Direct detection of the kinetic Sunyaev-Zel'dovich effect in galaxy clusters

We report the direct detection of the kinetic Sunyaev-Zel'dovich effect in galaxy clusters with a 3.8 sigma significance level. The measurement is performed by stacking the Planck map at 217 GHz at the positions of galaxy clusters from the Wen-Han-Liu (WHL) catalog. To avoid the cancellation of positive and negative kSZ signals, we use the large scale distribution of the SDSS galaxies to estimate the peculiar velocities of the galaxy clusters along the line-of-sight and incorporate the sign in the (velocity weighted) stacking of the kSZ signals. Using this technique, we are able to measure the kSZ signal around galaxy clusters beyond 3R500. Assuming a standard beta-model, we also find that the gas fraction within R500 is f(gas,500) = 0.13 +- 0.03 for the clusters with the mass of M500 ~ 0.9 * 10^14 Msun/h, and is slightly lower than the universal baryon fraction. We compare this result to predictions from the Magneticum cosmological hydrodynamic simulations as well as other kSZ and X-ray measurements, where most of them show a lower gas fraction than the universal value for the same mass of clusters.


Introduction
Galaxy clusters are the largest gravitationally bound structures in the Universe and have been used as probes of cosmology and astrophysics. These massive objects imprint their signature on the cosmic microwave background (CMB) through the Sunyaev-Zel'dovich (SZ) effect (Sunyaev & Zeldovich 1970, 1972, 1980. The SZ effect is caused by the scattering of CMB photons by hot, ionized plasma in the intra-cluster medium (ICM), giving rise to a change in the CMB temperature. The SZ effect can be classified into two contributions: the thermal Sunyaev-Zel'dovich (tSZ) and kinetic Sunyaev-Zel'dovich (kSZ) effect (e.g Diaferio et al. 2000).
The tSZ effect is caused by the scattering of CMB photons by free electrons with thermal motions in the objects, resulting in a characteristic spectral distortion to the CMB blackbody spectrum. It allows to trace gas pressure in the objects, and has been well characterized through measurements on individual massive clusters (e.g., Plagge et al. 2010;Bonamente et al. 2012;Sayers et al. 2013a;Ade et al. 2013a;Romero et al. 2015) and statistical measurements on massive to low-mass systems (e.g. Ade et al. 2013b;Greco et al. 2015;Vikram et al. 2017;Hill et al. 2018;Lim et al. 2018;Tanimura et al. 2019Tanimura et al. , 2020. The kSZ effect, in turn, is caused by the scattering of CMB photons off the electrons due to the object's bulk motion, leading to a Doppler shift of the CMB blackbody spectrum. While it is elusive due to its small amplitude and identical spectral shape to the CMB spectrum, kSZ has a great potential to constrain both cosmological and astrophysical models. From a cosmological point of view, peculiar velocities of galaxy clusters are given through measurements of the kSZ effect and they allow to estimate the amplitude of the growth rate of density fluctuations, which then help to constrain models of dark energy (Bhattacharya & Kosowsky 2008;Ma & Zhao 2014), modified gravity (Mueller et al. 2015a;Bianchini & Silvestri 2016) and massive neutrinos (Mueller et al. 2015b). From an astrophysical point of view, there is a debate whether a significant fraction of diffuse gas is present around halos as a circumgalactic medium, or whether the gas once expelled due to feedback processes such as star formation, supernovae and active galactic nuclei (AGN) is never accreted onto the halos (e.g., Ade et al. 2013b;Anderson et al. 2015;Le Brun et al. 2015). Since the kSZ effect is sensitive to the virialized gas and also to the gas surrounding halos, independent of the gas temperature (unlike the tSZ effect), it is well suited to study these baryons through the distribution of gas around galaxy clusters.
The detection of the kSZ signal has so far been made for a few individual systems (e.g., Sayers et al. 2013b;Adam et al. 2017) or by statistical measurements based on the pairwise method (e.g., Hand et al. 2012;Hernández-Monteagudo et al. 2015;Ade et al. 2016b;Soergel et al. 2016;De Bernardis et al. 2017) or cross-correlation method (Hill et al. 2016). However, the reported significance of these detections is limited to ∼2-4σ. To extract the kSZ signal, most of these statistical measurements rely on a matched filter (e.g., Soergel et al. 2016;Lim et al. 2020) or aperture photometry (e.g., Hernández-Monteagudo et al. 2015;Ade et al. 2016b;Schaan et al. 2016;De Bernardis et al. 2017;Sugiyama et al. 2018). However, due to the large uncertainty in the gas density profile in galaxy clusters, the kSZ signal extracted by a matched filter can be biased if the assumed profile is incorrect (Ferraro & Hensley 2015). Aperture photometry has a less dependence on the density pro-Article number, page 1 of 11 arXiv:2007.02952v1 [astro-ph.CO] 6 Jul 2020 A&A proofs: manuscript no. ksz file, however the extracted signal level changes depending on the aperture size due to the varying signal-to-noise on its size.
In present analysis, to extract the kSZ signal, we use a stacking method without making any assumption about the spatial distribution of gas around galaxy clusters nor setting any aperture. To avoid a cancellation of the kSZ signals when all the clusters are simply stacked, we estimate the peculiar velocities of the galaxy clusters along the line-of-sight (LOS), with which the sign of the kSZ signals is attributed during the stacking. The paper is organized as follows. Section 2 summarizes data sets used in our analyses. Section 3 explains the velocity reconstruction of galaxy clusters. Section 4 explains the stacking method to extract the kSZ signals. Possible systematic errors in our measurements are discussed in Section 5. The interpretation of the measurements is presented in Section 6. We end this paper with discussions and conclusions in Section 7 and Section 8.
Throughout this work, we adopt the ΛCDM cosmology in Komatsu et al. (2011) with Ω m = 0.272, Ω b = 0.046, and H 0 = 70.4 km s −1 Mpc −1 . The cosmological parameters are used to estimate peculiar velocities of galaxy clusters and distances to them, and our result may depend on the assumed cosmological parameters. However, we perform our data analysis with Planck cosmology in Ade et al. (2016a), and obtain consistent results. All masses are quoted in solar mass, and M ∆ is mass enclosed within a sphere of radius R ∆ such that the enclosed density is ∆ times the critical density at redshift z. Uncertainties are given at the 1σ confidence level. Wen et al. (2012) and Wen & Han (2015) identified a total of 158,103 Wen-Han-Liu galaxy groups and clusters from the SDSS galaxies in the redshift range between 0.05 and 0.8, of which 89% have spectroscopic redshifts (hereafter WHL galaxy cluster). The masses of the WHL galaxy clusters are estimated by the total luminosities and are calibrated by the masses of 1191 clusters estimated by X-ray or tSZ measurements. In our study, we use 30,431 WHL galaxy clusters that have spectroscopic redshifts at 0.25<z<0.55 and masses of M 500 > 10 13.5 h −1 M (see Sect. 4.2).

