Planck 2015 results. XXI. The integrated Sachs-Wolfe effect

# Planck 2015 results. XXI. The integrated Sachs-Wolfe effect

###### Key Words.:
Cosmology: observations – cosmic microwave background – large-scale structure of the Universe – dark engery – Galaxies: clusters: general – Methods: data analysis

This paper presents a study of the integrated Sachs-Wolfe (ISW) effect from the Planck 2015 temperature and polarization data release. This secondary cosmic microwave background (CMB) anisotropy caused by the large-scale time-evolving gravitational potential is probed from different perspectives. The CMB is cross-correlated with different large-scale structure (LSS) tracers: radio sources from the NVSS catalogue; galaxies from the optical SDSS and the infrared WISE surveys; and the Planck 2015 convergence lensing map. The joint cross-correlation of the CMB with the tracers yields a detection at where most of the signal-to-noise is due to the Planck lensing and the NVSS radio catalogue. In fact, the ISW effect is detected from the Planck data only at (through the ISW-lensing bispectrum), which is similar to the detection level achieved by combining the cross-correlation signal coming from all the galaxy catalogues mentioned above. We study the ability of the ISW effect to place constraints on the dark-energy parameters; in particular, we show that is detected at more than . This cross-correlation analysis is performed only with the Planck temperature data, since the polarization scales available in the 2015 release do not permit significant improvement of the CMB-LSS cross-correlation detectability. Nevertheless, the Planck polarization data are used to study the anomalously large ISW signal previously reported through the aperture photometry on stacked CMB features at the locations of known superclusters and supervoids, which is in conflict with CDM expectations. We find that the current Planck polarization data do not exclude that this signal could be caused by the ISW effect. In addition, the stacking of the Planck lensing map on the locations of superstructures exhibits a positive cross-correlation with these large-scale structures. Finally, we have improved our previous reconstruction of the ISW temperature fluctuations by combining the information encoded in all the previously mentioned LSS tracers. In particular, we construct a map of the ISW secondary anisotropies and the corresponding uncertainties map, obtained from simulations. We also explore the reconstruction of the ISW anisotropies caused by the large-scale structure traced by the 2MASS Photometric redshift survey (2MPZ) by directly inverting the density field into the gravitational potential field.

## 1 Introduction

This paper, one of a set associated with the 2015 release of data from the Planck1 mission, describes the detection and characterization of the integrated Sachs-Wolfe (ISW) effect using external (galaxy-survey catalogues) and internal (Planck lensing map) large-scale tracers. The 2015 Planck data release offers polarization information on the cosmic microwave background (CMB) for angular scales smaller than . Whenever possible, this polarization information is used to improve our characterization of the ISW signal.

The ISW effect (Sachs1967; Rees1968; Martinez1990b; Sugiyama1995) is a secondary anisotropy in the CMB, which is caused by gravitational interaction of CMB photons with the growing cosmic large-scale structure (LSS): {linenomath*}

 Θ=ΔTTCMB=−2c3∫χCMB0dχ∂Φ∂χ. (1)

Here, the fractional temperature perturbation is given as a line of sight integral over the time-evolving potentials in the LSS. The integral is expressed in terms of comoving distance , which is related to the scale factor according to , with the Hubble function and the speed of light . The integration is extended to the surface of last scattering corresponding to a redshift of in a CDM cosmology.

The ISW effect measures the rate of growth of gravitational potentials relative to universes with a critical density of matter through frequency shifts in the photon distribution. It is measured by cross-correlating with a tracer of the LSS, such as a galaxy catalogue or a reconstructed weak gravitational lensing map, in order to distinguish it from primary CMB anisotropies; this is because gravitational interaction conserves the Planckian shape of the photon spectrum. The ISW effect is generated at late times when the growth of structure is influenced by a cosmological constant, dark energy (Crittenden1996), modified gravity (Hu2002a), or spatial curvature (Kamionkowski1996).

