A&A 571, A1 (2014)
DOI: 10.1051
/
0004-6361
/
201321529
c
©
ESO 2014
Astronomy
&
Astrophysics
Planck 2013 results
Special feature
Planck
2013 results. I. Overview of products and scientific results
Planck Collaboration: P. A. R. Ade
116
, N. Aghanim
79
, M. I. R. Alves
79
, C. Armitage-Caplan
122
, M. Arnaud
96
, M. Ashdown
93
,
8
,
F. Atrio-Barandela
23
, J. Aumont
79
, H. Aussel
96
, C. Baccigalupi
114
, A. J. Banday
128
,
13
, R. B. Barreiro
89
, R. Barrena
88
, M. Bartelmann
126
,
103
,
J. G. Bartlett
1
,
91
, N. Bartolo
43
, S. Basak
114
, E. Battaner
131
, R. Battye
92
, K. Benabed
80
,
125
, A. Benoît
77
, A. Benoit-Lévy
32
,
80
,
125
, J.-P. Bernard
128
,
13
,
M. Bersanelli
47
,
68
, B. Bertincourt
79
, M. Bethermin
96
, P. Bielewicz
128
,
13
,
114
, I. Bikmaev
27
,
3
, A. Blanchard
128
, J. Bobin
96
, J. J. Bock
91
,
14
,
H. Böhringer
104
, A. Bonaldi
92
, L. Bonavera
89
, J. R. Bond
11
, J. Borrill
18
,
119
, F. R. Bouchet
80
,
125
, F. Boulanger
79
, H. Bourdin
49
, J. W. Bowyer
75
,
M. Bridges
93
,
8
,
85
, M. L. Brown
92
, M. Bucher
1
, R. Burenin
118
,
107
, C. Burigana
67
,
45
, R. C. Butler
67
, E. Calabrese
122
, B. Cappellini
68
,
J.-F. Cardoso
97
,
1
,
80
, R. Carr
54
, P. Carvalho
8
, M. Casale
54
, G. Castex
1
, A. Catalano
98
,
95
, A. Challinor
85
,
93
,
15
, A. Chamballu
96
,
20
,
79
, R.-R. Chary
76
,
X. Chen
76
, H. C. Chiang
37
,
9
, L.-Y Chiang
84
, G. Chon
104
, P. R. Christensen
110
,
51
, E. Churazov
103
,
118
, S. Church
121
, M. Clemens
63
,
D. L. Clements
75
, S. Colombi
80
,
125
, L. P. L. Colombo
31
,
91
, C. Combet
98
, B. Comis
98
, F. Couchot
94
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95
, B. P. Crill
91
,
111
, M. Cruz
25
,
A. Curto
8
,
89
, F. Cuttaia
67
, A. Da Silva
16
, H. Dahle
87
, L. Danese
114
, R. D. Davies
92
, R. J. Davis
92
, P. de Bernardis
46
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67
, G. de Zotti
63
,
114
,
T. Déchelette
80
, J. Delabrouille
1
, J.-M. Delouis
80
,
125
, J. Démoclès
96
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72
, J. Dick
114
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92
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89
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130
,
103
,
H. Dole
79
,
78
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68
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91
,
14
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79
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80
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122
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55
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85
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80
,
125
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103
,
H. K. Eriksen
87
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80
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95
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6
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87
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15
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94
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67
,
69
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13
,
128
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S. Foley
56
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128
,
13
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81
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65
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37
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67
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55
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1
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79
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22
,
T. C. Gaier
91
, S. Galeotta
65
, J. Gallegos
55
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80
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56
, K. Ganga
1
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1
,
101
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88
, T. Ghosh
79
,
M. Giard
128
,
13
, G. Giardino
57
, M. Gilfanov
103
,
118
