The Astrophysical Journal, 825:24 (13pp), 2016 July 1 doi:10.3847/0004-637X/825/1/24 © 2016. The American Astronomical Society. All rights reserved. TOWARD A TOMOGRAPHIC ANALYSIS OF THE CROSS-CORRELATION BETWEEN PLANCK CMB LENSING AND H-ATLAS GALAXIES F. Bianchini1,2,3, A. Lapi1,2,3,4, M. Calabrese1,5, P. Bielewicz1,6, J. Gonzalez-Nuevo7, C. Baccigalupi1,2, L. Danese1, G. de Zotti1,8, N. Bourne9, A. Cooray10, L. Dunne9,11,12, S. Eales11, and E. Valiante11 1 Astrophysics Sector, SISSA, Via Bonomea 265, I-34136 Trieste, Italy; [email protected] 2 INFN—Sezione di Trieste, Via Valerio 2, I-34127 Trieste, Italy 3 INAF—Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34131, Trieste, Italy 4 Dipartimento di Fisica, Università “Tor Vergata,” Via della Ricerca Scientifica 1, I-00133 Roma, Italy 5 INAF, Osservatorio Astronomico di Brera, via E. Bianchi 46, I-23807 (LC), Italy 6 Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland 7 Departamento de Física, Universidad de Oviedo, C. Calvo Sotelo s/n, E-33007 Oviedo, Spain 8 INAF—Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy 9 Scottish Universities Physics Alliance (SUPA), Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ, UK 10 Department of Physics and Astronomy, University of California, Irvine CA 92697, USA 11 School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, UK 12 Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand Received 2015 November 16; revised 2016 April 28; accepted 2016 April 29; published 2016 June 27 ABSTRACT We present an improved and extended analysis of the cross-correlation between the map of the cosmic microwave background (CMB) lensing potential derived from the Planck mission data and the high-redshift galaxies detected by the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS) in the photometric redshift range zph 1.5. We compare the results based on the 2013 and 2015 Planck datasets, and investigate the impact of different selections of the H-ATLAS galaxy samples. Significant improvements over our previous analysis have been achieved thanks to the higher signal-to-noise ratio of the new CMB lensing map recently released by the Planck collaboration. The effective galaxy bias parameter, b, for the full galaxy sample, derived from a joint +0.15 analysis of the cross-power spectrum and of the galaxy auto-power spectrum is found to be b = 3.54-0.14. Furthermore, a first tomographic analysis of the cross-correlation signal is implemented by splitting the galaxy sample into two redshift intervals: 1.5 zph < 2.1 and zph 2.1. A statistically significant signal was found for both bins, indicating a substantial increase with redshift of the bias parameter: b =2.89 0.23 for the lower and +0.24 fi b = 4.75-0.25 for the higher redshift bin. Consistent with our previous analysis, we nd that the amplitude of the +0.14 Λ cross-correlation signal is a factor of 1.45-0.13 higher than expected from the standard CDM model for the assumed redshift distribution. The robustness of our results against possible systematic effects has been extensively discussed, although the tension is mitigated by passing from 4 to 3σ. Key words: cosmic background radiation – galaxies: high-redshift – gravitational lensing: weak – methods: data analysis 1. INTRODUCTION both the geometry of the universe and to the growth of the LSS. Lensing also introduces non-Gaussian features in the CMB Over the past two decades, a wide set of cosmological anisotropy pattern which can be exploited to get information on observations (Weinberg 2008, p. 593) have allowed us to the intervening mass distribution (Hu & Okamoto 2002; Hirata summarize our understanding of the basic properties of the & Seljak 2003), which in turn may give hints on the early universe in the concordance cosmological model, known as the ( Λ fi stages of cosmic acceleration Acquaviva & Baccigalupi 2006; CDM model. Despite providing a good t to the observa- Hu et al. 2006). tional data, the model presents some puzzles as most of the On the other hand, since CMB lensing is an integrated content of the universe is in the form of dark components, quantity, it does not provide direct information on the evolution namely dark matter and dark energy, whose nature is still of the large-scale gravitational potential. However, the cross- mysterious. correlation between CMB lensing maps and tracers of LSS ( ) In this framework, cosmic microwave background CMB enables the reconstruction of the dynamics and of the spatial lensing science has emerged in the last several years as a new distribution of the gravitational potential, providing simulta- promising cosmological probe (Smith et al. 2007; Das et al. neous constraints on cosmological and astrophysical para- 2011; van Engelen et al. 2012, 2015; Planck Collaboration meters (Pearson & Zahn 2014), such as the bias