Galaxy catalog
The SDSS galaxies in Reid et al. (2016) are composed of 953,193 galaxies in the northern galactic hemisphere and of 372,542 in the southern galactic hemisphere, combining the LOWZ and CMASS galaxies. The completeness of the galaxies is stated to be 99% for CMASS and 97% for LOWZ. Spectroscopic information is available for all the galaxies and their redshifts extend up to z ∼ 0.8. We use the galaxies to compute the galaxy density field, which is then used to estimate peculiar velocities of the WHL clusters. To avoid a bias in the velocity calculation due to the magnitude limit at different redshifts, we limit our analysis to the range of 0.25<z<0.55, in which the number density of the galaxies in the survey volume is fairly flat (see Fig. 11 in Reid et al. 2016).

Planck maps
Planck produced all-sky maps in nine frequency bands from 30 to 857 GHz with the angular resolutions ranging from 31' to 5'. In our study for the detection of kSZ signal, we mainly use the 217 GHz frequency map from the Planck 2018 data release (Aghanim et al. 2018), since it corresponds to the null frequency of the tSZ effect. We also use, for comparison, the Planck CMB maps produced by four different component separation methods (Akrami et al. 2018): COMMANDER (Optimal Monte-carlo Markov chAiN Driven EstimatoR) (Eriksen et al. 2004(Eriksen et al. , 2008, NILC (Needlet Internal Linear Combination) (Delabrouille et al. 2009), SEVEM (Spectral estimation via expectation maximisation) (Martínez-González et al. 2003;Leach et al. 2008;Fernández-Cobos et al. 2012), and SMICA (Spectral Matching Independent Component Analysis) (Delabrouille et al. 2003;Cardoso et al. 2008). These maps are provided in HEALpix 1 format (Górski et al. 2005) with a pixel resolution of N side = 2048 (∼ 1.7 arcmin). To minimize the Galactic and extragalactic contamination, we apply the mask produced by the Planck team for the analysis of the CMB temperature maps, which also masks all the point sources detected at all the frequencies (see Table C.1 in Akrami et al. 2018). In addition, we use the sky mask provided by the Planck team for the analysis of the Compton y maps (Aghanim et al. 2016a), excluding the region around the Galactic plane and point sources. Combining these two masks excludes ∼50% of the sky.

Magneticum simulation
The Magneticum simulations are one of the largest cosmological hydrodynamical simulations (Hirschmann et al. 2014;Dolag 2015), based on the standard ΛCDM cosmology from Komatsu et al. (2011) with Ω m = 0.272, Ω b = 0.046, and H 0 = 70.4 km s −1 Mpc −1 . They provide several public data 2 (Ragagnin et al. 2017), of which we use the simulated kSZ lightcone map with an area of ∼1600 deg 2 (hereafter Magneticum lightcone). The corresponding cluster catalog with M 500 > 3 × 10 13 h −1 M at z 2 is also provided (Dolag et al. 2016;Soergel et al. 2018). In addition, they also provide the post-processed data of galaxy catalog and cluster catalog from the full simulations with a cube box of 640 3 h −1 Mpc. We use the post-processed data of "Box2b_hr" at z ∼ 0.42 (hereafter Magneticum snapshot), corresponding to the median redshift in our analysis range.

