Cosmological constraints on dark matter annihilation and decay: Cross-correlation analysis of the extragalactic $\gamma$-ray background and cosmic shear

We derive constraints on dark matter (DM) annihilation cross section and decay lifetime from cross-correlation analyses of the data from Fermi-LAT and weak lensing surveys that cover a wide area of $\sim 660$ squared degrees in total. We improve upon our previous analyses by using an updated extragalactic $\gamma$-ray background data reprocessed with the Fermi Pass 8 pipeline, and by using well-calibrated shape measurements of about twelve million galaxies in the Canada-France-Hawaii Lensing Survey (CFHTLenS) and Red-Cluster-Sequence Lensing Survey (RCSLenS). We generate a large set of full-sky mock catalogs from cosmological $N$-body simulations and use them to estimate statistical errors accurately. The measured cross-correlation is consistent with null detection, which is then used to place strong cosmological constraints on annihilating and decaying DM. For leptophilic DM, the constraints are improved by a factor of $\sim 100$ in the mass range of $O(1)\mathrm{TeV}$ when including contributions from secondary $\gamma$ rays due to the inverse-Compton upscattering of background photons. Annihilation cross sections of $⟨\sigma v⟩\sim {10}^{-23}{\mathrm{cm}}^3/\mathrm{s}$ are excluded for TeV-scale DM depending on channel. Lifetimes of $\sim 10^{25}\sec$ are also excluded for the decaying TeV-scale DM. Finally, we apply this analysis to wino DM and exclude the wino mass around 200 GeV. These constraints will be further tightened, and all the interesting wino DM parameter region can be tested, by using data from future wide-field cosmology surveys.

Figure 1

We plot the model IGRB-cosmic shear cross-correlation as a function of angle separation. We assume a DM particle mass of 100 GeV and ignore secondary $\gamma$ rays in this figure. The different colors represent different channels: $b\overline{b}$ (cyan) and ${\tau }^{+}{\tau }^{-}$ channel (gray). Top: DM annihilation with the canonical cross section of $⟨\sigma v⟩=3\times {10}^{-26}{\mathrm{cm}}^3/\mathrm{s}$. For each colored line, the shaded band indicates our conservative estimate of the theoretical uncertainty caused by the subhalo boost factor model. The solid line shows the total correlation function while the dashed line represents the so-called one-halo term (see text). Bottom: DM decay with decay rate of $3.3\times {10}^{-28}{\mathrm{s}}^{-1}$. The solid line shows the correlation function with proper modeling of nonlinear gravitational growth, while the dashed line represents the expected signal with linear growth of density perturbations. Note that we assume the source galaxy distribution of Ref. [7] and the $\gamma$-ray PSF as in Ref. [40].

Figure 2

The contributions from primary and secondary $\gamma$ rays to the cross-correlation function. Shown are the correlation expected from DM decay. We assume a DM particle mass of 1 TeV and a decay rate of $3.3\times {10}^{-28}{\mathrm{s}}^{-1}$ for the ${\mu }^{+}{\mu }^{-}$ model. The red dashed line shows the contribution from primary $\gamma$ rays, while the blue shows secondary $\gamma$ rays induced by the inverse-Compton upscattering of CMB photons by the decay products $e^{\pm }$. The solid line is the sum of the primary and secondary contributions.

Figure 3

Residual IGRB counts for energies $>1\mathrm{GeV}$ in the lensing survey regions. The isotropic components are calculated by subtracting the best-fit DGB and point sources from the raw photon counts in each ROI (see text). All maps comprise an area of $14°\times 14°$ and have been passed through a Gaussian filter of 0.3°.

Figure 4

Variance of the cross-correlation signals estimated from a set of randomized realizations, mock catalogs and observed maps. The red line shows the statistical error associated with the Poisson error due to the finite number of $\gamma$-ray photon counts. The gray line shows the statistical error associated with the intrinsic shape of source galaxies. The black line corresponds to a more realistic uncertainty incorporating the intrinsic shape and the sample variance of weak lensing.

Figure 5

Average spectrum of the IGRB (black solid line) obtained from a maximum-likelihood fit to the 16 different patches with the FermiTools analysis software. The green area represents an estimate of the systematic uncertainties as calculated with 8 different GALPROP models of the diffuse galactic background [62]. The grey band is the IGRB systematic uncertainty obtained in an all-sky study by the Fermi team [49].

Figure 6

Systematic uncertainties in our cross-correlation analysis. Each panel shows the difference in ${\xi }_{\mathrm{IGRB}-\mathrm{WL}}$ between the fiducial Galactic $\gamma$-ray template and an alternate Galactic $\gamma$-ray template (see text). The differences are normalized by the statistical uncertainty. The red line shows the average residual over eight galactic tempts, while the hatched region represents the range of maximum and minimum residuals for a given $\theta$.

Figure 7

The cross-correlation signal of the IGRB and cosmic shear. The top panel shows the ROIs within each of the CFHTLenS fields, while the bottom is the equivalent for RCSLenS. In both panels, each gray thin line represents the cross-correlation signals for a single ROI, while the symbols with error bars are the results combining several ROIs. The red circles show the results using tangential component of shear, while the black circles are for the cross component of shear as an indicator of systematics in lensing data. The error bars are based on the statistical uncertainties of 500 randomized shear catalogs, mock shear catalogs, and randomized photon count maps.

Figure 8

95% confidence level upper limits on the DM annihilation cross section as a function of DM particle mass. The three panels correspond to three different annihilation channels ($b\overline{b}$, ${\tau }^{+}{\tau }^{-}$, and ${\mu }^{+}{\mu }^{-}$). In each panel, constraints with (blue lines) and without (red) consideration of secondary $\gamma$ rays from inverse-Compton upscattering of CMB photons are shown. For each, the shaded band represents a conservative estimate of the theoretical uncertainty due to DM substructure. The black line shows the canonical cross section expected for thermal relic DM [65].

Figure 9

The same as Fig. 8, but for the 95% confidence level upper limit on the DM decay rate. The shaded band represents a conservative estimate of the theoretical uncertainty due to three-dimensional power spectrum of the DM distribution.

Figure 10

The confidence level derived from our cross-correlation analysis for a wino-like DM model [88]. We consider the annihilation channel of $W^{+}{W}^{-}$. The red line shows the constraint in absence of secondary emission, while the blue is with including the primary and secondary emissions. Note that the shaded regions represent the model uncertainty associated with DM substructures.