Constraining the baryon abundance with the kinematic Sunyaev-Zel’dovich effect: Projected-field detection using $Planck$, $WMAP$, and $unWISE$

The kinematic Sunyaev-Zel’dovich (kSZ) effect—the Doppler boosting of Cosmic Microwave Background (CMB) photons scattering off free electrons with nonzero line-of-sight velocity—is an excellent probe of the distribution of baryons in the Universe. In this paper, we measure the kSZ effect due to ionized gas traced by infrared-selected galaxies from the $unWISE$ catalog. We employ the “projected-field” kSZ estimator, which does not require spectroscopic galaxy redshifts. To suppress contributions from non-kSZ signals associated with the galaxies (e.g., dust emission and thermal SZ), this estimator requires foreground-cleaned CMB maps, which we obtain from $Planck$ and $WMAP$ data. Using a new “asymmetric” estimator that combines different foreground-cleaned CMB maps to maximize the signal-to-noise, we measure the ${\mathrm{kSZ}}^2$-galaxy cross-power spectrum for three subsamples of the $unWISE$ galaxy catalog. These subsamples peak at mean redshifts $z\approx 0.6$, 1.1, and 1.5, have average halo mass $\sim 1–5\times {10}^{13}{h}^{-1}{M}_{\odot }$, and in total contain over 500 million galaxies. After marginalizing over contributions from CMB lensing, we measure the amplitude of the kSZ signal $A_{{\mathrm{kSZ}}^2}=0.42\pm 0.31(\mathrm{stat})\pm 0.02(\mathrm{sys})$, $5.02\pm 1.01(\mathrm{stat})\pm 0.49(\mathrm{sys})$, and $8.23\pm 3.23(\mathrm{stat})\pm 0.57(\mathrm{sys})$, for the three subsamples, where $A_{{\mathrm{kSZ}}^2}=1$ corresponds to our fiducial theoretical model. The combined statistical significance of our kSZ detection exceeds $5\sigma$. Our theoretical model includes the first calculation of lensing magnification contributions to the ${\mathrm{kSZ}}^2$-galaxy cross-power spectrum, which are significant for the $z\approx 1.1$ and 1.5 subsamples. We discuss possible explanations for the excess kSZ signal associated with the $z\approx 1.1$ sample, and show that foreground contamination in the CMB maps is very unlikely to be the cause. From our measurements of $A_{{\mathrm{kSZ}}^2}$, we constrain the product of the baryon fraction $f_b$ and free electron fraction $f_{\mathrm{free}}$ to be $(f_b/0.158)(f_{\mathrm{free}}/1.0)=0.65\pm 0.24$, $2.24\pm 0.25$, and $2.87\pm 0.57$ at $z\approx 0.6$, 1.1, and 1.5, respectively, consistent with a large fraction of the cosmic baryon abundance existing in an ionized state at low redshifts.

Figure 1

The filter (used to extract the kSZ signal) and beam functions (to account for the finite resolution of the telescope), along with their product versus multipole moment used in the main analysis. See Eqs. (3), (4), and (5) for more details.

Figure 2

Top: bias-weighted redshift distributions $b(z)dn/dz$ (obtained by cross-correlation with BOSS and eBOSS surveys) for the blue (solid line), green (dashed line), and red (dotted line) $unWISE$ samples, as measured in [34]. Bottom: normalized statistical redshift distribution of the $unWISE$ galaxies for the blue (solid line), green (dashed line), and red (dotted line) obtained by dividing the curves from the top panel by a redshift dependent bias $b(z)$ function, and normalizing. See Table 1 for mean redshifts and other properties associated with these galaxy samples.

Figure 3

Multipole-dependent $\alpha$ values that null the cross-correlations of ${\delta }_g$ and $((1+\alpha )T_{\mathrm{LGMCA}}-\alpha T_{\mathrm{dust}})$ for each of the $unWISE$ maps. The $\alpha$ values are found for each of the 13 multipole bins, and then interpolated (using a CubicSpline) over the entire $\ell$ range used in the analysis.