Velocity reconstruction
The peculiar velocity of a galaxy cluster at the position, x, can be derived in the linear regime by where a is the scale factor, H(a) is the Hubble parameter, f (Ω) is the linear velocity growth rate given by f (Ω) Ω 0.545 m (Lahav et al. 1991;Wang & Steinhardt 1998;Linder 2005;Huterer & Linder 2007;Ferreira & Skordis 2010), and δ(y) is the overdensity of matter at the position y.
To compute the matter density field, δ(y), we use the galaxies in Sect. 2.2. Their redshift distances and J2000.0 coordinates are transformed into the comoving Cartesian coordinates: where α and δ refer to the J2000,0 right ascension and declination, respectively, and r(z) is the comoving distance at redshift z, with which a number density of galaxies is computed in the SDSS survey field. The galaxy density field can be connected to the matter density field by δ g = b δ through the galaxy bias, b. The galaxy bias was studied for the LOWZ galaxies (Parejko et al. 2013) and CMASS galaxies (White et al. 2011;Nuza et al. 2013;Rodríguez-Torres et al. 2016), showing b ∼ 2 at scales larger than 10 h −1 Mpc. Since a much larger scale of ∼240 h −1 Mpc, as later discribed, is considered in our study to calculate the peculiar velocity, we use b = 2. In practice, we place a galaxy cluster at the center in a cubic box of 240 3 h −1 Mpc, in which the box is divided by grid cells of 5 3 h −1 Mpc. If the cubic box for a galaxy cluster reaches the edge of the SDSS survey, we remove the galaxy cluster from our catalog because it may bias the velocity estimate. Then we place galaxies around the galaxy cluster in the box cells and calculate the overdensities of the galaxies. While finer grids may be better for the velocity estimate, we determine the size so that the grid size is large enough compared to the length expected from Redshift-space distortion (RSD): The RSD distortion for an typical velocity of 300 km/s is ∼3 h −1 Mpc at the redshift of interest in our analysis. Then the box cells are smoothed by a Gaussian kernel of 2 h −1 Mpc to remove sharp grid edges. By applying Eq. 1 to this cubic box, the peculiar velocity of a galaxy cluster can be obtained.
We check our velocity estimates of galaxy clusters using the Magneticum snapshot simulation, by comparing the computed velocities of the simulated galaxy clusters by Eq. 1 with the true velocities. To reproduce "real" data in the simulation, we remove the simulated galaxy clusters with M 500 < 10 13.5 h −1 M (minimum mass of the WHL clusters we use), and also remove the simulated galaxies with M * < 1.8×10 11 h −1 M , so that the number density of galaxies is same as the real data. In this simulation box, we calculate the 3D velocities of the simulated galaxy clusters and compare the velocities in the "LOS" direction, which is defined by placing an observer at the corner of the simulation box. In the comparison, we find that our velocity estimates are well correlated with the true ones as shown in Fig. 1 with an uncertainty of ∼180 km/s following a Gaussian distribution.
In addition, we check the effect of RSD on the velocity estimates using the Magneticum snapshot simulation, by including the RSD to the simulated galaxies. For simplicity, we do not reidentify galaxy clusters in the redshift space, but use the same galaxy clusters with their positions redshifted. Again by comparing the computed velocities of the simulated galaxy clusters with the true velocities, we find that our velocity estimates are well correlated with the true ones. An additional uncertainty of ∼80 km/s following a Gaussian distribution is found, but no significant bias is identified.

Analysis
To detect the kSZ signal, we apply a stacking method for the Planck HFI 217 GHz map or Planck CMB maps. However, due to the equal probability of positive or negative LOS velocity that cluster can have, the associated kSZ signal from clusters cancels out by a simple stacking. Therefore, to avoid the cancellation of equally likely positive and negative kSZ signals, we first perform the stacking after separating galaxy clusters depending on the directions of the LOS velocities estimated in Sect. 3.
In this paper, we define "positive" LOS direction as a radial direction from us: a positive motion is the motion moving away from us and a negative motion is the motion approaching us. It follows that when a galaxy cluster has a positive motion, the CMB is redshifted, resulting in a negative kSZ signal. On the other hand, when a galaxy cluster has a negative motion, the CMB is blueshifted, resulting in a positive kSZ signal.
Then the stacking is also performed for each cluster weighted by the LOS velocity. A positive kSZ signal weighted by a negative LOS velocity then has a negative signal and a negative kSZ signal weighted by a positive LOS velocity also has a negative signal. This allows to set the kSZ signal to a negative value, while other components are canceled out by the positive or negative LOS velocity with equal probability.

