A&A 617, A48 (2018) Astronomy https://doi.org/10.1051/0004-6361/201731489 & c ESO 2018 Astrophysics
Planck intermediate results LIII. Detection of velocity dispersion from the kinetic Sunyaev-Zeldovich effect
Planck Collaboration: N. Aghanim48, Y. Akrami50,51 , M. Ashdown58,4 , J. Aumont83, C. Baccigalupi70, M. Ballardini17,35 , A. J. Banday83,7 , R. B. Barreiro53, N. Bartolo23,54 , S. Basak75, R. Battye56, K. Benabed49,82 , J.-P. Bernard83,7 , M. Bersanelli26,39 , P. Bielewicz68,7,70 , J. R. Bond6, J. Borrill9,80 , F. R. Bouchet49,77 , C. Burigana38,24,41 , E. Calabrese73, J. Carron18, H.C. Chiang20,5 , B. Comis61, D. Contreras16, B. P. Crill55,8 , A. Curto53,4,58 , F. Cuttaia35, P. de Bernardis25, A. de Rosa35, G. de Zotti36,70 , J. Delabrouille1, E. Di Valentino49,77 , C. Dickinson56, J. M. Diego53, O. Doré55,8 , A. Ducout49,47 , X. Dupac29, F. Elsner65, T. A. Enßlin65, H. K. Eriksen51, E. Falgarone60, Y. Fantaye2,15 , F. Finelli35,41 , F. Forastieri24,42 , M. Frailis37, A. A. Fraisse20, E. Franceschi35, A. Frolov76, S. Galeotta37, S. Galli57, K. Ganga1, M. Gerbino81,69,25 , K. M. Górski55,84 , A. Gruppuso35,41 , J. E. Gudmundsson81,20 , W. Handley58,4 , F. K. Hansen51, D. Herranz53, E. Hivon49,82 , Z. Huang74, A. H. Jaffe47, E. Keihänen19, R. Keskitalo9, K. Kiiveri19,34 , J. Kim65, T. S. Kisner63, N. Krachmalnicoff70, M. Kunz11,48,2 , H. Kurki-Suonio19,34 , J.-M. Lamarre60, A. Lasenby4,58 , M. Lattanzi24,42 , C. R. Lawrence55, M. Le Jeune1, F. Levrier60, M. Liguori23,54 , P. B. Lilje51, V. Lindholm19,34 , M. López-Caniego29, P. M. Lubin21, Y.-Z. Ma56,72,67, ?, J. F. Macías-Pérez61, G. Maggio37, D. Maino26,39,43 , N. Mandolesi35,24 , A. Mangilli7, P. G. Martin6, E. Martínez-González53, S. Matarrese23,54,31 , N. Mauri41, J. D. McEwen66, A. Melchiorri25,44 , A. Mennella26,39 , M. Migliaccio79,45 , M.-A. Miville-Deschênes48,6 , D. Molinari24,35,42 , A. Moneti49, L. Montier83,7 , G. Morgante35, P. Natoli24,79,42 , C. A. Oxborrow10, L. Pagano48,60 , D. Paoletti35,41 , B. Partridge33, O. Perdereau59, L. Perotto61, V. Pettorino32, F. Piacentini25, S. Plaszczynski59, L. Polastri24,42 , G. Polenta3, J. P. Rachen14, B. Racine51, M. Reinecke65, M. Remazeilles56,48,1 , A. Renzi70,46 , G. Rocha55,8 , G. Roudier1,60,55 , B. Ruiz-Granados52,12 , M. Sandri35, M. Savelainen19,34,64 , D. Scott16, C. Sirignano23,54 , G. Sirri41, L. D. Spencer73, L. Stanco54, R. Sunyaev65,78 , J. A. Tauber30, D. Tavagnacco37,27 , M. Tenti40, L. Toffolatti13,35 , M. Tomasi26,39 , M. Tristram59, T. Trombetti38,42 , J. Valiviita19,34 , F. Van Tent62, P. Vielva53, F. Villa35, N. Vittorio28, B. D. Wandelt49,82,22 , I. K. Wehus55,51 , A. Zacchei37, and A. Zonca71 (Affiliations can be found after the references)
Received 2 July 2017 / Accepted 12 June 2018
ABSTRACT
Using the Planck full-mission data, we present a detection of the temperature (and therefore velocity) dispersion due to the kinetic Sunyaev- Zeldovich (kSZ) effect from clusters of galaxies. To suppress the primary CMB and instrumental noise we derive a matched filter and then convolve it with the Planck foreground-cleaned “2D-ILC ” maps. By using the Meta Catalogue of X-ray detected Clusters of galaxies (MCXC), we determine the normalized rms dispersion of the temperature fluctuations at the positions of clusters, finding that this shows excess variance compared with the noise expectation. We then build an unbiased statistical estimator of the signal, determining that the normalized mean temperature dispersion of 1526 clusters is h(∆T/T)2i = (1.64 ± 0.48) × 10−11. However, comparison with analytic calculations and simulations suggest that around 0.7 σ of this result is due to cluster lensing rather than the kSZ effect. By correcting this, the temperature dispersion is measured to be h(∆T/T)2i = (1.35 ± 0.48) × 10−11, which gives a detection at the 2.8 σ level. We further convert uniform-weight temperature dispersion into a measurement of the line-of-sight velocity dispersion, by using estimates of the optical depth of each cluster (which introduces additional uncertainty into the estimate). We find that the velocity dispersion is hv2i = (123 000 ± 71 000) ( km s−1)2, which is consistent with findings from other large-scale structure studies, and provides direct evidence of statistical homogeneity on scales of 600 h−1 Mpc. Our study shows the promise of using cross-correlations of the kSZ effect with large-scale structure in order to constrain the growth of structure. Key words. cosmic background radiation – large-scale structure of Universe – galaxies: clusters: general – methods: data analysis
