Planck 2013 results. XV. CMB power spectra and likelihood

Ade, P.A.R.; Wade, L.A.; Stolyarov, V.; Desert, F.X.; Knoche, J.; Giard, M.; Dupac, X.; Liguori, M.; Sanselme, L.; Matarrese, S.; Kurki-Suonio, H.; Mazzotta, P.; Coulais, A.; Gorski, K.M.; Vielva, P.; Tristram, M.; Gonzalez-Nuevo, J.; Bucher, M.; Mitra, S.; Tomasi, M.; Norgaard-Nielsen, H.U.; Leonardi, R.; Netterfield, C.B.; Vittorio, N.; Gaier, T.C.; Marinucci, D.; Paladini, R.; Mortlock, D.; Lindholm, V.; Perotto, L.; Franceschi, E.; Roudier, G.; Lopez-Caniego, M.; Pajot, F.; Santos, D.; Cardoso, J.F.; Nati, F.; Chiang, H.C.; Plaszczynski, S.; Crill, B.P.; Tuovinen, J.; Linden-Vornle, M.; Galeotta, S.; Reinecke, M.; Christensen, P.R.; Henrot-Versille, S.; Poutanen, T.; Wandelt, B.D.; Gratton, S.; Dickinson, C.; Natoli, P.; Rusholme, B.; Bonavera, L.; Maris, M.; Diego, J.M.; Giardino, G.; Maffei, B.; Chiang, L.Y.; Millea, M.; Sandri, M.; Delouis, J.M.; Battaner, E.; Tauber, J.A.; Riller, T.; Atrio-Barandela, F.; Lattanzi, M.; Puget, J.L.; Efstathiou, G.; Paoletti, D.; Bock, J.J.; Benabed, K.; Delabrouille, J.; Lesgourgues, J.; Martin, P.G.; Meinhold, P.R.; Pietrobon, D.; Jaffe, T.R.; Mennella, A.; Church, S.; Valenziano, L.; Osborne, S.; Maino, D.; Savini, G.; Dole, H.; Perrotta, F.; Pasian, F.; Douspis, M.; Pratt, G.W.; Polenta, G.; Starck, J.L.; Zonca, A.; Perdereau, O.; Bonaldi, A.; Ponthieu, N.; Cuttaia, F.; Moneti, A.; Lahteenmaki, A.; Pointecouteau, E.; Hobson, M.; Wehus, I.K.; Piacentini, F.; Villa, F.; Lamarre, J.M.; Rahlin, A.; O'Dwyer, I.J.; Bobin, J.; Munshi, D.; Shellard, E.P.S.; Martinez-Gonzalez, E.; Lilje, P.B.; Hansen, F.K.; Turler, M.; Dunkley, J.; Arnaud, M.; Molinari, D.; Hivon, E.; Sureau, F.; Davies, R.D.; Zacchei, A.; Marshall, D.J.; Stompor, R.; Ganga, K.; Rebolo, R.; Juvela, M.; Galli, S.; Bartlett, J.G.; Baccigalupi, C.; Pierpaoli, E.; Oxborrow, C.A.; Leach, S.; White, S.D.M.; Rowan-Robinson, M.; Benoit, A.; Le Jeune, M.; Knox, L.; Elsner, F.; Giraud-Heraud, Y.; Ricciardi, S.; Gjerlow, E.; Mendes, L.; Lawrence, C.R.; Clements, D.L.; Menegoni, E.; Ashdown, M.; Kiiveri, K.; Curto, A.; Suur-Uski, A.S.; Challinor, A.; Scott, D.; Mandolesi, N.; Novikov, I.; Bersanelli, M.; Partridge, B.; Barreiro, R.B.; Hornstrup, A.; Popa, L.; Lagache, G.; Yvon, D.; Harrison, D.; Rubino-Martin, J.A.; Hernandez-Monteagudo, C.; Kisner, T.S.; Holmes, W.A.; Melchiorri, A.; Chamballu, A.; Rachen, J.P.; Orieux, F.; Keihanen, E.; Hanson, D.; Frailis, M.; Hildebrandt, S.R.; Seiffert, M.D.; de Zotti, G.; Van