Modeling the track of the GD-1 stellar stream inside a host with a fermionic dark matter core-halo distribution

Abstract

Traditional studies of stellar streams typically involve phenomenological Lambda CDM halos or ad hoc dark matter (DM) profiles with different degrees of triaxiality, which preclude us from gaining insights into the nature and mass of the DM particles. Recently, the maximum entropy principle of halo formation has been applied to provide a DM halo model that incorporates the fermionic (quantum) nature of the particles while leading to DM profiles that depend on the fermion mass. These profiles develop a more general ``dense core - diluted halo'' morphology that can explain the Galactic rotation curve, while the degenerate fermion core can mimic the central massive black hole (BH). We model the GD-1 stellar stream using a spherical core-halo DM distribution for the host that simultaneously also explains the dynamics of the S-cluster stars through its degenerate fermion core without a central BH. We used two optimization algorithms in order to fit both the initial conditions of the stream orbit and the fermionic model. We modeled the baryonic potential with a bulge and two disks (thin and thick) with fixed parameters according to the recent literature. The stream observables were 5D phase-space data from the Gaia DR2 survey. We were able to find good fits for both the GD-1 stream and the S-stars for a family of fermionic core-halo profiles parameterized by the fermion mass. The particle masses are constrained in the range $56 keV c^ $, with a corresponding DM core of $ E3 $ Schwarzschild radii, to $360 keV c^ $, which corresponds to the most compact core of $5$ Schwarzschild radii prior to the gravitational collapse into a BH of about $ 4E6 Msun This work provides evidence that the fermionic profile is a reliable model for the massive central object and for the DM of the Galaxy. Remarkably, this model predicts a total Milky Way mass of $2.3 M_ odot $, which agrees with recent mass estimates obtained from Gaia DR3 rotation curves ( Gaia RC). In summary, with one single fermionic model for the DM distribution of the Milky Way, we obtain a good fit on three totally different distance scales of the Galaxy: $ $ kpc (central, S-stars), $ kpc (middle, GD-1), and $ 30$ kpc (boundary Gaia RC mass estimate).