1. Introduction CMB maps from the Atacama Cosmology Telescope (ACT). The detection of the kSZ effect has been further solidified using The kinetic Sunyaev-Zeldovich (hereafter kSZ; Sunyaev & Zeldovich 1972, 1980) effect describes the temperature aniso- the same pairwise momentum estimator with other CMB data, tropy of the cosmic microwave background (CMB) radiation including Wilkinson Microwave Anisotropy Probe (WMAP) due to inverse Compton scattering of CMB photons off a mov- 9-year W-band data, and Planck’s four foreground-cleaned maps ing cloud of electrons. The effect can be written as (Planck Collaboration Int. XXXVII 2016), and again more re- Z cently using a Fourier space analysis (Sugiyama et al. 2018). ∆T σT These measurements represent detections at the 2–3 σ level. In (rˆ) = − n (u · rˆ) dl, (1) T c e addition, De Bernardis et al.(2017) applied the pairwise mo- mentum estimator to the ACT data and 50 000 bright galaxies where σT is the Thomson cross-section, ne is the electron den- from BOSS DR11 catalogue, and obtained 3.6–4.1 σ C.L. de- sity, u · rˆ is the velocity along the line-of-sight, and dl is the tection. By using the same estimator to the South Pole Telescope path length in the radial direction. By adopting a so-called (SPT) data and Dark Energy Survey (DES) data, Soergel et al. “pairwise momentum estimator,” i.e., using the weights that (2016) achieved the detection of kSZ signal 4.2 σ C.L. More quantify the difference in temperature between pairs of galax- recently Li et al.(2018) detected the pairwise kSZ signal for ies, the effect was first detected by Hand et al.(2012) using 12 −1 BOSS DR13 low mass group (Mh . 10 h M ) by using the ? Corresponding author: Y.-Z. Ma, [email protected] 2D-ILC map (see Sect. 2.1.2). Besides the pairwise momentum
Article published by EDP Sciences A48, page 1 of 17 A&A 617, A48 (2018) estimator, in Planck Collaboration Int. XXXVII(2016) the kSZ field h∆T(u· nˆ)i, obtaining direct evidence of unbound gas outside temperature map (δT) was estimated from Planck full-mission the virial radii of the clusters. A follow-up paper modelled these data and cross-correlated with the reconstructed linear velocity results to reconstruct the baryon fraction and suggested that this field data (u · nˆ) from the Sloan Digital Sky Survey (SDSS-DR7) unbound gas corresponds to all baryons surrounding the galaxies to compute the correlation function h∆T(u · nˆ)i. For this cross- (Hernández-Monteagudo et al. 2015). Even though the large- correlation, 3.0–3.2 σ detections were found for the foreground- scale bulk flow and monopole flow were not detected in Planck cleaned Planck maps, and 3.8 σ for the Planck 217-GHz Collaboration Int. XIII(2014), the small-scale velocity dispersion map. Following Planck Collaboration Int. XXXVII(2016), in the nearby Universe, determined by the local gravitational Schaan et al.(2016) detected the aggregated signal of the kSZ potential field, might still be measurable. This is because the effect at 3.3 σ C.L. by cross-correlating the velocity field from velocity of each galaxy comprises two components, namely the BOSS samples with the kSZ map produced from ACT obser- bulk flow components, which reflect the large-scale perturba- vations. More recently, Hill et al.