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1 PDF hosted at the Radboud Repository of the Radboud University Nijmegen The foowing fu text is a preprint version which may differ from the pubisher's version. For additiona information about this pubication cick this ink. Pease be advised that this information was generated on and may be subject to change.

2 Astronomy & Astrophysics manuscript no. cibip c ESO 2013 September 3, 2013 arxiv: v1 [astro-ph.co] 2 Sep 2013 Panck 2013 Resuts. XXX. Cosmic infrared background measurements and impications for star formation Panck Coaboration: P. A. R. Ade 89, N. Aghanim 62, C. Armitage-Capan 94, M. Arnaud 75, M. Ashdown 72,7, F. Atrio-Barandea 20, J. Aumont 62, C. Baccigaupi 88, A. J. Banday 97,11, R. B. Barreiro 69, J. G. Bartett 1,70, E. Battaner 99, K. Benabed 63,96, A. Benoît 60, A. Benoit-Lévy 27,63,96, J.-P. Bernard 11, M. Bersanei 37,52, M. Bethermin 75, P. Bieewicz 97,11,88, K. Bagrave 10, J. Bobin 75, J. J. Bock 70,12, A. Bonadi 71, J. R. Bond 10, J. Borri 15,91, F. R. Bouchet 63,96, F. Bouanger 62, M. Bridges 72,7,66, M. Bucher 1, C. Burigana 51,35, R. C. Buter 51, J.-F. Cardoso 76,1,63, A. Cataano 77,74, A. Chainor 66,72,13, A. Chambau 75,17,62, X. Chen 59, H. C. Chiang 29,8, L.-Y Chiang 65, P. R. Christensen 84,40, S. Church 93, D. L. Cements 58, S. Coombi 63,96, L. P. L. Coombo 26,70, F. Couchot 73, A. Couais 74, B. P. Cri 70,85, A. Curto 7,69, F. Cuttaia 51, L. Danese 88, R. D. Davies 71, R. J. Davis 71, P. de Bernardis 36, A. de Rosa 51, G. de Zotti 48,88, J. Deabrouie 1, J.-M. Deouis 63,96, F.-X. Désert 55, C. Dickinson 71, J. M. Diego 69, H. Doe 62,61, S. Donzei 52, O. Doré 70,12, M. Douspis 62, X. Dupac 43, G. Efstathiou 66, T. A. Enßin 80, H. K. Eriksen 67, F. Finei 51,53, O. Forni 97,11, M. Fraiis 50, E. Franceschi 51, S. Gaeotta 50, K. Ganga 1, T. Ghosh 62, M. Giard 97,11, Y. Giraud-Héraud 1, J. Gonzáez-Nuevo 69,88, K. M. Górski 70,101, S. Gratton 72,66, A. Gregorio 38,50, A. Gruppuso 51, F. K. Hansen 67, D. Hanson 81,70,10, D. Harrison 66,72, G. Heou 12, S. Henrot-Versié 73, C. Hernández-Monteagudo 14,80, D. Herranz 69, S. R. Hidebrandt 12, E. Hivon 63,96, M. Hobson 7, W. A. Homes 70, A. Hornstrup 18, W. Hovest 80, K. M. Huffenberger 100, A. H. Jaffe 58, T. R. Jaffe 97,11, W. C. Jones 29, M. Juvea 28, P. Kabera 6, E. Keihänen 28, J. Kerp 6, R. Keskitao 24,15, T. S. Kisner 79, R. Kneiss 42,9, J. Knoche 80, L. Knox 31, M. Kunz 19,62,3, H. Kurki-Suonio 28,47, F. Lacasa 62, G. Lagache 62, A. Lähteenmäki 2,47, J.-M. Lamarre 74, M. Langer 62, A. Lasenby 7,72, R. J. Laureijs 44, C. R. Lawrence 70, R. Leonardi 43, J. León-Tavares 45,2, J. Lesgourgues 95,87, M. Liguori 34, P. B. Lije 67, M. Linden-Vørne 18, M. López-Caniego 69, P. M. Lubin 32, J. F. Macías-Pérez 77, B. Maffei 71, D. Maino 37,52, N. Mandoesi 51,5,35, M. Maris 50, D. J. Marsha 75, P. G. Martin 10, E. Martínez-Gonzáez 69, S. Masi 36, S. Matarrese 34, F. Matthai 80, P. Mazzotta 39, A. Mechiorri 36,54, L. Mendes 43, A. Mennea 37,52, M. Migiaccio 66,72, S. Mitra 57,70, M.-A. Mivie-Deschênes 62,10, A. Moneti 63, L. Montier 97,11, G. Morgante 51, D. Mortock 58, D. Munshi 89, J. A. Murphy 83, P. Nasesky 84,40, F. Nati 36, P. Natoi 35,4,51, C. B. Netterfied 22, H. U. Nørgaard-Niesen 18, F. Novieo 71, D. Novikov 58, I. Novikov 84, S. Osborne 93, C. A. Oxborrow 18, F. Paci 88, L. Pagano 36,54, F. Pajot 62, R. Paadini 59, D. Paoetti 51,53, B. Partridge 46, F. Pasian 50, G. Patanchon 1, O. Perdereau 73, L. Perotto 77, F. Perrotta 88, F. Piacentini 36, M. Piat 1, E. Pierpaoi 26, D. Pietrobon 70, S. Paszczynski 73, E. Pointecouteau 97,11, G. Poenta 4,49, N. Ponthieu 62,55, L. Popa 64, T. Poutanen 47,28,2, G. W. Pratt 75, G. Prézeau 12,70, S. Prunet 63,96, J.-L. Puget 62, J. P. Rachen 23,80, W. T. Reach 98, R. Reboo 68,16,41, M. Reinecke 80, M. Remazeies 62,1, C. Renaut 77, S. Ricciardi 51, T. Rier 80, I. Ristorcei 97,11, G. Rocha 70,12, C. Rosset 1, G. Roudier 1,74,70, M. Rowan-Robinson 58, J. A. Rubiño-Martín 68,41, B. Rushome 59, M. Sandri 51, D. Santos 77, G. Savini 86, D. Scott 25, M. D. Seiffert 70,12, P. Serra 62, E. P. S. Sheard 13, L. D. Spencer 89, J.-L. Starck 75, V. Stoyarov 7,72,92, R. Stompor 1, R. Sudiwaa 89, R. Sunyaev 80,90, F. Sureau 75, D. Sutton 66,72, A.-S. Suur-Uski 28,47, J.-F. Sygnet 63, J. A. Tauber 44, D. Tavagnacco 50,38, L. Terenzi 51, L. Toffoatti 21,69, M. Tomasi 52, M. Tristram 73, M. Tucci 19,73, J. Tuovinen 82, M. Türer 56, L. Vaenziano 51, J. Vaiviita 47,28,67, B. Van Tent 78, P. Vieva 69, F. Via 51, N. Vittorio 39, L. A. Wade 70, B. D. Wandet 63,96,33, M. White 30, S. D. M. White 80, B. Winke 6, D. Yvon 17, A. Zacchei 50, A. Zonca 32 (Affiiations can be found after the references) Received June 17, 2013; accepted XX, 2013 ABSTRACT We present new measurements of cosmic infrared background (CIB) anisotropies using Panck. Combining HFI data with IRAS, the anguar auto- and cross-frequency power spectrum is measured from 143 to 3000 GHz, and the auto-bispectrum from 217 to 545 GHz. The tota areas used to compute the CIB power spectrum and bispectrum are about 2240 and 4400 deg 2, respectivey. After carefu remova of the contaminants (cosmic microwave background anisotropies, Gaactic dust and Sunyaev-Zedovich emission), and a compete study of systematics, the CIB power spectrum is measured with unprecedented signa to noise ratio from anguar mutipoes 150 to The bispectrum due to the custering of dusty, star-forming gaaxies is measured from 130 to 1100, with a tota signa to noise ratio of around 6, 19, and 29 at 217, 353, and 545 GHz, respectivey. Two approaches are deveoped for modeing CIB power spectrum anisotropies. The first approach takes advantage of the unique measurements by Panck at arge anguar scaes, and modes ony the inear part of the power spectrum, with a mean bias of dark matter haos hosting dusty gaaxies at a given redshift weighted by their contribution to the emissivities. The second approach is based on a mode that associates star-forming gaaxies with dark matter haos and their subhaos, using a parametrized reation between the dust-processed infrared uminosity and (sub-)hao mass. The two approaches simutaneousy fit a auto- and cross- power spectra very we. We find that the star formation history is we constrained up to redshifts around 2, and agrees with recent estimates of the obscured star-formation density using Spitzer and Hersche. However, at higher redshift, the accuracy of the star formation history measurement is strongy degraded by the uncertainty in the spectra energy distribution of CIB gaaxies. We aso find that the mean hao mass which is most efficient at hosting star formation is og(m eff /M ) = 12.6 and that CIB gaaxies have warmer temperatures as redshift increases. The CIB bispectrum is steeper than that expected from the power spectrum, athough we fitted by a power aw; this gives some information about the contribution of massive haos to the CIB bispectrum. Finay, we show that the same hao occupation distribution can fit a power spectra simutaneousy. The precise measurements enabed by Panck pose new chaenges for the modeing of CIB anisotropies, indicating the power of using CIB anisotropies to understand the process of gaaxy formation. Key words. Cosmoogy: observations Gaaxies: star formation Cosmoogy: arge-scae structure of Universe Infrared: diffuse background 1

3 1. Introduction This paper, one of a set associated with the 2013 reease of data from the Panck 1 mission (Panck Coaboration I 2013), describes new measurements of the cosmic infrared background (CIB) anisotropy power spectrum and bispectrum, and their use in constraining the cosmic evoution of the star formation density and the uminous-dark matter bias. The reic emission from gaaxies formed throughout cosmic history appears as a diffuse, cosmoogica background. The CIB is the far-infrared part of this emission and it contains about haf of its tota energy (Doe et a. 2006). Produced by the stearheated dust within gaaxies, the CIB carries a weath of information about the process of star formation. Because dusty, star-forming gaaxies at high redshift are extremey difficut to detect individuay (e.g., Bain et a. 1998; Lagache et a. 2003; Doe et a. 2004; Fernandez-Conde et a. 2008; Nguyen et a. 2010), the CIB represents an exceptiona too for studying these objects and for tracing their overa distribution (Knox et a. 2001). The anisotropies detected in this background ight trace the arge-scae distribution of star-forming gaaxies and, to some extent, the underying distribution of the dark matter haos in which gaaxies reside. The CIB is thus a direct probe of the interpay between baryons and dark matter throughout cosmic time. The CIB has a redshift depth which compements current optica or near infrared measurements. This characteristic can be used to expore the eary buid-up and evoution of gaaxies, one of the biggest frontiers in cosmoogy. Indeed the hope is to be abe to use CIB anisotropies to improve our understanding of eary gas accretion and star formation, and to assess the impact of gaaxies on reionization. As dusty star-forming gaaxies start to be found up to very high redshift (e.g., z = 6.34, Riechers et a. 2013), this objective may be reachabe, even if quantifying the z 5 6 contribution to CIB anisotropy measurements to isoate the high-redshift part wi be very chaenging. As a start, CIB anisotropies can be used to measure the cosmic evoution of the star formation rate density (SFRD) up to z 6. Quantifying the SFRD at high redshift (z > 2.5) is a chaenging endeavour. Currenty, most of the measurements rey on the UV ight emerging from the high-redshift gaaxies themseves (e.g., Bouwens et a. 2009; Cucciati et a. 2012). To estimate their contribution to the tota SFRD one needs to appy the proper conversion between the observed UV rest-frame uminosity and the ongoing SFR. This conversion factor depends on the physica properties of the stear popuation (initia mass function, metaicities and ages) and on the amount of dust extinction, and is thus rather uncertain. Despite the significant amount of effort aimed at better understanding the UV-continuum sope distribution at high redshift, this remains one of the main imitation to SFRD measurements. The uncertainty on this conversion sometimes eads to significant revision of the SFRD (e.g., Behroozi et a. 2012; Bouwens et a. 2012; Casteano et a. 2012). Remarkaby, the estimates are now routiney made up to z 8 (e.g., Oesch et a. 2012a), and have even been pushed up to z 10 (Oesch et a. 2012b). One of the key questions, is how to quantify the contribution of the dusty, Corresponding author: G. Lagache guiaine.agache@ias. u-psud.fr 1 Panck ( is a project of the European Space Agency (ESA) with instruments provided by two scientific consortia funded by ESA member states (in particuar the ead countries France and Itay), with contributions from NASA (USA) and teescope refectors provided by a coaboration between ESA and a scientific consortium ed and funded by Denmark. star-forming gaaxies to the SFRD at high redshift. Since it is mosty impossibe to account for this contribution on the basis of optica/near-ir surveys, the best approach is to use the dusty gaaxy uminosity function measurements. However, such measurements at high redshift are chaenging with the current data, and this is where the CIB anisotropies, with their unmatched redshift depth, come into pay. The SFRD from dusty, star-forming gaaxies can be determined from their mean emissivity per comoving unit voume, as derived from CIB anisotropy modeing. The way gaaxies popuate dark matter haos is another ingredient that enters into the CIB anisotropy modeing. In particuar, the gaaxy bias the reationship between the spatia distribution of gaaxies and the underying dark matter density fied is a resut of the varied physics of gaaxy formation which can cause the spatia distribution of visibe baryons to differ from that of dark matter. If gaaxy formation is mainy determined by oca physica processes (such as hydrodynamics), the gaaxy bias is then approximatey constant on arge scaes (Coes 1993), and the gaaxy density fuctuations are thus proportiona to those of the dark matter. The proportionaity coefficient here is usuay caed as the inear bias factor, b. Its dependence on the uminosity, morphoogy, mass, and redshift of gaaxies provides important cues to how gaaxies are formed. However, the inear biasing parameter is at best a crude approximation, since the true bias is ikey to be nontrivia, i.e., non-inear and scae dependent, especiay at high redshift. At high redshift, the biasing becomes more pronounced, as predicted by theory (e.g., Kaiser 1986; Mo & White 1996; Wechser et a. 1998), and confirmed by the strong custering of dusty star-forming gaaxies (e.g., Steide et a. 1998; Bain et a. 2004; Cooray et a. 2010). CIB anisotropies can be used to constrain the biasing scheme for dusty star-forming gaaxies, which is crucia for understanding the process and history of gaaxy formation. However, measuring the CIB anisotropies is not easy. First, the instrument systematics, pipeine transfer function and beams have to be very we understood and measured. One can take advantage of recent experiments such as Hershe and Panck, for which diffuse emission is measured with better accuracy than their IRAS and Spitzer predecessors. Second, extracting the CIB requires a very accurate component separation. Gaactic dust, CMB anisotropies, emission from gaaxy custers through the therma Sunyaev Zedovich (tsz) effect, and point sources a have a part to pay. In cean regions of the sky, Gaactic dust dominates for mutipoes 200. This has a steep power spectrum (with a sope of about 2.8) and exhibits spatia temperature variations, and thus spectra energy distribution (SED) spatia variations. Distinguishing Gaactic from extragaactic dust is very difficut, as their SEDs are quite simiar, and both their spatia and spectra variations do not exhibit any particuar features. Currenty, the best approach is to rey on a Gaactic tempate; taking another frequency is not recommended as CIB anisotropies aso contribute. Taking a gas tracer as a spatia tempate is the best one can do, even if it has the drawback of not tracing the dust in a interstear medium phases. The CMB is very probematic at ow frequency, since its power spectrum is about 5000 and 500 times higher at = 100 than the CIB at 143 and 217 GHz, respectivey. For Panck at 217 GHz the CMB dominates the CIB for a ; at 353 GHz it dominates for < 1000; and at 545 GHz its power is 25 times ower at = 100 than the CIB. Any CMB tempate (taken from ow-frequency data or from compex component separation agorithms) wi be contaminated by residua foreground emission that wi have to be corrected for. At Panck frequencies ν > 200 GHz the tsz effect can be safey ignored, being cose to zero at 217 GHz and