Filtering CMB
The amplitude of the kSZ signal around galaxy clusters is of order of ∼1 uK dominated by the primordial CMB fluctuations of order of ∼ 50 uK. To extract the kSZ signal, present at the cluster scales, i.e. small angular scales, we apply a spatial filter to the Planck maps. The angular size of the virial radius of the WHL galaxy clusters is 2.2 -10.5 arcmin. Therefore, we filter out angular scales above 15 arcmin ( ∼ 720) in Fourier space, using a smooth function with its response of one below 15 arcmin ( ∼720) and zero above 30 arcmin ( ∼360). The effect of the filter is shown in Fig. 2 for a simulated power spectrum of the primordial CMB fluctuations. With this filter, the standard deviation of the primordial CMB fluctuations is reduced to ∼ 40 uK.

Stacking
We stack the filtered Planck maps at the positions of the WHL galaxy clusters and construct the stacked radial profile. In practice, we place a galaxy cluster at the center of 2-dimensional grids in "scaled" angular distance in the range of −10 < θ/θ 500 < 10, divided into 10 × 10 bins, where θ 500 is the angular radius of a galaxy cluster calculated with R 500 provided in the catalog. The Planck maps are scaled accordingly and data are placed on the 2dimensional grids, while data in the masked region are not used. In this process, if more than 20% of the region within 10 × θ 500 around a galaxy cluster is masked, the galaxy cluster is removed from our catalog, because a large mask may bias our measured A&A proofs: manuscript no. ksz profile. We repeat this for the selected 30,431 galaxy clusters and compute the stacked radial profile. In the upper left panel of Fig. 3, the stacked radial profile of the galaxy clusters using the Planck HFI 217 GHz map is shown in black. The stacked profile includes all the Galactic and extragalactic emissions at the frequency, in which the cosmic infrared background (CIB) is dominant at small scales as shown in Appendix A. In this step, no velocity weighting is applied and hence positive and negative kSZ signals are canceled out.
To extract the kSZ signals of the galaxy clusters, we stack the galaxy clusters with positive (16,338 clusters) and negative (14,093 clusters) LOS motions separately. As expected, the original stacked profile with all the galaxy clusters (30,431 clusters) is separated into two: one with stacked positive kSZ signal as shown in black dash-dotted line in the upper left panel of Fig. 3 and the other with stacked negative kSZ signal as shown in black dashed line. Since, in these profiles, the Galactic and extragalactic components are included with the same amount on average, we can extract the kSZ signals by taking the differences of the two separated profiles relative to the original one, shown in blue and red line in the lower left panel of To confirm whether the separated signals are originated from the kSZ or not, we check the correlation between the amplitude of the separated signals and the LOS velocity, which is only expected for the kSZ but not for other components such as CMB, CIB and tSZ. In the upper middle and right panel of Fig. 3, the stacking is performed for the galaxy clusters with the absolute LOS velocity larger than 100 km/s or 200 km/s, and the separated signals are shown in blue and red in the lower panels. The results show that the amplitude of the separated signals increases along with the amplitude of the velocity cut. This trend clearly supports that the separated signals are originated from the kSZ.
We assess the uncertainties of the stacked profile through bootstrap resampling. We draw a random sampling of the galaxy clusters with replacement and re-calculate one stacked profile for the new set of galaxy clusters. We repeat this process 1,000 times and produce the bootstrapped 1,000 stacked profiles, with which the covariance between different radial bins are computed. In Fig. 3, the 1σ statistical uncertainty is represented via the width of the lines, which is a square root of diagonal terms of the covariance matrix.

Comparison with hydrodynamic simulations
We compare our measured kSZ signal with predictions from the Magneticum hydrodynamic simulation. For comparison, we perform the same stacking analysis with the simulated kSZ map and galaxy clusters from the Magneticum lightcone simulation, as we did with the real data. The mass and redshift distribution of the simulated galaxy clusters are matched to the real data. However, since a galaxy catalog is not provided in the Magneticum lightcone simulation, we add uncertainties to the LOS velocities of the simulated galaxy clusters randomly using a Gaussian function with the standard deviation of 260 km/s (see Sect. 3). Based on the LOS velocities including the uncertainties, the simulated galaxy clusters are separated according to their positive or negative motions and they are stacked with the simulated kSZ map separately. (Some cancellation of the kSZ signal due to the uncertainties of the LOS velocities are included in the kSZ profile from the simulation as in the real data.) The result is shown in green dashed line in Fig. 4 and compared to the data profile. In the left panel, we see that our measured kSZ profiles with positive and negative LOS motions are consistent with the ones from the simulation. We also apply additional LOS-velocity cuts of 100 km/s or 200 km/s to the simulated galaxy clusters in the middle and right panel, respectively. Our measured kSZ profiles show a similar amount of correlation between the amplitude of the kSZ signal and LOS velocity with the predictions from the simulation.