(2016) cross-correlated the tions, and a small-scale velocity dispersion component, which squared kSZ fields from WMAP and Planck, and the projected reflects perturbations due to the local gravitational potential galaxy overdensity from the Wide-field Infrared Survey Explorer (see, e.g., Watkins et al. 2009; Feldman et al. 2010; Ma & Scott (WISE), which led to a 3.8 σ detection. With advanced ACTPol 2013, 2014). Therefore, although the bulk flow of the galaxy and a future Stage-IV CMB experiment, the signal-to-noise ratio clusters is constrained to be less than 254 km s−1, the total veloc- (S/N) of the kSZ squared field and projected density field could ity dispersion can still be large enough to be detected. With that reach 120 and 150, respectively (Ferraro et al. 2016), although motivation, in this paper we will look at a different aspect than these authors also cautioned that the results should be corrected in the previous two papers, namely focusing on 1-point statistics for a bias due to lensing. These previous attempts to make vari- of Planck data to constrain the temperature and velocity disper- ous kinds of kSZ measurement are summarized in Table1. sion due to the kSZ effect. This topic is relevant for large-scale There has been a lot of previous work investigating how structure, since the velocity dispersion that we are trying to mea- to use kSZ measurements to determine the peculiar velocity sure can be used as a sensitive test for galaxy formation models field. This idea was first proposed by Haehnelt & Tegmark (Ostriker 1980; Davies et al. 1983; Kormendy & Bender 1996; (1996), suggesting that on small angular scales the peculiar Kormendy 2001; MacMillan et al. 2006) and moreover, a numer- velocities of clusters could be inferred from CMB obser- ical value for the small-scale dispersion often has to be assumed vations. Aghanim et al.(2001) estimated the potential un- in studies of large-scale flows (e.g., Ma et al. 2011; Turnbull et certainty of the kSZ measurements due to contamination al. 2012). Providing such a statistical test through Planck’s full- by the primary CMB and thermal Sunyaev-Zeldovich (here- mission foreground-cleaned maps is the main aim of the present after tSZ) effect. In Holzapfel et al.(1997), the peculiar ve- paper. locities of two distant galaxy clusters, namely Abell 2163 This paper is organized as follows. In Sect.2, we describe the (z = 0.201) and Abell 1689 (z = 0.181), were estimated through Planck CMB data and the X-ray catalogue of detected clusters of millimetre-wavelength observations (the SZ Infrared Experi- galaxies. In Sect.3, we discuss the filter that we develop to con- ment, SuZIE). Furthermore, Benson et al.(2003) estimated volve the observational map, and the statistical methodology that the bulk flow using six galaxy clusters at z > 0.2 from the we use for searching for the kSZ temperature-dispersion signal. SuZIE II experiment in three frequency bands between 150 Then we present the results of our search along with relevant sta- and 350 GHz, constraining the bulk flow to be <1410 km s−1 at tistical tests. In Sect.4, we discuss the astrophysical implications 95% CL. In addition, Kashlinsky & Atrio-Barandela(2000) and of our result, the conclusions being presented in the last section. Kashlinsky et al.(2008, 2009) estimated peculiar velocities Throughout this work, we adopt a spatially flat, ΛCDM cos- on large scales and claimed a “dark flow” (∼>1000 km s−1) mology model, with the best-fit cosmological parameters given on Gpc scales. However, by combining galaxy cluster cata- by Planck Collaboration XIII(2016): Ωm = 0.309; ΩΛ = 0.691; logues with Planck nominal mission foreground-cleaned maps, ns = 0.9608; σ8 = 0.809; and h = 0.68, where the Hubble constant −1 −1 Planck Collaboration Int. XIII(2014) constrained the cluster is H0 = 100 h km s Mpc . velocity monopole to be 72 ± 60 km s−1 and the dipole (bulk flow) to be <254 km s−1 (95% CL) in the CMB rest frame. This indicates that the Universe is largely homogeneous on Gpc 2. Data description scales, consistent with the standard Λ cold dark matter (ΛCDM) 2.1. Planck maps scenario with adiabatic initial conditions1. This work represents