Tent, B.; Gruppuso, A.; White, M.; Donzelli, S.; Remazeilles, M.; Spencer, L.D.; Kneissl, R.; Ringeval, C.; Keskitalo, R.; Jones, W.C.; Macias-Perez, J.F.; Leon-Tavares, J.; Finelli, F.; Colombo, L.P.L.; Rocha, G.; Sygnet, J.F.; Noviello, F.; Dore, O.; Burigana, C.; Combet, C.; Pagano, L.; Gudmundsson, J.E.; Naselsky, P.; Migliaccio, M.; Bouchet, F.R.; Kunz, M.; Masi, S.; Lubin, P.M.; Paci, F.; Prezeau, G.; Sudiwala, R.; Paykari, P.; Novikov, D.; Jewell, J.; Bielewicz, P.; Patanchon, G.; Armitage-Caplan, C.; Calabrese, E.; Moss, A.; Lasenby, A.; Boulanger, F.; Prunet, S.; Terenzi, L.; Couchot, F.; Bernard, J.P.; de Rosa, A.; Bond, J.R.; Matthai, F.; Danese, L.; Jaffe, A.H.; Butler, R.C.; Laureijs, R.J.; Toffolatti, L.; Aumont, J.; Herranz, D.; Aghanim, N.; Eriksen, H.K.; Benoit-Levy, A.; Varis, J.; Sutton, D.; Tucci, M.; Colombi, S.; Miville-Deschenes, M.A.; Fraisse, A.A.; Leahy, J.P.; Tavagnacco, D.; de Bernardis, P.; Morgante, G.; Ensslin, T.A.; Forni, O.; Rosset, C.; Davis, R.J.; Montier, L.; Catalano, A.; Valiviita, J.; Renault, C.; Piat, M.; Bridges, M.; Helou, G.; Ristorcelli, I.; Banday, A.J.; Borrill, J.; Hurier, G.; Hovest, W.; Huffenberger, K.M.; Gregorio, A.

doi:10.1051/0004-6361/201321573

Article
Report number	arXiv:1303.5075 ; CERN-PH-TH-2013-128 ; CERN-PH-TH-2013-128
Title	Planck 2013 results. XV. CMB power spectra and likelihood
Author(s)	Ade, P.A.R. (Cardiff U.) ; Aghanim, N. (Paris, Inst. Astrophys.) ; Armitage-Caplan, C. (Oxford U.) ; Arnaud, M. (DAPNIA, Saclay) ; Ashdown, M. (Cambridge U., KICC ; Cambridge U.) ; Atrio-Barandela, F. (Salamanca U.) ; Aumont, J. (Paris, Inst. Astrophys.) ; Baccigalupi, C. (SISSA, Trieste) ; Banday, A.J. (Toulouse III U. ; IRAP, Toulouse) ; Barreiro, R.B. (Cantabria Inst. of Phys.) ; Bartlett, J.G. (APC, Paris ; Caltech) ; Battaner, E. (Granada U.) ; Benabed, K. (Paris, Inst. Astrophys. ; Paris U., VI-VII) ; Benoit, A. (LPSC, Grenoble) ; Benoit-Levy, A. (University Coll. London ; Paris, Inst. Astrophys. ; Paris U., VI-VII) ; Bernard, J.P. (IRAP, Toulouse) ; Bersanelli, M. (Milan U. ; Brera Observ.) ; Bielewicz, P. (Toulouse III U. ; IRAP, Toulouse ; SISSA, Trieste) ; Bobin, J. (DAPNIA, Saclay) ; Bock, J.J. (Caltech) ; Bonaldi, A. (Manchester U.) ; Bonavera, L. (Cantabria Inst. of Phys.) ; Bond, J.R. (Canadian Inst. Theor. Astrophys.) ; Borrill, J. (LBL, Berkeley ; UC, Berkeley) ; Bouchet, F.R. (Paris, Inst. Astrophys. ; Paris U., VI-VII) ; Boulanger, F. (Paris, Inst. Astrophys.) ; Bridges, M. (Cambridge U., KICC ; Cambridge U. ; Cambridge U., Inst. of Astron.) ; Bucher, M. (APC, Paris) ; Burigana, C. (Bologna Observ. ; Ferrara U.) ; Butler, R.C. (Bologna Observ.) ; Calabrese, E. (Oxford U.) ; Cardoso, J.F. (LTCI, Paris ; APC, Paris ; Paris, Inst. Astrophys.) ; Catalano, A. (LPSC, Grenoble ; LERMA, Ivry) ; Challinor, A. (Cambridge U., Inst. of Astron. ; Cambridge U., KICC ; Cambridge U., DAMTP) ; Chamballu, A. (DAPNIA, Saclay ; Paris, Inst. Astrophys.) ; Chiang, L.Y. (Taipei, Inst. Astron. Astrophys.) ; Chiang, H.C. (Princeton U. ; KwaZulu