at 3PN, and the contribution of spin to the spectral shift factor in the full relativistic model. These models are compared with each other and with a ray tracing in general relativity to determine the necessary PN effects and orders according to the orbital configurations. I simulate the star S2 as well as a hypothetical star S2/10 (same orbital parameters as S2 but with a semi-major axis ten times smaller) to probe the strong field regime. I also calculate the differences in right ascension, declination, and radial velocity obtained with different coordinate systems for the same set of osculating orbital elements. Finally, I evaluate the potential of a combined adjustment of the orbits of known S stars and the new star S301 to constrain the amplitude and orientation of the spin.
Results : We identify three precession speeds at the orbital scale, reflecting the displacement of the periastron in the plane and the reorientation out of the plane of the osculating ellipse, and give their expressions to the 2PN order as well as the corresponding integrated angular shifts. The choice of coordinate system can lead to deviations in RA, DEC, and RV comparable to current instrumental precision, which requires specifying the time of osculation and the coordinate system used with the orbital elements. Among known stars, S301 has a spin sensitivity comparable to S2/10 ; a joint adjustment with other stars of varying orientations reduces degeneracy and could shorten the observation time required to constrain the spin parameters of Sgr A*. Furthermore, our predictions indicate that, if only the spin magnitude is adjusted, it can be constrained with an accuracy of about 1σ ≃ 0.1 by 2032, 0.05 by 2034, and 0.03 by 2036. Similar performances are obtained when all spin parameters are adjusted simultaneously. Astrometry remains the main source of constraints, but spectroscopy becomes a major asset if radial velocity accuracy reaches ∼2 km/s, as expected with MICADO. Overall, spin detection appears robust as long as sufficient observational follow-up is available, with spin orientation playing a decisive role. Combining astrometric and spectroscopic data from several stars is therefore the most promising strategy.
