[Paper Review] Unified description of dark matter at the center and in the halo of the Galaxy

Neven Bilić, Gary B. Tupper+1 more|arXiv (Cornell University)|Nov 19, 2001

Cosmology and Gravitation Theories2 references3 citations

TL;DR

This paper proposes a unified model of galactic dark matter using a self-gravitating, finite-temperature fermion gas with a mass of ~15 keV, successfully describing both the Galactic halo's flat rotation curve and the supermassive compact dark object at the center. The model achieves a consistent fit to observed mass distributions and rotation curves using Thomas-Fermi theory with a central degeneracy parameter η₀ = 28 and temperature T = 3.75 meV.

ABSTRACT

We consider a self-gravitating ideal fermion gas at nonzero temperature as a model for the Galactic halo. The Galactic halo of mass ~ 2 x 10^12 Msol enclosed within a radius of ~ 200 kpc implies the existence of a supermassive compact dark object at the Galactic center that is in hydrostatic and thermal equilibrium with the halo. The central object has a maximal mass of ~ 2.3 x 10^6 Msol within a minimal radius of ~ 18 mpc for fermin masses ~ 15 keV.

Motivation & Objective

• To unify the description of dark matter in the Galactic halo and at the galactic center using a single physical model.
• To investigate whether a self-gravitating fermion gas at finite temperature can simultaneously explain the observed rotation curve and the mass-radius properties of the central compact object.
• To determine the fermion mass and thermodynamic parameters that yield consistent mass estimates within 50 kpc and 200 kpc, and within 18 mpc of the Galactic center.
• To assess the viability of 15 keV fermions (e.g., sterile neutrinos or axinos) as dark matter candidates consistent with cosmological closure and astrophysical constraints.

Proposed method

• Adapts Thomas-Fermi theory for self-gravitating fermion gases to finite temperature, incorporating thermal and degeneracy effects.
• Uses the equation of state for a degenerate, non-relativistic fermion gas to model the halo and central object, with temperature T = 3.75 meV and central degeneracy parameter η₀.
• Applies the virial theorem and spherical collapse model to estimate the maximal radius and minimal density of a virialized halo at turnaround time.
• Constructs the total mass distribution by summing contributions from the halo (modeled via fermion gas), bulge (spherically symmetric with parameters r₀ = 2.67 kpc, h), and disk (with scale length r₀ = 13.5 kpc and circular velocity Θ₀ = 100 km/s).
• Fits the model to observational rotation curve data from Merrifield and Olling, adjusting η₀ to match observed circular velocities.
• Evaluates the mass enclosed within 18 mpc (central object) and 50/200 kpc (halo) using the derived fermion gas distribution and compares with observational estimates.

Experimental results

Research questions

• RQ1 Can a single self-gravitating fermion gas model at finite temperature describe both the Galactic halo and the central compact dark object?
• RQ2 What fermion mass and thermodynamic parameters (T, η₀) yield a consistent fit to the observed rotation curve and mass estimates within 50 kpc and 200 kpc?
• RQ3 Does the model predict a central object mass and radius consistent with the observed 2.6 × 10⁶ M☉ within 18 mpc?
• RQ4 Is a 15 keV fermion mass compatible with cosmological closure and astrophysical constraints, such as overclosure and X-ray limits?
• RQ5 Can the same fermion species explain both the diffuse halo and the compact central object without requiring different particle types?

Key findings

• A fermion mass of m ≈ 15 keV maximizes the central object mass within 18 mpc, yielding M_c ≈ 2.27 × 10⁶ M☉ for η₀ between 20 and 28, closely matching the observed mass of ~2.6 × 10⁶ M☉.
• With T = 3.75 meV and η₀ = 28, the model reproduces the observed Galactic rotation curve, including contributions from the halo, bulge, and disk.
• The total mass within 50 kpc is M₅₀ = 5.04 × 10¹¹ M☉, and within 200 kpc is M₂₀₀ = 2.04 × 10¹² M☉, consistent with estimates from satellite galaxies and globular clusters.
• The central object radius is estimated at ~21 light-days (~7 × 10⁴ R_S), well within the upper limit of 22 light-days from stellar motion, confirming its non-black-hole nature.
• The model shows that a fermion gas at finite temperature can avoid gravitational collapse via supercooling, maintaining a metastable state near the gravothermal collapse threshold.
• A 15 keV fermion with g = 2 is consistent with a sterile neutrino or axino, potentially explaining the observed dark matter density without overclosing the universe.