Ruling Out Spiky WIMP Dark Matter using Indirect Searches

Abstract

The dark matter (DM) density profile in the innermost region of the Galaxy remains an open question. In particular, while adiabatic growth of the supermassive black hole Sgr A$^\ast$ at the Galactic Center (GC) can induce a 'spike' in central DM density, the existence of such a spike is still under debate. Here we present new constraints on the spike slope $γ_{\rm sp}$ using conventional DM indirect detection searches. We first recast existing photon and neutrino line searches, which include the contribution from the GC region, into constraints on the thermally-averaged DM annihilation cross section $\langleσv\rangle$ in the presence of a DM spike. We then derive new bounds on the spike profile for a generic Weakly Interacting Massive Particle (WIMP) DM scenario, where the thermal freeze-out mechanism fixes the annihilation cross-section at $\langleσv\rangle\sim (2-3) \times 10^{-26}~{\rm cm}^3~{\rm s}^{-1}$. We find that for DM annihilation to photons, constraints from Fermi-LAT and MAGIC rule out spike profiles at the GC for a broad range of WIMP DM masses from 10 GeV to 100 TeV. Our result holds even if the photon channel constitutes only $1\%$ of the total annihilation rate. For the neutrino channel, we use the IceCube data to constrain the existence of an extremely steep spike in the $\mathscr{O}(1-10)$ TeV DM mass range. Our analysis can be easily extended to other annihilation channels.

Figures (7)

• Figure 1: Illustration of the spike+halo construction for the Milky Way DM density as a function of the distance from the GC, for an NFW profile with DM mass of $m_\chi = 10$ GeV (black), and in the presence of DM spike (with slopes $\gamma_{\rm sp} =$ 2, 2.25 and 2.5, shown by the thin dotted, dashed and solid lines, respectively), for $m_\chi = 10$ GeV (blue), and $10^5$ GeV (red). The different spike parameters lead to different DM densities for $r \leq R_{\rm sp}$. The annihilation-regulated behavior for $r \leq R_{\rm sat}$ (the saturation radius) is illustrated for a fixed value of $\langle \sigma v\rangle = 2.2 \times 10^{-26}\;{\rm cm}^3\, {\rm s}^{-1}$. For larger DM masses, the value of the saturation density $\rho_{\rm sat}$ is higher, which leads to the DM spike continuing till smaller values of $R_{\rm sat}$.
• Figure 2: The impact of the spiky DM profile on the annihilation $J$-factor as a function of the maximum angular cutoff $\theta_{\max}$. We show results for an NFW profile with DM mass of $m_\chi \geq 10$ GeV (black curve), and in the presence of a DM spike (with slopes $\gamma_{\rm sp} = 2, \, 2.25$ and $2.5$), for $m_\chi = 10$ GeV (blue curves) and $10^5$ GeV (red curves). In the presence of a DM spike, the $J$-factor asymptotically reaches a large value at a smaller value of $\theta_{\max}$, when compared against the NFW profile.
• Figure 3: Comparison of Fermi-LAT constraints for two angular regions centered on the GC. The NFW constraints are taken from Ref. Foster:2022nva, where the blue (black) curve corresponds to constraints from observation within $1^\circ$ ($30^\circ$) of the GC. The green (purple) band corresponds to a recast of the NFW constraints to those corresponding to a spiky DM profile. In the presence of a steep DM spike, the relative enhancement of $J$-factor is larger at smaller $\theta_{\max}$. As a result, for steep spikes with $\gamma_{\rm sp}\in [2.25,\,2.5]$, the $(0-1)^\circ$ limits become stronger than those from $(0-30)^\circ$.
• Figure 4: Left panel: Constraints on DM annihilation cross section $\langle \sigma v\rangle$ from gamma-ray line searches toward the GC, as a function of the DM mass. The black solid line for Fermi-LAT corresponds to an observation window of $(0-30)^\circ$ and the black dashed curve for MAGIC up to $1.1^\circ$ around the GC, for an NFW profile. The cyan and green curves show our spike recast using Eq. \ref{['eq:recast_equation']} for GS-like spike benchmarks. For the rescaled Fermi-LAT constraints, we obtain the results from the inner $(0-1)^\circ$ annulus results in Ref. Foster:2022nva. Right panel: Upper bounds on the spike slope $\gamma_{\rm sp}$ for a thermal relic freeze-out WIMP, for DM annihilation to photons. The different shades correspond to photon-line annihilation branching ratios $f_{\rm BR}=1$, $0.1$, and $0.01$. For all three branching ratios, a GS spike with $\gamma_{\rm sp}\in [2.25, 2.5]$ is effectively ruled out for the thermal freeze-out scenario.
• Figure 5: Left panel: Constraints on DM annihilation to neutrinos from IceCube. The black curve shows the IceCube limit obtained for the NFW profile parametrization used in this work, while the green curves show our spike reinterpretation for GS-like spike slopes of $\gamma_{\rm sp}=2.25$ and $\gamma_{\rm sp} = 2.5$, with the shaded region denoting intermediate values of $\gamma_{\rm sp}$. The thermal relic benchmark is shown in gray. Right panel: Constraints on $\gamma_{\rm sp}$ assuming a thermal relic freeze-out annihilation cross section into neutrinos, shown as a function of the DM mass $m_\chi$. The strongest constraint occurs in the $m_\chi \sim (1.8- 3.9)$ TeV window, reaching $\gamma_{\rm sp}\simeq 2.35$.