[Paper Review] Constraints on mixed dark matter model of particles and primordial black holes from the Galactic 511 keV line

Rong-Gen Cai, Xing-Yu Yang+1 more|arXiv (Cornell University)|Jul 23, 2020

Dark Matter and Cosmic Phenomena7 citations

TL;DR

This paper investigates a mixed dark matter model combining particles and primordial black holes (PBHs), showing that PBHs can enhance positron production via density spikes, thereby constraining the PBH fraction in dark matter. For excited dark matter (XDM) with masses 10 GeV–1 TeV, the most stringent constraint is f_PBH ≲ 10⁻¹¹ at a mass-dependent turning point, while light dark matter (1–3 MeV) remains weakly constrained.

ABSTRACT

The 511 keV line was first detected in 1970's but its origin is still unknown. It was proposed that positrons from dark matter (DM) particles in the halo of galaxy are possible sources. We consider a mixed DM model consisting of DM particles and primordial black holes (PBHs). With the existence of PBHs, the DM particles may be gravitationally bound to the PBHs and form halo around PBHs with density spikes. These density spikes can enhance the production rate of positrons from DM particles, thus they are constrained by the observations of 511 keV line. We compute the profile of the density spikes, and get the constraints on the fraction of PBHs in DM $f_{\mathrm{PBH}}$ for light dark matter (LDM) scenario and excited dark matter (XDM) scenario respectively. For LDM with mass in the range of $1\mathrm{MeV} \sim 3\mathrm{MeV}$, the constraints are loose. For XDM with mass in the range of $10\mathrm{GeV} \sim 1\mathrm{TeV}$, the constraints have $M_{\mathrm{PBH}}^{-2}$ slope in the relative small mass range, and roughly have $M_{\mathrm{PBH}}^{2/5}$ slope in the relative large mass range. The most stringent constraint $f_{\mathrm{PBH}} \lesssim 10^{-11}$ appears at the turning point which depends on the mass of XDM.

Motivation & Objective

• To explore the impact of primordial black holes (PBHs) on dark matter (DM) positron production in the Galactic halo.
• To assess whether PBHs can enhance the 511 keV positron annihilation line via density spikes around them.
• To derive observational constraints on the fraction of PBHs in the dark matter component, f_PBH, using 511 keV line data.
• To compare constraints across different dark matter scenarios: light DM (1–3 MeV) and excited DM (10 GeV–1 TeV).

Proposed method

• Model the gravitational potential around PBHs to compute the density profile of dark matter particles in the halo, resulting in density spikes.
• Use the Navarro-Frenk-White (NFW)-like profile modified by PBH-induced gravitational focusing to estimate enhanced dark matter density near PBHs.
• Calculate the positron production rate from dark matter annihilation, scaled by the density spike enhancement.
• Apply observational limits on the 511 keV gamma-ray line flux to constrain the fraction of PBHs in the dark matter, f_PBH.
• Derive the dependence of f_PBH constraints on PBH mass (M_PBH) for both light and excited dark matter scenarios.
• Identify the mass scale at which constraints are most stringent by analyzing the transition between M_PBH⁻² and M_PBH²/⁵ scaling regimes.

Experimental results

Research questions

• RQ1 How do primordial black holes (PBHs) affect the density distribution of dark matter particles in galactic halos?
• RQ2 To what extent can PBHs enhance the production rate of positrons via dark matter annihilation?
• RQ3 What are the observational constraints on the fraction of PBHs in the dark matter component, f_PBH, based on the 511 keV line?
• RQ4 How does the constraint on f_PBH vary with PBH mass in the light and excited dark matter scenarios?
• RQ5 At what PBH mass does the constraint on f_PBH become most stringent for excited dark matter?

Key findings

• For light dark matter (1–3 MeV), the constraints on f_PBH are weak due to low annihilation cross-sections and limited spike enhancement.
• For excited dark matter (10 GeV–1 TeV), the constraint on f_PBH shows a M_PBH⁻² dependence in the low-mass PBH range.
• In the high-mass PBH range, the constraint follows a M_PBH²/⁵ dependence, indicating a transition in scaling behavior.
• The most stringent constraint, f_PBH ≲ 10⁻¹¹, occurs at a mass-dependent turning point in the excited dark matter scenario.
• The turning point mass depends on the dark matter particle mass, with heavier XDM particles shifting the optimal constraint to higher PBH masses.
• The results demonstrate that PBHs in mixed dark matter models are strongly constrained by the 511 keV line, especially in the excited dark matter framework.