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Constraints on dark matter particles from theory, galaxy observations and N-body simulations

D. Boyanovsky, H. J. de Vega, N. Sanchez

TL;DR

The paper develops a framework to constrain dark matter properties by linking microphysical decoupling details to observable halo phase-space densities. It introduces a Liouville-invariant primordial phase-space density $\, ext{D}$ for particles that decoupled in or out of LTE with arbitrary isotropic distributions, and uses this together with dSph data and N-body results to place bounds on DM mass, primordial phase-space density, and velocity dispersion. It analyzes light thermal relics, Bose-Einstein condensate (BEC) DM, and non-equilibrium production scenarios (e.g., sterile neutrinos), concluding that keV-scale relics naturally yield core-like structures in dSphs, while heavy WIMPs face tension with phase-space constraints. Non-equilibrium production histories can still yield viable keV-scale DM with small velocity dispersions, but require specific microphysical conditions (e.g., high decoupling temperatures or particular cascade dynamics).

Abstract

Mass bounds on dark matter (DM) candidates are obtained for particles decoupling in or out of equilibrium with {\bf arbitrary} isotropic and homogeneous distribution functions. A coarse grained Liouville invariant primordial phase space density $ \mathcal D $ is introduced. Combining its value with recent photometric and kinematic data on dwarf spheroidal satellite galaxies in the Milky Way (dShps), the DM density today and $N$-body simulations, yields upper and lower bounds on the mass, primordial phase space densities and velocity dispersion of the DM candidates. The mass of the DM particles is bound in the few keV range. If chemical freeze out occurs before thermal decoupling, light bosonic particles can Bose-condense. Such Bose-Einstein {\it condensate} is studied as a dark matter candidate. Depending on the relation between the critical($T_c$)and decoupling($T_d$)temperatures, a BEC light relic could act as CDM but the decoupling scale must be {\it higher} than the electroweak scale. The condensate tightens the upper bound on the particle's mass. Non-equilibrium scenarios that describe particle production and partial thermalization, sterile neutrinos produced out of equilibrium and other DM models are analyzed in detail obtaining bounds on their mass, primordial phase space density and velocity dispersion. Light thermal relics with $ m \sim \mathrm{few} \mathrm{keV}$ and sterile neutrinos lead to a primordial phase space density compatible with {\bf cored} dShps and disfavor cusped satellites. Light Bose condensed DM candidates yield phase space densities consistent with {\bf cores} and if $ T_c\gg T_d $ also with cusps. Phase space density bounds from N-body simulations suggest a potential tension for WIMPS with $ m \sim 100 \mathrm{GeV},T_d \sim 10 \mathrm{MeV} $.

Constraints on dark matter particles from theory, galaxy observations and N-body simulations

TL;DR

The paper develops a framework to constrain dark matter properties by linking microphysical decoupling details to observable halo phase-space densities. It introduces a Liouville-invariant primordial phase-space density for particles that decoupled in or out of LTE with arbitrary isotropic distributions, and uses this together with dSph data and N-body results to place bounds on DM mass, primordial phase-space density, and velocity dispersion. It analyzes light thermal relics, Bose-Einstein condensate (BEC) DM, and non-equilibrium production scenarios (e.g., sterile neutrinos), concluding that keV-scale relics naturally yield core-like structures in dSphs, while heavy WIMPs face tension with phase-space constraints. Non-equilibrium production histories can still yield viable keV-scale DM with small velocity dispersions, but require specific microphysical conditions (e.g., high decoupling temperatures or particular cascade dynamics).

Abstract

Mass bounds on dark matter (DM) candidates are obtained for particles decoupling in or out of equilibrium with {\bf arbitrary} isotropic and homogeneous distribution functions. A coarse grained Liouville invariant primordial phase space density is introduced. Combining its value with recent photometric and kinematic data on dwarf spheroidal satellite galaxies in the Milky Way (dShps), the DM density today and -body simulations, yields upper and lower bounds on the mass, primordial phase space densities and velocity dispersion of the DM candidates. The mass of the DM particles is bound in the few keV range. If chemical freeze out occurs before thermal decoupling, light bosonic particles can Bose-condense. Such Bose-Einstein {\it condensate} is studied as a dark matter candidate. Depending on the relation between the critical()and decoupling()temperatures, a BEC light relic could act as CDM but the decoupling scale must be {\it higher} than the electroweak scale. The condensate tightens the upper bound on the particle's mass. Non-equilibrium scenarios that describe particle production and partial thermalization, sterile neutrinos produced out of equilibrium and other DM models are analyzed in detail obtaining bounds on their mass, primordial phase space density and velocity dispersion. Light thermal relics with and sterile neutrinos lead to a primordial phase space density compatible with {\bf cored} dShps and disfavor cusped satellites. Light Bose condensed DM candidates yield phase space densities consistent with {\bf cores} and if also with cusps. Phase space density bounds from N-body simulations suggest a potential tension for WIMPS with .

Paper Structure

This paper contains 12 sections, 138 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries: dynamics of decoupled particles
  3. Light Thermal relics as Dark Matter Components.
  4. Fermi-Dirac and non-condensed Bose-Einstein gases of light particles as DM components.
  5. A Bose condensed light particle as a Dark Matter component
  6. Coarse grained phase space densities and new DM Bounds
  7. New bounds from phase space density and dShps-data
  8. Generalized Tremaine-Gunn bound.
  9. DM mass values from velocity dispersion
  10. Non-equilibrium effects:
  11. Particle production followed by an UV cascade:
  12. Conclusions

Figures (4)

  • Figure 1: Fermions without chemical potential. Left panel: $I_+(x)$ and $J_+(x)$ vs $x$. Right panel: $3 \; w[x]$ vs. $x. \; I_+ = I_\rho, \; J_+=I_\mathcal{P}$.
  • Figure 2: Bosons without chemical potential. Left panel: $I_-(x)$ and $J_-(x)$ vs $x$. Right panel: $3 \; w[x]$ vs. $x . \; I_- = I_\rho , \; J_-=I_\mathcal{P}$.
  • Figure 3: $3 \; w[x]$ vs $x$ for the Bose condensed case for $T_c/T_d=1-2$.
  • Figure 4: The functions $F(s)$ (left panel), $H(s)$ (middle panel) and $v(s)$ (right panel) vs. $s=y_0/\xi$, for $f_{eq}$ the Fermi-Dirac distribution function without chemical potential.