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Cosmology with the Cosmic Microwave Background Temperature-Polarization Correlation F A&A 602, A41 (2017) Astronomy DOI: 10.1051/0004-6361/201629815 & c ESO 2017 Astrophysics Cosmology with the cosmic microwave background temperature-polarization correlation F. Couchot1, S. Henrot-Versillé1, O. Perdereau1, S. Plaszczynski1, B. Rouillé d’Orfeuil1, M. Spinelli1; 2, and M. Tristram1 1 Laboratoire de l’Accélérateur Linéaire, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France e-mail: [email protected] 2 Department of Physics and Astronomy, University of the Western Cape, Robert Sobukwe Road, Bellville 7535, South Africa Received 30 September 2016 / Accepted 14 February 2017 ABSTRACT We demonstrate that the cosmic microwave background (CMB) temperature-polarization cross-correlation provides accurate and robust constraints on cosmological parameters. We compare them with the results from temperature or polarization and investigate the impact of foregrounds, cosmic variance, and instrumental noise. This analysis makes use of the Planck high-` HiLLiPOP likelihood based on angular power spectra, which takes into account systematics from the instrument and foreground residuals directly modelled using Planck measurements. The temperature-polarization correlation (TE) spectrum is less contaminated by astrophysical emissions than the temperature power spectrum (TT), allowing constraints that are less sensitive to foreground uncertainties to be derived. For P ΛCDM parameters, TE gives very competitive results compared to TT. For basic ΛCDM model extensions (such as AL, mν, or Neff ), it is still limited by the instrumental noise level in the polarization maps. Key words. cosmic background radiation – cosmological parameters – methods: data analysis 1. Introduction spectrum level in the likelihood. Most of the results presented in Planck Collaboration XIII(2016) are based on TT angular The results from the Planck satellite have recently demon- power spectra which present the higher signal-to-noise ratio. strated the consistency between the temperature and the polar- However, foreground residuals in temperature combine several ization data (Planck Collaboration XIII 2016). Adding the infor- different components which are difficult to model in the power mation coming from the velocity gradients of the photon–baryon spectra domain as they are both non-homogeneous and non- fluid through the polarization power spectra to the measure- Gaussian. Any mismatch between the foreground model and the ment of the temperature fluctuations improves the constraints data can thus result in a bias on the estimated cosmological pa- on cosmological parameters and helps break some degenera- rameters and, in all cases, will increase their posterior width. On cies. One of the best examples is the measurement of the the contrary, in polarization, even though the signal-to-noise ra- reionization optical depth using the large-scale signature that tio is lower, the only foreground that affects the Planck data is reionization leaves in the EE polarization power spectrum the polarized emission of the Galactic dust. As we show, this al- (Planck Collaboration Int. XLVII 2016). Moreover, as suggested lows for a precise reconstruction of the cosmological parameters in Galli et al.(2014), for a cosmic variance limited experiment, (especially with TE spectra) with less impact from foreground polarization power spectra alone can provide tighter constraints uncertainties. on cosmological parameters than the temperature power spec- trum, while for an experiment with Planck-like noise, constraints The cosmological parameters reconstructed with TT spectra should be comparable. are compared to those obtained independently with TE and EE. In this paper, we discuss in greater detail the constraints on In each case, we detail the foreground modelling and the prop- cosmological parameters obtained with the Planck 2015 polar- agation of its uncertainties. We use the High-` Likelihood on ization data (including foregrounds and systematic residuals). Polarized Power spectra (HiLLiPOP) likelihood which is based We find that the level of instrumental noise allows for an accurate on the Planck data in temperature and polarization. HiLLiPOP reconstruction of cosmological parameters using temperature- is one of the four high-` likelihoods developed within the Planck TE polarization cross-correlation C` only. Constraints from Planck consortium for the 2015 release and is briefly presented and EE polarization spectrum are dominated by instrumental noise. compared to others in Planck Collaboration XIII(2016). It is a In addition, we investigate the robustness of the cosmological full temperature+polarization likelihood based on cross-spectra interpretation with respect to astrophysical residuals. from Planck maps at 100, 143, and 217 GHz. It is based on a In the Planck analysis (Planck Collaboration XV 2014; Gaussian approximation of the C` likelihood which is well suited Planck Collaboration XI 2016), the foreground contamination for multipoles above ` = 30. In contrary