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Modeling dark matter halos with self-interacting fermions

Fabian Hernandez-Gutierrez, Juan Barranco

TL;DR

This paper tests a core–halo dark matter framework in which self-interacting, degenerate fermions form a dense core and the surrounding halo can be either a thermally equilibrated perfect fluid or an NFW envelope. It derives the equation of state including self-interactions, solves the TOV equations for the degenerate core, and fits galactic rotation data to constrain the fermion mass $m_f$ and interaction strength $y$. The results show that with $m_f$ around 39–45 eV and $y$ in the range $10^2$–$10^4$ (depending on halo type), a single fermion species plus a galaxy-dependent central density $\rho_0$ can describe LSB, Milky Way, and SPARC rotation curves, though halo surface density and total mass depend on the halo model. These findings highlight the potential of self-interacting fermionic dark matter to reconcile galactic-scale observations with a quantum-pressure-supported core, while emphasizing model-dependent signatures in halo structure that could distinguish between halo types.

Abstract

In this work we study the possibility of modeling the dark matter content in galaxies as a core-halo model consisting of self-gravitating, self-interacting fermions. For the core of the halo, the dark matter fermions are degenerate, while for the halo we have considered two possibilities: the fermions have thermalized as a perfect fluidor they will follow a standard cold dark matter Navarro-Frenk-White profile. The core density profile is obtained by solving the Tolman-Oppenheimer-Volkoff equations, and their properties are determined by the fermion mass, the central density and the interaction strength. The mass of the fermion and the strength of the fermion self-interaction is fixed by doing a $χ^2$ analysis to fit that fit the rotational curves of Low Surface Brightness galaxies. It was found that the fermion mass should be in the range $38.73~\rm{eV}< m_{f} < 42.11~\rm{eV}$ and the interparticle strength in the range $269.69 < y <348.48$ at $68$ C.L. in order to reproduce the rotational curves adequately, in the case when the halo is modeled as a thermalized ideal gas. Similar values are obtained if the halo is modeled following a Navarro-Frenk-White case, namely $41.54 ~\rm{eV} < m_{f} <49.87 ~\rm{eV}$ and $5606.06< y < 17484.84$. Once fixed the values of the mass of the fermion $m_f$ and the interaction strength $y$, we tested the core-halo model with data from the Milky Way and the SPARC database. We have found good agreement between the data and the core-halo models, varying only one free parameter: the central density. Thus a single fermion can fit hundreds of galaxies. Nevertheless, the dark matter halo surface density relation or the halo total mass and radius depend strongly on the model for the halo.

Modeling dark matter halos with self-interacting fermions

TL;DR

This paper tests a core–halo dark matter framework in which self-interacting, degenerate fermions form a dense core and the surrounding halo can be either a thermally equilibrated perfect fluid or an NFW envelope. It derives the equation of state including self-interactions, solves the TOV equations for the degenerate core, and fits galactic rotation data to constrain the fermion mass and interaction strength . The results show that with around 39–45 eV and in the range – (depending on halo type), a single fermion species plus a galaxy-dependent central density can describe LSB, Milky Way, and SPARC rotation curves, though halo surface density and total mass depend on the halo model. These findings highlight the potential of self-interacting fermionic dark matter to reconcile galactic-scale observations with a quantum-pressure-supported core, while emphasizing model-dependent signatures in halo structure that could distinguish between halo types.

Abstract

In this work we study the possibility of modeling the dark matter content in galaxies as a core-halo model consisting of self-gravitating, self-interacting fermions. For the core of the halo, the dark matter fermions are degenerate, while for the halo we have considered two possibilities: the fermions have thermalized as a perfect fluidor they will follow a standard cold dark matter Navarro-Frenk-White profile. The core density profile is obtained by solving the Tolman-Oppenheimer-Volkoff equations, and their properties are determined by the fermion mass, the central density and the interaction strength. The mass of the fermion and the strength of the fermion self-interaction is fixed by doing a analysis to fit that fit the rotational curves of Low Surface Brightness galaxies. It was found that the fermion mass should be in the range and the interparticle strength in the range at C.L. in order to reproduce the rotational curves adequately, in the case when the halo is modeled as a thermalized ideal gas. Similar values are obtained if the halo is modeled following a Navarro-Frenk-White case, namely and . Once fixed the values of the mass of the fermion and the interaction strength , we tested the core-halo model with data from the Milky Way and the SPARC database. We have found good agreement between the data and the core-halo models, varying only one free parameter: the central density. Thus a single fermion can fit hundreds of galaxies. Nevertheless, the dark matter halo surface density relation or the halo total mass and radius depend strongly on the model for the halo.

Paper Structure

This paper contains 11 sections, 25 equations, 11 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Equation of state for degenerate fermions with self-interaction
  3. Self-gravitating ultralight fermions as Dark matter halos
  4. Fitting Low Surface Brightness galaxies
  5. No Self-interaction ($y=0$)
  6. With Self-interaction $y \ne 0$
  7. The Milky Way Rotational Curve
  8. Fitting the SPARC Database
  9. Discussion
  10. Conclusions
  11. Results from fits to SPARC dataset

Figures (11)

  • Figure 1: Relative difference (in %) between the equation of state and its approximation as a function of fermion mass $m_f$ and interaction strength $y$. The color map shows the contour levels of the relative difference. The black error bars indicate the combined best-fit values (with 1$\sigma$ uncertainties) obtained from fits to six LSB galaxies, for the NFW halo (top) and the perfect-fluid halo (bottom). The green rectangles correspond to the 1$\sigma$ confidence regions of the individual galaxy fits.
  • Figure 2: Density and mass profiles of the self-gravitating system composed of self-interacting degenerate fermions. The left panel shows the changes produced by different values of the fermion mass, with fixed values of $y=100$, $\rho_{0}=30\ GeV/cm^{3}$. The right panel shows the influence of the self-interaction parameter $y$, with $m_{f}=30\ eV$, $\rho_{0}=30\ GeV/cm^{3}$ .
  • Figure 3: Contours of the masses of the fermion and central densities allowed by the fit to the rotational curves of the 6 LSB galaxies studied, in the case of no self-interaction. The darker and lighter regions correspond to the 68% and 95% confidence limits, respectively. The fully degenerate model is shown in green, while the semi-degenerate fermion with a NFW halo (left panel) and with a perfect-fluid halo (right panel) are shown in blue.
  • Figure 4: Comparison of fits for the perfect-fluid (a) and NFW (b) halo models. Top panels: contour for the 68% and 95% confidence limits for the three possible cases: a self-interacting fermion with halo (red), a non-interacting fermion with halo (green), and the fully degenerate fermion (blue). Bottom panels: $\chi^{2}$ as a function of the fermion mass for each of the same models.
  • Figure 5: Masses and interaction parameters allowed to fit the rotational curve data of the different galaxies studied. The contours represent the 68% (darker shade) and 95% (lighter shade) confidence limits. In red we present the contours for the case with a perfect fluid halo, in blue the NFW halo case.
  • ...and 6 more figures