Black Holes and WIMPs: All or Nothing or Something Else

Abstract: We consider constraints on primordial black holes (PBHs) in the mass range $( 10^{-18}\text{-}10^{15} )\,M_{\odot}$ if the dark matter (DM) comprises weakly interacting massive particles (WIMPs) which form halos around them and generate $\gamma$-rays by annihilations. We first study the formation of the halos and find that their density profile prior to WIMP annihilations evolves to a characteristic power-law form. Because of the wide range of PBH masses considered, our analysis forges an interesting link between previous approaches to this problem. We then consider the effect of the WIMP annihilations on the halo profile and the associated generation of $\gamma$-rays. The observed extragalactic $\gamma$-ray background implies that the PBH DM fraction is $f^{}_{\rm PBH} \lesssim 2 \times 10^{-9}\,( m_{\chi} / {\rm TeV} )^{1.1}$ in the mass range $2 \times 10^{-12}\,M_{\odot}\,( m_{\chi} / {\rm TeV} )^{-3.2} \lesssim M \lesssim 5 \times 10^{12}\,M_{\odot}\,( m_{\chi} / {\rm TeV} )^{1.1}$, where $m_{\chi}$ and $M$ are the WIMP and PBH masses, respectively. This limit is independent of $M$ and therefore applies for any PBH mass function. For $M \lesssim 2\times 10^{-12}\,M_{\odot}\,( m_{\chi}/ {\rm TeV} )^{-3.2}$, the constraint on $f^{}_{\rm PBH}$ is a decreasing function of $M$ and PBHs could still make a significant DM contribution at very low masses. We also consider constraints on WIMPs if the DM is mostly PBHs. If the merging black holes recently discovered by LIGO/Virgo are of primordial origin, this would rule out the standard WIMP DM scenario. More generally, the WIMP DM fraction cannot exceed $10^{-4}$ for $M > 10^{-9}\,M_{\odot}$ and $m_{\chi} > 10\,$GeV. There is a region of parameter space, with $M \lesssim 10^{-11}\,M_{\odot}$ and $m_{\chi} \lesssim 100\,$GeV, in which WIMPs and PBHs can both provide some but not all of the DM, so that one requires a third DM candidate.

• The paper finds that WIMP halos form around primordial black holes, evolving into a characteristic power-law density profile before significant annihilation.
• It establishes stringent gamma-ray observational limits, constraining the PBH dark matter fraction to fPBH ≲ 2×10⁻⁹ (mχ/TeV)^1.1 over key mass ranges.
• The analysis implies that neither standard WIMP nor PBH models alone can account for all dark matter, suggesting the need for an additional dark matter candidate.

Overview of "Black Holes and WIMPs: All or Nothing or Something Else"

This paper investigates the constraints on primordial black holes (PBHs) and weakly interacting massive particles (WIMPs) as candidates for dark matter (DM). The authors explore a wide range of PBH masses, from $10^{-18}$ to $10^{15} M_{\odot}$, and WIMP masses, from 10 GeV to 1 TeV. In doing so, they address the possibility that these PBHs and WIMPs might form halos and generate $\gamma$-rays through annihilations, contributing to observable extragalactic and Galactic $\gamma$-ray backgrounds.

Key Findings

• Formation of WIMP Halos: The paper outlines the formation of WIMP halos around PBHs that occur prior to WIMP annihilations. It finds that these halos evolve into a characteristic power-law density profile. This evolution is driven by the interplay between gravitational influences of PBHs and cosmic structural formation.
• Constraints from $\gamma$-ray Observations: There are stringent constraints on the fraction of dark matter that can comprise PBHs due to the observed $\gamma$-ray background. Specifically, the PBH DM fraction must be $$f_{\rm PBH} \lesssim 2 \times 10^{-9} ( m_{\chi} / {\rm TeV} )^{1.1}$$ over certain mass ranges.
• Implications for the DM Composition: The constraints imply that neither conventional WIMPs nor massive PBHs alone can account for all the dark matter under standard assumptions. This suggests a potential need for a third DM candidate if some DM is composed of both WIMPs and PBHs.

Implications and Discussion

These results have significant implications for the theoretical understanding of dark matter. If PBHs were the source of recent gravitational-wave events observed by LIGO/Virgo, they could not coexist with substantial amounts of WIMP dark matter under standard scenarios. The authors argue that this could necessitate a "third DM candidate," such as axions or sterile neutrinos, to account for the entirety of dark matter.

From a theoretical standpoint, the constraints on WIMP annihilation rates around PBHs also question the suitability of hybrid models that include both components as major contributors to the DM density. The authors speculate that if PBHs were involved in the LIGO/Virgo events, standard WIMP models would be untenable, emphasizing a shift toward non-baryonic MACHOs or other unconventional DM hypotheses.

Future Directions

The paper outlines several directions for future research:

1. Further refinement of the PBH mass function constraints could illuminate how PBHs contribute to observed $\gamma$-ray backgrounds.
2. Investigations into the implications of non-standard cosmologies or other DM candidates could provide insights into our understanding of dark matter.
3. Continued analysis on tidal stripping and other astrophysical processes may clarify the stability and evolution of potential WIMP halos in galaxies harboring PBHs.

Overall, this study provides a comprehensive analysis of the constraints and interplay between PBHs and WIMPs as dark matter sources. It highlights the importance of observational data in shaping theoretical models of dark matter composition and the necessity for novel approaches beyond conventional frameworks.