The most direct way of detecting the ISW effect is the determination of the cross-correlation or the cross-angular power spectrum between the CMB temperature and the density of tracer objects such as galaxies. In this way, the first detection was reported by Boughn2004 which was subsequently refined by many groups on the basis of WMAP data, yielding values for the detection significance in excess of (e.g., Fosalba2003; Nolta2004; Corasaniti2005; Padmanabhan2005; Vielva2006; Giannantonio2006b; Cabre2007; Rassat2007; McEwen2007; Giannantonio2012). Corresponding constraints on cosmological parameters were derived for standard models with a cosmological constant and for dark energy models (e.g., Pietrobon2006a; McEwen2007; Vielva2006; Giannantonio2008a; Ho2008; Xia2009b), as well as for models with modified gravity (e.g., Zhao2010). A Bayesian ISW detection method, which estimates the ISW amplitude conditionally to the observed LSS, can be expected to provide 10 % better signal-to-noise ratio compared to a direct CMB-LSS cross-correlation study (Frommert2008), as used traditionally and in this psper beacuse of its lower computational complexity.

In fact, using the ISW signal alone (but fixing the remaining cosmological parameters), the dark energy density parameter was estimated to be with an error of about 20 % (e.g., Nolta2004; Vielva2006; Giannantonio2006b), the dark energy equation of state parameter was found to be close to  (e.g., Vielva2006; Giannantonio2006b; Ho2008), and tests on spatial flatness yielded upper limits of a few percent for  (e.g., Ho2008; Li2010), thus confirming the concordance cosmological model.

The presence of systematics at large angular scales in LSS surveys and their possible impact on ISW studies was first emphasized in Hernandez2010 and formally addressed in Giannantonio2012 and Hernandez2014. The ISW analysis with the Planck data release in 2013 (planck2013-p14) was consistent with WMAP results using the NVSS radio catalogue and catalogues of tracer objects derived with optical SDSS data, while lowering the claimed detection levels to smaller numbers (from down to around ). In addition, a non-zero correlation between the reconstructed CMB-lensing map as an LSS tracer and the microwave background was reported for the first time, using the non-vanishing bispectrum of the CMB anisotropies on the relevant scales. The strength of this correlation was measured to be , and provides further evidence for a late-time accelerated expansion of the Universe, as theoretically shown by Hu2002b and Okamoto2003.

An alternative method for detecting the ISW effect is the stacking of CMB fields at the positions of known superstructures; if the ISW effect is associated with regions of large density, it should be possible to reduce the noise due to primary, uncorrelated CMB anisotropies by superposition and to reach a reduction inversely proportional to the square root of the number of stacked fields. Detections using this method range between and , based on WMAP data (e.g., Granett2008a; Papai2010a) and on Planck data (planck2013-p14).

A third application of the ISW effect is the reconstruction of a large-scale map of projected gravitational potentials (Barreiro2008). Using the correlation between temperature anisotropies and a map of the tracer density, it is possible to estimate these secondary temperature anisotropies directly.

The purpose of this paper is the measurement of the ISW effect with the full Planck 2015 data set and to establish the corresponding constraints on cosmological parameters. In principle, including polarization data allows us to reduce the error bars in estimating angular cross-power spectra (Frommert2009), and it provides a separation of the temperature anisotropies into those correlated and uncorrelated with polarization, through which the secondary nature of the ISW effect can be better investigated. Furthermore, the reconstruction of the weak lensing potential is improved, and a better template for cross-correlation is provided. However, as mentioned above, the current polarization information provided in the CMB maps of the 2015 Planck data release is limited to angular scales smaller than (more precisely, only multipoles are kept, with a cosine transition in the range ). This limits the amount of information on the ISW effect that can be obtained from the polarization data, since this secondary anisotropy is mostly significant on the largest angular scales. Therefore, in this paper, polarization is not used for the CMB cross-correlation with LSS tracers, although it is considered in the analysis of the CMB anisotropies stacked on the positions of known superstructures.