Natal U.) ; Christensen, P.R. (Bohr Inst.) ; Church, S. (Stanford U., Phys. Dept.) ; Clements, D.L. (Imperial Coll., London) ; Colombi, S. (Paris, Inst. Astrophys. ; Paris U., VI-VII) ; Colombo, L.P.L. (UCLA ; Caltech) ; Combet, C. (LPSC, Grenoble) ; Couchot, F. (Orsay, LAL) ; Coulais, A. (LERMA, Ivry) ; Crill, B.P. (Caltech) ; Curto, A. (Cambridge U. ; Cantabria Inst. of Phys.) ; Cuttaia, F. (Bologna Observ.) ; Danese, L. (SISSA, Trieste) ; Davies, R.D. (Manchester U.) ; Davis, R.J. (Manchester U.) ; de Bernardis, P. (Rome U.) ; de Rosa, A. (Bologna Observ.) ; de Zotti, G. (Padua Observ. ; SISSA, Trieste) ; Delabrouille, J. (APC, Paris) ; Delouis, J.M. (Paris, Inst. Astrophys. ; Paris U., VI-VII) ; Desert, F.X. (Grenoble Observ.) ; Dickinson, C. (Manchester U.) ; Diego, J.M. (Cantabria Inst. of Phys.) ; Dole, H. (Paris, Inst. Astrophys. ; IUF, Paris) ; Donzelli, S. (Brera Observ.) ; Dore, O. (Caltech) ; Douspis, M. (Paris, Inst. Astrophys.) ; Dunkley, J. (Oxford U.) ; Dupac, X. (ESA, Madrid) ; Efstathiou, G. (Cambridge U., Inst. of Astron.) ; Elsner, F. (Paris, Inst. Astrophys. ; Paris U., VI-VII) ; Ensslin, T.A. (Garching, Max Planck Inst.) ; Eriksen, H.K. (Oslo U.) ; Finelli, F. (Bologna Observ. ; INFN, Bologna) ; Forni, O. (Toulouse III U. ; IRAP, Toulouse) ; Frailis, M. (Trieste Observ.) ; Fraisse, A.A. (Princeton U.) ; Franceschi, E. (Bologna Observ.) ; Gaier, T.C. (Caltech) ; Galeotta, S. (Trieste Observ.) ; Galli, S. (Paris, Inst. Astrophys.) ; Ganga, K. (APC, Paris) ; Giard, M. (Toulouse III U. ; IRAP, Toulouse) ; Giardino, G. (ESTEC, Noordwijk) ; Giraud-Heraud, Y. (APC, Paris) ; Gjerlow, E. (Oslo U.) ; Gonzalez-Nuevo, J. (Cantabria Inst. of Phys. ; SISSA, Trieste) ; Gorski, K.M. (Caltech ; Warsaw U.) ; Gratton, S. (Cambridge U., KICC ; Cambridge U., Inst. of Astron.) ; Gregorio, A. (Trieste U. ; Trieste Observ.) ; Gruppuso, A. (Bologna Observ.) ; Gudmundsson, J.E. (Princeton U.) ; Hansen, F.K. (Oslo U.) ; Hanson, D. (Rutherford ; Caltech ; Canadian Inst. Theor. Astrophys.) ; Harrison, D. (Cambridge U., Inst. of Astron. ; Cambridge U., KICC) ; Helou, G. (Caltech) ; Henrot-Versille, S. (Orsay, LAL) ; Hernandez-Monteagudo, C. (CEFCA, Teruel ; Garching, Max Planck Inst.) ; Herranz, D. (Cantabria Inst. of Phys.) ; Hildebrandt, S.R. (Caltech) ; Hivon, E. (Paris, Inst. Astrophys. ; Paris U., VI-VII) ; Hobson, M. (Cambridge U.) ; Holmes, W.A. (Caltech) ; Hornstrup, A. (Denmark, Tech. U.) ; Hovest, W. (Garching, Max Planck Inst.) ; Huffenberger, K.M. (Miami U.) ; Hurier, G. (Paris, Inst. Astrophys. ; LPSC, Grenoble) ; Jaffe, T.R. (Toulouse III U. ; IRAP, Toulouse) ; Jaffe, A.H. (Imperial Coll., London) ; Jewell, J. (Caltech) ; Jones, W.C. (Princeton U.) ; Juvela, M. (Helsinki U.) ; Keihanen, E. (Helsinki