Null tests and significance
To estimate the significance of the detected kSZ signal from the 30,431 WHL galaxy clusters, we stack the filtered Planck maps at the positions of the clusters in the same way, as described above, with each cluster weighted by the LOS velocity as where T i (R) is the temperature value of i-th cluster at the radial distance, R, and i,LOS is the LOS velocity of i-th cluster. In this process, the kSZ signals with positive and negative LOS velocities end up with the same sign: a positive kSZ signal weighted by a negative LOS velocity has a negative signal and a negative kSZ signal weighted by a positive LOS velocity also has a negative signal. Therefore, the kSZ signals can be stacked without suffering any cancellation, while other components are canceled out. In addition, a cluster with a low LOS velocity (that is, a weaker kSZ signal) is underweighted in the stacking. The stacked radial profile with the additional weight is shown in Fig. 5 with the uncertainties estimated by bootstrap. A coherent angular pattern is seen, which is mainly due to our filter coupling with kSZ and CMB (as seen later in the null test in Fig. 6 and the model profile in Fig. 7). We will evaluate this velocity-weighted kSZ profile from now on. We perform a Monte Carlo-based null test to assess the significance of our measurements. In the null test, we displace the centers of the galaxy clusters at random positions on the sky and then the Planck maps are stacked at these random positions. We repeat this 1000 times to assess the rms fluctuations of the foreground and background signals. The result shows that the average of the null-test profiles is consistent with zero, as shown in   Fig. 6 with the rms fluctuations. This suggests that our measurements are unbiased. We see the same coherent angular pattern in the null test as seen in the data profile in Fig. 5, which is due to our filter coupling with CMB.
We estimate the significance of the measured kSZ signal to the null hypothesis. The signal-to-noise ratio (S/N) can be estimated as where where T data (R i ) is the temperature value at the R i bin of the data kSZ profile, T null (R i ) is the temperature value at the R i bin of the null-test profile, and C i j is the covariance matrix of the data profile, estimated by the bootstrap resampling. By measuring the kSZ signal up to 4 × θ 500 , the S/N value is estimated to be 3.8σ.

Systematics
In this section, we perform multiple tests to estimate potential systematics in our measurements. We performed one null test by displacing the galaxy clusters at random positions on the Planck maps in Sect. 4.4. We also carry out additional null tests in this section. Subsequently, we check the contamination in our measured kSZ signals due to the CMB, tSZ and CIB, respectively.

Additional null tests
We perform two additional null tests as follows: -We randomly shuffle the LOS velocities of the galaxy clusters, then the clusters are stacked with weights based on the shuffled LOS velocities. This is done to test the effect of correlation between LOS velocities and clusters. One shuffling may not be enough to remove the correlation, therefore we repeat the random velocity shuffling 1,000 times and evaluate the mean and standard deviation of the 1,000 stacked profiles with shuffled velocities. -We perform the stacking with a noise map produced by (T HM1 217 − T HM2 217 )/2, where T HM1 (2) 217 is the half mission 1(2) Planck map at 217 GHz.
The associated results are shown in the middle (yellow) and right (green) panel of Fig. 6 with the uncertainties. As expected, the obtained profiles are both consistent with zero. Including the null test performed in Sect. 4.4, all three null tests suggest that our measurements of the kSZ effect are unbiased.

Contamination from Galactic and extragalactic emissions
The kSZ signal is only a subdominant component and the measurement may be contaminated by Galactic as well as extragalactic emissions such as CMB, tSZ and CIB. The CMB, the Galactic emissions and instrumental noises are uncorrelated with cluster positions and they are added as noise in our measurements. The tSZ and CIB are correlated with clusters, but it can be assumed that they are uncorrelated with their LOS velocities and canceled out in our analysis. As a whole, no bias is expected due to other components. For a further check, we compare the kSZ signal extracted with the Planck 217 GHz map to the kSZ signals extracted with the Planck CMB maps produced by different component separation methods such as NILC, SMICA, SMICA-noSZ, SEVEM and COMMANDER. Note that the Galactic and extragalactic components are not cleaned in the Planck 217 GHz map, but cleaned in the Planck CMB maps. The extracted kSZ signals are all consistent as shown in Fig. 5, regardless of the maps we analyze with or without the Galactic and extragalactic components. This result suggests that the contamination to our measurements from the Galactic and extragalactic components is minor.

Contamination of the CMB
While we have shown that the contamination to our measured kSZ signals from the Galactic and extragalactic components is minor, the contamination from the CMB may still be present at some level. This is because our null tests performed by the random displacements and velocity shuffling of galaxy clusters show statistically no bias by considering 1,000 realizations, but the CMB is one realization in real and the cancellation by stacking may not be sufficient for the real CMB. Therefore we estimate a possible level of contamination only from the CMB by simulating 100 CMB maps with different realizations using the PYCAMB 3 interface to the CAMB 4 code (Lewis et al. 2000). We repeat our stacking analysis for the simulated 100 CMB maps, producing 100 CMB profiles. The mean of the 100 CMB profiles is consistent with zero and its standard deviation is ∼ 18% of the amplitude of our measured kSZ signal. Thus, while the CMB contamination may be present at some level, it should not be significant.