The paper is organized as follows. In Sect. 2 we present the data used in this work (both for the CMB and the LSS tracers). The cross-correlations of these tracers are investigated in Sect. LABEL:sec:xcorr. In Sect. LABEL:sec:stack we present the results of the stacking analysis using temperature and polarization data. The recovery of the ISW anisotropy map is described in Sect. LABEL:sec:recov. Finally, we discuss our main results and their cosmological implications in Sect. LABEL:sec:discussion.

## 2 Data sets

In this section we describe the data sets and the simulations used throughout the paper. In Sect. 2.1 we describe the CMB related data (temperature and polarization anisotropies), whereas the LSS data sets are discussed in Sect. 2.2, including galaxy, cluster and void catalogues from redshift and photometric surveys, and the Planck lensing map. In Sect. LABEL:sec:data_sims we explain the specific simulations performed to study the CMB-LSS cross-correlation.

### 2.1 CMB data

There are four major Planck foreground-cleaned CMB temperature and polarization maps, namely, the COMMANDER, NILC, SEVEM, and SMICA maps, named after their respectively generating component separation methods (see planck2014-a11, for details). All these maps are used here, in comparison, in order to test the robustness of our results. Together with the common  and  Stokes parameter polarization maps, the Planck 2015 data release also provides -mode maps based on the four component separation methods. In addition, the SEVEM method also provides foreground-cleaned CMB maps at specific frequencies, in temperature at 100, 143, and 217 GHz, and in polarization at 70, 100, and 143 GHz.

The Planck 2015 CMB maps are provided at different resolutions (planck2014-a11). In this paper we consider two different resolutions, depending on the application. First, maps with a HEALPix (gorski2005) resolution parameter = 64 (FWHM = arcmin) are adopted for studying the CMB-LSS cross-correlation (Sect. LABEL:sec:xcorr) and for recovering the ISW anisotropies (Sect. LABEL:sec:recov). Second, = 512 (FWHM = arcmin) maps are used to study the ISW effect through the stacking of CMB maps on the positions of known superstructures (Sect. LABEL:sec:stack). Each resolution has an associated set of masks, one for temperature (called UT78, = 74 % at  = 512), another for  and  Stokes parameters (called UPB77, = 76 % at  = 512), and a final one for the -mode ( = 45 % at  = 512). The parameter indicates the fraction of the sky that is retained after masking.

In addition, there are 1000 simulations associated with each delivered map, which allow us to characterize the instrumental properties of Planck CMB maps. In the context of this work, these simulations are used for the stacking analyses in Sect. LABEL:sec:stack. The other ISW studies require specific coherent simulations between the CMB and the LSS tracers. These simulations are described in Sect. LABEL:sec:data_sims.

As mentioned in Sect. 1, the polarized CMB maps of the 2015 release have been high-pass filtered (see planck2014-a08; planck2014-a11, for details). In particular, all the multipoles with were removed, and a cosine transition between was imposed. Obviously, this high-pass filtering very much limits the usefulness of the polarization information for the ISW analyses. More precisely, the expected 16 % increase of the ISW detection significance by exploiting polarization information in the CMB-LSS cross-correlation (Frommert2009) depends, mainly, on the filtered-out scales (up to for , and for ). In addition, the approach to derive the -correlated () and the -uncorrelated () maps (see below), are based on an -mode map, with a corresponding mask that, as mentioned above, covers significantly less sky (45%) than the temperature one (74%). Therefore, in practice, there is no real gain in the signal-to-noise level. Nevertheless, some of the information kept at smaller scales may still be useful for particular analyses such as the stacking of the CMB anisotropies on the positions of known superstructures. First, because these structures are within the part of the sky covered by the  and  maps and, second, because the multipole range that mainly contributes to the angular scales of the stacked profiles corresponds to smaller scales than those for the CMB-LSS cross-correlation. For that reason, the polarization information is not used in the ISW study through the correlation of the CMB and the LSS tracers (Sect. LABEL:sec:xcorr), but it was considered in the stacking analyses (Sect. LABEL:sec:stack). A final study of the ISW effect using full polarization information is expected to be done with the next Planck data release.