U.) ; Keskitalo, R. (UC, Berkeley ; LBL, Berkeley) ; Kiiveri, K. (Helsinki U. ; Helsinki Inst. of Phys.) ; Kisner, T.S. (LBL, Berkeley) ; Kneissl, R. (European Southern Obs., Chile) ; Knoche, J. (Garching, Max Planck Inst.) ; Knox, L. (UC, Davis) ; Kunz, M. (Geneva U. ; Paris, Inst. Astrophys. ; African Inst. Math. Sci., Cape Town) ; Kurki-Suonio, H. (Helsinki U. ; Helsinki Inst. of Phys.) ; Lagache, G. (Paris, Inst. Astrophys.) ; Lahteenmaki, A. (Aalto U. ; Helsinki Inst. of Phys.) ; Lamarre, J.M. (LERMA, Ivry) ; Lasenby, A. (Cambridge U. ; Cambridge U., KICC) ; Lattanzi, M. (Ferrara U.) ; Laureijs, R.J. (ESTEC, Noordwijk) ; Lawrence, C.R. (Caltech) ; Le Jeune, M. (APC, Paris) ; Leach, S. (SISSA, Trieste) ; Leahy, J.P. (Manchester U.) ; Leonardi, R. (ESA, Madrid) ; Leon-Tavares, J. (Turku U. ; Aalto U.) ; Lesgourgues, J. (CERN ; LPHE, Lausanne) ; Liguori, M. (Padua U.) ; Lilje, P.B. (Oslo U.) ; Lindholm, V. (Helsinki U. ; Helsinki Inst. of Phys.) ; Linden-Vornle, M. (Denmark, Tech. U.) ; Lopez-Caniego, M. (Cantabria Inst. of Phys.) ; Lubin, P.M. (UC, Santa Barbara) ; Macias-Perez, J.F. (LPSC, Grenoble) ; Maffei, B. (Manchester U.) ; Maino, D. (Milan U. ; Brera Observ.) ; Mandolesi, N. (Bologna Observ. ; ASI, Rome ; Ferrara U.) ; Marinucci, D. (Rome U.) ; Maris, M. (Trieste Observ.) ; Marshall, D.J. (DAPNIA, Saclay) ; Martin, P.G. (Canadian Inst. Theor. Astrophys.) ; Martinez-Gonzalez, E. (Cantabria Inst. of Phys.) ; Masi, S. (Rome U.) ; Matarrese, S. (Padua U.) ; Matthai, F. (Garching, Max Planck Inst.) ; Mazzotta, P. (Rome U.) ; Meinhold, P.R. (UC, Santa Barbara) ; Melchiorri, A. (Rome U. ; INFN, Rome) ; Mendes, L. (ESA, Madrid) ; Menegoni, E. (Rome U.) ; Mennella, A. (Milan U. ; Brera Observ.) ; Migliaccio, M. (Cambridge U., Inst. of Astron. ; Cambridge U., KICC) ; Millea, M. (UC, Davis) ; Mitra, S. (Pune U. ; Caltech) ; Miville-Deschenes, M.A. (Paris, Inst. Astrophys. ; Canadian Inst. Theor. Astrophys.) ; Molinari, D. (Bologna Observ.) ; Moneti, A. (Paris, Inst. Astrophys.) ; Montier, L. (Toulouse III U. ; IRAP, Toulouse) ; Morgante, G. (Bologna Observ.) ; Mortlock, D. (Imperial Coll., London) ; Moss, A. (Nottingham U.) ; Munshi, D. (Cardiff U.) ; Naselsky, P. (Bohr Inst.) ; Nati, F. (Rome U.) ; Natoli, P. (Ferrara U. ; ASDC, Frascati ; Bologna Observ.) ; Netterfield, C.B. (Toronto U.) ; Norgaard-Nielsen, H.U. (Denmark, Tech. U.) ; Noviello, F. (Manchester U.) ; Novikov, D. (Imperial Coll., London) ; Novikov, I. (Bohr Inst.) ; O'Dwyer, I.J. (Caltech) ; Orieux, F. (Paris, Inst. Astrophys.) ; Osborne, S. (Stanford U., Phys. Dept.) ; Oxborrow, C.A. (Denmark, Tech. U.) ; Paci, F. (SISSA, Trieste) ; Pagano, L. (Rome U. ; INFN, Rome) ; Pajot, F. (Paris, Inst. Astrophys.) ; Paladini, R. (Caltech) ; Paoletti, D. (Bologna