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98
, Y. Giraud-Héraud
1
, E. Gjerløw
87
, J. González-Nuevo
89
,
114
, K. M. Górski
91
,
132
,
S. Gratton
93
,
85
, A. Gregorio
48
,
65
, A. Gruppuso
67
, J. E. Gudmundsson
37
, J. Haissinski
94
, J. Hamann
124
, F. K. Hansen
87
, M. Hansen
110
,
D. Hanson
105
,
91
,
11
, D. L. Harrison
85
,
93
, A. Heavens
75
, G. Helou
14
, A. Hempel
88
,
52
, S. Henrot-Versillé
94
, C. Hernández-Monteagudo
17
,
103
,
D. Herranz
89
, S. R. Hildebrandt
14
, E. Hivon
80
,
125
, S. Ho
34
, M. Hobson
8
, W. A. Holmes
91
, A. Hornstrup
21
, Z. Hou
40
, W. Hovest
103
, G. Huey
42
,
K. M. Hu
ff
enberger
35
, G. Hurier
79
,
98
, S. Ili
́
c
79
, A. H. Ja
ff
e
75
, T. R. Ja
ff
e
128
,
13
, J. Jasche
80
, J. Jewell
91
, W. C. Jones
37
, M. Juvela
36
, P. Kalberla
7
,
P. Kangaslahti
91
, E. Keihänen
36
, J. Kerp
7
, R. Keskitalo
29
,
18
, I. Khamitov
123
,
27
, K. Kiiveri
36
,
61
, J. Kim
110
, T. S. Kisner
100
, R. Kneissl
53
,
10
,
J. Knoche
103
, L. Knox
40
, M. Kunz
22
,
79
,
4
, H. Kurki-Suonio
36
,
61
, F. Lacasa
79
, G. Lagache
79
, A. Lähteenmäki
2
,
61
, J.-M. Lamarre
95
, M. Langer
79
,
A. Lasenby
8
,
93
, M. Lattanzi
45
, R. J. Laureijs
57
, A. Lavabre
94
, C. R. Lawrence
91
, M. Le Jeune
1
, S. Leach
114
, J. P. Leahy
92
, R. Leonardi
55
,
J. León-Tavares
58
,
2
, C. Leroy
79
,
128
,
13
, J. Lesgourgues
124
,
113
, A. Lewis
33
, C. Li
102
,
103
, A. Liddle
115
,
33
, M. Liguori
43
, P. B. Lilje
87
,
M. Linden-Vørnle
21
, V. Lindholm
36
,
61
, M. López-Caniego
89
, S. Lowe
92
, P. M. Lubin
41
, J. F. Macías-Pérez
98
, C. J. MacTavish
93
, B. Ma
ff
ei
92
,
G. Maggio
65
, D. Maino
47
,
68
, N. Mandolesi
67
,
6
,
45
, A. Mangilli
80
, A. Marcos-Caballero
89
, D. Marinucci
50
, M. Maris
65
, F. Marleau
83
,
D. J. Marshall
96
, P. G. Martin
11
, E. Martínez-González
89
, S. Masi
46
, M. Massardi
66
, S. Matarrese
43
, T. Matsumura
14
, F. Matthai
103
, L. Maurin
1
,
P. Mazzotta
49
, A. McDonald
56
, J. D. McEwen
32
,
108
, P. McGehee
76
, S. Mei
59
,
127
,
14
, P. R. Meinhold
41
, A. Melchiorri
46
,
70
, J.-B. Melin
20
,
L. Mendes
55
, E. Menegoni
46
, A. Mennella
47
,
68
, M. Migliaccio
85
,
93
, K. Mikkelsen
87
, M. Millea
40
, R. Miniscalco
56
, S. Mitra
74
,
91
,
M.-A. Miville-Deschênes
79
,
11
, D. Molinari
44
,
67
, A. Moneti
80
, L. Montier
128
,
13
, G. Morgante
67
, N. Morisset
73
, D. Mortlock
75
, A. Moss
117
,
D. Munshi
116
, J. A. Murphy
109
, P. Naselsky
110
,
51
, F. Nati
46
, P. Natoli
45
,
5
,
67
, M. Negrello
63
, N. P. H. Nesvadba
79
, C. B. Netterfield
26
,
H. U. Nørgaard-Nielsen
21
, C. North
116
, F. Noviello
92
, D. Novikov
75
, I. Novikov
110
, I. J. O’Dwyer
91
, F. Orieux
80
, S. Osborne
121
, C. O’Sullivan
109
,
C. A. Oxborrow
21
, F. Paci
114
, L. Pagano
46
,
70
, F. Pajot
79
, R. Paladini
76
, S. Pandolfi
49
, D. Paoletti
67
,
69
, B. Partridge
60
, F. Pasian
65
, G. Patanchon
1
,
P. Paykari
96
, D. Pearson
91
, T. J. Pearson
14
,
76
, M. Peel
92
, H. V. Peiris
32
, O. Perdereau
94
, L. Perotto
98
, F. Perrotta
114
, V. Pettorino
22
, F. Piacentini
46
,
M. Piat
1
, E. Pierpaoli
31
, D. Pietrobon
91
, S. Plaszczynski
94
, P. Platania
90
, D. Pogosyan
38
, E. Pointecouteau
128
,
13
, G. Polenta
5
,
64
, N. Ponthieu
79
,
72
,
L. Popa
82
, T. Poutanen
61
,
36
,
2
, G. W. Pratt
96
, G. Prézeau
14
,
91
, S. Prunet
80
,
125
, J.-L. Puget
79
, A. R. Pullen
91
, J. P. Rachen
28
,
103
, B. Racine
1
,
A. Rahlin
37
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104
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129
, R. Rebolo
88
,
19
,
52
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103
, M. Remazeilles
92
,
79
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1
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98
, A. Renzi
114
, A. Riazuelo
80
,
125
,
S. Ricciardi
67
, T. Riller
103
, C. Ringeval
86
,
80
,
125
, I. Ristorcelli
128
,
13
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103
, G. Rocha
91
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14
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1
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1
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47
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68