the third contribution of the 2.1.1. Maps from the Planck Legacy Archive 2 Planck Collaboration to the study of the kSZ effect. In In this work we use the publicly released Planck 2015 data3. The Planck Collaboration Int. XIII(2014) we focused on constrain- kSZ effect gives rise to frequency-independent temperature fluc- ing the monopole and dipole of the peculiar velocity field, tuations that are a source of secondary anisotropies. The kSZ ef- which gives constraints on the large-scale inhomogeneity of the fect should therefore be present in all CMB foreground-cleaned Universe. In the second paper, Planck Collaboration Int. XXXVII products. Here we investigate the four Planck 2015 foreground- (2016), we calculated the pairwise momentum of the kSZ effect cleaned maps, namely the Commander, NILC, SEVEM, and SMICA and cross-correlated this with the reconstructed peculiar velocity maps. These are the outputs of four different component- 1 Although in principle one could still have an isocurvature perturba- separation algorithms (Planck Collaboration Int. XXXVII 2016) tion on very large scales (Turner 1991; Ma et al. 2011). and have a resolution of θFWHM = 5 arcmin. SMICA uses a 2 Planck (http://www.esa.int/Planck) is a project of the European spectral-matching approach, SEVEM adopts a template-fitting Space Agency (ESA) with instruments provided by two scientific consor- method to minimize the foregrounds, NILC is the result of an tia funded by ESA member states and led by Principal Investigators from internal linear combination approach, and Commander uses a France and Italy, telescope reflectors provided through a collaboration parametric, pixel-based Monte Carlo Markov chain technique to between ESA and a scientific consortium led and funded by Denmark, and additional contributions from NASA (USA). 3 From the Planck Legacy Archive, http://pla.esac.esa.int
A48, page 2 of 17 Planck Collaboration: Velocity dispersion from the kSZ effect
Table 1. Recent measurements of the kinetic Sunyaev-Zeldovich effect with cross-correlations of various tracers of large-scale structure.
Method Reference kSZ data Tracer type Tracer data Significance Pairwise Hand et al.(2012) a ACT Galaxies (spec-z) BOSS III/DR9 2.9 σ temperature Planck Collaboration Int. XXXVII(2016) Planck Galaxies (spec-z) SDSS/DR7 1.8–2.5 σ difference Hernández-Monteagudo et al.(2015) WMAP Galaxies (spec- z) SDSS/DR7 3.3 σ Soergel et al.(2016) SPT Clusters (photo- z) 1-yr DES 4.2 σ De Bernardis et al.(2017) ACT Galaxies (spec- z) BOSS/DR11 3.6–4.1 σ Sugiyama et al.(2018) b Planck Galaxies (spec-z) BOSS/DR12 2.45 σ Li et al.(2018) b Planck Galaxies (spec-z) BOSS/DR12 1.65 σ c kSZ × vpec Planck Collaboration Int. XXXVII(2016) Planck Galaxy velocities SDSS/DR7 3.0–3.7 σ Schaan et al.(2016) c ACT Galaxy velocities BOSS/DR10 2.9 σ, 3.3 σ kSZ2 × projected Hill et al.(2016), Planck, Projected WISE 3.8–4.5 σ density field Ferraro et al.(2016) d WMAP overdensities catalogue kSZ dispersion This work Planck Clusters MCXC 2.8 σ
Notes. “Spec-z” and “photo-z” mean galaxy surveys with spectroscopic or photometric redshift data, respectively. “DES” stands for Dark En- ergy Survey. (a) A p-value of 0.002 is quoted in the original paper, which we convert to S/N by using Eq. (C.3). (b) The differences between Sugiyama et al.(2018) and Li et al.(2018) are that the former used a Fourier-space analysis and a density-weighted pairwise estimator, while the latter used a real-space analysis and a uniform-weighting pairwise momentum estimator. (c) Galaxy peculiar velocities form SDSS/DR7 in Planck Collaboration Int. XXXVII(2016) and BOSS /DR10 in Schaan et al.