Abstract The Galactic Centre black hole provides a naive environment for understanding unknown matter distribution and new gravitational physics. For this stellar orbits in the nuclear star cluster are reliable probes. We investigate different dark matter mass profiles through pericentre shift of stellar orbits near the black hole. We also study capability of existing and upcoming astrometric facilities to detect dark matter induced precession and to distinguish between several dark matter profiles. Parameters of different dark matter density profiles are estimated by using the most recent upper bound on dark mass near the black hole. These profiles are then used for calculating the gravitational potential and hence the relativistic pericentre shift of both low and high eccentricity orbits of 13 S-stars. We use the recently measured deviation parameter fsp for investigating competition between dark matter and gravitational physics within S2’s orbit. The astrometric shift of the pericentres has been calculated and compared with existing and upcoming astrometric capabilities of large and extremely large telescopes. The orbit of S2 is found to be insensitive to dark matter induced precession. Low eccentricity and wider orbits are prominent probes for measuring dark matter induced precession which is accessible to present and upcoming astrometric facilities such as Keck, GRAVITY and TMT. The existing and upcoming facilities can distinguish between different dark matter profiles for some stars and hence they posses the capability to distinguish between possible formation histories of the central region of our Galaxy.
Paul et al. (2026) studied this question.