4 100 times beow the CIB power spectrum at 353 GHz. However tsz contamination can come from the use of a CMB tempate that contains residua tsz power. At 100 GHz, based on the tsz power spectrum measured in Panck Coaboration XXI (2013) and the CIB mode deveoped in Panck Coaboration XVIII (2011), we estimate the tsz power spectrum to be 10 times higher than the CIB. The correction of any tsz contamination wi be made difficut by the intrinsic correation between the CIB and tsz signas (Addison et a. 2012; Reichardt et a. 2012). Finay, as bright point sources wi put extra power at a scaes in the power spectrum, point sources need to be carefuy masked up to a we-controed fux density eve. This step is compicated by the extragaactic source confusion that imits the depth of source detection for current far-infrared and submiimetre space missions. The pioneering studies in CIB anisotropy measurement with Hersche-SPIRE (Ambard et a. 2011) and Panck- HFI (Panck Coaboration XVIII 2011) are now extended in Viero et a. (2013b) for the former, and in this paper for the atter. The new Panck measurements benefit from arger areas, ower instrument systematics, and better component separation. They are not imited to auto-power spectra but aso incude frequency cross-spectra, from 143 to 857 GHz (and 3000 GHz with IRAS), and extend to bispectra at 217, 353 and 857 GHz. These more accurate measurements pose new chaenges for the modeing of CIB anisotropies. Our paper is organized as foows. We present in Sect. 2 the data we are using and the fied seection. Section 3 is dedicated to the remova of the background CMB and foreground Gaactic dust. We detai in Sect. 4 how we estimate the power spectrum and bispectrum of the residua maps, and their bias and errors. In the same section, resuts on CIB power spectra and bispectra are presented. In Sect. 5, we describe our modeing and show the constraints obtained on the SFRD, and the custering of high-redshift, dusty gaaxies. In Sect. 6, we discuss the 143 GHz anisotropies, the frequency decoherence, the comparison of our measurements with previous determinations, the SFRD constraints, and the CIB non-gaussianity. We concude in Sect. 7. The appendices give some detais about the Hi data used to remove Gaactic dust (Appendix A), the CIB anisotropy modeing (Appendices B and C), and aso present the power spectra and bispectra tabes (Appendix D). Throughout the paper, we adopt the standard ΛCDM cosmoogica mode as our fiducia background cosmoogy, with parameter vaues derived from the best-fit mode of the CMB power spectrum measured by Panck (Panck Coaboration XVI 2013): {Ω m, Ω Λ, Ω b h 2, σ 8, h, n s } = {0.3175, , , , , }. We aso adopt a Sapeter initia mass function (IMF). 2. Data sets and fieds 2.1. Panck HFI data We used Panck channe maps from the six HFI frequencies: 100, 143, 217, 353, 545, and 857 GHz. These are N side = 2048 HEALPix 2 maps (Górski et a. 2005), corresponding to a pixe size of We made use of the first pubic reease of HFI data that corresponds to temperature observations for the nomina Panck mission. The characteristics of the maps and how they were created are described in detai in the two HFI data processing and caibration papers (Panck Coaboration VI 2013; Panck Coaboration VIII )). At 857, 545, and 353 GHz, we use the zodiaca ight subtracted maps (Panck Coaboration XIV 2013). Some reevant numbers for the CIB anaysis are given in Tabe 1. Maps are given in units either of MJy sr 1 (with the photometric convention νi ν =constant 3 ) or K CMB, the conversion between the two can be exacty computed knowing the bandpass fiters. The mean coefficients used to convert frequency maps in K CMB units to MJy sr 1 are computed using noise-weighted band-average spectra transmissions. The mean conversion factors are given in Tabe 1. The map-making routines do not average individua detector maps, but instead combine individua detector data, weighted by the noise estimate, to produce singefrequency channe maps. As portions of the sky are integrated for different times by different detectors, the reative contribution of a given detector to a channe-average map varies for different map pixes. The effects of this change on the channe-average transmission spectra is very sma, being of the order of 0.05 % for the nomina survey coverage (Panck Coaboration IX 2013; Panck Coaboration ES 2013). As in Panck Coaboration XVIII (2011), the instrument noise power spectrum on the sma extragaactic fieds (see Sect. 2.3) is estimated with the jack-knife difference maps, which are buit using the first and second haves of each pointing period (a haf-pointing period is of the order of 20 minutes). The haf-ring maps give an estimate of the noise that is biased ow (by a coupe of percent) due to sma correations induced by the way the timeines have been degitched. However, as discussed in Panck Coaboration VI (2013), the bias is significant ony at very high mutipoes. As we stop our CIB power spectra measurements at = 3000, we can safey ignore this bias. For the arger GASS fied (see Tabe 2), we directy compute the cross-spectra between the two haf-maps to get rid of the noise (assuming that the noise is uncorreated between the two hafmaps). The effective beam window functions, b, are determined from panet observations, foding in the Panck scanning strategy, as described in Panck Coaboration VII (2013). Because of the non-circuar beam shape, the detector combinations, and the Panck scanning strategy, the effective b (ν) of each channe map appicabe to the smaest patches considered here varies across the sky. These variations are, however, ess than 1% at = 2000 and average out when considering many different patches, or arger sky areas. We wi therefore ignore them and consider a singe b (ν) for each frequency channe. Because of their experimenta determination, the b (ν) are sti affected by systematic uncertainties, which can be represented by a sma set of orthogona eigen-modes and whose reative standard deviation can reach 0.5% at = 2000 for ν = 857 GHz. This uncertainty is accounted for in the error budget IRIS data Our anaysis uses far-infrared data at 3000 GHz (100 µm) from IRAS (IRIS, (Mivie-Deschênes & Lagache 2005)). During its 10-month operation period, IRAS made two surveys of 98% of the sky and a third one of 75% of the sky. Each survey, caed an HCON for Hours CONfirmation, consisted of two coverages of the sky separated by up to 36 hours. The first two HCONs (HCON-1 and HCON-2) were carried out concurrenty, whie 3 The convention νi ν =constant means that the MJy sr 1 are given for a source with a spectra energy distribution I ν ν 1. For a source with a different spectra energy distribution a coour correction has to be appied (see Panck Coaboration IX 2013). 3

5 Tabe 1. Conversion factors, absoute caibration and inter-frequency reative caibration errors, beam FWHM and point source fux cuts, for HFI and IRIS. Here 2013 means the first pubic reease of Panck maps. Band Map version Conversion factors Abs. ca. error Re. ca. error FWHM Fux cut [GHz] K CMB /MJy sr 1 [νi ν = const.] [%] [%] [arcmin] [mjy] ± ± ± ± ± ± ± ± ± ± ± ± IRIS the third survey (HCON-3) began after the first two were competed. Due to exhaustion of the iquid heium suppy, the third HCON coud not be competed. We use the HCON difference maps to estimate the instrument noise power spectrum (just as we use the haf-pointing-period maps to estimate the instrument noise power spectrum for HFI). As for HFI at high frequencies, the IRIS 3000 GHz map is given in MJy sr 1 with the photometric convention νi ν =constant. The beam at 3000 GHz is not as we characterized as the HFI beams. The IRIS effective FWHM is about 4.3 (Mivie-Deschênes & Lagache 2005). We estimate the FWHM uncertainty using different measurements of the point spread function (PSF) coming from seected point sources used to study the PSF in the ISSA expanatory suppement, and the power spectrum anaysis from Mivie-Deschênes et a. (2002). The dispersion between those estimates gives an uncertainty of 0.5 on the FWHM Extragaactic fieds with high anguar resoution Hi data Foowing the successfu approach of Panck Coaboration XVIII (2011), we do not remove Gaactic dust by fitting for a power-aw power spectrum at arge anguar scaes, but rather use an independent, externa tracer of diffuse dust emission, the Hi gas. From 100 µm to 1 mm, at high Gaactic atitude and outside moecuar couds a tight correation is observed between far-infrared emission from dust and the 21-cm emission from gas 4 (e.g. Bouanger et a. 1996; Lagache et a. 1998; Panck Coaboration XXIV 2011). Hi can thus be used as a tracer of cirrus emission in our fieds, and indeed it is the best tracer of diffuse interstear dust emission. Athough Panck is an a-sky survey, we restricted our CIB anisotropy measurements to a few fieds at high Gaactic atitude, where Hi data at an anguar resoution cose to that of HFI are avaiabe. The 21-cm Hi spectra used here were obtained with: (1) the Parkes 64-m teescope; (2) the Effesberg 100-m radio Teescope; and (3) the 100-m Green Bank Teescope (GBT). Fied characteristics are given in Tabe 2. Further detais on the Hi data reduction and fied seection are given in Appendix A. The HEALPix HFI maps were reprojected onto the sma Hi GBT and EBHIS maps by binning the origina HEALPix data into Hi map pixes (Sanson-Famsteed, or SFL projection with pixe size of 3.5 for a fieds). An average of sighty more than four HEALPix pixes were averaged for each sma map pixe. For the GASS fied, the HFI data were convoved to the Hi anguar resoution (16.2 ), and then degraded to N side = 512. We have 11 fieds (one EBHIS, nine GBT and one GASS). The tota area used to compute the CIB power spectrum is about 4 The Pearson correation coefficient is > 0.9 (Lagache et a. 2000) deg 2, 16 times arger than in Panck Coaboration XVIII (2011) Point sources: fux cut and masks We use the Panck Cataogue of Compact Sources (PCCS, Panck Coaboration XXVIII 2013) to identify point sources with signa-to-noise ratio greater or equa to 5 in the maps, and we create point-source masks at each frequency. We mask out a circuar area of 3 σ radius around each source (where σ=fwhm/2.35). The point sources to be removed have fux densities above a chosen threshod. The threshod is determined using the number counts dn/ds on the ceanest 30% of the sky and by measuring the fux density at which we observe a departure from a Eucidean power aw; this departure is a proxy for measuring the fux density regime where the incompeteness starts to be measurabe. In practice, this departure often corresponds to about 80% of competeness (e.g., Panck Coaboration Int. VII 2013). The uncertainty on fux densities comes from the form of the dn/ds sope. Fux density cuts and a-sky effective beam widths are given in Tabe 1. For IRIS at 3000 GHz, we use the IRAS faint source cataogue (Moshir 1992) and we mask a sources with S 3000 > 1 Jy. 3. Extracting CIB from Panck -HFI and IRIS maps One of the most difficut steps in extracting the CIB is the remova of the Gaactic dust and the CMB. CMB anisotropies contribute significanty to the tota HFI map variance in a channes at frequencies up to and incuding 353 GHz. Gaactic dust contributes at a frequencies but is dominant at high frequencies. One approach is to keep a the components and search for the best-fit mode of the CIB in a ikeihood approach, accounting for CMB and dust (e.g., as a power aw). This is the phiosophy of the method deveoped for the ow-frequency data anaysis to extract the cosmoogica parameters (Panck Coaboration XV 2013; Panck Coaboration XVI 2013). However, with such an approach, the compexity of the ikeihood and the number of parameters and their degeneracies prevent the use of advanced modes for the custered CIB (modes beyond a simpe power aw). We thus decided to use another approach, based on tempate remova. To remove the CMB in the fieds retained for our anaysis, we used a simpe subtraction technique (as in Panck Coaboration XVIII 2011). This method enabes us to reiaby evauate CMB and foreground component residuas, noise contamination, and to easiy propagate errors (for exampe cross-caibration errors). It aso guarantees that high-frequency CIB anisotropy signas wi not eak into ower frequency, CMBfree maps. For the Gaactic dust, the present work focuses on 4

6 Tabe 2. CIB fied description: centre (in Gaactic coordinates), size, mean and dispersion of Hi coumn density. The given area is the size used for the CIB power spectrum computation (i.e., removing the area ost by the masking). The GASS Mask2 is not used for CIB power spectrum anaysis but for some tests on the quaity of our component separation, and for the measurement of the bispectrum. Mask2 incudes a of Mask1. Radio Teescope Fied name b Area Mean N(Hi) σ N(Hi) [deg] [deg] [deg 2 ] [10 20 cm 2 ] [10 20 cm 2 ] Effesberg EBHIS GBT N AG SP LH Bootes NEP SPC SPC MC Parkes GASS Mask GASS Mask very cean regions of the sky, for which Gaactic foregrounds can be monitored using anciary Hi observations. We describe in this section the remova of the two components. Some corrections are made at the map eve, others can ony be done at the power spectrum eve CMB remova A ow-frequency map as a CMB tempate The extraction of CIB anisotropies at ow frequency is strongy imited by our abiity to separate the CIB from the CMB. As a matter of fact, at mutipoe 100, the CIB anisotropy power spectrum represents about 0.2% and 0.04% of the CMB power spectrum at 217 and 143 GHz, respectivey. We decided in this paper to use the HFI owest frequency channe (100 GHz) as a CMB tempate. It has the advantage of being an interna tempate, meaning its noise, data reduction processing, photometric caibration, and beam are a we known. It aso has an anguar resoution cose to the higher HFI frequency channes. Foowing Panck Coaboration XVIII (2011), we removed the CMB contamination in the maps at ν 353 GHz. At 545 GHz as the CMB power represents ess than 5% of the CIB power, we removed the CMB in harmonic space. Using a owest possibe frequency channe as a CMB tempate ensures the owest CIB contamination, since the CIB SED is decreasing as ν 3.4 (Gispert et a. 2000). Contrary to what was done in Panck Coaboration XVIII (2011), where they used the 143 GHz channe as a CMB tempate, we used the HFI 100 GHz map. This is a good compromise between being a ow frequency tempate, and having an anguar resoution cose to the higher frequency HFI channes. Note that using the 100 GHz channe was not feasibe in Panck Coaboration XVIII (2011) as the data were too noisy, and the fied area too sma (140 versus 2240 deg 2 ). As detaied in Panck Coaboration XVIII (2011), we appied a Wiener fiter to the 100 GHz map, designed to minimize the contamination of the CMB tempate by instrument noise. Errors in reative photometric caibration (between channes) are accounted for in the processing, as detaied in Sect. 4.1 and Sect Foowing Panck Coaboration XVIII (2011), two corrections have to be appied to the measured CIB power spectra when using such a CMB tempate. First we need to remove the extra instrument noise that has been introduced by the CMB remova. This is done through: ( ) 2 N CMBres (ν) = N (ν 100 ) w 2 b (ν), (1) b (ν 100 ) with ν equa to 143, 217 or 353 GHz. b (ν) is the beam window function, w is the Wiener fiter, and N (ν 100 ) is the noise power spectrum of the 100 GHz map. It is computed in the same way as in the other frequency channes, using the haf-pointing period maps. Second, owing to the ower anguar resoution of the 100 GHz channe compared to 143, and 217 and 353 GHz, we aso have to remove the CMB contribution that is eft cose to the anguar resoution of the 143, 217 and 353 GHz channes: C CMBres (ν) = C CMB (ν) F 2 b2 (ν) (1 w ) 2, (2) with F being the pixe and reprojection transfer function (detaied in Sect. 4.1). Note that Eqs. 1 and 2 are the corrections for the auto-power spectra. They are easiy transposabe to cross-power spectra CMB tempate contamination to the CIB The ow-frequency channe CMB tempate has the disadvantage of being contaminated by the CIB and the tsz effect (the Gaactic dust is removed using our dust mode detaied in the foowing section, and IR and radio point sources are masked). Indeed the cross-spectra between the estimated CIB maps at ν and ν invove the a m product: a ν m aν m = { a CIB,ν m { a CIB,ν m + a SZ,ν m + a SZ,ν m w ( ν a CIB,100 m w ν ( a CIB,100 m )} + a SZ,100 m + a SZ,100 m )}, (3) where w ν is either zero if ν 545, or the Wiener fiter appied to the 100 GHz map (w ) if ν 353. Besides the signa C ν ν CIB that we want to measure, Eq. 3 invoves three additiona contributions that we have to correct for: tsz tsz; spurious CIB CIB; and CIB tsz correations. We discuss each of them in this section. 5

7 Tabe 3. SZ correction (Eq. 12) to be appied to the CIB measurements at 217 and 353 GHz, in Jy 2 sr 1 [νi ν uncertainty on C SZcorr is of order 10%, whie the uncertainty on C CIB SZcorr is about a factor of two. = constant]. The C SZcorr C CIB SZcorr C SZcorr C CIB SZcorr C SZcorr C CIB SZcorr CIB CIB spurious correations From Eq. 3, the CIB CIB spurious contribution reads C ν ν CIBcorr = w νc 100 ν CIB w ν C 100 ν CIB + w ν w ν C CIB. (4) Using a mode of CIB anisotropies, we can compute C ν ν CIBcorr. This correction incudes both the shot noise and the custered CIB anisotropies. The correction wi be taken into account when searching for the best-fit CIB mode: for each reaization of our CIB anisotropy modes (detaied in Sects. 5.4 and 5.5) we wi compute C ν ν CIBcorr. To iustrate the order of magnitude of the correction, we can use the mode constructed in Panck Coaboration XVIII (2011) to fit the eary Panck CIB measurements, and the shot-noise eves given in Sect. 5.1, and compute C ν ν CIBcorr when subtracting the 143 GHz map instead of the 100 GHz map as a CMB tempate. Note that this comparison is ony indicative, since this CIB mode at 143 and 100 GHz is an extrapoation of the power spectrum using the custering parameters of the 217 GHz best-fit mode, and the emissivities computed using the same empirica mode of gaaxy evoution. We show this comparison for the power spectrum in Fig 1. We see from this figure that the CIB obtained using the 143 GHz map as a CMB tempate is about 1.6 times ower than the CIB obtained using the 100 GHz map. Appying the correction (Eq. 4) argey decreases this discrepancy (compare the two dashed ines 5 ). Note that the correction is aso non negigibe when using the 100 GHz map: it is a factor 1.15 for 50 < < 700. This justifies appying the correction systematicay when fitting for our best CIB modes. We can extend the check on the impact of the choice of CMB map using the cross-correation between the CIB and the distribution of dark matter, via the ensing effect on the CMB (Panck Coaboration XVIII 2013). We specificay compared the cross-correation for the CIB at 217 GHz obtained using our two Wiener-fitered 100 and 143 GHz maps. We reached the same concusion as before, and retrieved the same underestimate of the CIB when using the Wiener-fitered 143 GHz rather than 100 GHz CMB map. Finay, we note that an aternative method of removing the CMB contamination was extensivey tested; this was based on an interna inear combination of frequency maps, combined (or not) with a needet anaysis. However, such CMB maps are often not suited to our purposes because they are, among other probems, contaminated by the CIB that has eaked from the highfrequency channes that are used in the component separation 5 Note that the two curves have not exacty the same eve as the corrections inked to the tsz contributions are not the same when using the two CMB tempates, and they are not appied for this pot. Fig. 1. Power spectrum of the residua map (map dust CMB) at 217 GHz obtained in the GASS fied with different CMB tempates: the 100 GHz Wiener-fitered map (red points); the 143 GHz Wiener-fitered map (bue points); and the SMICA map (orange points). These CMB maps are contaminated by both CIB anisotropies and shot noise. For the CIB measured using Wiener-fitered CMB maps, we can easiy compute the correction to appy to recover the true CIB, using a mode of the CIB anisotropies. Such corrected power spectra are shown with the dashed ines (using the CIB mode from Panck Coaboration XVIII 2011). They are ony indicative, since the correction strongy depends on the CIB mode. process. We compare the CIB obtained using the 100 GHz and SMICA CMB maps (Panck Coaboration XII 2013) in Fig. 1. We see that they are compatibe within 1 σ (red-dashed ine and orange points). Again this comparison is ony indicative, since the SMICA CMB map main contaminants are SZ, shot noise from point sources, and CIB 6 ; those contaminants have not been corrected for here, because the correction woud need fuy reaistic simuations. From Eq. 3, the tsz tsz spurious con- tsz tsz correation tribution reads C ν ν SZcorr = Cν ν SZ + w νw ν C SZ w ν C ν 100 SZ w ν C ν 100 SZ. (5) 6 The contamination of the SMICA CMB map by foregrounds has been computed by running SMICA on the FFP6 simuations. 6