Contamination of the tSZ
The contamination of the tSZ can also be estimated quantatively by applying our stacking analysis to the Planck all-sky y maps provided in the Planck 2015 data release 5 (Aghanim et al. 2016a). We use the y map from the modified internal linear combination algorithm (MILCA) (Hurier et al. 2013), but the result is consistent using the y map from needlet independent linear combination (NILC) (Remazeilles et al. 2013). The Compton y parameter in the Planck HFI 217 GHz map can be calculated with its frequency dependence, given by where g(ν) = x coth(x/2) − 4 with x = hν/(k B T CMB ), h is the Planck constant, k B is the Boltzmann constant and T CMB is the CMB temperature. At 217 GHz, T CMB g(ν) = 0.187 is given in Aghanim et al. (2016a) for the conversion from the Compton y parameter to CMB temperature. The result of stacking the y map shows that the tSZ contamination is ∼1% of the amplitude of our measured kSZ signal and hence negligible.

Contamination of the CIB
Similarly, we estimate the level of contamination from the CIB by stacking the Planck all-sky CIB maps provided in Aghanim et al. (2016b). However, since the CIB map at 217 GHz was not produced, we scaled the Planck CIB map at 353 GHz to the one at 217 GHz with the power-law spectral index of β ∼ 1.1 (Tucci et al. 2016). The result of stacking the CIB map shows that the CIB contamination is ∼8% of the amplitude of our measured kSZ signal and not significant. Hideki Tanimura et al.: Direct detection of the kinetic Sunyaev-Zel'dovich effect in galaxy clusters Fig. 6. Velocity-weighted kSZ radial profile around the 30,431 WHL clusters with the Planck temperature map at 217 GHz (black), compared to three null tests. In left panel, the clusters are displaced at random positions on the Planck map, and then stacked. This process is repeated 1,000 times and the mean of the 1,000 random samples is computed (cyan). The 1σ uncertainty is estimated by computing a standard deviation of the 1,000 random sample. In middle panel, the LOS velocities of the clusters are shuffled randomly and then the clusters are stacked. This process is repeated 1,000 times and the mean of the 100 velocity-shuffled profiles is computed (yellow). The 1σ uncertainty is estimated by computing a standard deviation of the 1,000 velocity-shuffled profiles. In right panel, the clusters are stacked with a noise map, produced by (T HM1 217 − T HM2 217 )/2, where T HM1 (2) 217 is the half mission 1(2) Planck map at 217 GHz (green). The 1σ uncertainty is estimated by a bootstrap resampling.

Interpretation
The CMB temperature fluctuation caused by the kSZ effect is given by where σ T is the Thomson scattering cross section, c is the speed of light, n e is the electron number density, v ·n represents the peculiar velocity of electrons along the line of sight. In the final transformation, the integral, τ = σ T n e dl, is performed along the line of sight under the approximation that the typical correlation length of LOS velocities (given by ·n) is much larger than the density correlation length, and thus the LOS velocity term can be pulled out of the kSZ integral. This is justified by Ade et al. (2016b) who found that the typical correlation length of peculiar velocities is 80-100 h −1 Mpc, well above the typical galaxy correlation length of ∼5h −1 Mpc. Physical properties of gas can be estimated by considering a β model (Cavaliere & Fusco-Femiano 1978) for a gas(electron) density profile, given by n e (r) = n e,0 1 + where n e,0 is the central electron density, r is the cluster radial extension, and r c is the core radius of the electron distribution. In our study, we use β = 0.86 and r c = 0.2 × R 500 from the measurements of the South Pole Telescope clusters (Plagge et al. 2010). We can express the data profile as a geometrical projection of the density profile with n e (r), where R is the tangential distance from a galaxy cluster. (We express the 3D distance with a lowercase letter r, and the 2D distance on a map with an uppercase letter R.) We fit this model to the measured kSZ profile by using the average of the LOS velocities (in absolute value) of the WHL galaxy clusters estimated in Sect. 3. However, the average velocity is overestimated due to the uncertainties of the LOS velocities. (The Gaussian distribution of the estimated LOS velocities have a larger standard deviation than the distribution of the true LOS velocities due to the uncertainties.) The average velocity can be corrected with the uncertainty of the LOS velocities investigated in Sect. 3. The uncertainty of the LOS velocities also induces the decrease in the amplitude of the measured kSZ signal, because it causes some cancellation of the kSZ signal. This can be corrected analytically with the uncertainty of the LOS velocities estimated in Sect. 3. Including these corrections in the model, we fit the model to the data. The result of the model fitting is shown in red in Fig. 7. The reduced χ 2 value is 1.2. Note that we see a coherent angular pattern in the model profile similar to the data profile, which is due to our filter coupling with kSZ as described in Sect. 4.4. Defining the optical depth of a galaxy cluster within R 500 as τ e,500 = R 500 0 σ T n e (r) dV, the fitting result provides an average optical depth of the WHL clusters as τ e,500 = (2.0 ± 0.5) × 10 −3 .
Offsets between cluster centers from optical data and centers of gas distribution in clusters may have an impact on the estimated optical depth. In Rozo & Rykoff (2014), the offsets between X-ray cluster centers (proxy of gas center) and optical cluster centers were studied, and they showed that ∼ 70% of the WHL clusters have offsets less than ∼ 0.1 Mpc to X-ray clusters. The length corresponds to ∼ 0.2 arcmin at the median redshift of our sample (z ∼ 0.44) and smaller than the angular resolution of the Planck maps (∼ 5 arcmin). To check the contribution of this offset to the measurement of the optical depth, we randomly displace the centers of the WHL clusters by distances drawn from a Gaussian distribution with the standard deviation of ∼ 0.1 Mpc and repeat the stacking. The result shows that the amplitude of our measured kSZ profile decreases only by ∼ 1% and the effect is minor.
We can also estimate a total gas mass in a galaxy cluster defined as M gas,500 = R 500 0 n e (r) µ e m p dV, where µ e = 1.148 is the mean molecular weight of electrons (Arnaud et al. 2010), and m p is the mass of proton. Through Article number, page 7 of 11 A&A proofs: manuscript no. ksz our measurement of the optical depth, the average gas mass in the WHL clusters can be estimated to be M gas,500 ∼ 1.0 × 10 13 h −1 M . This provides the gas mass fraction of f gas,500 = M gas,500 /M 500 = 0.13 ± 0.03 for our sample with the average mass of M 500 ∼ 0.9 × 10 14 h −1 M . The Magneticum simulation also provides gas masses of the simulated clusters within R 500 , and it shows the gas mass of M gas,500 ∼ 1.2×10 13 h −1 M for the cluster with M 500 ∼ 0.9×10 14 h −1 M (average mass of our cluster sample). It corresponds to the gas mass fraction of f gas,500 ∼ 0.13 and is consistent with our result, f gas,500 = 0.13 ± 0.03.

