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

TL;DR

This work assesses whether a horizonless fermionic dark matter core-halo around Sgr A* can reproduce the dynamics of the S-cluster and G-sources as an alternative to a black hole. Using MCMC and Bayesian evidence, it contrasts fermion masses $m c^2 = 56$ keV and $m c^2 = 300$ keV against a Schwarzschild BH, while enforcing MW halo constraints from Gaia DR3 to fit the Galactic rotation curve. For S2, the 56 keV core is slightly favored over 300 keV, but all three central potentials predict similar orbital parameters within current observational uncertainties; for G-objects, no universal preference emerges. A robustness test shows the results are stable against plausible outer halo variations, underscoring the need for higher-precision data, especially for stars closer to Sgr A*, to statistically distinguish between the competing potentials.

Abstract

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.

Figures (11)

• Figure 1: RAR-DM energy density profiles for fermions of $mc^2=56$ and $300$ keV for the same boundary conditions for the MW halo and core mass $M_{\rm c}$. The core compactness increases with the fermion mass. The blue band corresponds to the location of the most relevant S-stars and G-objects.
• Figure 2: Top: Observed and theoretical orbits of S2 star. Bottom: radial velocity, Right Ascension, and Declination as a function of time. The astrometric measurements were taken from 2019Sci...365..664D. For a better visualization of the orbit at the apocentre and pericentre, see figure 2 in 2022MNRAS.511L..35A.
• Figure 3: Observed and theoretical orbits for the G-cluster stars. coloured lines correspond to the best-fit orbits modelled with $\mathcal{M}_{1a}$ of 56 keV fermions. Dashed black lines correspond to the best-fit orbits modelled with $\mathcal{M}_{0a}$ a BH. The astrometric measurements are taken from 2020Natur.577..337C2023ApJ...943..183P.
• Figure 4: Observed and theoretical right ascension, declination, and radial velocity for the G-cluster stars. The astrometric measurements are taken from 2020Natur.577..337C2023ApJ...943..183P. As in figure \ref{['fig:G-orbits']}, coloured lines correspond to model $\mathcal{M}_{1a}$, and black dashed lines to model $\mathcal{M}_{0a}$.
• Figure 5: MW Rotation curve. Data and models reads: S2 (red pentagon), G2 (violet diamond), Inner Bulge (dashed blue line), Bulge (dashed olive line), Disk (dot-dashed orange line), fermionic DM with $mc^2=300$ keV (dotted black line), full MW (solid light-blue line) and halo data are taken from sofue_rotation_2013 (yellow squares) and Jiao2023 (green circles).