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1
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95
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75
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88
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52
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131
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76
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12
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67
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98
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98
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36
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61
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112
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126
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30
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ff
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91
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14
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79
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15
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37
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39
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100
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1
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74
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116
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96
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8
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57
,?
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ff
olatti
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94
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22
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73
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56
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92
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, N. Welikala
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41
(A
ffi
liations can be found after the references)
Received 21 March 2013
/
Accepted 17 May 2014
?
Corresponding author: e-mail:
jtauber@cosmos.esa.int
Article published by EDP Sciences
A1, page 1 of 48
A&A 571, A1 (2014)
ABSTRACT
The European Space Agency’s
Planck
satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14 May
2009 and has been scanning the microwave and submillimetre sky continuously since 12 August 2009. In March 2013, ESA and the Planck
Collaboration released the initial cosmology products based on the first 15.5 months of
Planck
data, along with a set of scientific and technical
papers and a web-based explanatory supplement. This paper gives an overview of the mission and its performance, the processing, analysis, and
characteristics of the data, the scientific results, and the science data products and papers in the release. The science products include maps of
the cosmic microwave background (CMB) and di
ff
use extragalactic foregrounds, a catalogue of compact Galactic and extragalactic sources, and
a list of sources detected through the Sunyaev-Zeldovich e
ff
ect. The likelihood code used to assess cosmological models against the
Planck
data
and a lensing likelihood are described. Scientific results include robust support for the standard six-parameter
Λ
CDM model of cosmology and
improved measurements of its parameters, including a highly significant deviation from scale invariance of the primordial power spectrum. The
Planck
values for these parameters and others derived from them are significantly di
ff
erent from those previously determined. Several large-scale
anomalies in the temperature distribution of the CMB, first detected by WMAP, are confirmed with higher confidence.
Planck
sets new limits on
the number and mass of neutrinos, and has measured gravitational lensing of CMB anisotropies at greater than 25
σ
.
Planck
finds no evidence
for non-Gaussianity in the CMB.
Planck
’s results agree well with results from the measurements of baryon acoustic oscillations.