8 We can make expicit the frequency dependence of the tsz and write T ν SZ (θ, φ) = g ν a SZ m, (6) where g ν is the conversion factor from the tsz Compton parameter y to CMB temperature units. Hence m Panck Coaboration: CIB anisotropies with Panck C ν ν SZ = g2 νc SZ. (7) Eq. 5 then becomes C ν ν SZcorr = C { SZ gν g ν + w ν w ν g g 100(w ν g ν + w ν g ν ) }. (8) We compute C SZcorr using the tsz power spectrum, C SZ, and the conversion factors, g ν, given in Panck Coaboration XXI (2013). The uncertainty on C SZ is about 10%. From Eq. 3, the tsz CIB spurious con- tsz CIB correation tribution reads C ν ν CIB SZcorr = C ν ν CIB SZ + ν Cν CIB SZ w νc 100 ν CIB SZ w ν C100 ν CIB SZ w ν C ν 100 CIB SZ w ν Cν 100 CIB SZ + 2w νw ν C CIB SZ, (9) where C ν ν CIB SZ is the notation for the cross-spectrum between CIB(ν) and SZ(ν ). This correction is highy dependent on the mode used to compute the cross-correation between tsz and CIB; we use the mode from Addison et a. (2012). We made the assumption that C ν ν CIB SZ = acib m (ν)asz m (ν ) = g ν φ(ν)c CIB SZ, (10) where φ(ν) is the ampitude of the power spectrum of the CIB correated with the tsz, C CIB SZ, taken from Addison et a. (2012). This paper aso provides exampes of cross-spectra, with a reference frequency at 150 GHz. We use this reference frequency and power spectrum ratios to compute C ν ν SZ CIB foowing C ν ν SZ CIB = φ(ν ) φ(150) g ν C SZ CIB g. (11) 150 We show in Fig. 2 the measured CIB, C ν ν CIB (measured), together with the corrected one: C ν ν CIB = Cν ν CIB (measured) { C ν ν SZcorr + Cν ν CIB SZcorr}. (12) We aso show the ratio of the corrections to the measured CIB, and give the vaues of the corrections at 217 and 353 GHz in Tabe 3. We see that tsz contamination is the highest for the combination, with a contamination of the order of 15%. It is ess than 5% and 1% for and , respectivey. The tsz power spectrum measured by Panck Coaboration XXI (2013) is uncertain by 10%, whie tsz CIB is uncertain by a factor of two (Addison et a. 2012). Hopefuy, where the contamination is important (i.e., ), the dominant contribution to the CIB comes from C ν ν SZcorr. Hereafter, we therefore appy the correction coming from the tsz contamination to the measured CIB, and add the uncertainties of the correction quadraticay to the CIB uncertainties. When cross-correating maps at 353 GHz and above 545 GHz, the correction inked to the tsz contamination is dominated by the term C ν ν CIB SZcorr, which is highy uncertain. The correction is about 3%, < 1%, 4% and < 2% for the , , and cross-power spectra, respectivey. Athough sma, for consistency with the case ν 353 GHz and ν 353 GHz, we aso appy the tszreated corrections to the measured CIB when ν 353 GHz and ν 545 GHz. Fig. 2. Top: Residua map (a.k.a CIB) auto- and cross-spectra measured at 217 and 353 GHz (circes). The dashed ines represent the measured power spectra corrected for the tsz contamination (both tsz and tsz CIB, see Eq. 8 and 9, respectivey). Bottom: Absoute vaue of the ratio C ν ν SZcorr /Cν ν CIB [measured] (continuous ine) and C ν ν CIB SZcorr /Cν ν CIB [measured] (dot-dashed ine, negative). The highest contamination is for the power spectrum, where the tota correction represents about 15% of the measured CIB power spectrum. For C ν ν SZcorr, the uncertainty is about 10%. On the contrary, C ν ν CIB SZcorr is poory constrained, as the mode used to compute it is uncertain by a factor of two Dust mode Many studies, using mosty IRAS and COBE data, have reveaed the strong correation between the far-infrared dust emission and 21-cm integrated emission at high Gaactic atitudes. In particuar, Bouanger et a. (1996) studied this reation over the whoe high Gaactic atitude sky and reported a tight dust-hi correation for N HI < cm 2. For higher coumn densities the dust emission systematicay exceeds that expected by extrapoating the correation. Examining specific high Gaactic atitude regions, Arendt et a. (1998), Reach et a. (1998), Lagache et a. (1998) and Lagache et a. (1999) found infrared excesses with respect to N HI, with a threshod varying from 1.5 to cm 2. Panck Coaboration XXIV (2011) presented the resuts from the comparison of Panck dust maps with GBT Hi observations in 14 fieds covering more than 800 deg 2. They showed that the brighter fieds in their sampe, with an average Hi coumn density greater than about cm 2, show significant excess dust emission compared to the Hi coumn density. Regions of excess ie in organized structures that suggest the presence of hydrogen in moecuar form. Because of this, we restrict our CIB anaysis to the ceanest part of the sky, with mean N HI < cm 2. 7

9 Constructing dust maps As detaied in Panck Coaboration XXIV (2011), Panck Coaboration XVIII (2011) and in Appendix A, we constructed integrated Hi emission maps of the different Hi veocity components observed in each individua fied: the oca component, typica of high-atitude Hi emission, intermediate-veocity couds (IVCs), and high-veocity couds (HVCs), if present. To remove the cirrus contamination from HFI maps, we determined the far-ir to miimetre emission of the different Hi components. We assumed that the HFI maps, I ν (x, y), at frequency ν can be represented by the foowing mode I ν (x, y) = α i νnhi i (x, y) + C ν(x, y), (13) i where NHI i (x, y) is the coumn density of the ith Hi component, α i ν is the far-ir to mm versus Hi correation coefficient of component i at frequency ν and C ν (x, y) is an offset. The correation coefficients α i ν (often caed emissivities) were estimated using χ 2 minimization given the Hi, HFI and IRIS data, as we as the mode (Eq. 13). We removed from the HFI and IRIS maps the Hi veocity maps mutipied by the correation coefficients. For EBHIS and GBT fieds, we considered ony one correation coefficient per fied and per frequency. The remova was done at the HFI and IRIS anguar resoutions, even though the Hi map is of ower resoution ( 10 ). This is not a probem because cirrus, with a roughy k 2.8 power-aw power spectrum (Mivie-Deschênes et a. 2007), has negigibe power between the Hi (GBT and EBHIS) and HFI and IRIS anguar resoutions, in comparison to the power in the CIB. The correation of the dust emission with the different Hi veocity components and its variation from fied to fied is iustrated in Fig. 5 of Panck Coaboration XVIII (2011). For the GASS fied, due to its arge size the dust mode needs to take into account variations of the dust emissivity across the fied. We make use of an anaysis of the dust-togas correation over the southern Gaactic cap (b < 30 ) (Panck Coaboration XXXI 2013) using Hi data from the GASS southern sky survey (Kabera et a. 2010). The Panck- HFI maps are ineary correated with Hi coumn density over an area of 7500 deg 2 covering a of the southern sky (δ < 0 ) at b < 30 (17% of the sky). We use HFI maps corrected for the mean vaue of the CIB (Panck Coaboration VIII 2013). The Panck maps and Hi emission at Gaactic veocities are correated over circuar patches with 15 diameters, centered on a HEALPix grid with Nside=32. The inear regression is iterated to identify and mask sky pixes that depart from the correation. At microwave frequencies the correation coefficients (α ν ) and offsets (C ν ) derived from this inear correation anaysis incude a significant CMB contribution that comes from the chance correation of the cosmic background with the Hi emission. This contribution is estimated by assuming that the SED of dust emission foows a modified backbody spectrum for 100 ν 353 GHz. The fit is performed on the differences α ν α 100GHz that are CMB-free for each sky area when expressed in units of K CMB. This yieds vaues of the correations coefficients corrected for CMB, α c ν. The detaied procedure is described in Panck Coaboration et a (2013). In this section we expain how the resuts of this study are used to buid a mode of the dust contribution to the sky emission. To make the dust mode in the GASS fied, we start by buiding a map of the dust emission to Hi coumn density ratio, interpoating the vaues of α c ν, corrected for the CMB, using HEALPix sky pixes with a Gaussian kerne. The 1σ width of this convoution kerne is equa to the pixe size 1.8 of the HEALPix grid for Nside=32. To reduce the data noise at ν < 353 GHz we use the modified backbody fits to α ν α 100GHz and not the measured vaues of α ν. This yieds a set of six maps of the dust emission per unit Hi coumn density for a HFI frequencies from 100 to 857 GHz. We aso buid a set of Gaactic offset maps from the offsets C ν of the Panck-Hi correation. These offsets comprise contributions from Gaactic dust and the CMB. We subtract the CMB contribution assuming that the SED of the dust contribution to C ν is the same as that of α c ν for each sky area. For each frequency, the dust mode is the product of the dust emission per unit Hi coumn density times the Hi map, pus the Gaactic offset map. The anguar resoution of the mode is that of the Hi map (16.2 ). As for the smaer EBHIS and GBT fieds, the mode in the GASS fied ony accounts for the emission of dust in Hi gas. Couds with a significant fraction of moecuar gas produce ocaized regions with positive residua emission. The histogram of residua emission at 857 GHz aso shows a non-gaussian extension towards negative vaues (as observed in the EBHIS fied, see Appendix A.3). In the maps these pixes correspond to ocaized Hi couds with no (or a weak) counterpart in the Panck map. In the GASS survey, these couds are ikey to be part of the Mageanic Stream, with radia veocities within the range used to buid the Gaactic Hi map. For the anaysis of the CIB we mask pixes with positive and negative residuas arger than 3 σ. To be conservative this first mask is sighty enarged, and apodized. It covers about 4400 deg 2 (Mask2 in Tabe 2). This mask sti contains some regions with N HI cm 2 and thus potentia IR emission from moecuar gas couds. To measure the CIB power spectrum, a regions with N HI cm 2 are further masked (Mask1). The fina area is about 1900 deg Dust map uncertainties The uncertainties estimated for the emissivities by the eastsquares fit method are substantiay underestimated, as they do not take into account systematic effects associated with the CIB and the CMB, nor the spatia variation of the emissivity inside a patch (or a fied). We use the GASS fied to estimate the error we have on the dust mode. For this fied, we have the arge-scae variations (at 15 ) of the dust emissivities. We make the hypothesis that the measured variations extend to smaer anguar scaes, with a distribution on the sky given by a power spectrum with a sope 2.8, simiar to that of the dust emission. Within this assumption, we simuate mutipe maps of the dust emissivity that a match the dispersion of the dust emissivity measured at 857 GHz. For each reaization, we obtain a dust map at 857 GHz by mutipying the dust emissivity map by the GASS map of Gaactic Hi. Dust maps at other frequencies are obtained by scaing the 857 GHz fux using the mean dust SED given in Panck Coaboration XXXI (2013). These simuations provide a good match to the Gaactic residuas of the dust-hi correation characterized in Panck Coaboration XXXI (2013). We obtain simuated maps of the sky emission adding reaizations of the HFI instrument noise, CIB and CMB to the dust maps. We perform on the simuated sky maps the same correation anaysis with Hi as that done on the Panck maps. For each simuation, we obtain vaues of the dust emissivity that we compare with the input emissivity map averaged over each sky patch. We find that there is no systematic difference between the vaues derived from the correation anaysis and the input vaues of the dust 8

10 anaysis. Mask2 contains higher-coumn density regions, so it is not suitabe for CIB-ony anaysis, but is usefu, for exampe, when cross-correating the CIB with other arge-scae structure tracers (when dust contamination is ess of a probem, e.g., Panck Coaboration XVIII 2013) and for the bispectrum measurement at ow frequencies. As expected, the power spectra of residua maps computed using Mask2 are in excess compared to the CIB. Whatever the frequency, this excess represents about 5-10% of the cirrus power spectrum at ow. This eads to a CIB from Mask2 that is overestimated by a factor of 1.5 at 857 GHz and 1.2 at 217 GHz, for 200, compared to the CIB from Mask1. Taking such a residua at the 5-10% eve of the dust power spectrum (as observed between Mask1 and Mask2) woud ony strongy affect the first two bins, at = 53 and 114. This is consistent with the simuation anaysis (see Fig. 3). We wi thus not use those bins when searching for the best CIB mode, and we consider those points as upper imits. Fig. 3. Power spectrum anaysis of the simuations made at 857 GHz in the GASS fied to characterize cirrus residuas. The bue and red diamonds compare the power spectrum of our simuated and HFI maps, respectivey, whie the bue and orange dots are the simuated and recovered CIB, respectivey. The recovered CIB is biased by cirrus residuas at ow mutipoes. The measured CIB (obtained on the GASS Mask1 fied, dispayed with a but cirrus error bars) shows the same behaviour at ow mutipoes. Thus the measurements in the first two bins have to be considered as upper imits. As discussed in Sect , the simuations are used to compute the error bars inked to the cirrus remova. emissivities. The fractiona error, i.e., the standard deviation of the difference between measured and the input vaues divided by the mean dust emissivity, is 13% of the mean dust emissivity at 857 GHz (Panck Coaboration XXXI 2013). This error increases sighty towards ower frequencies up to 16 and 21% for the 143 and 100 GHz channes. We show in Fig. 3 the power spectrum of the recovered CIB, compared to the input CIB. We see that it is strongy biased by Gaactic dust residuas in the first two mutipoe bins. These points have thus to be considered as upper imits. For the other points, we use the simuations to set the error bars inked to the Gaactic dust remova. The observed inear correation between the sigmas of dust residuas and N HI is used to compute the power spectrum of Gaactic dust residuas for each fied, foowing C Fied = C GASS Gaactic dust residuas HI > < NFied < N GASS HI > 2. (14) One of the main issues when using Hi coumn density as a dust tracer is the presence of dark gas (Panck Coaboration XIX 2011; Panck Coaboration XXIV 2011), ionised gas (Lagache et a. 2000), and emissivity variation at scaes smaer that those probe by the correation anaysis. The dust contribution of the dark gas becomes rapidy visibe (not ony at high frequencies), when N HI cm 2. In addition to the simuations discussed in the previous section, we investigated the contribution of dust residuas by computing the CIB power spectra on the GASS fied, using Mask1 and Mask2. Mask1 is very conservative and is our nomina mask for CIB 3.3. CMB and Gaactic dust ceaned maps We show in Fig. 4, one exampe of the ceaning process, from the frequency to the CIB maps, for the SPC5 fied. The bottom row shows the residua CIB maps, smoothed to 10. In Fig. 5 are shown the CIB maps in a part of the GASS fied, at 16.2 resoution. We see from both figures that common structures, corresponding to CIB anisotropies, are ceary visibe. As previousy noticed (Panck Coaboration XVIII 2011), the three intermediate frequencies (353, 545 and 857 GHz) show highy correated structures. On the contrary, the 3000 GHz data on one hand, and the 217 GHz on the other, revea a decoherence, which can be attributed to the redshift distribution of the CIB anisotropies. We wi come back to this decoherence by measuring the correation coefficients in Sect There are two frequencies where extracting the CIB from the frequency maps is particuary chaenging. At 3000 GHz, the cirrus contamination is the highest and we observe more spatia variations of the dust Hi emissivity which are difficut to manage. This is due to the contamination at 3000 GHz data by a hotter dust component, which may be inked to the so-caed very sma grains in some interstear fiaments. Consequenty, we have not tried to extract the CIB in the GASS fied at 3000 GHz, and the Bootes fied has been discarded for the CIB anaysis due to interstear dust residuas (due to one IVC component, which has both a high emissivity and a hot spectrum; P. Martin, private communication). Moreover, the EBHIS fied is right in the midde of the missing IRAS observation. It is thus aso not used for the CIB anaysis. In the end, the tota area used to compute the CIB power spectrum at 3000 GHz is 183 deg 2. At 143 GHz, we expect the correated CIB anisotropies in brightness to be about 1 2% of the CMB anisotropies for mutipoes (whie it is about 3 15% at 217 GHz). The remova of the CMB has thus to be extremey accurate. Moreover, the expected CIB is ower than the instrument noise. Constraints can ony be obtained on the arge GASS fied that is more immune to noise. We see from Fig. 5 that the 143 GHz CIB map shows some structures that are correated with the higher CIB frequency maps. We discuss in Sect. 6.1 our attempt to obtain some constraints at this frequency. We used two different approaches to measure the CIB power spectra according to the size of the fieds: (i) for the EBHIS and GBT fat-sky fieds, we used an updated version of 9

11 Fig. 4. Maps of the roughy 25 deg 2 of the SPC5 fied, from eft to right: 143, 217, 353, 545, 857 and 3000 GHz. From top to bottom: raw HFI and IRIS maps; CMB-ceaned maps; residua maps (CMB- and cirrus-ceaned); point source masks; and residua maps smoothed at 10 to highight the CIB anisotropies. The joint structures ceary visibe (bottom row) correspond to the anisotropies of the CIB. POKER (Ponthieu et a. 2011), and we computed the error bars using Monte Caro simuations (Sect. 4.1); (ii) for the GASS fied, we used Xspect (Tristram et a. 2005), a method that was first deveoped for the Archeops experiment to obtain estimates of the anguar power spectrum of the CMB temperature anisotropies, incuding anaytica error bars (Sect. 4.2). Having two competey different pipeines and a many fieds with various dust and CMB contaminations (and noise contributions), is extremey vauabe, as it aows us to test the robustness of our approach. 4. Anguar power spectrum and bispectrum 4.1. Cross-correation pipeine for the EBHIS and GBT fieds To determine the cross-correation between the CIB observed at two frequencies, ν 1 and ν 2, we used a modified version of POKER (Ponthieu et a. 2011). POKER is an agorithm that determines the power spectrum of a map, corrects for mask aiasing and computes the covariance between each power spectrum bin via a Monte Caro approach. It has been used to measure the power spectrum of the CIB as observed by Panck- HFI (Panck Coaboration XVIII 2011) and is described in detai therein. In the foowing, we wi ca auto-power spectrum C ν 1 the usua anguar power spectrum and cross-power spectrum its generaization to two different frequencies defined as C ν 1ν aν 1 m aν 2 m + a ν 1 m aν 2 m = (2π) 2 C ν 1ν 2 δ δ mm, (15) where a ν m are the Fourier coefficients of the CIB anisotropy at the observation frequency ν. We take a common mask for both frequencies and it is straightforward to generaize the agebra presented in Ponthieu et a. (2011) and Panck Coaboration XVIII (2011) to obtain an unbiased estimate of the cross-power spectrum: C ν 1ν 2 b Mbb 1 ˆP ν 1ν 2 b N ν 1ν 2, instr b N ν 1ν 2, res b. (16) b Here ˆP ν 1ν 2 b denotes the binned pseudo-cross-power spectrum of the maps at frequencies ν 1 and ν 2, and M bb is the so-caed mode-mixing matrix that is described in detai in Eq. 24 of Panck Coaboration XVIII (2011) and its appendix. We reca that it incudes the mode-couping effects induced by the mask, 10

