Improved Constraints on Dark Matter Annihilations Around Primordial Black Holes

TL;DR

This work analyzes scenarios where particle dark matter coexists with primordial black holes and revisits gamma-ray constraints, extending prior s-wave analyses to velocity-dependent annihilations with ⟨σv⟩ ∝ $v^2$ or $v^4$ while using refined PBH halo profiles. It combines a careful treatment of PBH halo density structures with a z-dependent extragalactic gamma-ray flux calculation to derive f_MAX bounds for s-, p-, and d-wave annihilations, showing that velocity suppression generally weakens bounds but nonzero s-wave fractions can restore significant constraints. The paper also highlights the importance of the halo stripping radius and the role of kinetic decoupling in shaping the DM halo, as well as the potential discrepancies with previous analyses. Overall, the results indicate that velocity-dependent annihilations allow larger PBH dark-matter fractions than s-wave scenarios, but a complete picture requires considering mixed annihilation channels, redshift evolution, and more complex PBH mass distributions.

Abstract

Cosmology may give rise to appreciable populations of both particle dark matter and primordial black holes (PBH) with the combined mass density providing the observationally inferred value $Ω_{\rm DM}\approx0.26$. However, previous studies have highlighted that scenarios with both particle dark matter and PBH are strongly excluded by $γ$-ray limits for particle dark matter with a velocity independent thermal cross section $\langleσv\rangle\sim3\times10^{-26}{\rm cm}^3/{\rm s}$, as is the case for classic WIMP dark matter. Here we extend these existing studies on $s$-wave annihilating particle dark matter to ascertain the limits from diffuse $γ$-rays on velocity dependent annihilations which are $p$-wave with $\langleσv \rangle\propto v^2$ or $d$-wave with $\langleσv \rangle\propto v^4$, which we find to be considerably less constraining. Furthermore, we highlight that even if the freeze-out process is $p$-wave it is relatively common for (loop/phase-space) suppressed $s$-wave processes to actually provide the leading contributions to the experimentally constrained $γ$-ray flux from the PBH halo. This work also utilyses a refined treatment of the PBH dark matter density profile and outlines an improved application of extra-galactic $γ$-ray bounds.

Figures (14)

• Figure 1: These plots indicate the relevant length scales which dictate the scaling laws of the PBH halo profiles for different PBH masses $M_\bullet$ and under different assumptions (adopting the style of Boudaud:2021irr (Fig. 7)). Left: We show how the PBH halo profiles vary between the various regimes neglecting particle dark matter annihilations and assuming a halo terminal radius to be $r_T=r_{\rm eq}$, following Boudaud:2021irr. Centre: We highlight the impact of including particle dark matter annihilations for $s$-wave annihilations, as studied in Section \ref{['4.2']}. Comparing to the left panel we observe that much of the parameter space with non-trivial scaling laws is replaced by a constant central density core. In the case of $p$-wave annihilations, the boundary is shifted by about an order of magnitude and the inner profile is rising instead of constant, however, the qualitative properties of this plot mostly remain unchanged. Right: The PBH profile will be generically stripped through close encounters with astrophysical bodies, the figure shows how the scaling regions are altered assuming that the PBH resides in the Galactic Bulge, see Section \ref{['3.4']}, note that in this case only the constant density core remains.
• Figure 2: Left. The dark matter density profile around the PBH of Boudaud et al.Boudaud:2021irr (dashed), the impact of including annihilation labelled "This work" (solid), and also compare to the alternatively derived profile of Carr et al.Carr:2020mqm which includes dark matter annihilations (grey dashed). In all cases dark matter annihilation is assumed to be $s$-wave, other parameter values are stated. Observe that with dark matter annihilations the density profile features an inner plateau and then falls with a power-law profile at increasing radial distance. Right. A comparison of three density profiles with the same parameters, but assuming only $s$-wave, $p$-wave and $d$-wave annihilations. The velocity dependence of the annihilation cross section translates into the radial dependence of the central density profile.
• Figure 3: The annihilation rate, $\Gamma_{\bullet}$, as function of PBH mass $M_{\bullet}$ with a halo extending to $r_T\sim r_{\rm eq}$. We plot $\Gamma_{\bullet}$ assuming that the dominant annihilation channel is either $s$-wave (left), $p$-wave (center), or $d$-wave (right) and for each we show three different dark matter mass choices as indicated. We assume the annihilation rate sets the relic density of particle dark matter $\Omega_{\rm pDM}$ with $\Omega_{\rm pDM}\approx0.26$. As a cross-check, notice that the powerlaw breaks for $m_\chi = 1$ TeV in the s-channel plot at $M_{\bullet} \sim 10^{-11} M_\odot$, corresponding to the switch over for the outer density profile apparent in the central plot of Figure \ref{['Fig:length']}.
• Figure 4: Examples of the extragalactic differential flux as a function of energy for dark matter with $m_\chi = 1$ TeV and PBH mass of $M_{\bullet} \sim 10^{-9} M_\odot$ for $s$-wave (left) and $p$-wave annihilation (right, note different $y$-axis scale), fixing $f_{\rm PBH}=2.8\times10^{-8}$. We overlay this with the Fermi-LAT data extragalactic $\gamma$-ray background Fermi-LAT:2015qzw. By design, for $s$ wave $f_{\rm PBH}=f_{\rm MAX}$ (as defined by our criteria) and one can see that the flux in this case saturates the upper limit of the observed $\gamma$-ray background.
• Figure 5: The upper bound on the fractional abundance of PBH $f_{\rm PBH}\lesssim f_{\rm MAX}$ from extragalactic $\gamma$-rays as the PBH mass $M_\bullet$ is varied for different dark matter scenarios. We show three choices of the dark matter mass, assuming that the dominant annihilation channel is $s$-wave (left), $p$-wave (centre), and $d$-wave (right). We assume that the same annihilation channel sets the relic density of the particle dark matter. The grey region indicates $M_\bullet-f_{\rm PBH}$ parameter space for which PBH populations are excluded by evaporations, lensing, gravitational waves, or distortions of the CMB (see e.g. Carr:2020xqk).