Planck
finds a
lower Hubble constant than found in some more local measures. Some tension is also present between the amplitude of matter fluctuations (
σ
8
)
derived from CMB data and that derived from Sunyaev-Zeldovich data. The
Planck
and WMAP power spectra are o
ff
set from each other by an
average level of about 2% around the first acoustic peak. Analysis of
Planck
polarization data is not yet mature, therefore polarization results are
not released, although the robust detection of
E
-mode polarization around CMB hot and cold spots is shown graphically.
Key words.
cosmology: observations – cosmic background radiation – space vehicles: instruments – instrumentation: detectors
1. Introduction
The
Planck
satellite
1
(Tauber et al. 2010a; Planck Collaboration I
2011) was launched on 14 May 2009 and observed the sky
stably and continuously from 12 August 2009 to 23 October
2013.
Planck
’s scientific payload comprised an array of 74 de-
tectors sensitive to frequencies between 25 and 1000 GHz, which
scanned the sky with angular resolution between 33
′
and 5
′
.
The detectors of the Low Frequency Instrument (LFI; Bersanelli
et al. 2010; Mennella et al. 2011) are pseudo-correlation ra-
diometers, covering bands centred at 30, 44, and 70 GHz. The
detectors of the High Frequency Instrument (HFI; Lamarre et al.
2010; Planck HFI Core Team 2011a) are bolometers, covering
bands centred at 100, 143, 217, 353, 545, and 857 GHz.
Planck
images the whole sky twice in one year, with a combination of
sensitivity, angular resolution, and frequency coverage never be-
fore achieved.
Planck
, its payload, and its performance as pre-
dicted at the time of launch are described in 13 papers included
in a special issue of Astronomy & Astrophysics (Vol. 520).
The main objective of
Planck
, defined in 1995, is to mea-
sure the spatial anisotropies in the temperature of the cos-
mic microwave background (CMB), with an accuracy set by
fundamental astrophysical limits, thereby extracting essentially
all the cosmological information embedded in the temperature
anisotropies of the CMB.
Planck
was also designed to measure
to high accuracy the CMB polarization anisotropies, which en-
code not only a wealth of cosmological information, but also
provide a unique probe of the early history of the Universe dur-
ing the time when the first stars and galaxies formed. Finally,
Planck
produces a wealth of information on the properties of ex-
tragalactic sources and on the dust and gas in the Milky Way
(see Fig. 1). The scientific objectives of
Planck
are described in
detail in Planck Collaboration (2005). With the results presented
here and in a series of accompanying papers (see Fig. 2),
Planck
has already achieved many of its planned science goals.
This paper presents an overview of the
Planck
mission, and
the main data products and scientific results of
Planck
’s second
1
Planck
(
http://www.esa.int/Planck
) is a project of the
European Space Agency (ESA) with instruments provided by two sci-
entific consortia funded by ESA member states (in particular the lead
countries, France and Italy) with contributions from NASA (USA), and
telescope reflectors provided in a collaboration between ESA and a sci-
entific consortium led and funded by Denmark.
release
2
, based on data acquired in the period 12 August 2009
to 28 November 2010.
1.1. Overview of 2013 science results
Cosmology
– A major goal of
Planck
is to measure the key
cosmological parameters describing our Universe.
Planck
’s
combination of sensitivity, angular resolution, and frequency
coverage enables it to measure anisotropies on intermediate and
small angular scales over the whole sky much more accurately
than previous experiments. This leads to improved constraints
on individual parameters, the breaking of degeneracies between
combinations of other parameters, and less reliance on supple-
mentary astrophysical data than previous CMB experiments.
Cosmological parameters are presented and discussed in Sect. 9
and in Planck Collaboration XVI (2014).
The Universe observed by
Planck
is well-fit by a six-
parameter, vacuum-dominated, cold dark matter (
Λ
CDM)
model, and we provide strong constraints on deviations from this
model. The values of key parameters in this model are summa-
rized in Table 10. In some cases we find significant changes com-
pared to previous measurements, as discussed in detail in Planck
Collaboration XVI (2014).