to the Planck pub- is mitigated using masks which are adapted to each fre- lic likelihood (Planck Collaboration XIII 2016), the foreground quency, reducing the sky fraction to the region where the fore- description in HiLLiPOP directly relies on the Planck astro- ground emission is low. The residuals of diffuse foreground physical measurements. For the Λ cold dark matter (ΛCDM) emission are then taken into account using models at the cosmology, using a τ prior, it gives results very compatible Article published by EDP Sciences A41, page 1 of 24 A&A 602, A41 (2017) Planck 353 GHz map as a tracer of the thermal dust emission TT 4 in intensity. In practice, we smoothed the Planck 353 GHz map 10 EE to increase the signal-to-noise ratio before applying a thresh- ] TE old which depends on the frequency considered. Masks are then B ◦ M 3 2 apodized using a 8 Gaussian taper for power spectra estima- C 10 K tion. For polarization, Planck dust maps show that the diffuse µ [ emission is strongly related to the Galactic magnetic field at ` 2 C 10 large scales (Planck Collaboration Int. XIX 2015). However, at π the smaller scales which matter here (` > 50), the orientation 2 / ) 1 of dust grains is driven by local turbulent magnetic fields which 1 10 + produce a polarization intensity proportional to the total intensity ` ( dust map. We thus use the same Galactic mask for polarization ` 100 as for temperature. Molecular lines from CO produce diffuse emission on star -1 forming region. Two major CO lines at 115 GHz and 230 GHz 10 0 500 1000 1500 2000 2500 enter the Planck bandwidths at 100 and 217 GHz, respectively multipole ` (Planck Collaboration XIII 2014). We smoothed the Planck re- constructed CO map to 30 arcmin before applying a threshold at Fig. 1. Signal (solid line) versus noise (dashed line) for the Planck 2 K km s−1. The resulting masks are then apodized at 15 arcmin. cross-spectra for each mode TT, EE, and TE (in red, blue, and green, In practice, the CO masks are almost completely included in the respectively). Galactic masks, decreasing the accepted sky fraction only by a few percentage points. For point sources, the Planck 2013 and 2015 analyses mask with the Planck public likelihood, except for the (τ; As) pair which is more consistent with the low-` data. Consequently, it the sources detected with a signal-to-noise ratio above 5 in the Planck point-source catalogue (Planck Collaboration XXVI also shows a better lensing amplitude AL (see the discussion in Couchot et al. 2017). 2016) at each frequency (Planck Collaboration XVI 2014; The paper is organized as follows. In Sect.2, we describe the Planck Collaboration XI 2016). On the contrary, the masks power spectra used in this analysis. We discuss the Planck maps used in our analysis rely on a more refined procedure that and the sky region for the power spectra estimation. Section3 preserves Galactic compact structures and ensures the com- presents the likelihood functions both in temperature and in po- pleteness level at each frequency, but with a higher flux cut larization, and details the model of each associated foreground (340, 250, and 200 mJy at 100, 143, and 217 GHz, respec- emission. We then present in Sect.4 the results for the ΛCDM tively). The consequence is that these masks leave a slightly cosmological model and check the impact of priors on the as- greater number of unmasked extragalactic sources, but pre- serve the power spectra of the dust emission (as described in trophysical parameters. Section5 gives the results on the AL pa- rameter considered as an internal cross-check of the CMB like- Planck Collaboration Int. XXX 2016). For each frequency, we lihoods. Finally, in Sect.6, we demonstrate the impact of the mask a circular area around each source using a radiusp of three foreground parameters for the temperature likelihood and the TE times the effective Gaussian beam width (σ = FWHM= ln 8) at likelihood in terms of both the bias and the precision of the cos- that frequency. We apodize these masks with a Gaussian taper of mological parameters. FWHM = 15 arcmin. Finally, we also mask strong extragalactic objects including both point sources and nearby extended galaxies. The masked 2. Data set galaxies include the LMC and SMC and also M31, M33, M81, 2.1. Maps and masks M82, M101, M51, and CenA. The combined masks used are named M80, M70, and M55 The maps used in this analysis are taken from the Planck 2015 1 (corresponding to effective fsky = 72%; 62%; 48%), associ- data release and described in detail in Planck Collaboration VIII ated with the 100, 143, and 217 GHz channels, respectively (2016). We use two maps per frequency (A and B, one for (Fig.2). Tests have been carried out using more conserva- each half-mission) at 100, 143, and 217 GHz. The beam asso- tive Galactic masks (with fsky = 65%, 55%, and 40% for ciated with each map is provided by the Planck Collaboration 100, 143, and 217 GHz, respectively) showing perfectly com- (Planck Collaboration VII 2016). Figure1 compares the signal patible results with those of the smaller masks.
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