12 Fig. 5. Residua maps (Gaactic dust and CMB removed) at 16.2 anguar resoution, extracted from the area covered by the GASS Hi data (on Mask1). The patch covers the smoothing by the instrumenta beam, and the map pixeization (see beow). The two noise terms, N ν 1ν 2, instr b and N ν 1ν 2, res b, refer, respectivey, to the instrument noise and to the contribution of what can be considered as random components at the map eve, such as the CMB residuas of our component separation and the noise of the 100 GHz map that propagates to our maps (see Sect. 3.1). Of course, Eq. 16 appied to ν 1 = ν 2 gives the auto-power spectrum of the anisotropy, and we computed the two auto-spectra at ν 1 and ν 2 at the same time as the cross-power spectrum. We buit very simiar simuation and anaysis pipeines to those of Panck Coaboration XVIII (2011) to obtain our measures and their associated error bars. We here briefy reca the main steps of these pipeines and highight the modifications introduced by the generaization from auto-power spectra estimation to that of cross-power spectra. Anaysis pipeine. 1. In order to combine our measurements from different fieds, we define a common mutipoe binning. Above 200, we choose a ogarithmic binning / = 0.3, whie beow 200, we respect the generic prescription that bins of mutipoes shoud be arger than twice the mutipoe corresponding to the argest anguar scae contained in the fied. 2. We define a common weight map W ν 1ν 2 that masks out bright point sources found at both frequencies. Together with the mask, three different transfer functions must be accounted for in the computation of M bb (Eq. 24 of Panck Coaboration XVIII 2011): (i) the instrument beam transfer function that depends on the exact beam shape and the scan pattern on the observed fied, athough since the variation of beam transfer function is ess than 1% between our fieds, we take the same one for a of them (see Sect. 2.1); (ii) the HEALPix pixe window function; and (iii) the reprojection from HEALPix maps to the fat-sky maps used by POKER. The first transfer function comes from a dedicated anaysis (Panck Coaboration VII 2013). The second 11

13 one is provided by the HEALPix ibrary. The third one is computed via Monte Caro simuations: we simuate fu sky HEALPix maps of diffuse emission with a typica CIB power spectrum, reproject them on our observed patches and compute the anguar power spectra; the ratio between the measured and the input power spectrum gives the transfer function. This ratio is the same for a fieds (a in SFL projection with 3.5 pixes) within statistica error bars, so we compute the average and appy it to a fieds. 3. An estimate of the noise auto-power spectrum at ν 1 and ν 2 is obtained from jack-knife maps. Indeed, at each frequency, two maps can be buit using ony the first (respectivey, the second) haf of each Panck observation ring. The difference between these maps is dominated by instrumenta noise. Appying POKER to these difference maps gives an estimate of the instrument noise auto-power spectrum at each frequency N ν i, instr b. The noise contribution to the auto-power spectrum are negigibe at high frequencies. 4. N ν 1ν 2, res b is the contribution of CMB residuas both from the component separation and from the propagation of noise in the 100 GHz CMB map. We have estimates of each component of this residua power spectrum in space on the sphere (see. Sect. 3.1) and combine them into our measurement bins. 5. We now appy Eq. 16 to our data and determine their autoand cross-power spectra. Simuation pipeine. The simuation pipeine is essentia to provide the error bars on our estimates coming from the anaysis pipeine. We created 100 simuations of our data maps and computed their auto- and cross-power spectra. The dispersion of these spectra gives the compete covariance matrices of our binned auto- and cross-power spectra and their associated error bars. For each reaization we foow these steps. 1. The measured auto- and cross-power spectra are used as inputs to simuate CIB anisotropy maps at each frequency, with the appropriate correated component. To do so, we generate random Gaussian ampitudes x and y in Fourier space, such that: a ν 1 = x (C ν 1 )1/2 ; a ν 2 = x C ν 1ν 2 /(C ν 1 )1/2 + y { C ν 2ν 2 ( C ν 1ν 2 ) 2 } 1/2 /C ν For each frequency ν i, we simuate a noise map with the appropriate power spectrum ˆN ν i, instr and add it to the simuated signa map. 3. We add the simuations of CMB and 100 GHz noise residuas (Eqs.1 and 2), and of CMB residuas induced by reative caibration errors, so that we have a fina pair of maps at ν 1 and ν 2 that are a faithfu representation of our data. Error estimation. Statistica uncertainties due to instrument noise and component separation residuas are derived using the simuation pipeine. Systematic uncertainties incude mask aiasing effects, imperfect subtraction of foreground tempates, and beam and projection transfer function errors. We studied some fieds in common with Panck Coaboration XVIII (2011), with very simiar masks, and showed that the correction of mask effects by POKER eads to no more than 2% uncertainty on the resut. The transfer function due to the projection of spherica HEALPix maps to our square patch is determined via Monte Caro (see step 2 of the description of the anaysis pipeine). This process provides estimates F b of the transfer function in our measurement bins. However, we need an estimate of the transfer function F for a modes, to incude it in the derivation of M bb. We therefore construct a smooth interpoation of our measures. The projection transfer function pays the same roe as an extra instrumenta beam and enters the derivation of M bb. Roughy speaking, it damps the signa at high and correcting for this effect corresponds to dividing the measured power spectrum by the damping function. The statistica uncertainty on the determination of F is smaer than 1%, and hence eads to the same uncertainty on the C. Between the first anaysis of CIB anisotropies with Panck- HFI and this work, much progress has been achieved on the beam measurements (Panck Coaboration VII 2013). Based on this progress, we have better estimates of the beam shapes and better assessments of the uncertainties on these beam transfer functions, both for auto-spectra and for cross-spectra between different frequency bands. We used the eigenmodes to compute the beam transfer function uncertainties, which are a smaer than 0.55% in our anguar range. On the contrary, auto- and cross-spectra invoving IRIS suffer from a much arger beam uncertainty (0.5 for a FWHM of 4.3 ). The systematic uncertainties on the contribution of Gaactic dust residuas (see Sect ) are added ineary to the statistica error bars. An exampe of the error budget is given in Tabe Cross-correation pipeine for the GASS fied For the arge GASS fied, we used another strategy: Due to the size of the fied, which vioates the fat-sky approximation used for the EBHIS and GBT fieds, we compute the anguar auto- and cross-power spectra on the HEALPix maps, using the Xspect agorithm (Tristram et a. 2005). We appy the Gaactic dust mask discussed in Sect The power spectra are computed using maps at the HFI anguar resoution (N side = 2048). As the anguar resoution of the Hi map is 16, we use a hybrid method to remove the Gaactic dust. On arge anguar scaes ( 590), we remove the cirrus from the maps using Hi. On sma anguar scaes ( > 590), we remove an estimate of the dust power spectrum. This estimate comes from the dust mode that is fit on arge anguar scaes ( ) by a power aw, foowing Mivie-Deschênes et a. (2007), and then extrapoated to sma anguar scaes. The power-aw fit has been shown to be vaid for the whoe range of anguar scaes covered by our measurements (e.g., Mivie-Deschênes et a. 2010). As for the fat-sky fieds, the CMB is removed as described in Sect Statistica error bars are not computed using simuations but using anaytica formuations (see beow). Auto- and cross-power spectra. We used the maps buit from the first and second haves of each pointing period. As described in Tristram et a. (2005), the spherica harmonic coefficients from the cut-sky maps are corrected from the modecouping introduced by the mask, as we as the beam smoothing effect in the harmonic domain. The cross-power spectra are unbiased estimates of the anguar power spectrum, avoiding any correction for the instrument noise, contrary to our measurements done in Sect We computed the spectra using the same mu- 12

14 Tabe 4. Exampe of a power spectrum averaged for the fat fieds. This iustrates the order of magnitude of the different errors. The tota error contains the cosmic variance and instrumenta noise, and aso the cirrus residuas (CMB is negigibe at this frequency). The contribution of cirrus errors ony is given in the sixth coumn for comparison. The errors inked to the projection of the fieds on the tangentia pane and those due to the beam, athough systematic and not stochastic, are given for convenience in the same units as the tota power C, in coumns 7 and 8, respectivey. 857 GHz 857 GHz min max C Tota error Cirrus error Systematic errors [Jy 2 sr 1 ] [Jy 2 sr 1 ] [Jy 2 sr 1 ] [Jy 2 sr 1 ] Projection Beam tipoe binning as that of the fat fieds. We checked that the bin to bin correation was smaer than 1%. We show in Fig. 6 an exampe of a cross-power spectrum ( ) computed on maps for which the CMB has been removed. We aso show the power spectrum of the dust mode, fitted by a broken power aw. The sope of the dust power spectrum appears to fatten at 110, with a sope in the range 2.1 to 1.8 for < 110, and 2.8 to 2.7 for > 110, depending on the frequency. We compare the CIB power spectrum obtained by removing the dust at the map eve to that obtained by subtracting the fit of the dust mode power spectrum. For 200 we have exceent agreement. We aso see that for 700 the dust remova has a negigibe impact. At ow, where the dust correction is important, we chose to use the dust remova on the map, since it eads to a ower variance on the residua power spectrum, as shown in Pénin et a. (2012b). Indeed, the spatia subtraction removes each moment of the statistics, whereas the subtraction of the power spectrum ony removes the first two moments. At ow, errors on the fit are aso quite arge. We arbitrary decide to take the transition between the dust remova on the map and on the power spectrum at = 510. The exact choice of the mutipoe for the transition has no consequence on the resuting CIB power spectrum. Error bars. We quadraticay combine the foowing error terms to obtain the fina uncertainty on the GASS CIB power spectra: The error bars on the spectrum computed anayticay as described in Tristram et a. (2005), from the auto-power and cross-power spectra of the two maps. They incude both the samping variance (which dominates at arge scaes) and the instrumenta noise (which dominates at sma scaes). The errors inked to the CMB remova. Errors on the extra instrumenta noise that have been introduced by the CMB remova (see Eq. 1) are computed using the errors on the noise measurements at 100 GHz. For the error on the CMB contribution that is eft cose to the anguar resoution of the 143 and, 217 and 353 GHz channes (see Eq. 2), we use the theoretica cosmic variance estimate on the determination of the CMB power spectrum. Finay, we add the errors that come from the reative photometric caibration in the CMB remova. Fig cross-power spectrum in the GASS fied (using Mask1). The back ine is the cross-power spectrum of the dust mode, with error bars not shown for carity. The red points are the resut of a power-aw fit to the dust mode, using the bins of the CIB power spectrum. The CIB obtained by the spatia remova of the dust is shown in orange (note that it stops at 1000 due to the anguar resoution of the Hi data), whie the CIB obtained from the spectra remova of the dust (i.e., on the power spectrum) is shown in ight bue (diamonds). We see that the two methods give identica CIB for 300. In dark bue is the cross-power spectrum of the CMB-free frequency maps; the dust remova is negigibe for 700. For carity the points have been shifted by ± 3% and the error inked to the cirrus bias (see Sect 3.2.2) have not been added. As detaied in Sect , the uncertainty on the dust mode is derived from simuations. It is added ineary to the statistica error bars. For 510, we aso add the error on the dust mode fit. Beam errors are computed using the eigenmodes. They are the same as those detaied in Sect. 2.1 and

15 4.3. Bispectrum pipeine for the GASS fied The bispectrum b is the 3-point correation function in harmonic space: a 1 m 1 a 2 m 2 a 3 m 3 = b G m 1m 2 m , (17) with G m 1m 2 m the Gaunt integra (Sperge & Godberg 1999). It is a owest-order indicator of the non-gaussianity of the fied. The maps used are the same as for the power spectrum anaysis, but degraded to N side = 512. As the signa-to-noise ratio for bispectra is quite ow compared to that of power spectra, bispectra have to be measured on the argest possibe cean area of the sky. Here, we measure the bispectrum on GASS Mask2. We appy the binned bispectrum estimator described in Lacasa et a. (2012) and used for the Panck tsz map anaysis (Panck Coaboration XXI 2013) and non-gaussianity constraints (Panck Coaboration XXIV 2013). A arge bin size = 128 has been adopted to minimize mutipoe correations due to the mask. We used a mutipoe range min = 129 to max = 896, eaving six mutipoe bins and 43 bispectrum configurations ( 1, 2, 3 ) (accounting for permutation invariance and the trianguar condition). We ony considered auto-bispectra for simpicity, i.e., at a singe frequency (see Tabe D.3). For each frequency, we computed the auto-bispectra of the two maps buit using the two haf-pointing period rings, and average these bispectra for a raw estimate. The raw estimate has been then debiased from mask and beam effects using simuations. Specificay we generated simuations with a high eve of non-gaussianity and a bispectrum corresponding to the CIB prescription from Lacasa et a. (2012), computed the ratio of the bispectrum of the masked map to the fu-sky bispectrum, and finay averaged this ratio over simuations, finding a quick convergence especiay at high mutipoes. We found this ratio to be very cose to f sky b 1 (ν) b 2 (ν) b 3 (ν) (with b (ν) the beam window function), showing that the mutipoe correation is indeed negigibe for this bin size and bispectrum. We checked on the two haf maps that the Panck noise is cose to Gaussian, hence it does not bias our bispectrum estimates; it however increases their variance. The error estimates are the sum in quadrature of: cosmic variance computed with anaytica formuae and incuding the noise; dust residuas from (the absoute vaue of) the bispectrum of the dust mode, scaed to the residua dust ampitude found in Sect Note that beam errors are competey negigibe in the range of considered. The fu-sky cosmic variance of the bispectrum is composed of four terms: Cov(b 1 2 3, b ) = C C C C 6, (18) with (see Lacasa et a. 2012) Here C = (2+1) 123 4π C 1 C 2 C 3 ( 1 2 ) 2 δ 1 δ 1 2 δ (19) equiatera trianges = 2 isoscees trianges 1 genera trianges (20) and when the bispectrum is factorizabe C 3 3 = b b ( δ δ δ δ δ δ δ δ δ ) (21) C 2 4 and C 6 invove, respectivey, the map trispectrum and 6- point function. C is the cosmic variance in the weak non- Gaussianity imit, as considered, e.g., by Crawford et a. (2013) in their tsz and CIB non-gaussianity study; it produces a diagona covariance matrix, since it does not coupe the different configurations. C 3 3 is the bispectrum correction to the covariance matrix and coupes bispectrum estimates in different configurations. In the cosmic variance imited case, we found that incuding ony C woud noticeaby overestimate the detection significance. However when considering a error sources, C 3 3 has a sma impact on the SNR; hence we incude it in the foowing anaysis but negect higher order corrections C 2 4 and C 6. We use the f sky approximation, that is Cov = Cov fu sky / f sky, as the first mutipoes were discarded and we saw no mode couping with our arge bin size. The power spectrum used for C is the map auto-power spectrum, incuding the noise as necessary, debiased from the mask and beam effects. As described in Sect , the residua maps are contaminated by tsz contribution at 100 GHz eaking through the CMB ceaning process. Whie this contamination is negigibe compared to the CIB signa at 353 GHz and above, it is important at 217 GHz, where the contamination can be as arge as 40%, depending on the configuration and mutipoe. We derived the SZ bispectrum by measuring the bispectrum of the map of the Panck SZ custer cataogue (both custers and candidate custers from Panck Coaboration XXIX (2013) are considered). A 80% error on the ampitude of the tsz correction is added to the covariance measurement described previousy. This error is based on the reative difference between the bispectrum of the Panck SZ cataog of confirmed custers (Panck Coaboration XXIX 2013), the bispectrum of the Panck estimated tsz map, and the bispectrum of the Panck FFP6 SZ simuations (see the bispectrum anaysis in Panck Coaboration XXI 2013). The error is conservative as it takes for a mutipoes and configurations the maximum observed difference CIB power spectrum Figure 7 presents a summary of a the measured auto- and crosspower spectra on residua maps. Foowing the same covariance studies as in Panck Coaboration XVIII (2011), we combine our cross-power spectrum estimates on individua fieds f for each bin b into an average cross-power spectrum, using inverse variance weights, C ν ν b = f W f b P f,ν ν b f W f b, (22) with W f b = 1/σ 2 (P f,ν ν b ). These weights are estimated in the foowing way: 14

16 Fig. 7. Auto- and cross-power spectra of the CIB for each fied (but EBHIS, Bootes and GASS at 3000 GHz, see Sect. 3.3). For readabiity, error bars on individua measurements are not potted. For the case, measurements on the fat-sky fieds are noise dominated, and we thus use ony the resuts from the GASS fied. For dispay purpose, power spectra have been mutipied by the number given at the bottom-eft side of each pane. - Step 1: Ony statistica errors are used to compute a weighted average of the power spectra and their associated error bars on sma fieds. - Step 2: The projection error is added ineary to the error bar of step 1. - Step 3: For frequencies where observations on GASS are avaiabe, we average the GASS power spectrum and the sma fieds power spectrum. We here use inverse statistica variance weights for GASS, and the inverse variance derived from step 2 for the sma fieds. This gives the fina power spectrum estimate and a pseudo-statistica error bar. - Step 4: We compute the error due to beam uncertainties using the average power spectrum. We add this error ineary to the error derived on Step 3. - Step 5 : The bias induced by Gaactic dust residuas is ineary added to the error derived on Step 4 to obtain the fina tota error bar. The resuting power spectra and their errors are given in Tabe D.1. For the auto-power spectrum, ony the 15