factor b et al. 2013; Ade et al. 2014; Baxter et al. 2015; Planck relating fluctuations in luminous and dark matter. Collaboration et al. 2015). The large-scale structure (LSS) In the standard structure formation scenario, galaxies reside leaves an imprint on CMB anisotropies by gravitationally in dark matter halos (Mo et al. 2010), the most massive of deflecting CMB photons during their journey from the last which are the signposts of larger scale structures that act as scattering surface to us (Bartelmann & Schneider 2001; Lewis lenses for CMB photons. Bright sub-millimeter-selected & Challinor 2006). The net effect is a remapping of the CMB galaxies, which are thought to be the progenitors of present observables, dependent on the gravitational potential integrated day massive spheroidal galaxies, are excellent tracers of LSS along the line of sight (LOS). Thus, the effect is sensitive to and thus optimally suited for cross-correlation studies. 1 The Astrophysical Journal, 825:24 (13pp), 2016 July 1 Bianchini et al. Even more importantly, the sub-millimeter (sub-mm) flux Throughout this paper, we adopt the fiducial flat ΛCDM density of certain sources remains approximately constant with cosmology with best-fit Planck + WP + highL + lensing increasing redshift for z 1 (strongly negative K-correction), cosmological parameters as provided by Planck Collaboration so that sub-mm surveys have the power of piercing the distant et al. (2014b). Here, WP refers to WMAP polarization data at universe up to z 3–4, where the CMB lensing is most low multipoles, highL to the inclusion of high-resolution CMB sensitive to matter fluctuations. In contrast, the available large– data of the Atacama Cosmology Telescope (ACT) and South area optical/near-infrared galaxy surveys and radio source Pole Telescope (SPT) experiments, and lensing to the inclusion surveys reach redshifts only slightly above unity and therefore of Planck CMB lensing data in the parameter likelihood. pick up only a minor fraction of the CMB lensing signal whose contribution peaks at z > 1 and is substantial up to much 2. THEORY higher redshifts. Quasars allow us to extend investigations Both the CMB convergence field κ and the galaxy density much further, but are rare and therefore provide a sparse fluctuation field g along the LOS can be written as a weighted sampling of the large-scale gravitational field. integral over redshift of the dark matter density contrast δ: Previous cross-correlation studies involving CMB lensing z and galaxy or quasar density maps have been reported by many XdzWzzz(nnˆ)()(()= * X dc ˆ,,)() 1 authors (Smith et al. 2007; Hirata et al. 2008; Bleem et al. ò0 2012; Feng et al. 2012; Sherwin et al. 2012; Geach et al. 2013; where Xg= {}k, and WX ()z is the kernel related to a given Planck Collaboration et al. 2013; Giannantonio & Perci- field. The kernel Wk, describing the lensing efficiency of the val 2014; Allison et al. 2015; Bianchini et al. 2015; DiPompeo matter distribution, writes et al. 2015; Giannantonio et al. 2015; Kuntz 2015; Omori & Holder 2015; Pullen et al. 2015). 3W H 2 cc- ()z ( ) Wzk ()= m 0 ()()1.2+ zzc * () As pointed out by Song et al. 2003 , the CMB lensing 2c Hz() c kernel is well matched with the one of the unresolved dusty * galaxies comprising the cosmic infrared background (CIB) Here, c ()z is the comoving distance to redshift z, c is the since both are tracers of the large-scale density fluctuations in * comoving distance to the last scattering surface at z* 1090, the universe. In particular, Planck measurements suggest that H(z) is the Hubble factor at redshift z, c is the speed of light, Wm the correlation between the CMB lensing map and the CIB map and H0 are the present day values of matter density and Hubble at 545 GHz can be as high as 80% (Planck Collaboration et al. ) fi parameter, respectively. 2014a . Other statistically signi cant detections have been Assuming that the luminous matter traces the peaks of the ( ) ( ) recently reported by Holder et al. 2013 , Hanson et al. 2013 , dark matter distribution, the galaxy kernel is given by the sum ( ) POLARBEAR Collaboration et al. 2014 , and van Engelen of two terms: et al. (2015). Even though there are connections between these dN studies and the one presented here, one needs to bear in mind Wzg ()=+ bz ()m ()z .3 () that, differently from galaxy catalogs, the CIB is an integrated dz quantity and as such it prevents a detailed investigation of the The first term is related to the physical clustering of sources and temporal evolution of the signal. Moreover, the interpretation 14 of the measured cross-correlation is actually more challenging is the product of the bias factor b with the unit normalized / since the precise redshift distribution of the sources contribut- redshift distribution of sources, dN dz.