Constraints on the redshift evolution of astrophysical feedback with Sunyaev-Zel’dovich effect cross-correlations

An understanding of astrophysical feedback is important for constraining models of galaxy formation and for extracting cosmological information from current and future weak lensing surveys. The thermal Sunyaev-Zel’dovich effect, quantified via the Compton-$y$ parameter, is a powerful tool for studying feedback, because it directly probes the pressure of the hot, ionized gas residing in dark matter halos. Cross-correlations between galaxies and maps of Compton-$y$ obtained from cosmic microwave background surveys are sensitive to the redshift evolution of the gas pressure, and its dependence on halo mass. In this work, we use galaxies identified in year one data from the Dark Energy Survey and Compton-$y$ maps constructed from Planck observations. We find highly significant (roughly $12\sigma$) detections of galaxy-$y$ cross-correlation in multiple redshift bins. By jointly fitting these measurements as well as measurements of galaxy clustering, we constrain the halo bias-weighted, gas pressure of the Universe as a function of redshift between $0.15\lesssim z\lesssim 0.75$. We compare these measurements to predictions from hydrodynamical simulations, allowing us to constrain the amount of thermal energy in the halo gas relative to that resulting from gravitational collapse.

Figure 1

Cumulative contribution to the $⟨b{P}_e⟩$ integral from theoretical estimates (using AGN feedback pressure profile described in Sec. 2b) of Eq. (15) as a function of halo mass. Most contribution to the integral comes from halos in the range $10^{13}$ to $10^{15}$ $M_{\odot }/h$. There is significant contribution to $⟨b{P}_e⟩$ from halos with $M<{10}^{14}{M}_{\odot }/h$; for current data, correlation analyses of the type considered here are the only way to probe this halo mass range.

Figure 2

Redshift distributions of Y1 redMaGiC galaxies used in this analysis. The galaxy sample is divided into five redshift bins, which are identical to the ones used in DES Collaboration et al. [30]. We only use the first four of these bins in the present analysis, as described in Sec. 3a. The integral of each curve over $dz$ is equal to the number of galaxies in the bin. In total, the sample contains approximately 600 000 galaxies.

Figure 3

Frequency scaling of the halo-CIB correlation in the Websky mocks for different halo selections in redshift (dashed) and mass (dot-dashed). Measurements are shown relative to the fiducial CIB model, as described in the text. We also show the frequency scaling of the CIB in the Sehgal simulations (green solid curve), and the measurements from Planck Collaboration et al. [35] (blue points with error bars). For frequencies less than 545 GHz (i.e., the frequency range used in this analysis, corresponding to the unshaded region in this plot), departures from our fiducial CIB model are less than 20%, and are consistent with the Planck measurements.

Figure 4

Galaxy-$y$ cross-correlation measurements with reconstructed $y$ maps from the Sehgal simulations. We show results for the halo bin with $2\times {10}^{13}{M}_{\odot }/h<M_h<3\times {10}^{13}{M}_{\odot }/h$ and $0.15<z<0.3$. The results for other redshift bins are similar. We find that our $y$ reconstruction methods are sufficient to recover an essentially unbiased estimate of the $\mathrm{halo}\text{−}y$ cross-correlation over the scales of interest.

Figure 5

Left panel shows the ratio of $⟨b{P}_e⟩$ inferred in simulations from measurements with redMaGiC galaxies to that inferred from halos. For both the Buzzard (blue) and MICE (orange) simulations, the redMaGiC galaxies and halos lead to consistent determinations of $⟨b{P}_e⟩$. This supports the notion that the measurements are sufficiently far in the two-halo regime that the inference of $⟨b{P}_e⟩$ is independent of the halo-galaxy connection. The right panel shows the measurements of $⟨b{P}_e⟩$ in the Buzzard simulation compared to the theoretical prediction.

Figure 6

Measurements of the galaxy autocorrelation (top row) and Compton-y galaxy cross-correlation (bottom row) at different redshift bins corresponding to four redshift bins used in the analysis. The solid line is the best-fit to the fiducial model of $\mathrm{Compton}\text{−}y$, which is generated after removing 545 and 857 GHz frequency channels from the analysis. Only data in the unshaded regions are used for fitting. These scale cut choices are validated in Sec. 4e

Figure 7

The $\mathrm{galaxy}\text{−}y$ cross-correlation function over the scales of interest when the component separation method used to estimate $y$ is varied. We show the correlation measurements for the highest signal to noise redshift bin, $0.45<z<0.6$, but results for the other redshift bins are similar. We find that the estimated correlation function does not vary significantly when the $y$ estimation choices are varied. Together with our validation with simulations, this constitutes strong evidence that our correlation measurements are not significantly biased by astrophysical contaminants in the estimated $y$.

Figure 8

Constraints on the redshift evolution of the bias weighted pressure of the Universe [Eq. (15)]. We compare the data points obtained from this work with Vikram et al. [15] and theory curves corresponding to shock heating model as described in Ref. [26]. For theory curves, all models are evaluated for $\mathrm{\Delta }=500$ and for various choices of $R_{\max }/R_{\mathrm{\Delta }}$.

Figure 9

Constraints on the thermal energy of the gas as a function of redshift. The parameter $\alpha$ defined in Eq. (28), measures the fractional departure of the gas thermal energy from the predictions of a model that only includes gravitational energy. Large $\alpha$ means that some process must have contributed extra thermal energy to the gas, while negative $\alpha$ means that the gas must have cooled. In our model, the addition (or deficit of) thermal energy impacts all halos below a threshold mass, $M_{\mathrm{th}}$. We show the results for $M_{\mathrm{th}}\to \infty$ (region between blue solid curves) and for $M_{\mathrm{th}}={10}^{14}{M}_{\odot }$ (region between orange-red dashed curves). The $⟨b{P}_e⟩$ measurements presented in this work are sensitive to halos with $10^{13}\lesssim M\lesssim {10}^{15}{M}_{\odot }$, as shown in Fig. 1.

Figure 10

Cross-correlation of reconstructed $\mathrm{Compton}\text{−}y$ with the halos in Websky mocks for various reconstruction methods. We correlate halos satisfying $0.3<z<0.45$ and $2\times {10}^{13}{M}_{\odot }/h<M_h<3\times {10}^{13}{M}_{\odot }/h$. The points labelled ‘input’ correspond to the true $\mathrm{halo}\text{−}y$ cross-correlation in the absence of any contamination. The other points show the results of applying component separation to simulated sky maps that include the CIB signal. In all cases, we use frequencies 100, 143, 217, and 343 GHz. We find that the choice of $\mathrm{unit}\text{−}y$, null-CMB leads to no significant bias in the inferred $\mathrm{halo}\text{−}y$ cross-correlation.

Figure 11

Top panel shows the log of the absolute value of the final covariance matrix. Bottom panel shows the corresponding cross-correlation matrix.

Figure 12

Multidimensional parameter constraints from the model fits to data. The first four parameters are galaxy bias for each of the four redshift bin used in this analysis and next four are bias weighted pressure corresponding to the same bins.