Measurement of the thermal Sunyaev-Zel’dovich effect around cosmic voids

We stack maps of the thermal Sunyaev-Zel’dovich effect produced by the Planck Collaboration around the centers of cosmic voids defined by the distribution of galaxies in the CMASS sample of the Baryon Oscillation Spectroscopic Survey, scaled by the void effective radii. We report a first detection of the associated cross-correlation at the $3.4\sigma$ level: voids are under-pressured relative to the cosmic mean. We compare the measured Compton-$y$ profile around voids with a model based solely on the spatial modulation of halo abundance with environmental density. The amplitude of the detected signal is marginally lower than predicted by an overall amplitude ${\alpha }_v=0.67\pm 0.2$. We discuss the possible interpretations of this measurement in terms of modeling uncertainties, excess pressure in low-mass halos, or nonlocal heating mechanisms.

Figure 1

Relative contribution to the average electron pressure from halos of different mass at different distances from the void center (here $r_v$ is the effective void radius). Due to the suppressed growth of structure inside the void, the electron pressure is mostly supported by low-mass halos.

Figure 2

2-dimensional stacked tSZ signal in polar coordinates measured around the CMASS voids (top left) and three random mock void catalogs (top right and bottom). The data exhibit a noticeable average decrement below $\theta \lesssim 0.7{\theta }_v$, where ${\theta }_v$ is the angle subtended by the void effective radius.

Figure 3

Radial tSZ profile around voids estimated from the CMASS void catalog (red circles with error bars). The dashed black line corresponds to the theoretical expectation based on the model described in Sec. 2, while the solid black line corresponds to the best-fit model found by scaling the fiducial prediction by an amplitude ${\alpha }_v$.

Figure 4

Covariance matrix of the measured radial tSZ profile around voids (see Fig. 3). The covariance matrix is estimated from the 1,000 CMASS mock void catalogues and contains significant off-diagonal elements that need to be accounted for in the analysis. These are caused by the beam smoothing of the $y$ maps and by the mixing of scales associated with the effective map rescaling with each void’s size before stacking.

Figure 5

Radial tSZ profile around voids estimated from the CMASS void catalog using the MILCA $y$ map (red circles with error bars) and the NILC $y$ map (blue squares with error bars). The solid black line corresponds to the best-fit rescaling of the theoretical expectation described in Section to the MILCA map. The black diamonds with error bars show the best-fit dust leakage computed by scaling the stacked void signal on the Planck 545 GHz map by a constant factor ${\alpha }_{\mathrm{CIB}}$ estimated as described in Sec. 4c. The gray band around these data shows the dust leakage allowed by the $1\sigma$ uncertainty on ${\alpha }_{\mathrm{CIB}}$. Finally, the yellow line shows the mean signal measured from the mock catalogues and subtrated from our measurements. Note that the true mean signal is not directly measurable, and therefore this measured mean has no meaningful physical interpretation.

Figure 6

Radial tSZ profile around voids estimated from the CMASS void catalog using the MILCA $y$ map (red circles with error bars) via our fiducial analysis, and estimated by applying an ILC at the cross-correlation level to measurements of the void cross-correlation with the six Planck HFI frequency maps. The yellow squares show the result for a standard (tSZ-preserving, variance-minimizing) ILC applied to the cross-correlation measurements, while the black diamonds show the result when the ILC additionally deprojects a fiducial CIB component. The consistency of the yellow and black points indicate that the ILC is already removing CIB contamination effectively. Although the direct HFI–void cross-correlation measurements are noisier than our fiducial results, they demonstrate robustness to possible CIB contamination.

Figure 7

Summary of void-related quantities. Top: relative density of galaxies around void as estimated from the CMASS data (dashed) and associated relative matter density after correcting for the CMASS galaxy bias (solid). Middle: effective expansion rate as a fraction of the expansion rate outside the void (i.e., $\eta (r)$ in Eq. (a1). Bottom: electron pressure in the void as a fraction of the mean pressure outside. In this model voids have a negligible pressure, and therefore the negative differential tSZ flux in void measured in this work is effectively dominated by the mean electron pressure outside the void (with a negative sign).