(2016) are obtained by reconstructing the linear peculiar velocity field from the density field. (d) Here “kSZ2” means the squared kSZ field. project out foregrounds (Planck Collaboration XII 2014; Planck weighted linear combination of the Planck frequency maps. T P9 Collaboration IX 2016; Planck Collaboration X 2015). All of Specificallys ˆCMB(rˆ) = w x(rˆ) = i=1 wi xi(rˆ), under the condi- these maps are produced with the intention of minimizing the tion that the scalar product of the weight vector w and the CMB foreground contribution, but there could nevertheless be some P9 scaling vector a is equal to unity, i.e., i=1 wiai = 1, which guar- residual contamination from the tSZ effect, as well as other fore- antees the conservation of CMB anisotropies in the filtering. grounds (e.g., the Galactic kSZ effect, see Waelkens et al. 2008). However, 2D-ILC (Remazeilles et al. 2011a) generalizes the We use the HEALPix package (Górski et al. 2005) to visualize standard NILC method by offering an additional constraint for and mainpulate the maps. the ILC weights to be orthogonal to the tSZ emission law b, while guaranteeing the conservation of the CMB component. 2.1.2. The 2D-ILC map The 2D-ILC CMB estimate is thus given by T The 2D-ILC Planck CMB map has the additional benefit sˆCMB(rˆ) = w x(rˆ), (3) of being constructed to remove contamination from the tSZ such that the variance of Eq. (3) is minimized, with effect, provided that the tSZ spectral energy distribution is T perfectly known across the frequency channels. The 2D-ILC w a = 1, (4) CMB map has been produced by taking the Planck 2015 data wT b = 0. (5) and implementing the “constrained ILC” method developed in Remazeilles et al.(2011a). This component-separation approach Benefiting from the knowledge of the CMB and tSZ spectral sig- was specifically designed to cancel out in the CMB map any natures, the weights of the 2D-ILC are constructed in order to residual of the tSZ effect towards galaxy clusters by using spec- simultaneously yield unit response to the CMB emission law a tral filtering, as we now describe. (Eq. (4)) and zero response to the tSZ emission law b (Eq. (5)). The residual contamination from Galactic foregrounds and in- For a given frequency band i, the Planck observation map xi can be modelled as the combination of different emission com- strumental noise is controlled through the condition (Eq. (3)). ponents: The exact expression for the 2D-ILC weights was derived in Remazeilles et al.(2011a) by solving the minimization problem xi(rˆ) = ai sCMB(rˆ) + bi stSZ(rˆ) + ni(rˆ), (2) (Eqs. (3)–(5)): T −1 T −1 T −1 T −1 where sCMB(rˆ) is the CMB temperature anisotropy at pixel rˆ, b Cx b a Cx − a Cx b b Cx sˆ (rˆ) = x(rˆ), (6) s (rˆ) is the tSZ fluctuation in the same direction, and n (p) CMB 2 tSZ i T −1 T −1 T −1 is a “nuisance” term including instrumental noise and Galac- a Cx a b Cx b − a Cx b tic foregrounds at frequency i. The CMB fluctuations scale with i j D E frequency through a known emission law parameterized by the where Cx = xi x j are the coefficients of the frequency- vector a, with nine components, accounting for the nine Planck frequency covariance matrix of the Planck channel maps; in frequency bands. The emission law of the tSZ fluctuations is also practice we compute this locally in each pixel p as known and can be parameterized by the scaling vector b in the i j X C (p) = x (p0)x (p0). (7) Planck frequency bands. The kSZ signal is implicitly included x i j 0 in the CMB fluctuations, since CMB anisotropies and kSZ fluc- p ∈D(p) tuations share the same spectral signature. Here the pixel domain D(p) (referred to as “super pixels”) Similar to the standard NILC method (Basak & Delabrouille around the pixel p is determined by using the following proce- 2012, 2013), the 2D-ILC approach makes a minimum-variance- dure: the product of frequency maps xi and x j is convolved with
A48, page 3 of 17 A&A 617, A48 (2018) a Gaussian kernel in pixel space in order to avoid sharp edges at the boundaries of super pixels that would create spurious power (Basak & Delabrouille 2012, 2013). Before applying the 2D-ILC filter (Eq. (6)) to the Planck
2015 data, we first pre-process the data by performing point- source “in-painting” and wavelet decomposition, in order to optimize the foreground cleaning. In each Planck chan- nel map we mask the point-sources detected at S/N > 5 in