Wiener filtering and multi-tracer techniques for dark matter cross-correlations between gamma-ray emission and galaxy catalogs

Abstract

Cross-correlations between a gravitational tracer of dark matter and the contribution to the unresolved gamma-ray background (UGRB) from the radiation produced by the annihilation of the particles responsible for the dark matter, have been established as a powerful tool to investigate the particle physics nature of dark matter. Cross-correlations of the UGRB with galaxy catalogs, cluster catalogs and weak lensing have indeed been measured. In this paper we study statistical techniques that could improve the sensitivity of the cross-correlation techniques on the bounds that can be set to the particle dark matter physical properties. The two methods that we investigate are the application of a Wiener filter and the exploitation of the full multi-tracer information. After identifying the optimal strategies, we show that the adoption of a Wiener filter in the cross-correlation analysis can improve the sensitivity to the dark matter annihilation rate by a factor of 2/2.5 as compared to the standard analysis where no filter is applied. The inclusion of the full multi-tracer information can improve the sensitivity up to a factor of 5 for dark matter masses below about 50 GeV, the Wiener filter remaining the best option for heavier dark matter.

Figures (8)

• Figure 1: Gamma-ray window functions $W_\gamma(z)$ as a function of redshift for the total emission (red lines) from unresolved astrophysical sources (blazars, misaligned active galactic nuclei, flat spectrum radio quasars and star forming galaxies), together with a few representative examples from dark matter emission in the $b\bar{b}$ channel, namely: $m_{\rm DM} = 10$ GeV (red), $m_{\rm DM} = 100$ GeV (green) and $m_{\rm DM} = 1000$ GeV (blue). In all cases the cross section is set at its "thermal" value $\langle\sigma_{\rm ann} v\rangle_{\rm th} = 3\times 10^{-26}$ cm$^{-3}$ s$^{-1}$. The three panels refer to the gamma-ray emission in three different energy bins; from left to right: number 6, 9 and 12 of Table \ref{['tab:Fermi_energy_bins']}.
• Figure 2: Gamma-ray window functions $W_\gamma(E)$ as a function of energy for the total emission (red lines) from unresolved astrophysical sources (blazars, misaligned active galactic nuclei, flat spectrum radio quasars and star forming galaxies), together with a few representative examples from dark matter emission in the $b\bar{b}$ channel, namely: $m_{\rm DM} = 10$ GeV (red), $m_{\rm DM} = 100$ GeV (green) and $m_{\rm DM} = 1000$ GeV (blue). In all cases the cross section is set at its "thermal" value $\langle\sigma_{\rm ann} v\rangle_{\rm th} = 3\times 10^{-26}$ cm$^{-3}$ s$^{-1}$. The three panels refer to the gamma-ray emission in three different redshift bins; from left to right: $z = 0.025$, $z = 0.5$, $z = 1$.
• Figure 3: Galaxy survey window functions vs redshift. The black lines shows the 2MRS window function $W_g(\chi)$ without applying weights (standard case). The remaining lines show the 2MRS window functions $W_{wg}(\chi)$ with the weights applied. The colors differentiate the dark matter mass (red is for $m_{\rm DM} = 10$ GeV, green for $m_{\rm DM} = 100$ GeV and yellow for $m_{\rm DM} = 1000$ GeV -- in all cases the cross section is set at its "thermal" value $\langle\sigma_{\rm ann} v\rangle = 3\times 10^{-26}$ cm$^{-3}$ s$^{-1}$) while the three panels, from left to right, refer to the Fermi-LAT energy bins number 6, 9 and 12. The unweighted window functions are clearly the same in each panel.
• Figure 4: Some representative cases of the product between the galaxy window function $W_g(\chi)$ and the gamma-rays window function $W_\gamma(\chi)$, in the unweighted (standard) case (solid lines) and when weights are applied (dashed lines). In all cases, the gamma-ray window function adds the astrophysical sources contribution to a DM signal, which refers to: $m_{\rm DM} = 10$ GeV (red lines), $m_{\rm DM} = 100$ GeV (green) and $m_{\rm DM} = 1000$ GeV (yellow). In all cases the cross section is set at its "thermal" value $\langle\sigma_{\rm ann} v\rangle = 3\times 10^{-26}$ cm$^{-3}$ s$^{-1}$. From left to right, the panels refer to the Fermi-LAT energy bins number 6, 9 and 12. The quantity $W_g(\chi)$$W_\gamma(\chi)$ determines the cross-correlation signal, as in Eq. (\ref{['eq:APS']}).
• Figure 5: Contribution from each multipole to the SNR$^2$ (Eq. (\ref{['eq:SNR_ell']}), upper panels) and to the $\varDelta\chi^2$ of Eq. (\ref{['eq:delta_chi_2']}) (lower panels) in the unweighted case. The left panels refer to the gamma-rays $\otimes$ galaxies cross-correlation $(\gamma g$) case, the central panels to the multi-tracer case that combines gamma-rays $\otimes$ galaxies cross-correlation with galaxies auto-correlation ($\gamma g$ + $gg$) and the right panels to the multi-tracer case that combines gamma-rays $\otimes$ galaxies cross-correlation, galaxies auto-correlation and gamma rays auto-correlation ($\gamma g$ + $gg$ + $\gamma\gamma$). In each upper panel, the black lines refer to gamma-ray emission from astrophysical sources only. The red, yellow and green lines stand for gamma-ray emission from astrophysical sources and dark matter, for three representative dark matter mass values: 10 GeV (red), 100 GeV (yellow) and 1000 GeV (green). The annihilation cross section $\langle\sigma_{\rm ann} v\rangle$ for the three cases is 0.05, 0.5 and 5 times the "thermal" value $\langle\sigma_{\rm ann} v\rangle_{\rm th} = 3\times 10^{-26}$ cm$^{-3}$ s$^{-1}$, respectively.