17 Fig. 8. Comparison between the CMB- and dust-free map power spectra obtained from the anaysis of the fat fieds (328 deg 2, red diamonds) and GASS (1914 deg 2, back dots). From top to bottom: ; ; ; and measurement on the GASS fied is considered, as the measurement in the fat-sky fieds is noise dominated. Note aso that the ast bin for a measurements invoving the subtraction of the 100 GHz CMB tempate is = 1956, due to the anguar resoution of Panck-HFI at 100 GHz. To obtain the CIB power spectra, the estimates obtained from the CMB- and dust-free maps (Tabe D.1) have to be corrected for SZ contaminations (Eqs. 5 and 9), and for the spurious CIB contamination (Eq. 4) induced by our CMB tempate. This ast contamination is computed using our best-fit mode described in Sect Moreover, foowing Sects and 3.2.3, the first two bins at mutipoes = 53 and 114 have to be considered as upper imits. CIB power spectrum vaues are given in Tabe D.2. The errors contain a the terms: statistica uncertainty; beam and projection uncertainty; cirrus bias; and errors from the SZ correction. CIB power spectra are shown on the figure comparing the measurements with the mode (Fig. 12). Comparison with previous recent measurements are shown and discussed in Sect The power spectra from the fat-sky and GASS fieds have been obtained using two independent pipeines. The fieds have different Gaactic dust and point sources contamination, as we as instrument noise eves, and between GASS and the fat-sky fieds, different pixeization and projection. Comparing combined power spectra obtained on a fat-sky fieds to that obtained on GASS is thus a powerfu consistency check on our determination of power spectra and error bars. We show on Fig. 8 this comparison for an arbitrary set of frequencies. The power spectra are aways compatibe within 1 σ. Of course, due to the much arger area of the GASS fied, the CIB measured in GASS has much smaer cosmic variance errors CIB bispectrum We measure the bispectrum ony at 217, 353 and 545 GHz. The bispectrum at 143 GHz is noise-dominated and is moreover highy contaminated by tsz and extragaactic radio point sources. At 857 GHz, as we are using Mask2, Gaactic dust residuas contaminate the bispectrum in most configurations. In particuar, the residuas produce a rising bispectrum at high mutipoes. In the foowing, we are thus not considering the 857 GHz frequency for the anaysis. At 217, 353 and 545 GHz, the bispectrum is measured in 38, 40 and 36 configurations, respectivey. We show in Fig. 9 the measured CIB bispectrum at 353 GHz for some particuar configurations, namey equiatera (,, ), orthogona isoscees (,, 2), fat isoscees (,, 2), and squeezed ( min,, ). The bispectrum decreases with scae and exhibits a peak in the squeezed configurations, as predicted by Lacasa et a. (2012). In Tabe 5, we give the significance of the detection for the three frequencies used, with either the average significance per configuration or the significance of the tota bispectrum, when accounting for the whoe covariance matrix. The bispectrum is significanty detected at each frequency individuay. Moreover, these measurements represent the first detection of the CIB bispectrum per configuration, permitting us to probe the scae and configuration dependence of the bispectrum, as we as its frequency behaviour. The bispectrum vaues are given in Tabe D.3. Tabe 5. Detection significance of the bispectra at each frequency. Note that the mean SNR per configuration and the tota SNR are not directy inked by the square root of the configuration numbers as the covariance matrix is not diagona. Band Mean SNR per configuration Tota SNR 217 GHz GHz GHz Interpreting CIB power spectrum measurements Once the CMB and Gaactic dust have been removed, there are three astrophysica contributors to the power spectrum at the HFI frequencies: two from dusty star-forming gaaxies (with both shot noise, C ν ν d,shot, and custering, Cν ν d,cust (), components); and one from radio gaaxies (with ony a shot-noise component, C ν ν r,shot, the custering of radio sources being negigibe, e.g., Ha et a. 2010). The measured CIB power spectrum C ν ν measured () is thus C ν ν measured () = Cν ν d,cust () + Cν ν d,shot + Cν ν r,shot. (23) In this section, we first discuss the shot-noise contributions. We then present how we can mode C ν ν d,cust (). Two approaches are considered. The first one is the simpest, and use ony the arge scae CIB measurements to fit for a inear mode. The second one is based on the hao-mode formaism. Our main goa is to use CIB anisotropies to measure the SFRD and effective bias redshift evoution Shot noise from dusty star forming and radio gaaxies The shot noise arises from samping of a background composed of a finite number of sources, and as such is decouped from the correated term. The anguar resoution of the HFI instrument is not high enough to measure the shot-noise eves. As demonstrated in Panck Coaboration XVIII (2011), the noninear contribution to the power spectrum is degenerate with the shot-noise eve (on the scaes probed by Panck). Since our data by themseves are not sufficient to expore this degeneracy, we need to rey on a mode to compute the shot noise. 16

18 Auto-power spectrum The shot-noise eve at frequency ν can be easiy computed using monochromatic gaaxy number counts. Let us consider a fux interva [S k, S k + S k ]. The number of sources per unit soid ange, n k in this fux interva is and the variance is, n k = dn ds S k (24) σ 2 B k = n k S 2 k. (25) Summing a fux intervas gives the variance on the tota contribution to the CIB: σ 2 B = n k S k 2 = dn ds S k 2 S k. (26) k When we take the imit of S k tending to zero, this sum becomes the integra S c σ 2 B = dn ds S 2 ds. (27) 0 Here S c is the fux cut above which bright sources are detected and can be removed. This cut is mandatory, since the integra does not converge in the Eucidian regime, dn ds S 2.5, which is the case at bright fuxes for star-forming gaaxies Cross-power spectrum We now consider two frequencies ν and ν. The number of sources n k in the fux density and redshift intervas [S k, S k + S k ] and [z, z + z ], is n k = dn ds dz S k z (28) Considering a sma redshift interva, the covariance between the two frequencies can be approximated as: σ ν1 ν 2,k = n k S ν,k S ν,k = n k S 2 ν,k R νν,k, (29) where R νν,k is the mean coour for the considered gaaxy popuation in the considered fux density and redshift interva. Using a mean coour per fux density and redshift interva is not a strong assumption as ong as S k and z are sma. Summing over fux densities, redshifts and the gaaxy popuation gives σ νν = n pop,k S ν,k 2 R νν,pop,k, (30) with the integra imit σ νν = pop pop S ν =0 k z=0 H(S ν < S c ν, R ν ν,pops ν < S c ν ) dn pop ds ν dz S 2 νr ν ν,pop ds ν dz. (31) Here H(P 1, P 2 ) is equa to 1 when P 1 and P 2 are both true, and 0 otherwise, and S c ν and S c ν are the fux cuts in the frequency bands ν and ν. They are given in Tabe 1. We use this formaism to compute the radio gaaxy shot noise. For the star-forming dusty gaaxy shot noise, we rey on the formaism detaied in Béthermin et a (their appendix B) Shot-noise vaues We use the Béthermin et a. (2012a) mode to compute the starforming dusty gaaxy shot noise, C ν ν d,shot (Eq. 23). The mode is in rather good agreement with the number counts measured by Spitzer and Hersche (e.g., Genn et a. 2010). It aso gives a reasonabe CIB redshift-distribution, which is important for the cross-spectra. Since this mode is based on observations that have typica caibration uncertainties of <10%, the estimations of the shot-noise eves (being proportiona to the square of caibration factor) cannot be accurate to more than 20%. As uncertainties in the fux cuts induce uncertainties in the shot noise that are negigibe (ess than 3% at a frequencies), we take 20% as the shot-noise uncertainty. For extragaactic radio sources, we use the Tucci et a. (2011) mode (more specificay, the one referred as C2Ex in the paper) to compute C ν ν r,shot (Eq. 23). The predictions for high frequency number counts are based on a statistica extrapoation of fux densities of radio sources from ow frequency data (1 5 GHz). In particuar, this mode considers physicay based recipes to describe the compex spectra behaviour of bazars, which dominate the mm-wave counts at bright fux densities. It is abe to give a good fit to a bright extragaactic radio source data avaiabe so far: number counts up to 600 GHz; and spectra index distributions up to at east GHz (see Tucci et a. 2011; Panck Coaboration Int. VII 2013; López-Caniego et a. 2012). As for the dusty gaaxies, we consider an error of 20% on the shot-noise computation from the mode. But contrary to dusty gaaxies, the shot noise for the radio popuation depends strongy on the fux cut (Panck Coaboration XVIII 2011). Accordingy, we add to the 20% mentioned above, a shot-noise error taken to be the shot-noise variations as we change the fux cut, considering the fux cut errors given in Tabe 1. The shot-noise eves for the HFI fux cuts given in Sect. 2.4, are isted in Tabes 6 and Basics of CIB correated anisotropy modeing The anguar power spectrum of CIB correated anisotropies is defined as: δi ν m δiν m = C ν ν d,cust () δ δ mm, (32) where ν and ν denote the observing frequencies and I ν,ν the measured intensity at those frequencies. In a fat universe, the intensity is reated to the comoving emissivity j via I ν = dz dχ a j(ν, z) (33) dz = dz dχ ( ) dz a j(ν, δ j(ν, z) z) 1 +, j(ν, z) where χ(z) is the comoving distance to redshift z, and a = 1/(1+ z) is the scae factor. Combining Eqs. 32 and 33 and using the Limber approximation, we obtain C ν ν d,cust () = dz χ 2 dχ dz a2 j(ν, z) j(ν, z)p ν ν j (k = /χ, z), (34) where P ν ν j is the 3-D power spectrum of the emissivities and is defined as foows: δ j(k, ν)δ j(k, ν ) = (2π) 3 j(ν) j(ν )P ν ν j (k)δ 3 (k k ). (35) In the context of CIB anisotropy modeing, the simpest version of the so-caed hao mode, which provides one view of 17

19 Tabe 6. Shot-noise eves C ν ν d,shot (fat power-spectra) for star-forming gaaxies (in Jy2 sr 1 ) computed using the Béthermin et a. (2012a) mode. To obtain the shot noise in Jy 2 sr 1 for our photometric convention νi ν = constant, a coour correction, given in Sect. 5.2, has to be appied ± ± ± ± ± ± ± ± ± ± ± ± ± ±12 16 ± ± 5 56± 11 35± 7 15 ± 3 4.3± ± ± 2 20± 4 12± 2 5.4± ± ± ±0.03 Tabe 7. Shot-noise eves C ν ν r,shot (fat power-spectra) for radio gaaxies (in Jy2 sr 1 ) computed using the Tucci et a. (2011) mode. To obtain the shot noise in Jy 2 sr 1 for our photometric convention νi ν = constant, a coour correction has to be appied. It is however ower than 1% (see Sect. 5.2) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 1.97 the arge-scae structure of the Universe as cumps of dark matter, consists of equating P j with the gaaxy power spectrum P gg. This is equivaent to assuming that the CIB is sourced equay by a gaaxies, so that the spatia variations in the emissivities trace the gaaxy number density, δ j/ j = δn ga / n ga. (36) The dark matter haos are popuated through a hao occupation distribution (HOD) prescription. Utimatey, P gg (k, z) is written as the sum of the contributions of gaaxies within a singe dark matter hao ( 1h ) and gaaxies beonging to two different haos ( 2h ): P gg (k, z) = P 1h (k, z) + P 2h (k, z). (37) On arge scaes P 2h reduces to a constant bias (squared) times the inear theory power spectrum, whie the 1-hao contribution encapsuates the non-inear distribution of matter. In this paper, we deveoped two approaches for the modeing of CIB anisotropies. The first one (Sect. 5.4) is very simpe, and takes advantage of the accurate measurement of CIB anisotropies with Panck and IRIS at arge anguar scaes. As an aternative to the HOD mode for P gg we use a constant bias mode in which P gg (k, z) = b 2 eff P in(k, z), where b eff is a redshift- and scae-independent bias and P in (k) is the inear theory, darkmatter power spectrum. The second one (Sect. 5.5) uses the anisotropies at a anguar scaes, and takes advantage of the frequency coverage of our measurements, to constrain a hao mode with a uminositymass dependence. As a matter of fact, the mode described above, which assumes that emissivity density traces gaaxy number density (Eq. 36), impies that a gaaxies contribute equay to the emissivity density, irrespective of the masses of their host haos. It assumes that a gaaxies have the same uminosity, which is a crude assumption, as the uminosity and the custering strength are cosey reated to the mass of the host hao. Fig. 9. CIB bispectrum at 353 GHz in some particuar configurations (back points, in Jy 3 sr 1 ). The red curve is the CIB bispectrum predicted from the power spectrum (best-fit mode from Sect. 5.5) foowing Lacasa et a. (2012). The yeow curve is a power-aw fit (as given in Tabe 13). See Sect. 6.5 for more detais. 18

20 Before embarking in the detais of our modes buiding and fitting, we want to stress that the purpose of the foowing sections is to buid as physica a mode as possibe that reproduces our measurements. To do so, we wi buid on the arge amount of works in the astrophysica iterature that expoited the simpifying concept of hao-mode. We hope that this way our work wi have wider impact. Nevertheess, it has to be emphasized that these modes are very phenomenoogica and muti-faceted. To some extent, there is no such thing as a hao mode as there are many hidden assumptions standing on uneven grounds. For exampe, in our approach we wi rey on a concentration prescription as a function of mass and redshift and use it a the way to a redshift of 6, thus pushing in a regime where it has not been vaidated. The same hods for our ansatz for the L M reation and more generay the concept of HOD. To expore the dependence of our concusions on these hidden assumptions is a work that goes we beyond the scope of this paper and woud certainy require a arge use of simuations. To incude these assumptions as Bayesian priors in our fit coud be an approach but woud aso certainy miss serious conceptua imitations. As such, we chose, in this current modeing effort to just make our assumptions cear and justify our fixed vaues when possibe. This approach eaves a degree of uncertainty unaccounted for in our error budget and shoud be keep in mind when interpreting our resuts Fitting for a mode The power spectra that are computed by the modes need to be coour-corrected, from a CIB SED to our photometric convention νi ν = constant. We use the CIB SED from Béthermin et a. (2012a) to compute the coour corrections. They are equa to 1.076, 1.017, 1.119, 1.097, 1.068, 0.995, and at 100, 143, 217, 353, 545, 857, and 3000 GHz, respectivey. The correction to the power spectra foows C mode,ν,ν cc ν cc ν = C measured,ν,ν. (38) We use the same coour corrections (cc) for both the star-forming gaaxy shot noise and the CIB power spectrum. For the radio gaaxy shot noise we use a power aw S ν ν α, with α = 0.5. This is the average spectra index for radio sources that mainy contribute to the shot-noise power spectra. With such an SED, we find that the coour corrections are a ower than 0.7% for 100 ν 857 GHz. We thus negect them. To search for our best-fit mode, we foow this scheme. 1. Take the residua map power spectra, as given in Tabe D Discard the first two bins at mutipoes = 53 and 114 (foowing Sect and 3.2.3). 3. Correct for SZ-reated residuas, C ν ν SZcorr, and Cν ν CIB SZcorr, foowing Eqs. 8, 9, 12, and add the errors of these corrections quadraticay to the error bars given in Tabe D Appy the coour correction to convert the theoretica mode from measured Jy 2 sr 1 to Jy 2 sr 1 [νi ν = constant] (Eq. 38). 5. Compute the χ 2 vaue between the theoretica mode and the observations, further appying the correction C ν ν CIBcorr (Eq. 4), and adding caibration errors, as described in the next item. 6. The caibration uncertainties are treated differenty than the CIB power spectra error bars. We use an approach simiar to the gaaxy number counts mode of Béthermin et a. (2011). A caibration factor f ca is introduced. It has an initia vaue of 1, but can vary inside a Gaussian prior, centred on the caibration errors given in Tabe 1. We add a term to the χ 2 that takes into account the estimated caibration uncertainties: χ 2 ca = bands( f ca 1) 2 /σ 2 ca, where σ2 ca are the caibration errors. The C computed for the mode is thus modified according to C ca,ν ν = f ca ν fν ca C mode,ν ν Constraints on SFRD and effective bias from the arge-ange inear scaes Fitting the inear mode to the data Panck is a unique probe of the arge-scae anisotropies of the CIB. At 1000, the custering is dominated by the correation between dark matter haos (the 2-hao term, e.g., Panck Coaboration XVIII 2011). Panck data thus give the opportunity to put new constraints on both star-formation history and custering of star-forming gaaxies, using ony the inear part of the power spectra. In this modeing, we consider ony the 2- hao contribution to the cross-power spectrum between maps at frequency ν and ν (or auto-spectrum if ν = ν ), which can be written as C 2h,ν,ν = dz χ 2 dχ dz a2 b 2 eff (z) j(ν, z) j(ν, z)p in (k = /χ, z), (39) and we fit ony for 600. Here b eff is the effective bias of infrared gaaxies at a given redshift, i.e., the mean bias of dark matter haos hosting infrared gaaxies at a given redshift weighted by their contribution to the emissivities. This term impicity takes into account the fact that more massive haos are more custered. The ink between this simpe approach and the HOD approach of Sect. 5.5 is discussed in Appendix C. We compute P in (k) using CAMB ( The emissivities j(ν, z) are derived from the star formation density ρ SFR foowing (see Appendix B) j(ν, z) = ρ SFR(z)(1 + z)s ν,eff (z)χ 2 (z), (40) K where K is the Kennicutt (1998) constant (SFR/L IR = M yr 1 for a Sapeter IMF) and S ν,eff (z) the mean effective SED of a infrared gaaxies at a given redshift. They are deduced from the Béthermin et a. (2012a) mode (see Appendix B). These SEDs are a mixture of secuary star-forming gaaxies and starburst gaaxies. The dust temperature here increases with redshift foowing the measurements of Magdis et a. (2012) (see Sect. 6.4 for a discussion about the choice of the SED ibrary for the modeing and the impact on the resuts). There are degeneracies between the evoution of the bias and of the emissivities. In order to break them, we put some priors on the foowing quantities. The oca infrared uminosity density, ρ SFR (z = 0) = (1.95 ± 0.3) 10 2 M yr 1 (Vaccari et a. 2010), converted using the H 0 vaue measured by Panck). The oca bias of infrared gaaxies, b = 0.84 ± 0.11 (Saunders et a. 1992), converted using σ 8 measured by Panck. The mean eve of the CIB deduced from gaaxy number counts, nw m 2 sr 1 at 3000 GHz from Berta et a. (2011), nw m 2 sr 1 at 857 GHz, and nw m 2 sr 1 at 545 GHz from Béthermin et a. (2012c), and finay > 0.27 nw m 2 sr 1 from Zemcov et a. (2010) at 353 GHz. These vaues are coour-corrected from PACS, SPIRE and SCUBA to Panck and IRAS, using the Béthermin et a. (2012a) mode. 19