Discussion
The kSZ effect is sensitive to cosmological parameters such as the growth rate of density perturbations. However, we find that our result is consistent using the WMAP and Planck cosmology and the current level of our kSZ detection does not allow to constrain cosmological parameters. Therefore we have used our measurement of the kSZ signal to constrain the average optical depth (or gas mass) of the cluster sample. Our result is compared to other measurements as follows.
Gas masses in groups and clusters of galaxies were studied in the X-ray by Gonzalez et al. (2013). They combined measurements with XMM-Newton and Chandra observations from Vikhlinin et al. (2006), Sun et al. (2009) andSanderson et al. (2013), and showed the X-ray gas fraction within R 500 as a function of M 500 . The relation shows f gas,500 ∼ 0.1 at M 500 ∼ 1.3 × 10 14 M (average mass of our sample), which is slightly lower than our result of f gas,500 = 0.13 ± 0.03, but consistent within our measurement uncertainties.
Gas in halos was studied with the kSZ in Ade et al. (2016b). They detected the pairwise kSZ signal at the positions of central galaxies from the SDSS DR7 data using the Planck and WMAP maps and measured an average optical depth of τ = (1.4 ± 0.5) × 10 −4 . This value is one order of magnitude lower then our value of τ e,500 = (2.0 ± 0.5) × 10 −3 , but it can be attributed to the difference in halo mass: the halo mass of their sample is M 500 ∼ 0.3 × 10 14 M and it is significantly lower than the average mass of our sample, M 500 ∼ 1.3 × 10 14 M .
A similar study to Ade et al. (2016b) was performed with the kSZ in Soergel et al. (2016) using clusters with photometric redshifts. They detected the pairwise kSZ signal by combining a cluster catalog from the Dark Energy Survey (DES) with the CMB map from the South Pole Telescope Sunyaev-Zel'dovich Survery (SPT-SZ) and measured an average optical depth of τ = (3.75 ± 0.89) × 10 −3 for the clusters with M 500 ∼ (1 − 3) × 10 14 M . This value is higher than our value of τ e,500 = (2.0 ± 0.5) × 10 −3 , but it may be again related to the difference in mass: the average mass of our cluster sample, M 500 ∼ 1.3×10 14 M , corresponds to the lower end of their cluster mass range. They also estimated the gas mass fraction within R 500 to be f gas,500 = 0.08 ± 0.02 assuming a β model for the density distribution. Our value of f gas,500 = 0.13 ± 0.03 is slightly higher than their result, but consistent within ∼ 1.4σ when we consider the uncertainties of both measurements. Lim et al. (2020) also detected the kSZ signals from galaxy groups and cluster in the mass range of 2 × 10 12 M < M 500 < 2 × 10 14 M by combining the cluster catalog from Yang et al. (2007) and the Planck frequency maps at 100, 143 and 217 GHz. Surprisingly, their results show that the gas fraction in halos is about the universal baryon fraction in their cluster mass range ( f gas ∼ 0.17). To compare with their results, we convert our measurements to their estimator of K 500 , which is the intrinsic kSZ signal, scaled to redshift z = 0 and to a fixed angular diameter distance. Our value translates into K 500 = (0.9 ± 0.3) × 10 −2 at M 500 ∼ 1.3 × 10 14 M , and the value is lower than their value by more than 1σ.
The gas mass fraction in halos, estimated with the kSZ signals in Lim et al. (2020), is relatively higher than our result. In addition, their result is not consistent with those of Soergel et al. (2016) and the X-ray measurements by Gonzalez et al. (2013). One possibility may be due to the filter they use to extract the kSZ signals. Indeed, Lim et al. (2020) used a matched filter to extract the kSZ signal, which may induce a bias, if the assumed profile is incorrect (Ferraro & Hensley 2015). However, given the large Planck beam, they did not find a significant bias in their results by testing with an incorrect profile. In addition, while they assume the β profile from Plagge et al. (2010), we used the same β profile and find that it fits well our measured kSZ profiles with the minimum χ 2 of 1.2. Therefore, the assumed profile does not explain the difference. On the other hand, our measured kSZ profiles show extended kSZ signal beyond R 500 and it does not seem to match the Lim et al. (2020)'s result that the gas fraction within R 500 of halos is about the universal baryon fraction. However, the beam of the Planck maps (∼ 5 arcmin) is equivalent to the average angular size of our cluster sample (∼ 4 arcmin) and it prevents a definitive conclusion. Another possibility to explain the different results may be due to the difference of cluster redshifts. Lim et al. (2020) study a cluster sample at z < 0.12, while our sample is at z ∼ 0.44 and the sample in Soergel et al. (2016) is at z ∼ 0.5. Thus, the evolution of the gas in halos may explain the difference in the kSZ measurements. However the X-ray measurement in Gonzalez et al. (2013) also study local clusters at z ∼ 0.1 and the evolution does not seem to explain the difference. So far, the reason of the difference is unknown. To confirm it, measurements of gas in common halos with multiple probes would be needed.