Observ. ; INFN, Bologna) ; Partridge, B. (Haverford Coll.) ; Pasian, F. (Trieste Observ.) ; Patanchon, G. (APC, Paris) ; Paykari, P. (DAPNIA, Saclay) ; Perdereau, O. (Orsay, LAL) ; Perotto, L. (LPSC, Grenoble) ; Perrotta, F. (SISSA, Trieste) ; Piacentini, F. (Rome U.) ; Piat, M. (APC, Paris) ; Pierpaoli, E. (UCLA) ; Pietrobon, D. (Caltech) ; Plaszczynski, S. (Orsay, LAL) ; Pointecouteau, E. (Toulouse III U. ; IRAP, Toulouse) ; Polenta, G. (ASDC, Frascati ; Rome Observ.) ; Ponthieu, N. (Paris, Inst. Astrophys. ; Grenoble Observ.) ; Popa, L. (Bucharest, Inst. Space Science) ; Poutanen, T. (Helsinki Inst. of Phys. ; Helsinki U. ; Aalto U.) ; Pratt, G.W. (DAPNIA, Saclay) ; Prezeau, G. (Caltech) ; Prunet, S. (Paris, Inst. Astrophys. ; Paris U., VI-VII) ; Puget, J.L. (Paris, Inst. Astrophys.) ; Rachen, J.P. (Nijmegen U. ; Garching, Max Planck Inst.) ; Rahlin, A. (Princeton U.) ; Rebolo, R. (IAC, La Laguna ; CSIC, Madrid ; Laguna U., Tenerife) ; Reinecke, M. (Garching, Max Planck Inst.) ; Remazeilles, M. (Paris, Inst. Astrophys. ; APC, Paris) ; Renault, C. (LPSC, Grenoble) ; Ricciardi, S. (Bologna Observ.) ; Riller, T. (Garching, Max Planck Inst.) ; Ringeval, C. (Louvain U. ; Paris, Inst. Astrophys. ; Paris U., VI-VII) ; Ristorcelli, I. (Toulouse III U. ; IRAP, Toulouse) ; Rocha, G. (Caltech) ; Rosset, C. (APC, Paris) ; Roudier, G. (APC, Paris ; LERMA, Ivry ; Caltech) ; Rowan-Robinson, M. (Imperial Coll., London) ; Rubino-Martin, J.A. (IAC, La Laguna ; Laguna U., Tenerife) ; Rusholme, B. (Caltech) ; Sandri, M. (Bologna Observ.) ; Sanselme, L. (LPSC, Grenoble) ; Santos, D. (LPSC, Grenoble) ; Savini, G. (University Coll. London) ; Scott, D. (British Columbia U.) ; Seiffert, M.D. (Caltech) ; Shellard, E.P.S. (Cambridge U., DAMTP) ; Spencer, L.D. (Cardiff U.) ; Starck, J.L. (DAPNIA, Saclay) ; Stolyarov, V. (Cambridge U. ; Cambridge U., KICC ; Stavropol, Astrophys. Observ.) ; Stompor, R. (APC, Paris) ; Sudiwala, R. (Cardiff U.) ; Sureau, F. (DAPNIA, Saclay) ; Sutton, D. (Cambridge U., Inst. of Astron. ; Cambridge U., KICC) ; Suur-Uski, A.S. (Helsinki U. ; Helsinki Inst. of Phys.) ; Sygnet, J.F. (Paris, Inst. Astrophys.) ; Tauber, J.A. (ESTEC, Noordwijk) ; Tavagnacco, D. (Trieste Observ. ; Trieste U.) ; Terenzi, L. (Bologna Observ.) ; Toffolatti, L. (Oviedo U. ; Cantabria Inst. of Phys.) ; Tomasi, M. (Brera Observ.) ; Tristram, M. (Orsay, LAL) ; Tucci, M. (Geneva U. ; Orsay, LAL) ; Tuovinen, J. (MilliLab) ; Turler, M. (Geneva U.) ; Valenziano, L. (Bologna Observ.) ; Valiviita, J. (Helsinki Inst. of Phys. ; Helsinki U. ; Oslo U.) ; Van Tent, B. (Orsay, LPT) ; Varis, J. (MilliLab) ; Vielva, P. (Cantabria Inst. of Phys.) ; Villa, F. (Bologna Observ.) ; Vittorio, N. (Rome U.) ; Wade, L.A. (Caltech) ; Wandelt, B.D. (Paris, Inst. Astrophys. ; Paris U., VI-VII ; Illinois U., Urbana) ; Wehus, I.K. (Caltech) ; White, M. (UC, Berkeley) ; White, S.D.M. (Garching, Max Planck Inst.) ; Yvon, D. (DAPNIA, Saclay) ; Zacchei, A. (Trieste Observ.) ; Zonca, A. (UC, Santa Barbara)
