Detection of Cross-Correlation between Gravitational Lensing and $\gamma$ Rays

In recent years, many $\gamma$-ray sources have been identified, yet the unresolved component hosts valuable information on the faintest emission. In order to extract it, a cross-correlation with gravitational tracers of matter in the Universe has been shown to be a promising tool. We report here the first identification of a cross-correlation signal between $\gamma$ rays and the distribution of mass in the Universe probed by weak gravitational lensing. We use data from the Dark Energy Survey Y1 weak lensing data and the Fermi Large Area Telescope 9-yr $\gamma$-ray data, obtaining a signal-to-noise ratio of 5.3. The signal is mostly localized at small angular scales and high $\gamma$-ray energies, with a hint of correlation at extended separation. Blazar emission is likely the origin of the small-scale effect. We investigate implications of the large-scale component in terms of astrophysical sources and particle dark matter emission.

Figure 1

DES Y1 (solid, used in this Letter) and final (dashed) sky coverage superimposed on the Fermi-LAT $\gamma$-ray map for photons in the 1–10 GeV energy range. The Galactic plane and point-source emissions are clearly visible. The plot is in McBryde-Thomas flat polar quartic projection.

Figure 2

Measurement and model of the cross-correlation between $\gamma$-ray photons and gravitational shear. The points in both figure parts show the measured cross-correlation, averaged over all redshift and energy bins, while the fits are done across all dimensions. The lines refer the best-fit results for the phenomenological model (left) and for the physical model (right), averaged the same way.

Figure 3

(Left) Constraints on the normalization and spectral index parameters of the phenomenological model (the redshift dependence parameters are unconstrained and not shown in the plot). (Right) Constraints on the parameters of the dark matter and blazar models described in Eq. (5). The blazar model assumes a single population matching the properties of Fermi resolved sources. The dark matter model assumes annihilation in the ${\tau }^{+}{\tau }^{-}$ channel. In both panels, 2D contours refer to the 68% and 95% C.L. regions. The dashed and solid vertical lines in the 1D subplots denote the 68% and 95% C.L. constraints of the 1D profile likelihood distributions.

Figure 4

(Left) Energy scaling of the measured signal and best-fit models, in terms of the matched filter amplitude $\mathcal{A}$ of the cross-correlation between gravitational shear and $\gamma$ rays (see text for its definition). The amplitude is divided by the size of the corresponding energy bin $\mathrm{\Delta }{E}_a$ and multiplied by the measured photon intensity $⟨I_a⟩$ in the same bin, to show the physical differential scaling in energy. (Right) Redshift scaling of the measured signal and models, again in terms of the matched filter amplitude $\mathcal{A}$ introduced in the text.