21 Fig. 10. (Cross-) power spectra of the CIB measured by IRAS and Panck, and the inear mode. Data points are shown in back. The data used to fit the inear mode are represented by diamonds ( 600). High- points are not dispayed as they are not used. The cyan dash-three-dot ine (often confounded with the red continuous ine) is the best-fit CIB inear mode. For competeness, we aso show on this figure the shot-noise eve given in Tabe 6 (orange dashed ine) and the 1-hao term predicted by Béthermin et a (green dot-dashed ine). The red ine is the sum of the inear, 1-hao and shot-noise components. It contains the spurious CIB introduced by the CMB tempate (see Sect ). The bue ong-dashed ine represents the CIB inear best-fit mode pus 1-hao and shot noise terms. It is corrected for the CIB eakage in the CMB map, simiary to the cyan ine. When the CIB eakage is negigibe, the bue ong-dashed ine is the same as the red continuous ine. In this simpe anaysis, we want to measure ony two quantities: the effective bias and its evoution with redshift, b eff (z); and the star formation density history, ρ SFR (z). Inspired by the redshift evoution of the dark matter hao bias, we chose the foowing simpe parametric form for the evoution of the effective bias: b eff (z) = b 0 + b 1 z + b 2 z 2. (41) For the star formation history, the vaues of ρ SFR at z = 0, 1, 2 and 4 are free parameters, and we connect these points assuming a power aw in (1+z), using the two ast points to extrapoate ρ SFR at z > 4. We perform a Monte Caro Markov chain anaysis of the goba parameter space. We assume Gaussian uncorreated error bars for uncertainties, which are a inear combination 20

22 of statistica and beam errors. The caibration uncertainties are treated foowing the method described Sect To be independent of the exact eve of the Poisson and 1- hao power spectrum in our inear anaysis, we fit ony for 600 measurements. For such s, contamination by the Poisson and 1-hao terms is ower than 10% (except for where it reaches 25% at =502, see Fig. 10). We nevertheess add to our mode the sma correction due to the 1-hao and Poisson terms, as derived from the Béthermin et a. (2013) mode. Panck Coaboration: CIB anisotropies with Panck Resuts With a best-fit χ 2 vaue of 35 for 41 degrees of freedom, we obtain a very good fit to the data. In Tabe 8 we quote median vaues and marginaized imits for the parameters. The posterior vaue of parameters for which we imposed a Gaussian prior (oca effective bias and SFRD, pus caibration factors) are a within the 1 σ range of the prior vaues (except the 857 GHz caibration factor which is at 1.2σ). Fig. 11 shows the evoution of the star formation density with redshift (upper pane). Our derived star formation history nicey agrees with the infrared measurements of the dust-obscured star-formation rate density of Rodighiero et a. (2010) and Magnei et a. (2011), up to z 2. At higher redshift, our determination is marginay compatibe (2σ) with Gruppioni et a. (2013), but in very good agreement with the recent work of Burgarea et a. (2013) at z=3. We aso compared our measurements with the UV estimate of star formation (not corrected for dust-attenuation) from Bouwens et a. (2007), Cucciati et a. (2012), and Reddy & Steide (2009). Beow z 3, the buk of the UV ight emitted by young, short-ived stars is reprocessed in the infrared. Above this redshift, we find that the star formation probed in the UV and IR regimes have roughy an equa contribution. The infrared regime aone is thus no onger a good measure of the tota star-formation rate density. We aso studied the evoution of the effective bias (ower pane of Fig. 11). We measure an increase of the bias with redshift. In Fig. 11 we compare the evoution of the gaaxy dark matter bias with that of dark matter haos of various mass (from Tinker et a. 2008). Our resuts are compatibe with the track of dark matter haos with M, corresponding to the hao mass of maxima efficiency of star formation, as found in recent works (e.g., Béthermin et a. 2012b, Wang et a. 2013, and Behroozi et a. 2013, and compatibe with the reated ensing magnification study of Hidebrandt et a. 2013) Hao mode for CIB anisotropies The hao mode is a standard approach to describe the custering of matter at a scaes (Cooray & Sheth 2002). Starting from the assumption that a gaaxies ive in dark matter haos, the custering power spectrum can be considered as the sum of two components: the 1-hao term (abeed P 1h ), due to correations of gaaxies within the same hao, is responsibe for the smascae custering; whie the 2-hao term (P 2h ), sourced by gaaxy correations in different haos, describes the arge-scae custering. The gaaxy power spectrum is competey characterized by four main ingredients: the hao bias between dark matter and haos; the hao density profie, describing the spatia distribution of dark matter inside a given hao; the hao mass function, specifying the number density of haos with a given mass; and a pre- Fig. 11. Evoution of the star formation density (upper pane) and effective bias as a function of redshift (ower pane), as constrained by the inear part of the power spectra. In both panes, the median reaization of the mode is represented with a red ine, the ±1 σ confidence region with a dark orange area, and the ±2 σ region with a ight orange area. In the upper pane, we added the measurements of obscured star formation from infrared (Magnei et a. 2011, squares), (Rodighiero et a. 2010, asterisks), (Cucciati et a. 2012, diamonds), (Gruppioni et a. 2013, crosses), and unobscured star formation from uncorrected UV (Bouwens et a. 2007, trianges; Reddy & Steide 2009, circes). In the ower pane, we aso pot the evoution of the dark matter hao bias for dark matter hao mass of M (dashed ine), M (dot-dashed ine), and M (three-dots-dashed ine). scription for fiing dark matter haos with gaaxies, the so-caed Hao Occupation Distribution (HOD). A common assumption in the simpest versions of the hao mode is that a gaaxies have the same uminosity, regardess of their host dark matter hao (Viero et a. 2009; Ambard et a. 2011; Panck Coaboration XVIII 2011; 21

23 Tabe 8. Summary of the parameters of the inear mode. The vaues are obtained through an MCMC anaysis (median and 68% confidence imits, CL). Parameter Definition Median vaue ρ SFR (z = 0) z = 0 star formation density M yr 1 ρ SFR (z = 1) z = 1 star formation density M yr 1 ρ SFR (z = 2) z = 2 star formation density M yr 1 ρ SFR (z = 4) z = 4 star formation density M yr 1 b 0 Effective bias at z = b 1 First order evoution b 2 Second order evoution f ca 3000 Caibration factor at 3000 GHz f ca 857 Caibration factor at 857 GHz f ca 545 Caibration factor at 545 GHz f ca 353 Caibration factor at 353 GHz f ca 217 Caibration factor at 217 GHz Xia et a. 2012; Viero et a. 2013b). However, as has aready been pointed out in Shang et a. (2012), both gaaxy custering and gaaxy uminosity are inked to host hao mass so that, in a statistica way, gaaxies situated in more massive haos have more stear mass and are more uminous. The ack of such a ink between gaaxy uminosity and host hao mass in the mode can ead to an interpretation of the custering signa on sma anguar scaes being due to a significant overabundance of sateite haos (as in Ambard et a. 2011) with respect to what is found in numerica simuations (see discussion in Shang et a. 2012; Viero et a. 2013b). However, this can instead be due to a smaer number of gaaxies, but with higher uminosity. In this paper, we assume a hao mode with a gaaxy uminosity-hao mass reation simiar to the one introduced in Shang et a. (2012) and aso used in Viero et a. (2013b). We define haos as overdense regions with a mean density equa to 200 times the mean density of the Universe and we assume an NFW profie (Navarro et a. 1997) for the hao density profie, with a concentration parameter as in Cooray & Sheth (2002). Fitting functions of Tinker et a. (2008) and the associated prescription for the hao bias (see Tinker et a. 2010) wi be used for the hao and sub-hao mass functions, respectivey. In the next sub-sections we wi introduce the hao mode that we use and we wi describe how our anaysis constrains its main parameters A hao mode with uminosity dependence The reation between the observed fux S ν and the uminosity of a source at a comoving distance χ(z) is given by: S ν = (1 + z)l ν(1+z), (42) 4πχ 2 (z) and the gaaxy emissivity j ν (z) can be written as j ν (z) = dl dn dl (L, z) L (1+z)ν 4π, (43) where dn/dl denotes the infrared gaaxy uminosity function. In genera, in order to mode the gaaxy uminosity hao mass reation, we shoud introduce a scatter describing the probabiity density P(L M) for a hao (or a sub-hao) of mass M to host a gaaxy with uminosity L (as in the conditiona uminosity function modes of, e.g., Yang et a. 2003, Yang et a. 2005, Cooray & Miosavjević 2005, Cooray 2006, Ambard & Cooray 2007, and De Bernardis & Cooray 2012). In order to keep the anaysis as simpe as possibe, we negect any scatter and introduce L cen,ν(1+z) (M H, z) (for centra gaaxies) and L sat,ν(1+z) (m SH, z) (for sateite gaaxies), where M H and m SH denote the hao and sub-hao masses, respectivey, Eq. 43 can be re-written as: j ν (z) = dm dn dm (z) 1 { Ncen L cen,(1+z)ν (M H, z) (44) 4π dn + dm SH dm (m SH, z)l sat,(1+z)ν (m SH, z) }, where dn/dm denotes the sub-hao mass function and N cen is the number of centra gaaxies inside a hao. Introducing fν cen and fν sat for centra and sateite gaaxies, L cen,(1+z)ν (M H, z) ν (M, z) = N cen, (45) 4π f cen f sat ν (M, z) = M M min dm dn dm (m SH, z M) (46) L sat,(1+z)ν(m SH, z), 4π then the power spectrum of CIB anisotropies at observed frequencies ν, ν can be written as P 1h,νν (k, z) = P 2h,νν (k, z) = Here D ν (k, z) = 1 j ν j ν { f cen ν M min dm dn dm (M, z) f sat (M, z)u(k, M, z) ν + f cen sat (M, z) fν (M, z)u(k, M, z) ν (47) + fν sat (M, z) fν sat (M, z)u2 (k, M, z) }, 1 D ν (k, z)d ν (k, z)p in (k, z). (48) j ν j ν dm dn b(m, z)u(k, M, z) (49) M min dm { fν cen (M, z) + fν sat (M, z) }, with u(k, M, z) being the Fourier transform of the hao density profie Parameterizing the L M reation In the simpest version of the hao mode, where gaaxies residing in haos of different masses have the same uminosity, the gaaxy power spectrum is fuy determined by the HOD, namey the function describing the number of centra and sateite gaaxies in each dark matter hao. In the mode used here, the power spectrum depends, additionay, on the function L (1+z)ν (M H, z), where M denotes the hao mass. The uminosity L (1+z)ν (M H, z) depends on three variabes: the redshift z; the mass of the host (sub)hao; and the observing frequency ν. We wi consider the foowing assumptions about the structure of the uminositymass reation L(M). 22

24 We assume no difference between haos and sub-haos with the same mass, so that L(M H, z) = L(m SH, z), for M H = m SH. Whie recent studies (e.g., Rodríguez-Pueba et a. 2012, 2013) show some indication that sateite gaaxies tend to have sighty more stear mass than centra gaaxies with the same hao mass, these resuts depend on the subhao mass definition used; in particuar, the uminosity-mass reation for sateites and centra gaaxies has been found to be not very different when the mass of the subhao is defined at the time of accretion (as done in this paper). A very simpe functiona form (see Bain et a. 2003, and reference therein) is assumed for gaaxy SEDs: { ν Θ(ν, z) β B ν (T d (z)) ν < ν 0 ; ν γ (50) ν ν 0. Here B ν denotes the Panck function, whie the emissivity index β gives information about the physica nature of dust and in genera depends on grain composition, temperature distribution of tunneing states and waveength-dependent excitation (e.g., Meny et a. 2007). The power-aw function is used to temper the exponentia Wien tai at high frequencies and obtain a shaower SED shape, more in agreement with observations. The temperature is assumed to be a function of redshift according to T d T 0 (1 + z) α. (51) This dependence of the temperature with redshift can be due to different physica processes, such as more compact geometries for gaaxies at high redshift (Magdis et a. 2012), a goba evoution of the SED (e.g., Addison et a. 2012; Béthermin et a. 2013) or the increase of the CMB temperature with redshift (Bain 1999). The SED functions at high and ow frequencies are connected smoothy at the frequency ν 0 satisfying dnθ(ν, z) dnν = γ. (52) The range of variation for the parameters α, γ, and ν is arge enough to ensure that we do not excude non-negigibe regions of the mutidimensiona parameter space; however we assume physicay motivated priors for both the temperature (T 0 in the range K, see measurements in e.g., Dunne et a. 2000, Chapman et a. 2005, Ambard et a. 2010, and Hwang et a. 2010) and the emissivity index (β in the range ). The correct choice of β is a matter of debate; measurements of Miky Way dust, and in externa gaaxies (e.g., Bosei et a. 2012), give vaues in the range 1 2, but aowing for some degree of correation between dust temperature and emissivity index (see, e.g., Paradis et a. 2010) it is possibe to obtain β > 2 for ow dust temperatures (T d 18K). On the theoretica side, whie modes for both insuating and conducting materias naturay give β = 2 at ong waveengths (e.g., Draine & Lee 1984), significant deviations from the vaue β = 2 occur when accounting for the disordered structure of the amorphous dust grains (Meny et a. 2007). Indeed, some authors (Shang et a. 2012; Viero et a. 2013b) aow for vaues β > 2 when fitting CIB data. In this anaysis we prefer to be conservative and, since we assume the condition T d > 20 K, we aso impose β 2; this wi aow us to draw soid concusions on the other parameters of the mode, avoiding regions of the parameter space whose physica interpretation is questionabe. We assume a redshift-dependent, goba normaization of the L M reation of the form Φ(z) = (1 + z) δ. (53) The parameter δ wi be aowed to vary in the range 0 7. Such a redshift dependence can be justified considering the evoution of the specific far infrared uminosity (L IR /M ) with redshift: if the ratio of stear mass to hao mass evoves ony midy with redshift (see e.g., Neistein et a. 2011), then the ratio L IR /M H shoud evove approximatey as the specific infrared uminosity. The semi-anaytic gaaxy formation mode of De Lucia & Baizot (2007) shows the evoution of such a quantity with redshift as a power aw with a sope of about 2.5, whie observations performed by Oiver et a. (2010) indicate a much steeper sope, around 4.4. We assume a og-norma function for the dependence of the gaaxy uminosity on hao mass: 1 Σ(M, z) = M (2πσ 2 e (og 10 (M) og 10 (Meff))2/2σ2 L/M. (54) L/M )1/2 Here M eff describes the peak of the specific IR emissivity, whie the parameter σ L/M describes the range of hao masses used for producing the IR uminosity; we wi assume that σ 2 L/M = 0.5 throughout this paper and we checked that resuts do not significanty change when assuming σ 2 L/M = 0.65, as in Béthermin et a. (2012b). The reason for choosing a og-norma functiona form is that star formation is active ony over a given range of hao masses, being suppressed at both the ow- and the highmass end by mechanisms such as photoionization, supernovae heating, feedback from active gaactic nucei and viria shocks (see e.g., Benson et a. 2003; Croton et a. 2006); it is then possibe to identify a peak in the L M reation, which describes the maximum in the average infrared emissivity per unit mass. At the ow mass end, we assume a minimum mass M min, which is a free parameter in the range M, and we assume L = 0 for M < M min. The equation for the uminosity-mass reation can finay be written as L (1+z)ν (M, z) = L 0 Φ(z)Σ(M, z)θ[(1 + z)ν], (55) where L 0 is a free normaization parameter (which being not physicay meaningfu wi not be further discussed) Method and data used In order to constrain the main parameters of our mode, we fit for a tota of 121 data points of the 15 possibe combinations of Panck auto- and cross-power spectra at 217, 353, 545, 857 and 3000 GHz, considering the mutipoe range We use the same procedure as described in Sect. 5.3 in order to coour-correct our mode to the photometric convention νi ν = constant and to incude the corrections due to CIB oversubtraction and SZ-reated residuas (see points 1 6 in Sect. 5.3). There are two main differences with respect to the inear mode anaysis outined above (Sect. 5.4): we keep a the caibration parameters fixed at f ca = 1, which assumption is justified by the anaysis using the inear mode, aowing us not to dea with too many parameters; 23

25 Fig. 12. (Cross-) power spectra of the CIB anisotropies measured by Panckand IRAS, compared with the best-fit extended hao mode. Data points are shown in back. The red ine is the sum of the inear, 1-hao and shot-noise components, which is fitted to the data. It contains the spurious CIB introduced by the CMB tempate (see Sect ). The orange dashed, green dot-dashed, and cyan three-dots-dashed ines are the best-fit shot-noise eve, the 1-hao and the 2-hao terms, respectivey. They are corrected for the CIB eakage in the CMB. The sum of the three is the bue ong-dashed ine. When the CIB eakage is negigibe, the bue ong-dashed ine is the same as the red continuous ine. we assume the same prior on the star formation rate density (Vaccari et a. 2010) as in the inear mode but we do not use any constraints on the bias at redshift zero. We aso assume fat priors on the mean eve of the CIB at 545 and 857 GHz. We perform a Monte Caro Markov chain anaysis of the goba parameter space using a modification of the pubicy avaiabe code CosmoMC (Lewis & Bride 2002). We consider variations in the foowing set of eight hao mode parameters: P {α, β, γ, δ, M eff, M min, T 0, L 0 }. (56) We assume the shot-noise eves given by the sum of the vaues quoted in Tabes 6 and 7, from Béthermin et a. (2012a) 24

