2024A&A...686A.179L

Context. Current constraints on distributed matter in the innermost Galactic centre (such as a cluster of faint stars and stellar remnants, dark matter, or a combination thereof) based on the orbital dynamics of the visible stars closest to the central black hole typically assume simple functional forms for the distributions.
Aims. We aim to take a general model-agnostic approach in which the form of the distribution is not constrained by prior assumptions on the physical composition of the matter. This approach yields unbiased, entirely observation-driven fits for the matter distribution and places constraints on our ability to discriminate between different density profiles (and consequently between physical compositions) of the distributed matter.
Methods. We constructed a spherical shell model with the flexibility to fit a wide variety of physically reasonable density profiles by modelling the distribution as a series of concentric mass shells. We tested this approach in an analysis of mock observations of the star S2.
Results. For a sufficiently large and precise data set, we find that it is possible to discriminate among several physically motivated density profiles. However, for data coming from current and expected next generation observational instruments, the potential for profile distinction will remain limited by the precision of the instruments. Future observations will still be able to constrain the overall enclosed distributed mass within the apocentre of the probing orbit in an unbiased manner. We interpret this in the theoretical context of constraining the secular versus non-secular orbital dynamics.
Conclusions. Our results show that while stellar data over multiple orbits of currently known stars will eventually yield model-agnostic constraints for the overall amount of distributed matter within the probe's apocentre in the innermost Galactic centre, an unbiased model distinction made by determining the radial density profile of the distribution is, in principle, out of the measurement accuracy of the current and next-generation instruments. Constraints on dark matter models will therefore remain subject to model assumptions and will not be able to significantly downsize the zoo of candidate models.