The primary CMB temperature anisotropies act effectively as a noise source for the measurement of secondary CMB anisotropies by increasing its cosmic variance. This is true for the ISW effect, which does not produce a notable -mode polarization. Hence, polarization data permit us to identify the part of the primary temperature anisotropies that is correlated with the -mode polarization, and to remove it from the maps. The resulting CMB temperature map, partly cleaned form primary anisotropies, provides up to a 16 % better signal-to-noise ratio for secondary fluctuations (Frommert2009). To this end, we separate the temperature map in two components: an -correlated () and an -uncorrelated () part. Following the approach of Frommert2009, we have produced these maps from the delivered CMB inputs described above. An estimation of the -correlated temperature anisotropies () is given, in terms of its spherical harmonic coefficients , by {linenomath*}

 aTE−cℓm=aEℓmwℓ, (2)

where the filter is defined by the and the angular power spectra: {linenomath*}

 wℓ=CTEℓ+FTEℓCEEℓ+FEEℓ+NEEℓ, (3)

with , , and representing the angular power spectra of the CMB, residual foregrounds, and noise, respectively. Hence, the  map is given by: {linenomath*}

 TE−c(\@vec^n)=ℓmax∑ℓ=0ℓ∑m=−ℓaTE−cℓmYℓm(\@vec^n), (4)

with the spherical harmonic functions. The  map is build by subtraction: . The above procedure is performed by applying an apodized version of the corresponding masks. In Fig. 1 we show the , , and  maps for SEVEM. In practice, the determination of the filter is not straightforward; although the CMB and noise contributions can be obtained directly from the Planck best-fit cosmological model (planck2014-a15) and the FFP8 simulations (planck2014-a14; planck2014-a11), information about the residual foregrounds () present in the CMB temperature and polarization is also needed. We verified that the expected CMB and noise power spectra account well for the observed and the angular power spectra at . Although the foreground spectra are not fully known, their impact is minor on these scales due to the large mask imposed on the -mode map and the high-pass filtering applied to the polarization data. However, at smaller angular scales some foreground residuals exist.

An alternative way to construct such a filter to reduce primary anisotropies is to extract the relevant correlation functions directly from the data. In particular, we have constructed filters using a smooth fit of the filter constructed as the ratio of the and the angular power spectra of the different CMB component separation maps. The procedure followed to build the filter distinguishes between high- and low- regimes. For small scales (), we compute the ratio of and obtained from the data using an apodized mask, which is afterwards smoothed following the Savitzky-Golay procedure (Savitzky1964). In the low- regime () the filter is constructed using the average value obtained from 1000 simulations of CMB plus noise, using the same apodized mask. The resulting filters (solid lines) are shown in Fig. 2; for comparison, the corresponding theoretical filters, computed only from the instrumental properties and the Planck fiducial angular power spectra, are also plotted (dashed lines).

### 2.2 LSS tracers

As mentioned in Sect. 1, tracers of the gravitational potential of the LSS are required to extract the secondary ISW anisotropies from the dominant primary CMB anisotropies. These tracers are used to perform the CMB-LSS cross-correlation, but also for studying the ISW effect through the stacking of the CMB anisotropies on the position of known superstructures (such as clusters or voids), and for producing a map of the ISW anisotropies.

We have included three additional galaxy catalogues with respect to to the ones used in planck2013-p14, which were the radio NVSS catalogue and the optical luminous galaxies (SDSS-CMASS/LOWZ) as well as the main photometric galaxy sample (SDSS-MphG) catalogues from the Sloan Digital Sky Survey (SDSS). These additional catalogues consist of star forming galaxies (WISE-GAL), of active galactic nuclei (AGN; WISE-AGN), both sets taken from the catalogue of extragalactic sources detected by the Wide-Field Infrared Survey Explorer (WISE, see Wright2010), and of photometric redshifts (2MPZ) obtained from the Two Micron All Sky Survey Extended Source Catalogue (2MASS-XSC), WISE and SuperCOSMOS data sets. This last catalogue is only used to build an estimation of the ISW anisotropies based on a reconstruction of the gravitational potential from the 3D distribution of the galaxies (see Appendix. LABEL:sec:appen). The reason is that the expected CMB-LSS cross-correlation signal is very low to be used in this cross-correlation study but, however, the galaxy redshift estimation error is sufficiently low to attempt the gravitational potential reconstruction. Finally, we also cross-correlate the Planck lensing map as a LSS tracer with the CMB. In particular, we use the lensing convergence map (Kappa) obtained in planck2014-a17.