With the
Planck
data, we: (a) firmly establish deviation from
scale invariance of the primordial matter perturbations, a key
indicator of cosmic inflation; (b) detect with high significance
lensing of the CMB by intervening matter, providing evidence
for dark energy from the CMB alone; (c) find no evidence
for significant deviations from Gaussianity in the statistics of
CMB anisotropies; (d) find a deficit of power on large angu-
lar scales with respect to our best-fit model; (e) confirm the
anomalies at large angular scales first detected by WMAP; and
2
In January of 2011, ESA and the
Planck
Collaboration released to the
public a first set of scientific data, the Early Release Compact Source
Catalogue (ERCSC), a list of unresolved and compact sources extracted
from the first complete all-sky survey carried out by
Planck
(Planck
Collaboration VII 2011). At the same time, initial scientific results re-
lated to astrophysical foregrounds were published in a special issue of
Astronomy & Astrophysics (Vol. 520, 2011). Since then, more than 12
“Intermediate” papers have been submitted for publication to A&A con-
taining further astrophysical investigations by the Collaboration.
A1, page 2 of 48
Planck Collaboration:
Planck
2013 results. I.
Fig. 1.
Composite, multi-frequency, full-sky image released by
Planck
in 2010. Made from the first nine months of the data, it illustrates artistically
the multitude of Galactic, extragalactic, and cosmological components of the radiation detected by its payload. Unless otherwise specified, all full-
sky images in this paper are Mollweide projections in Galactic coordinates, pixelised according to the
HEALPix
(Górski et al. 2005) scheme.
(f) establish the number of neutrino species to be consistent with
three.
The
Planck
data are in remarkable accord with a flat
Λ
CDM
model; however, there are tantalizing hints of tensions both inter-
nal to the
Planck
data and with other data sets. From the CMB,
Planck
determines a lower value of the Hubble constant than
some more local measures, and a higher value for the ampli-
tude of matter fluctuations (
σ
8
) than that derived from Sunyaev-
Zeldovich data. While such tensions are model-dependent, none
of the extensions of the six-parameter
Λ
CDM cosmology that
we explored resolves them. More data and further analysis may
shed light on such tensions. Along these lines, we expect sig-
nificant improvement in data quality and the level of systematic
error control, plus the addition of polarization data, from
Planck
in 2014.
A more extensive summary of cosmology results is given in
Sect. 9.
Foregrounds
– The astrophysical foregrounds measured by
Planck
to be separated from the CMB are interesting in their
own right. Compact and point-like sources consist mainly of
extragalactic infrared and radio sources, and are released in
the
Planck
Catalogue of Compact Sources (PCCS; Planck
Collaboration XXVIII 2014). An all-sky catalogue of sources
detected via the Sunyaev-Zeldovich (SZ) e
ff
ect, which will be-
come a reference for studies of SZ-detected galaxy clusters, is
given in Planck Collaboration XXIX (2014).
Seven types of unresolved foregrounds must be removed or
controlled for CMB analysis: thermal dust emission; anoma-
lous microwave emission (likely due to tiny spinning dust
grains); CO rotational emission lines (significant in at least
three HFI bands); free-free emission; synchrotron emission; the
clustered cosmic infrared background (CIB); and SZ secondary
CMB distortions. For cosmological purposes, we achieve robust
separation of the CMB from foregrounds using only
Planck
data
with multiple independent methods. We release maps of: thermal
dust
+
fluctuations of the CIB; integrated emission of carbon
monoxide; and synchrotron
+
free-free
+
spinning dust emis-
sion. These maps provide a rich source for studies of the inter-
stellar medium (ISM). Other maps are released that use ancillary
data in addition to the
Planck
data to achieve more physically
meaningful analysis.
These foreground products are described in Sect. 8.