26 Resuts With a best-fit χ 2 of and 98 degrees of freedom, we obtain a remarkaby good fit to the data. In Tabe 9 we quote mean vaues and marginaized imits for the mode parameters. In the foowing, we comment on the resuts obtained for some parameters of the mode and for some derived quantities. Peak mass M eff The mean vaue of the most efficient hao mass for generating the CIB, og(m eff /M ) = 12.6 ± 0.1, is in good agreement with resuts obtained from a simiar anaysis using Hersche CIB data at 250, 350 and 500 µm (Viero et a. 2013b), and with other anayses, using previous Panck and Hersche data (e.g., Shang et a. 2012; Xia et a. 2012), whie it is sighty higher than resuts from other observations and simuations (e.g., Moster et a. 2010; Behroozi et a. 2012; Béthermin et a. 2012b; Wang et a. 2013). We aso checked for a possibe redshift evoution of M eff (which can be justified in the framework of the so-caed downsizing idea), performing an MCMC run with the functiona form M eff = M 0 (1 + z) q, (57) The arge degeneracy between M 0 and q eads to very high vaues of M 0. The bias and SFRD have the same redshift evoution as in the case q = 0, but with much arger error bars (they are mutipied by a factor of 6 for exampe for the bias). Constraints on the dust temperature Parameterizing the average dust temperature of sources as T d (z) = T 0 (1 + z) α, (58) Fig. 13. Evoution of the star formation density (upper pane) and effective bias as a function of redshift (ower pane), as constrained from our extended hao mode. In both panes, the median reaization of the mode is represented with a red ine, the ±1 σ confidence region in dark orange, and the ±2 σ region in ight orange. In the upper pane the reported data are the same as in Fig. 11. In the ower pane, we aso pot the evoution of the dark matter-hao bias for dark matter hao masses of M (dashed ine), M (dot-dashed ine), and M (threedots-dashed ine). and Tucci et a. (2011), respectivey, and we assume fat priors around them with width given by their 1σ error. The tota number of free parameters in our anaysis is then 23, consisting of the sum of eight hao mode parameters pus 15 shot-noise parameters. Whie it is tempting to fix the shot-noise power spectra to their theoreticay modeed vaues (in order not to dea with too many parameters and keep the anaysis as simpe as possibe), we beieve that, since these vaues are not very tighty constrained by their underying modes, it is better to et them vary as free parameters around their best estimates. the data suggest a redshift evoution of the temperature, with T 0 = (24.4 ± 1.9) K and α = 0.36 ± Such a trend, impying some kind of SED evoution, has been aso found in e.g., Addison et a. (2012); Viero et a. (2013b). Experimenta resuts from different surveys appear to have been quite contradictory, with systematics paying a critica roe (e.g., Chapman et a. 2005; Coppin et a. 2008; Pascae et a. 2009; Ambard et a. 2010; Hwang et a. 2010; Chapin et a. 2011). But recenty, some consensus has emerged on a scenario with an increase of dust temperature with redshift (Magdis et a. 2012; Viero et a. 2013a). The increase of temperature may be expained by a harder interstear radiation fied at earier times (see Magdis et a. 2012, for a detaied discussion). Constraints on the bias Gaaxies are considered as a biased tracer of the dark matter fied. The gaaxy overdensity δ g (k, z) is assumed to trace the underying dark matter fied δ dm (k, z) via δ g (k, z) = b(k, z)δ dm (k, z), (59) where b(k, z) is the gaaxy bias, which in genera can depend not ony on scae and redshift but aso on uminosity, spectra type and coour. On arge scaes, the bias is generay assumed to be scae-independent; however, both numerica simuations (Kauffmann et a. 1999) and recent resuts from gaaxygaaxy ensing and gaaxy custering aso indicate an increase of the bias with redshift (e.g., Mandebaum et a. 2012), whie Tegmark & Peebes (1998) show that the bias must be cose to unity when approaching z = 0. The combination of CMB and arge-scae custering data yieds a bias parameter b 1 (Verde et a. 2002) whie Saunders et a. (1992) found bσ 8 = 25

27 Tabe 9. Mean vaues and marginaized 68% CL for hao mode parameters and shot-noise eves (in Jy 2 sr 1 ). Parameter Definition Mean vaue α SED: redshift evoution of the dust temperature 0.36 ± 0.05 T 0 [K] SED: dust temperature at z = ± 1.9 β SED: emissivity index at ow frequency 1.75 ± 0.06 γ SED: frequency power aw index at high frequency 1.7 ± 0.2 δ Redshift evoution of the normaization of the L M reation 3.6 ± 0.2 og(m eff )[M ] Hao mode most efficient mass 12.6 ± 0.1 M min [M ] Minimum hao mass unconstrained S Shot noise for 3000 GHz 3000 GHz 9585 ± 1090 S Shot noise for 3000 GHz 857 GHz 4158 ± 443 S Shot noise for 3000 GHz 545 GHz 1449 ± 176 S Shot noise for 3000 GHz 353 GHz 411 ± 48 S Shot noise for 3000 GHz 217 GHz 95 ± 11 S Shot noise for 857 GHz 857 GHz 5364 ± 343 S Shot noise for 857 GHz 545 GHz 2702 ± 124 S Shot noise for 857 GHz 353 GHz 953 ± 54 S Shot noise for 857 GHz 217 GHz 181 ± 6 S Shot noise for 545 GHz 545 GHz 1690 ± 45 S Shot noise for 545 GHz 353 GHz 626 ± 19 S Shot noise for 545 GHz 217 GHz 121 ± 6 S Shot noise for 353 GHz 353 GHz 262 ± 8 S Shot noise for 353 GHz 217 GHz 54 ± 3 S Shot noise for 217 GHz 217 GHz 21 ± ± 0.11 for IRAS gaaxies, which, assuming σ 8 = 0.8, gives b In Fig. 11 we show our estimate of the redshift dependent bias; it is remarkabe that, without assuming any prior on the vaue of the bias at redshift zero, we are abe to obtain a very good fit to observations, with b(z = 0) = 1.1 ± Constraints on star formation history The mean vaue and 68% CL bounds on the cosmic star formation rate density ρ SFR are potted in Fig. 11. The parameter ρ SFR has been computed foowing Eq. 40, repacing s ν,eff (z) by the hao mode SED as given in Eq. 50. We use the Kennicutt (1998) constant to convert infrared uminosity to star formation rate (SFR/L IR = M yr 1 for a Sapeter IMF). As can be seen from Fig. 11, the star formation rate densities predicted by both modes used in this paper are in very good agreement for redshifts z 2 whie there is a significant difference at higher redshifts. Interestingy, Behroozi et a. (2012) reports a compiation of resuts, showing how measurements performed before 2006 predict quite a high vaue for the high redshift SFRD (then more compatibe with the hao mode resuts, see aso the compiation in Hopkins & Beacom 2006), whie measurements performed after 2006 and obtained with different assumptions about the dust present at z > 3, show a rapid decrease of the SFRD, which then becomes more compatibe with resuts obtained using the inear mode. In an attempt to reproduce the break in the SFRD seen in Fig. 14 for the inear mode, we aso imposed the condition δ = 0 at redshift z = 2 in the redshift normaization parameter Φ(z) of the L M reation. Such a condition has aready been considered in Shang et a. (2012) and, whie it is motivated by some observations, it is aso hard to expain from a theoretica point of view (e.g., Weinmann et a. 2011). In this case, we are abe to obtain ower vaues of the SFRD at high redshifts (see Fig. 13), but at the price of sighty degrading the quaity of the fit. We finay note that another potentia reason for the discrepancy found at high redshift can be the difference in the inferred bias evoution between the inear mode and the hao mode: in fact, a ower vaue of the bias at high redshift (as found in the context of the hao mode) can be compensated by higher vaues for the SFRD in the same redshift range. We wi come back to the SFRD discussion in Sect Finay, we are aso abe to determine the mean CIB intensity at the Panck frequencies considered in the anaysis. The vaues obtained are presented in Tabe 10. Athough higher, they are compatibe, within the 95% CL, with resuts obtained from number counts measurements (Béthermin et a. 2012c). Tabe 10. Derived estimates of the CIB intensity from the extended hao mode. Band νi ν [nw m 2 sr 1 ] 3000 GHz 13.1 ± GHz 7.7 ± GHz 2.3 ± GHz 0.53 ± GHz ± CIB-CMB ensing cross-correation We tested the vaidity of our approach by comparing the predictions for our best-fit modes with the measurements of the cross-correation between the CIB and the CMB ensing potentia presented in Panck Coaboration XVIII (2013). For the inear mode, we computed the cross-correation foowing: C νφ = b eff (z) j(ν, z) 3 2 Ω rmm, H 2 0 ( χ χ χ χ ) P in (k = /χ, z)dχ, (60) where χ is the comoving distance to the CMB ast-scattering surface. We use a simiar equation for the extended hao mode. Figure 15 shows a comparison between the mode and the data. The hao mode (as we as its variant with a break in the temperature and goba normaization of the L M reation at redshift z 4, see Sect. 6.4) agrees remarkaby we with the mea- 26

28 Fig. 14. Marginaized constraints on the star formation rate density, as derived from our extended hao mode described in Sect. 5.5 (red continuous ine with ±1 and ±2 σ orange dashed areas). It is compared with mean vaues computed imposing the condition δ(z 2) = 0 (back ong-dashed ine), or the combined conditions δ(z z break ) = 0 and T(z = z break ) = T(z break ), where z break is found to be 4.2 ± 0.5 (bue dashed ine). The vioet points with error bars are the SFR density determined from the modeing of the CIB-CMB Lensing cross correation by Panck Coaboration XVIII (2013). surements for a channes. The inear mode gives a higher prediction at 217 and 353 GHz (athough compatibe with the data points at the 1 σ eve). 6. Discussion 6.1. The 143 GHz case Removing the CMB anisotropy at 143 GHz is very probematic, since the CMB power spectrum is about 5000 higher than the CIB at = 100. However, thanks to the exceptiona quaity of the Panck data, and the accuracy of the 100 and 143 GHz reative photometric caibration, we can obtain significant measurements, using the same method to cean the maps and measure the power spectra as for the other channes. We show the measurements in Fig. 16, together with the best-fit CIB mode. This estimate has been obtained by correcting the measurements for the SZ and spurious CIB (induced by the use of the 100 GHz map as a CMB tempate). Those corrections are important, especiay for power spectra at ow frequencies. For exampe, for , the SZ-reated corrections decrease the measurements by 10 20%, whie the correction for the spurious CIB increases the measurements by 30 60%. Since these corrections are arge, we have not attempted to incude the 143 GHz measurements when constraining the mode. We show in Fig. 16 a comparison between extrapoation of the hao best-fit mode to the 143 GHz cross-power spectra and our CIB power-spectrum estimates. The 143 ν cross-power spectra agree quite we for < 1000, at east for ν 353 GHz. The CIB power spectrum ies about 2 σ above the prediction at intermediate scaes ( = 502 and 684). This CIB overestimate increases for the power spectrum, which is certainy the most difficut to obtain; this is in excess with respect to the prediction for 300 < < At this frequency, Fig. 15. Comparison between the measurements of the CIB and gravitationa potentia cross-correation given in Panck Coaboration XVIII (2013) (diamonds), with the predictions from our best-fit modes of the CIB cross-power spectra (red and bue soid ines for the inear and extended hao mode, respectivey). The other curves are the two variants of the extended hao mode with: (i) a break in the goba normaization of the L M reation fixed at redshift z = 2 (bue 3-dot-dashed curve); and (ii) a break in both the temperature evoution and normaization of the L M reation, found at redshift z = 4.2±0.5 (bue ong-dashed curve). however, the CIB auto-power spectrum measurements have to 27

29 a HFI bands with IRIS is quite ow, between about 0.2 and 0.32 (with a arge dispersion). This is expected, because the redshift distribution of CIB anisotropies evoves strongy between 3000 and 857 GHz, being biased towards higher redshifts at ower frequencies (e.g., Béthermin et a. 2013). Contrary to the range GHz the band correation strongy varies with at 143 GHz, decreasing from = 150 to 1000 (see Tabe 11). Such a decrease might be expected, based on the high shot-noise contribution at this frequency (see Fig. 16). Indeed, Béthermin et a. (2013) observe that the band correation is ower for the shot noise than for correated anisotropies; this mimics a scae dependence Comparison with recent measurements Fig. 16. CIB cross- and auto- power spectra obtained at 143 GHz (red points). To obtain the CIB, the ceaned CMB and Gaactic dust power spectra (back points, shifted in for carity) are corrected for SZ-reated residuas, C ν ν SZcorr and Cν ν CIB SZcorr (foowing Eqs. 8, 9, and 12), and for C ν ν CIBcorr (foowing Eq. 4, and computed using the extrapoation of the best-fit hao mode). The prediction of the hao mode is shown in bue (continuous for 2h+1h+shot noise; dashed for shot noise ony). be taken with caution, as the correction for the spurious CIB can be as high as 70%, and is thus highy mode dependent Frequency decorreation Using the power spectrum measurements, we can quantify the frequency decoherence. We measure the correation between bands by averaging the quantity C ν ν /(C ν ν C ν ν ) 1/2 for 150 < < We restrict ourseves to this range to have ony the custered CIB contribution (not the shot noise). Resuts are given in Tabe 11. We see that the CIB for the four HFI frequencies (from 217 to 857 GHz) is very we correated, the worst case being between the 857 and 217 GHz channes, with a correation of about On the other hand, the correation of We now compare the CIB auto-spectrum measurements with the most recent measurements from Hersche-SPIRE (Viero et a. 2013b) and the earier measurements from Panck (Panck Coaboration XVIII 2011). We compute the SPIRE-HFI coour corrections using the CIB SED from Gispert et a. (2000) and the most recent bandpasses (see Panck Coaboration IX 2013). In order to compare with HFI at 857 and 545 GHz, the power spectra at 350 and 500 µm have to be mutipied by and 0.805, respectivey. We use the SPIRE power spectra with ony extended sources masked (such that the poisson contribution is the same in both measurements). We see from Fig. 17 that the agreement between the SPIRE and HFI measurements (red circes versus bue circes) is exceent at 857 GHz. At 545 GHz, athough compatibe within the error bars there is a sma difference, with the SPIRE power spectrum being higher than HFI by about 7% for 650 < < 1800 and by about 30% for 200 < < 600. Between the pubication of Panck Coaboration XVIII (2011) and this paper, the photometric caibration of the two high-frequency HFI channes has been modified (see Panck Coaboration VIII 2013). Using a panet-based caibration rather than a FIRAS-based caibration eads to a division of the caibration factors by 1.07 and 1.15 at 857 and 545 GHz, respectivey. After correcting for these factors, the two Panck CIB measurements agree within 1 σ at 545 GHz and within 2 σ at 857 GHz. At 217 GHz, the discrepancy we observe between the earier Panck CIB measurements and those presented in this paper is expained by the SZ and CIB contamination of the 143 GHz-based CMB tempate used in Panck Coaboration XVIII (2011). Note that with the new measurements, we do not improve the error bars, since the use of the 100 GHz channe as a CMB tempate adds more noise than the use of the 143 GHz channe. The apparent difference in shape between the CIB at 217 GHz and at higher frequencies has to be attributed to the shot noise, whose contribution reative to the correated part is higher at 217 GHz, making the measured CIB fatter at this frequency. For cross-power spectra, we can compare our determination with Hajian et a. (2012). We show on Fig. 18 the and Panck power spectra, and those obtained from the cross-correation between BLAST and ACT data. For this comparison, the shot noise contributions have been removed, as they are very different for BLAST, ACT and Panck. We do not appied any coor correction. Even if three points overap in scae, the comparison can be done ony on one point, as the ow- measurements from BLAST ACT are very noisy. For this =1750 point, the two measurements agree within 1σ. This pot ius- 28

30 Tabe 11. Frequency decoherence of the CIB, measured by averaging C νν /(C νν C ν ν ) 1/2 for 150 < < The error bars correspond to the standard deviation. The vaues at 143 GHz strongy depend on the correction of the spurious CIB (that has been introduced by the choice of our CMB tempate), which is highy mode dependent. The band correation is strongy varying with at 143 GHz, increasing as one goes from = 1000 to 150. The numbers in brackets at 143 GHz indicate this variation ± ± ± ± ± ± ± ± 0.10 [ ] ± ± ± 0.11 [ ] ± ± 0.11 [ ] ± 0.08 [ ] trates the compementarity between Panck and the high- measurements from ACT and SPT The history of star formation density The star formation histories recovered from the two different modeing approaches presented in Sects. 5.4 and 5.5 are consistent beow z = 2, and agree with recent estimates of the obscured star-formation density measured by Spitzer and Hersche. At higher redshift, there are discrepancies between our two modes and the estimate of Gruppioni et a. (2013). The inear mode is about 1 and 2 σ ower than their measurements at z = 2.5 and 3.5, respectivey, whie the hao mode ies about > 3 σ above these data points. Such estimates assume a shape for the infrared uminosity function. They are strongy dependent on the faint-end sope assumption, since no data are avaiabe beow the break of the uminosity function. This shows how measurement of the obscured star formation rate density at z > 3 is difficut. We investigated the origin of the discrepancy between the two modeing approaches. In particuar, we modified the hao mode in two ways to see how different assumptions on the parametrization of the mode can affect the resuts. 1. We fit the data by imposing the condition δ = 0 for redshifts z z break = 2 in the redshift normaization parameter Φ(z) of the uminosity-mass reation. This parametrization, athough degrading the quaity of the fit somewhat, decreases the SFRD by a factor of about 5 for z = 4, which is now compatibe with the inear mode SFRD (see Fig. 13). 2. We fit the data by imposing two conditions: δ = 0 for redshift z z break and T(z z break ) = constant = T(z break ) for z break in the range 2 5. We find z break = 4.2 ± 0.5, as can be seen in Fig. 13. In this case the SFRD is ony reduced at very high redshift, by a factor 3 at z = 6. Note that aowing for a redshift break in the redshift evoution of the temperature avoids reaching unphysicay high vaues at very high redshift. We aso show in Fig. 13 the SFRD measurements from the CIB-CMB ensing cross-correation (Panck Coaboration XVIII 2013). This compares favouraby with a high SFRD eve at high redshift. Part of the discrepancy between the two modeing approaches can aso be attributed to the effective bias. A higher bias, as that recovered at high redshift from the inear mode, favors a ower SFRD. We finay compared the SEDs used in the two approaches. The effective SEDs present a broader peak than the extended hao mode SEDs, because they take into account the dispersion in dust temperature and the mixing between secuary starforming gaaxies and episodic starbursts. At z > 2, there are discrepancies in the Rayeigh-Jeans regime between the two tempates, the effective SEDs being higher than the extended hao mode SEDs; this discrepancy increases with redshift. At z = 5, for the same L IR, the parametric SEDs of the hao mode emits about 3 times ess infrared ight than the effective SEDs (and hence about an order of magnitude ess fuctuations). This expains why this mode requires a much higher star formation rate density to fit CIB anisotropies than the inear mode 7. Foowing the parametrisation of Eq. 50, we fit the effective SEDs with a modified back body with a ν 1.75 emissivity aw to obtain the dust temperature. On Fig. 19, we show the redshift evoution of the temperature of the two tempates. Compared to the recent average temperatures of star-forming gaaxies found by Viero et a. (2013a) up to z 4, the temperature of the effective SEDs is a bit ow whie the temperature of the SEDs of the extended hao mode is a bit high. Knowing the SEDs of the gaaxies that are responsibe for the buk of the CIB is the principa imitation in our modeing framework. Accurate future measurement of the SEDs wi be crucia to propery estimate the obscured star formation rate density at high redshift from the CIB anisotropies. This is important if one wants to determine whether or not the buk of the star formation is obscured at high redshift, and whether the UV and Lyman-break gaaxy popuations are a compete tracer of the star formation in the eary Universe CIB non-gaussianity Lacasa et a. (2012) proposed a phenomenoogica prescription for the CIB bispectrum based on its power spectrum, namey b = α C 1 C 2 C 3, (61) where α is a dimensioness parameter quantifying the intrinsic eve of non-gaussianity. Using the best-fit power spectrum of the CIB mode described in Sect. 5.5, we fitted this parameter α through a χ 2 minimization using the covariance matrix described in Sect The resuting best-fit α, its error bar (computed using a Fisher matrix anaysis), and the χ 2 vaue of the best fit can be found in Tabe 12. Tabe 12. Best-fit ampitude parameter for the bispectrum prescription (Eq. 61), and the vaues of χ 2 and number of degrees of freedom associated with the fit. Band α χ 2 N dof 217 GHz (1.90 ± 0.5 ) GHz (1.21 ± 0.07) GHz (1.56 ± 0.06) We obtain the same SFRD if we fix in the inear mode the SEDs and effective bias to those obtained from the extended hao mode. 29