The redshift distributions of these catalogues are shown in Fig. 3. We note that lensing, NVSS, and WISE-AGN offer the widest redshift coverage. Some basic properties of the galaxy catalogues used (NVSS, WISE-AGN, WISE-GAL, SDSS-CMASS/LOWZ, SDSS-MphG, and 2MPZ) are summarized in Table 3.

For a better visualization, Wiener-filtered versions of the all-sky density projection of the external catalogues, as well as the Planck Kappa map, are shown in Fig. LABEL:fig:surveys_maps. These are constructed from the theoretical power spectra obtained as described in Sect. LABEL:sec:data_sims. In Fig. LABEL:fig:surveys_cls, we show the angular auto- and the cross-power angular spectra for all the LSS tracers: dashed lines and points correspond to the theoretical model and the data measurements, respectively (red for auto-spectra, and blue for cross-spectra); and grey areas represent the sampling uncertainties due to cosmic variance. All of these spectra have been corrected for the mask coupling following the MASTER approach (Hivon2002). Notice that the Planck lensing convergence map only contains information for multipoles  (see planck2014-a17, for details). The two maps based on the WISE catalogues (WISE-AGN and WISE-GAL) exhibit some extra signal at the largest scales. We identify this with some systematic effect present in these catalogues and, therefore, as a baseline, we only consider multipoles for these two surveys. This cut implies only a minor loss of the ISW signal, while permitting a more robust determination of it. The rest of the auto-spectra are in reasonably good agreement with the theoretical predictions. Notice that any mismatch on the auto-spectra could suffer, not only from systematic effects, but from an inaccurate description of the statistical properties of the catalogues. In this sense, cross-spectra are, in principle, less affected by systematics (at least, among catalogues from different experiments), and, therefore, are more useful for identifying possible problems in the adequacy of the galaxy redshift distribution and galaxy biases. We emphasise that, in this sense, the Planck Kappa map could in principle be a more robust LSS probe, since it does not suffer from these kinds of uncertainty and, therefore, its correlation with the rest of the surveys is very useful for highlighting potential issues related to the catalogue characterization. In this sense, from Fig. LABEL:fig:surveys_maps, it seems that the measured cross-correlation of the lensing potential with the galaxy catalogues is very good, indicating that, within the current uncertainties, the description of the surveys is accurate. The three maps (Kappa, WISE-AGN, and WISE-GAL) shown in Fig. LABEL:fig:surveys_maps do not include the cut multipoles.

Besides the galaxy surveys described above, we also use superstructure catalogues to study the ISW effect through the stacking of the CMB anisotropies on the positions of clusters and voids. We concentrate on the supercluster and void catalogue of Granett2008b, obtained from SDSS (GR0808), since, as shown in planck2013-p14, its reported strong signal would be a challenge for the standard CDM cosmology if it is solely caused by the ISW effect.

Below we provide a description of all these LSS tracers. For those catalogues already used in our previous publication (NVSS, SDSS-CMASS/LOWZ, SDSS-MphG, and GR0808) only a summary is provided; more detailed description can be found in planck2013-p14.

### Footnotes

1. Planck (http://www.esa.int/Planck) is a project of the European Space Agency (ESA) with instruments provided by two scientific consortia funded by ESA member states and led by Principal Investigators from France and Italy, telescope reflectors provided through a collaboration between ESA and a scientific consortium led and funded by Denmark, and additional contributions from NASA (USA).
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