Figure 4

Null tests on the LGMCA maps (noise maps in top panels and the $\alpha$-cleaned maps used in our main data analysis in the bottom panels). All are color coded based on the $unWISE$ colors: blue, red, and green, and include probabilities-to-exceed from fitting them to null. The green points are offset by $\ell =20$, and the red by $\ell =50$ with respect to the true multipole moment values, for visual purposes. Top left: cross-correlation between $T_{\text{noise}}$ and unWISE, where $T_{\text{noise}}$ is the ${\mathrm{LGMCA}}_{\text{noise}}$ map. Top right: cross-correlation between $T_{\text{noise}}^2$ and unWISE. Bottom left: cross-correlation of $(T_{\text{clean}}{T}_{\mathrm{dust}})$ and $unWISE$, where $T_{\mathrm{dust}}$ is the $Planck$ 857 GHz map. Bottom right: cross-correlation of $(T_{\text{clean}}{T}_{\mathrm{dust}})$ and $unWISE$, where $T_{\mathrm{dust}}$ is the $Planck$ 545 GHz map. All tests are consistent with null, which provides robust evidence that our $\alpha$-cleaned LGMCA map contains negligible thermal dust contamination from the $unWISE$ galaxies.

Figure 5

Cross-power spectra of the real-space product of the cleaned, filtered LGMCA map and the filtered SMICA map with each of the $unWISE$ galaxy density maps: blue, green, and red (data points in respective colors). The thin dashed curves show the best-fit CMB lensing contribution (including the lensing-galaxy and lensing-magnification bias terms), the black dotted shows the best-fit kSZ contribution (including the kSZ-galaxy and kSZ-magnification bias terms), and the pink stars show the lensing-subtracted residuals for illustration. The yellow solid curves in each plot show the total best-fit curves, which are the sum of best-fit lensing and best-fit kSZ contributions. The best-fit values for each of the free parameters in the theory model (the ${\mathrm{kSZ}}^2$ amplitude $A_{{\mathrm{kSZ}}^2}$, the galaxy bias $b_g$, and the magnification response $s$) are presented in the plot titles. Our fiducial model assumes $A_{{\mathrm{kSZ}}^2}=1$. The kSZ signal is detected at $1.4\sigma$, $5.0\sigma$, and $2.5\sigma$ significance, respectively, for the three $unWISE$ subsamples.

Figure 6

Fiducial model prediction for each of the $unWISE$ samples (color-coded). Each contribution (${\mathrm{kSZ}}^2$-galaxy cross-correlation, ${\mathrm{kSZ}}^2$-magnification bias cross-correlation, CMB lensing-galaxy cross-correlation, and CMB lensing-magnification bias cross-correlation) is plotted separately. The fiducial model assumes the ${\mathrm{kSZ}}^2$ amplitude $A_{{\mathrm{kSZ}}^2}=1$, and the values for the galaxy bias $b_g$ and the magnification response $s$ to be equal to the values measured in Ref. [34]. These values are given in the plot titles for ease of reference. The curves are slightly nonsmooth because we apply the same binning used in the data analysis to the theory curves here. Note the logarithmic scale on the vertical axis, as compared to the linear scale in Fig. 5.

Figure 7

Null tests on the ${\mathrm{LGMCA}}_{\text{clean}}$ map for the constant $\alpha$ cleaning. Both plots are color coded based on the $unWISE$ colors: blue, red, and green, and include their respective $p$-values (for 13 degrees of freedom) in the legend when fitting them to null. Green is offset by $\ell =20$, and red by $\ell =50$ with respect to the true multipole moment values, for visual purposes. Left: cross-correlation between $T_{\text{clean}}$ and $unWISE$. Right: cross-correlation between $T_{\text{clean}}{T}_{\mathrm{dust}}$ and unWISE, where $T_{\mathrm{dust}}$ is $Planck$ 545 GHz map.