Publication	2014-10-29
Imprint	22 Mar 2013
Number of pages	60
Note	Comments: This paper is one of a set associated with the 2013 release of data from the Planck mission. 62 pages, 64 figures, 12 tables This paper is one of a set associated with the 2013 release of data from the Planck mission. 62 pages, 64 figures, 12 tables
In:	Astron. Astrophys. 571 (2014) A15
DOI	10.1051/0004-6361/201321573
Subject category	Astrophysics and Astronomy
Accelerator/Facility, Experiment	PLANCK RE24
Abstract	We present the Planck likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations. We use this likelihood to derive the Planck CMB power spectrum over three decades in l, covering 2 <= l <= 2500. The main source of error at l <= 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher l's. For l < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz through a physically motivated Bayesian component separation technique. At l >= 50, we employ a correlated Gaussian likelihood approximation based on angular cross-spectra derived from the 100, 143 and 217 GHz channels. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on cosmological parameters. We find good internal agreement among the high-l cross-spectra with residuals of a few uK^2 at l <= 1000. We compare our results with foreground-cleaned CMB maps, and with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. The best-fit LCDM cosmology is in excellent agreement with preliminary Planck polarisation spectra. The standard LCDM cosmology is well constrained by Planck by l <= 1500. For example, we report a 5.4 sigma deviation from n_s /= 1. Considering various extensions beyond the standard model, we find no indication of significant departures from the LCDM framework. Finally, we report a tension between the best-fit LCDM model and the low-l spectrum in the form of a power deficit of 5-10% at l < 40, significant at 2.5-3 sigma. We do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent dataset. (Abridged)
Copyright/License	Preprint: © 2013-2024 CERN (License: CC-BY-3.0)

$The covariance matrix blocks used in the likelihood, accounting for the correlations between cross-spectra estimated from the 100, 143, and 217\,GHz channels. \emph{}$ $noimgDetectors used to make the maps for this analysis. Spider Web Bolometers (SWB) are used individually; Polarised Sensitive Bolometer pairs (PSBs, denoted a and b) are used in pairs, and we consider only the maps estimated from two pairs of PSBs. The relevant effective beams, and their uncertainties, are given in \cite{planck2013-p03c}.$