$X+y$: insights on gas thermodynamics from the combination of X-ray and thermal Sunyaev-Zel'dovich data cross-correlated with cosmic shear

Abstract

We measure the cross-correlation between cosmic shear from the third-year release of the Dark Energy Survey, thermal Sunyaev-Zel'dovich (tSZ) maps from Planck, and X-ray maps from ROSAT. We investigate the possibility of developing a physical model able to jointly describe both measurements, simultaneously constraining the spatial distribution and thermodynamic properties of hot gas. We find that a relatively simple model is able to describe both sets of measurements and to make reasonably accurate predictions for other observables (the tSZ auto-correlation, its cross-correlation with X-rays, and tomographic measurements of the bias-weighted mean gas pressure). We show, however, that contamination from X-ray AGN, as well as the impact of non-thermal pressure support, must be incorporated in order to fully resolve tensions in parameter space between different data combinations. We obtain simultaneous constraints on the mass scale at which half of the gas content has been expelled from the halo, $\mathrm{log}_{10}(M_c)=14.83^{+0.16}_{-0.23}$, on the polytropic index of the gas, $Γ=1.144^{+0.016}_{-0.013}$, and on the ratio of the central gas temperature to the virial temperature $α_T=1.30^{+0.15}_{-0.28}$.

Figures (11)

• Figure 1: Top: relative contribution from different halo masses to the bias weighted average $\langle bU\rangle$, which dominates the amplitude of the power spectrum on large scales. Bottom: relative contribution from different halo masses to the 1-halo power spectrum, which dominates the amplitude on small scales, at $k=1\,{\rm Mpc}^{-1}$. Results are shown at $z=0$ for the matter power spectrum (dotted black), for the matter-pressure cross correlation (dashed red), and for the correlation between matter and X-ray emissivity (solid blue). On small-scales, where baryonic effects are most relevant, cross-correlations between cosmic shear and X-ray emission from hot gas traces almost the same mass scales that the matter power spectrum is sensitive to.
• Figure 2: Angular cross-power spectra of the 4 DESY3 cosmic shear redshift bins with the ROSAT X-ray map (top panels) and the Planck 2015 Compton-$y$ map (bottom panels). We show theory predictions from the bestfit to $C_\ell^{\gamma X}$ (blue), $C_\ell^{\gamma y}$ (orange) and their combination (dashed green) where individual $\chi^2$ are listed in Table \ref{['tab:snr_det']}. For visualisation purpose, we used $D_\ell=\ell(\ell+1)C_\ell/2\pi$
• Figure 3: 2D marginalised posterior distributions for our minimal hydrodynamic model, derived from the X-ray-shear correlation (blue), from the tSZ-shear correlation (orange), and from their combination (green). Angular power spectrum predictions from best-fit models of these three data combinations are shown in Fig. \ref{['fig:shear_x_y_ps']}. Note that the constraint on $\alpha_T$ from the shear-tSZ correlation is fully driven by the prior bounds on $\mathrm{log}_{10}(M_c)$. Combined constraints are pulled towards lower $\Gamma$ values due to the higher SNR of the tSZ-shear correlation, following the X-ray-shear degeneracy line.
• Figure 4: 2D marginalised posterior distributions for $C_\ell^{\gamma X}$ alone and in combination with $C_\ell^{\gamma y}$ power spectra masking the brightest AGN (darkblue, green) or without masking it (lightblue, gray). The impact of our choice of masking brightest AGN is not significant enough to explain the discrepancy on the inferred polytropic index $\Gamma$.
• Figure 5: 2D marginalised posterior distributions in the $\Gamma - \mathrm{log}_{10}(M_c)$ plane for different analysis settings and data combinations. This figure highlights our most successful attempt at reconciling parameter constraints from the cross correlations studied in this article: marginalising over AGN contamination in X-ray data.