The dynamics of S-stars and G-sources orbiting a supermassive compact object made of fermionic dark matter

Surrounding Sgr A*, a cluster of young and massive stars coexist with a population of dust-enshrouded objects, whose astrometric data can be used to scrutinize the nature of Sgr A*. An alternative to the black hole (BH) scenario has been recently proposed in terms of a supermassive compact object composed of self-gravitating fermionic dark matter (DM). Such horizon-less configurations can reproduce the relativistic effects measured for S2 orbit, while being part of a single continuous configuration whose extended halo reproduces the latest GAIA-DR3 rotation curve. In this work, we statistically compare different fermionic DM configurations aimed to fit the astrometric data of S2, and five G-sources, and compare with the BH potential when appropriate. We sample the parameter spaces via Markov Chain Monte Carlo statistics and perform a quantitative comparison estimating Bayes factors for models that share the same likelihood function. We extend previous results of the S2 and G2 orbital fits for 56 keV fermions (low core-compactness) and show the results for 300 keV fermions (high core-compactness). For the selected S2 dataset, the former model is slightly favoured over the latter. However, more precise S2 datasets, as obtained by the GRAVITY instrument, remain to be analysed in light of the fermionic models. For the G-objects, no conclusive preference emerges between models. For all stellar objects tested, the BH and fermionic models predict orbital parameters that differ by less than 1%. More accurate data, particularly from stars closer to Sgr A*, is necessary to statistically distinguish between the models considered.

💡 Research Summary

This paper investigates whether the supermassive compact object at the Galactic centre (Sgr A*) can be described by a horizon‑less fermionic dark‑matter core‑halo configuration (the RAR model) instead of the conventional Schwarzschild black hole. The authors construct equilibrium solutions for self‑gravitating fermions with masses of 56 keV (low core compactness) and 300 keV (high core compactness), each reproducing the Milky Way rotation curve (GAIA‑DR3) and embedding a dense central core that could mimic a black hole. Using the latest astrometric and spectroscopic data for the S2 star and five dust‑enshrouded G‑objects (including the updated G2 orbit from Peißker et al. 2021), they perform Markov‑Chain Monte Carlo sampling of the model parameters and compute Bayes factors to compare the fermionic models with the black‑hole potential.

For S2, the 56 keV configuration yields a slightly higher Bayesian evidence than the 300 keV case, indicating a modest preference for a more extended fermion core, though the difference is not statistically decisive. For the G‑sources, the Bayes factors are essentially unity, showing no clear discrimination between the black‑hole and either fermionic model. In all cases the predicted orbital elements (semi‑major axis, eccentricity, inclination, etc.) differ by less than 1 % between the black‑hole and fermionic potentials, well within current measurement uncertainties.

A robustness test varying the outer halo boundary conditions (consistent with the GAIA‑DR3 rotation curve) shows that the core mass and radius remain stable, underscoring the internal consistency of the RAR solutions. The authors conclude that present‑day S‑star and G‑object data are insufficient to decisively favor one scenario over the other; higher‑precision astrometry (e.g., future GRAVITY+ observations), longer monitoring of stars with tighter pericentre passages, and complementary strong‑gravity probes such as Event Horizon Telescope imaging or gravitational‑wave detections will be required to test the fermionic core‑halo hypothesis and its implications for black‑hole formation from dark‑matter collapse.