Conclusion
In this paper, we have presented the first direct detection of the kSZ signal with a significance of 3.8σ. The measurement is per-formed by stacking the Planck temperature map at 217 GHz from the Planck 2018 data release at the positions of Wen-Han-Liu (WHL) galaxy clusters constructed from the SDSS galaxies. If all the clusters are simply stacked, the kSZ signals are canceled out due to the equal probability of clusters to show positive or negative kSZ signals. To avoid this cancellation, we estimate the peculiar velocities of the galaxy clusters along the LOS through the galaxy density field computed from the SDSS galaxies, which is related to the matter density field with the galaxy bias, b = 2, estimated in other studies. Using the LOS velocities as a weight in the stacking, the positive and negative kSZ signals are turned to the same sign and added up, while other components are canceled out by the positive or negative LOS velocity with equal probability. The measured kSZ signals show a clear correlation with the amplitude of the LOS velocities. As a result of the stacking, we obtain the average kSZ profile of the galaxy clusters with the mass of M 500 ∼ 0.9 × 10 14 h −1 M , showing an extended distribution of gas around the galaxy clusters beyond 3 × R 500 .
The kSZ signal is a subdominant component and our measurement may be contaminated by the Galactic and extragalactic emissions. The CMB, the Galactic emissions and instrumental noise are uncorrelated with cluster positions and they are added as noise in our measurements. The tSZ and CIB are correlated with clusters, but uncorrelated with their LOS velocities. We perform three different null tests. All the null tests are consistent with zero indicating that our measurements are unbiased. Possible level of contamination from the CMB, tSZ and CIB are also investigated and we do not find any significant contamination from these components.
Based on our kSZ measurement, we estimate the average optical depth and find τ e,500 = (2.0 ± 0.5) × 10 −3 for clusters with the mass of M 500 ∼ 0.9 × 10 14 h −1 M assuming a β model. It provides an average gas mass of the galaxy clusters to be M gas,500 ∼ 1.0 × 10 13 h −1 M , leading to the gas fraction of f gas,500 = 0.13 ± 0.03 within R 500 . We compare our results with the Magneticum hydrodynamic simulations and find a consistent result. We also compare our measurement of gas mass fraction for the clusters with the mass of M 500 ∼ 0.9 × 10 14 h −1 M with the result using X-rays (Gonzalez et al. 2013) and kSZ (Soergel et al. 2016). All these results show that the gas mass fraction is slightly lower than the cosmic baryon fraction. However, the result in Lim et al. (2020) show that the gas fraction in halos is about the universal baryon fraction down to the mass of 2 × 10 12 M . The reason of the difference is so far unknown, and measurements of gas in common halos with multiple probes would be needed to confirm it.