31 Fig. 18. Panck (red dots) and BLAST ACT (bue dots from Hajian et a. 2012) CIB power spectra. Ony the custered CIB is shown (the shot noises have been removed as they are very different in the two measurements). No coor corrections have been appied between HFI channes, and the 218 GHz (ACT) and 857 GHz (BLAST) channes. The y-axis for the cross-correation is in inear scae as the BLAST ACT measurement has negative vaues (due to the shot-noise remova). Fig. 17. Comparison of the CIB auto-power spectra measured using SPIRE (bue dots, Viero et a. 2013b), earier Panck data (Panck Coaboration XVIII 2011, back dots) and in this paper (red circes). The SPIRE data have been coour corrected to be compared with HFI (see text). The dashed ines show the Panck Coaboration XVIII (2011) CIB measurements, rescaed at 857 and 545 GHz by the photometric re-caibration factors ( and , for the power spectra at 857 and 545 GHz, respectivey, see Panck Coaboration VIII 2013). At 217 GHz, the difference between the back and red points is due to the tsz and CIB contamination of the CMB tempate that is now corrected 30 for. The consistency of α across frequencies shows that the measured bispectrum has a frequency dependence consistent with that of the power spectrum. The best-fit α vaues are consistent with the vaues predicted using the number counts mode of Béthermin et a. (2011). The best-fit αs are of the same order, athough a itte ower than those found by Lacasa et a. (2012) on simuations by Sehga et a. (2010), since they found α This indicates a ower eve of CIB non-gaussianity than in the simuations by Sehga et a. (2010). The χ 2 vaue of the fit shows that the prescription does not provide a very good mode of the data as frequency increases; visua inspection reveas that this mainy comes from the fact that the measured bispectrum has a steeper sope than the prescription. To quantify the sope of the measured bispectrum, we fit a power aw to the measurements, i.e., b = A n 1 2 3, (62) 3 0 where we chose as the pivot scae 0 = 320, which is the centre of the second mutipoe bin. Tabe 13 presents the obtained bestfit vaues for the ampitude A and the index n, as we as their error bars and correation (computed again with Fisher matrices) and the χ 2 vaue. The power aw provides a significanty better fit to the data than the prescription of Eq. 61, having ower best-fit χ 2 vaues. The indices obtained are coherent between frequencies, and significanty steeper than the Eq. 61 prescription, which is n 0.6 (since C 1.2 ). There is no sign of fattening of the bispectrum, showing that the shot-noise contribution is subdominant in this mutipoe range. This is consistent with shot-noise estimates based on the number counts mode of Béthermin et a. (2011). A detection of CIB non-gaussianity has recenty been reported by Crawford et a. (2013). In this paper, they used the

32 Tabe 13. Best-fit ampitude and index for a power-aw fit to the bispectra, as we as the associated correation, χ 2 vaue of the fit and number of degrees of freedom. Frequency A [Jy 3 sr 1 ] Index Correation χ 2 N dof 217 GHz (1.46 ± 0.68) ± % GHz (5.06 ± 0.49) ± % GHz (1.26 ± 0.09) ± % Fig. 19. Redshift evoution of the dust temperature of the effective SEDs used in the inear mode (bue continuous ine) and of the SEDs fit in the extended hao mode (red continuous ine with z break = 4.2, red dot-dashed ine without any redshift break). prescription proposed by Lacasa et a. (2012) to give the ampitude of the bispectrum. In comparison with this anaysis, we provide a higher detection significance, and at severa frequencies. Most importanty, we find an indication that the CIB bispectrum is steeper than the prescription of Lacasa et a. (2012), athough we fitted by a power aw. However, our steeper CIB bispectrum at 217 GHz, extrapoated up to =2000, is compatibe with Crawford et a. (2013) bispectrum measurement at =2000 within 1σ. The steeper sope may be an indication that the contribution of more massive haos to the CIB bispectrum is smaer than in the modes studied by Lacasa & Pénin (2013) and Pénin et a. (2013). 7. Concusions We have presented new measurements of the CIB anisotropies with Panck. Owing to the exceptiona quaity of the data, and using a compete anaysis of the different steps that ead to the CIB anisotropy power spectra, we have been abe to measure the custering of dusty, star-forming gaaxies at 143, 217, 353, 545, and 857 GHz, with unprecedented precision. For the fist time we aso measured the bispectrum from 130 to 900 at 217, 353, and 545 GHz. The CIB power spectrum is aso measured with IRAS at 3000 GHz. We worked on 11 independent fieds, chosen to have high anguar-resoution Hi data and ow foreground contamination. The tota areas used to compute the anguar power spectrum is about 2240 deg 2. This improves over previous Panck and Hersche anayses by more than an order of magnitude. For the bispectrum, the tota area is about 4400 deg 2. To obtain the CIB, the HFI and IRAS maps were ceaned using two tempates: Hi for Gaactic cirrus; and the Panck 100 GHz map for CMB. We used new Hi data that covers very arge portions of the sky. The arge areas forced us to buid a dust mode that takes into account the submiimetre Hi emissivity variations. However, because the Hi is not a perfect tracer of dust emission (e.g., the dark gas), and ceary contains dustdeficient couds, we had to reduce the sky fraction to the owest Hi coumn-density parts of the sky. The 100 GHz Panck channe, ceaned of Gaactic dust and sources, and then fitered, provides a good tempate for the CMB. This is because it has an anguar resoution cose to the higher frequency channes, from which we measure the CIB, and has the advantage of being an interna tempate, meaning that its noise, data reduction processing steps, photometric caibration, and beam are a we known. It has the drawback of contaminating CIB measurements with tsz signa and spurious CIB coming from the correation between the CIB at 100 GHz, and the CIB at higher frequency. The tsz and spurious CIB corrections are reativey sma for frequencies ν 217 GHz. At 143 GHz, whie the tsz and tsz CIB corrections are sti rather sma (ower than 20%), the spurious CIB is a very arge correction (between 30 and 70% at intermediate scaes) due to the high eve of CIB correation between 100 and 143 GHz. Thus, the 143 GHz CIB measurements strongy rey on the CIB mode used to compute the correction. Due to dust contamination at high frequency, as we as radio sources, SZ and CIB at ow frequency, we conservativey restrict our bispectrum measurement to the three frequencies 217, 353, and 545 GHz. We measure the bispectrum due to the custering of dusty star forming gaaxies from 130 to 900. It is detected with a very high significance, > 28 σ for a configurations, and even > 4.5 σ for individua configurations at 545 GHz. Such measurements are competey new; they open a window for constraining modes of CIB source emission that we have not yet fuy expored in this paper. We deveoped two approaches for modeing the CIB anisotropies. The first takes advantage of the accurate measurement of CIB anisotropies performed with Panck and IRIS at arge anguar scaes, and uses ony the inear part of the power spectra. The second approach uses the measurements at a anguar scaes, and takes advantage of the frequency coverage, to constrain a hao mode with a uminosity-mass dependence. We find that both modes give a very good fit to the data. Our main findings are as foows. The modes give strong constraints on the star formation history up to redshift 2.5. At higher redshift, the accuracy of the star formation history measurement is strongy degraded by the uncertainty on the SED of CIB gaaxies. An accurate measurement of SEDs of gaaxies that are responsibe for the buk of the CIB wi be crucia to estimate propery the obscured star-formation rate density at high redshifts from the CIB anisotropies. As found in other recent studies, haos of mass M eff = M appear to be the most efficient at activey forming stars. CIB gaaxies have warmer temperatures as redshift increases (T d (z) = 24.4 (1+z) 0.36 K in the extended hao mode). This is compatibe with the most recent Hersche observations, and can be expained by a harder interstear radiation fied in high-z gaaxies. The same hao occupation distribution can simutaneousy fit a power spectra. However, the 1-hao term is significanty reduced compared to previous studies (Pénin et a. 2012a; 31

33 Panck Coaboration XVIII 2011). This is due to a ower contribution to the custering from ow-z massive haos, as aso observed in Béthermin et a. (2013). We find that the CIB bispectrum is steeper than the prescription deveoped by Lacasa et a. (2012). Just ike the reduction of the 1-hao term in the power spectrum, this may be an indication that the contribution of massive haos to the CIB bispectrum is smaer than in the modes studied by Lacasa & Pénin (2013) and Pénin et a. (2013). The bispectrum is quite we fitted by a power aw. This can be used to provide vauabe constraints on the potentia contamination of measurements of the primordia CMB bispectrum on arge scaes. Whie our component separation process is successfu in extracting the CIB from the maps, the next step is to use a fu muti-frequency fitting procedure to separate the CIB power spectrum and bispectrum, from the tsz (and ksz) effects, the CMB, and the extragaactic source contribution. Simutaneousy taking into account a the components wi improve our abiity to separate them. The goa is to give unprecedented imits on the reionization history of the Universe, as we as understanding the history of star formation in dark matter haos. Acknowedgements. The deveopment of Panck has been supported by: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Itay); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MICINN and JA (Spain); Tekes, AoF and CSC (Finand); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerand); RCN (Norway); SFI (Ireand); FCT/MCTES (Portuga); and PRACE (EU). A description of the Panck Coaboration and a ist of its members with the technica or scientific activities they have been invoved into, can be found at esa.int/index.php?project=planck&page=panckcoaboration. 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Each subsequent scan is offset by 3.5 in the corresponding orthogona direction. This strategy resuts in a rectanguar region of the Hi sky samped every 3.5. Some of the regions have been scanned in this way mutipe times, in order to increase the signa-to-noise, and to investigate the stabiity of the system (Boothroyd et a. 2011). The spectra are first converted from their antenna temperature scae to a brightness temperature (T b ) scae. This invoves caibration and stray radiation corrections, as discussed in Boothroyd et a. (2011). A T b spectra for a corresponding region are assigned to a 3.5 Sanson-Famsteed-projection grid (SFL-projection) using convoution with an optimized tapered Besse function, in order to minimize noise on spatia scaes smaer than the beam (Mangum et a. 2007). Note that this observing strategy and gridding choice resuts in a fina cube resoution of , sighty broader than the inherent GBT 21-cm beam. Each spectrum is recorded using in-band frequencyswitching, resuting in veocity coverage of 450 km s 1 V LS R 355 km s 1, with very fat baseines. Any residua baseine is removed on a pixe-by-pixe basis by fitting the emissionfree channes in the fina caibrated cube using a third-order poynomia. The archiva LH2 fied was observed using a 3 grid pattern with the GBT spectra processor and was caibrated accordingy. As the residua baseine behaviour is different for the archiva data, ony a inear poynomia was fit to the emission-free channes. The rest of the processing was identica to that described above. The individua 0.8 km s 1 spectra channes of the cubes are integrated to convert the T b spectra into N HI maps: N HI (x, y) = v T b (x, y, v)τ(t s )δv, (A.1) where the sum is over a given veocity range, v, and δv is the 0.80 km s 1 channe spacing. The quantity τ is the opacity correction for spin temperature, T s : τ(t s ) = n(1 T b /T s ). (A.2) For the adopted vaue of T s = 80 K, these corrections are a ess than 5% for our CIB fieds (Panck Coaboration XVIII 2011). The veocity ranges over which the integrations are performed are seected using the observed veocity structure in each of the cubes. The modes presented here subdivide each cube into three veocity-seected components: a oca component; intermediate-veocity couds, IVCs; and high-veocity couds, HVCs. Divisions between components are distinguishabe by reductions in structure (as measured through the standard deviation of individua channe maps) as one progresses through the data cube, channe by channe. More detais can be found in Panck Coaboration XVIII (2011). A.2. GASS observations and data preparation The GASS survey is a 21-cm ine survey covering the southern sky for a decinations δ < 1. The observations were made with the mutibeam system on the 64-m Parkes Radio Teescope. The intrinsic anguar resoution of the data is 14.4 fu width at haf maximum (FWHM). The veocity resoution is 1.0 km s 1 and the usefu bandpass covers a veocity range v sr < 468 km s 1 for a of the observations; some data cover up to v sr < 500 km s 1. GASS is the most sensitive, highest anguar resoution arge-scae survey of Gaactic Hi emission ever made in the southern sky. The observations are described in McCure-Griffiths et a. (2009). We used data from the fina 33

35 Panck Coaboration: CIB anisotropies with Panck data reease (Kabera et a. 2010) that were corrected for instrumenta effects and radio-frequency interference (RFI). The data were gridded on a Cartesian grid on the Mageanic stream (MS) coordinate system as defined by Nidever et a. (2008). To minimize the noise and eiminate residua instrumenta probems, we cacuated a second 3-D data cube with a beam of 0.5 FWHM, smoothing at the same time in veocity by 8 km s 1. Emission beow a 5 σ eve of 30 mk in the smoothed data-cube was considered as insignificant and was accordingy zeroed. For detais in data processing and anaysis see Venzmer et a. (2012). When ooking at the Hi data cube in the southern sky, one of the most prominent structures is inked to hydrogen gas in the Mageanic stream, in the disks of the Mageanic couds, and in the stream s eading arm. In particuar, the Mageanic stream, stretches over 100 behind the Large and Sma Mageanic couds. We thus need to remove this contamination to be abe to use the Hi as a tracer of Gaactic dust. Aiming to separate Gaactic emission from the observations of the Mageanic system we cacuated the expected Miky Way emission according to the mode of Kabera & Dedes (2008). Veocities for components in direction towards the southern Gaactic poe were shifted by 5 km s 1 to mimic the apparent infa (see Weaver 1974). Comparisons between the emission and the mode at two particuar veocities in the Gaactic standard of rest frame are shown in Fig. A.1. The strong Gaactic emission can be traced to weak extended ine wings that are we represented by the mode. It is therefore feasibe to use the mode to predict regions in the 3-D data cube that are most probaby occupied by Miky Way emission. We used a cip eve of 60 mk, the owest isophote in Fig. A.1 that deineates the disk emission. Such a treatment extracts most of the Gaactic emission, however we must take into account the fact that at positions with strongy bended ines Mageanic emission aso gets incuded. A higher cip eve woud minimize this probem, athough, at the same time the wings of the Gaactic emission woud be affected. The chosen cip eve of 60 mk (comparabe to the instrumenta noise), is a good compromise. As the fina step in the reduction of the GASS data we integrated the Hi emission over the appropriate veocity range for each individua position in the Nside = 512 HEALPix database to obtain coumn densities of the Gaactic gas. To avoid any interpoation errors, we extracted profies from the origina GASS database; a intermediate data products that have been described above served ony to discriminate Gaactic emission from the Mageanic stream. Due to the finite beam size of the Parkes teescope and the Gaussian weighting that was used for the gridding, the effective resoution of the HEALPix data is FWHM. A.3. EBHIS observations and data anayses The Effesberg-Bonn Hi Survey (EBHIS) comprises an Hi sur vey of the entire northern sky for a decinations δ > 5 with the Effesberg 100-m teescope. The bandwidth of 100 MHz covers 1000 km s 1 vlsr 19,000 km s 1. This aows us to study the detaied Miky Way Hi structure as we as the oca Universe up to a redshift of z ' 0.07 (Kerp et a. 2011), with an effective veocity resoution of about 2.1 km s 1. We seected from the eary survey data a cean high Gaactic atitude fied. The observations of the fied of interest were performed during the summer of Foowing the standard observing strategy (Kerp et a. 2011) individua fieds of 25 deg2 were measured. In addition to the data reduction and caibration pipeine of Winke et a. (2010), the Hi data were corrected with an improved RFI mitigation detection agorithm and the absoute 34 Fig. A.1. Comparison of observed Hi emission with the Gaactic mode (back isophotes are for the expected emission at eves of 0.06, 0.6 and 6.0 K). Mageanic coordinates (ongitude and atitude) are used. Two exampes for channe maps at Gaactic standard of rest veocities of 19.8 and km s 1 are given. offsets between the individua fieds were minimized to a eve of NHI cm 2. As for the GBT fieds, the EBHIS data were put on a 3.50 SFL-projection grid. The overa Hi emission in this fied can be characterized by intermediate- and ow-veocity emission popuating the radia veocity range 80 km s 1 vlsr +20 km s 1. The area of interest is about 130 deg2 with Hi coumn densities beow NHI = cm 2. The tota Hi coumn density range is cm 2 NHI cm 2. Accordingy we expect infrared excess emission associated with moecuar hydrogen towards areas of NHI cm 2, whie the owcoumn density regions shoud aow us to study the emission associated with the CIB. In the first step we performed a inear fit of the EBHIS Hi data integrated across the veocity range 160 km s 1 vlsr +160 km s 1 to the HFI 857 GHz map: I857 = a NHI + b, for NHI cm 2. The residua map shows dust excess, as expected when the tota infrared emissivity traces Hi and H2 (Panck Coaboration XIX 2011; Panck Coaboration XXIV 2011). In agreement with our expectation dust excess couds