Figure 8

To assess the “additional cleaning factor” described in Appendix pp2, we show a comparison of the absolute value of $D_{\ell }$ for $\mathrm{LGMCA}\times unWISE$ and $D_{\ell }$ for an estimate of the dust-only contribution to $143\mathrm{GHz}\times unWISE$, where the latter has been obtained by rescaling from $Planck217\mathrm{GHz}\times unWISE$ using a dust SED determined from 217 and 545 GHz data (see the text for details). We show these quantities for each of the $unWISE$ maps (color-coded).

Figure 9

A comparison of the dust contamination present in the LGMCA map versus the best-fit kSZ signal from our analysis for each of the $unWISE$ maps. The dust is assessed by rescaling $(Planck545\mathrm{GHz}{)}^2\times unWISE$ down to 143 GHz and dividing by the “additional cleaning factors” from Table 7 squared. This demonstrates that any $unWISE$-correlated dust that is present in the LGMCA maps is negligible, and we can safely assume it is not a source of our detected signal.

Figure 10

The 2D and 1D marginalized posterior distributions of the $A_{{\mathrm{kSZ}}^2}$, $b_g$, and $s$ parameters for the fit to the cross-power spectra of the product of filtered ${\mathrm{LGMCA}}_{\text{clean}}$ and SMICA with each of the $unWISE$ galaxy maps (solid lines). This analysis imposes external priors on $b_g$ and $s$ derived from Ref. [34]. The $b_g$ priors are Gaussians with mean and $1\sigma$ width corresponding to the values in Table 4, while the $s$ priors are Gaussians centered at the values in Table 4 with a fractional standard deviation of 10%. The dashed curves are the posteriors of the same model fit, but without the external priors on $b_g$. Clockwise from top-left: $unWISE$ blue, green, and red.

Figure 11

Dimensionless CMB lensing-galaxy cross power spectrum (top panel) and galaxy auto power spectrum (bottom panel). Measurements from [34] are shown as the black data points with error bars. The halo model prediction ($1+2$-halo) is shown as the solid red lines. The 1-halo term contribution is shown as the dash-dotted red lines. The other curves (in green) show the contribution from lensing magnification bias and are computed according to Eqs. (6.4) and (6.5) of [34], using the matter power spectrum computed with Halofit. For this figure we use the green sample of $unWISE$ galaxies and carry out all the Halofit and halo model computations with class_sz.

Figure 12

Halo model predictions for the one-halo term contribution to $C_{\ell }^{{\mathrm{kSZ}}^2\times {\delta }_g}$ (top panel) and $C_{\ell }^{{\mathrm{kSZ}}^2\times {\mu }_g}$ (bottom panel) under three different assumptions: (i) fiducial halo model (dash-dotted red lines); (ii) velocity dispersion computed without nonlinear corrections in the matter power spectrum, i.e., using the linear matter power spectrum rather than Halofit in Eq. (d1) (dot-dot-dashed blue lines); (iii) a $\tau$-profile concentration twice as high as the fiducial model (green dashed lines). Note that as we change the concentration we keep the total mass fixed (see text). The solid black lines depict the templates used in the data analysis in the main part of this paper (see Fig. 6). For this figure we use the green sample of $unWISE$ galaxies and carry out all the halo model computations with class_sz. In future work we will compute the other halo-model contributions to these signals, beyond the one-halo term.

Figure 13

Dust null tests on the $\alpha$-cleaned SMICA-noSZ map, analogous to those shown in Fig. 4 for the $\alpha$-cleaned LGMCA map. We show the dust null tests for the $\alpha$-cleaned LGMCA and $\alpha$-cleaned SMICA-noSZ maps, and not for the original SMICA maps, since the latter has non-negligible tSZ residuals and thus only the former two maps can be used as primary maps in our estimator. All are color coded based on the $unWISE$ subsample colors: blue, red, and green, and the legends give the probabilities-to-exceed for fits to null. The green sample points are offset by $\ell =20$, and the red by $\ell =50$ with respect to the true multipole moment values, for visual purposes. Left: cross-correlation of $(T_{\text{clean}}{T}_{\mathrm{dust}})$ and $unWISE$, where $T_{\mathrm{dust}}$ is the $Planck$ 545 GHz map and ($T_{\text{clean}}$ is the clean SMICA-noSZ map. Right: cross-correlation of $(T_{\text{clean}}{T}_{\mathrm{dust}})$ and $unWISE$, where $T_{\mathrm{dust}}$ is the $Planck$ 857 GHz map and ($T_{\text{clean}}$ is the clean SMICA-noSZ map. Both are consistent with null.

Figure 14

Cross-power spectra of the real-space product of the cleaned, filtered SMICA-noSZ map and the filtered SMICA map with each of the $unWISE$ galaxy maps: blue, green, and red (data points in respective colors), analogous to our main analysis in Fig. 5. The thin dashed curves show the best-fit lensing contribution, the black dotted are kSZ and the pink stars the residuals. The yellow solid curves in each plot show the total best-fit curves. The best-fit values for the free parameters (the ${\mathrm{kSZ}}^2$ amplitude $A_{{\mathrm{kSZ}}^2}$, galaxy bias $b_g$, and the magnification response $s$) are presented in the plot titles. These results validate our main analysis.

Figure 15

Cross-power spectra of the real-space square of the cleaned, filtered LGMCA map with each of the $unWISE$ galaxy maps: blue, green, and red (data points in respective colors), analogous to our main analysis in Fig. 5. The thin dashed curves show the best-fit lensing contribution, the black dotted the kSZ and the pink stars the residuals. The yellow solid curves in each plot show the total best-fit curves. The best-fit values for the free parameters (the ${\mathrm{kSZ}}^2$ amplitude $A_{{\mathrm{kSZ}}^2}$, galaxy bias $b_g$, and the magnification response $s$) are presented in the plot titles. These results validate our main analysis, and also demonstrate that the “asymmetric” estimator employed in our fiducial analysis is robust to foregrounds, while generally yielding smaller error bars than the approach used in these plots (which matches that in H16).

Figure 16

Cross-power spectra of the real-space square of the cleaned, filtered SMICA-noSZ map with each of the $unWISE$ galaxy maps: blue, green, and red (data points in respective colors), analogous to our main analysis in Fig. 5. The thin dashed curves show the best-fit lensing contribution, the black dotted the kSZ and the pink stars the residuals. The yellow solid curves in each plot show the total best-fit curves. The best-fit values for the free parameters (the ${\mathrm{kSZ}}^2$ amplitude $A_{{\mathrm{kSZ}}^2}$, galaxy bias $b_g$, and the magnification response $s$) are presented in the plot titles. These results validate our main analysis, and again also verify the robustness of the asymmetric estimator used in our fiducial analysis.

Figure 17

A comparison of all the combinations of SMICA and SMICA-noSZ maps cross-correlated with the $unWISE$ maps (blue, green, and red, color-coded). The $(\mathrm{SMICA}\text{−}{\mathrm{noSZ}}_{\text{clean}}·\mathrm{SMICA})\times unWISE$ points are offset by $\ell =20$, and the ${\mathrm{SMICA}}_{\text{clean}}^2\times unWISE$ points are offset by $\ell =50$ with respect to the true multipole moment values, for visual purposes. All analyses yield consistent results with one another, and with our main analysis in Fig. 5, which validates the robustness of our analysis.

Figure 18

A comparison of all the combinations of SMICA and LGMCA maps cross-correlated with the $unWISE$ maps (blue, green, and red, color-coded). The $({\mathrm{LGMCA}}_{\text{clean}}·\mathrm{SMICA})\times unWISE$ points are offset by $\ell =20$, and the ${\mathrm{SMICA}}_{\text{clean}}^2\times unWISE$ points are offset by $\ell =50$ with respect to the true multipole moment values, for visual purposes. All analyses yield consistent results with one another, although the ${\mathrm{SMICA}}_{\text{clean}}^2$ results show some small differences, which are likely due to the tSZ residuals present in this map (hence why we do not use this map for our main analysis). Note that our main results from Fig. 5 are also shown here as the cyan, light green, and maroon points, and their consistency with the ${\mathrm{LGMCA}}_{\text{clean}}^2$ points validates the robustness of our analysis.