1.2. Features of the Planck mission
Planck
has an unprecedented combination of sensitivity, angu-
lar resolution, and frequency coverage. For example, the
Planck
detector array at 143 GHz has instantaneous sensitivity and an-
gular resolution 25 and three times better, respectively, than the
WMAP
V
band (Bennett et al. 2003; Hinshaw et al. 2013).
Considering the final mission durations (nine years for WMAP,
29 months for
Planck
HFI, and 50 months for
Planck
LFI),
the white noise at map level, for example, is 12 times lower
at 143 GHz for the same resolution. In harmonic space, the noise
level in the
Planck
power spectra is two orders of magnitude
lower than in those of WMAP at angular scales where beams
are unimportant (
` <
700 for WMAP and 2500 for
Planck
).
Planck
measures 2.6 times as many independent multipoles as
WMAP, corresponding to 6.8 times as many independent modes
(
`,
m
) when comparing the same leading CMB channels for the
two missions. This increase in angular resolution and sensitivity
results in a large gain for analysis of CMB non-Gaussianity and
cosmological parameters. In addition,
Planck
has a large overlap
in
`
with the high resolution ground-based experiments ACT
(Sievers et al. 2013) and SPT (Keisler et al. 2011). The noise
spectra of SPT and
Planck
cross at
`
∼
2000, allowing an excel-
lent check of the relative calibrations and transfer functions.
A1, page 3 of 48
A&A 571, A1 (2014)
HFI Processing
LFI Processing
LFI Beams &
window functs
LFI Calibration
LFI Systematics
HFI Calibration
Component
Separation
Overview of
products & results
Frequency Maps
Component Maps
Power Spectra
Parameters
Power Spectra
& Likelihood
Cosmological
Parameters
Catalogue of
compact sources
Lensing by
LSS
Catalogue of
SZ sources
Galactic CO
Consistency of
the Data
HFI Time Response
& Beams
HFI Spectral
Response
HFI Energetic
particle effects
Zodiacal
Emission
II
XIII
VI
XXXI
XII
XV
XXVIII
XXIX
XVI
XVII
XIV
X
IX
VII
IV
V
VIII
III
I
Lensing-IR
background
correlation
XVIII
Integrated
Sachs-Wolfe
effect
XIX
Cosmology from
SZ counts
XX
Compton para-
meter power
spectrum
XXi
Constraints on
inflation
XXII
Isotropy &
statistics of
the CMB
Primordial
non-Gaussianity
XXIII
XXIV
Strings &
other defects
XXV
Background
geometry &
topology
XXVi
Doppler boost-
ing of the
CMB
XXVii
All-sky model
of thermal dust
XI
Cosmic
Infrared
Background
XXX
Fig. 2.
Planck
papers published simultaneously with the release of the 2013 products. The title of each paper is abbreviated. The roman numerals
correspond to the sequence number assigned to each of the papers in the series; references include this number. Green boxes refer to papers
describing aspects of data processing and the 2013
Planck
products. Blue boxes refer to papers mainly dedicated to scientific analysis of the
products. Pink boxes describe specific 2013
Planck
products.
Increased sensitivity places
Planck
in a new situation. Earlier
satellite experiments (COBE
/
DMR, Smoot et al. 1992; WMAP,
Bennett et al. 2013) were limited by detector noise more than
systematic e
ff
ects and foregrounds. Ground-based and balloon-
borne experiments ongoing or under development (e.g., ACT,
Kosowsky 2003; SPT, Ruhl et al. 2004; SPIDER, Fraisse et al.
2013; and EBEX, Reichborn-Kjennerud et al. 2010), have far
larger numbers of detectors and higher angular resolution than
Planck
, but can survey only a fraction of the sky over a lim-
ited frequency range. They are therefore sensitive to foregrounds
and limited to analysing only the cleanest regions of the sky.
Considering the impact of cosmic variance, Galactic fore-
grounds are not a serious limitation for CMB temperature-based
cosmology at the largest spatial scales over a limited part (
<
0.5)
of the sky. Di
ff
use Galactic emission components have steep fre-
quency and angular spectra, and are very bright at frequencies
below 70 and above 100 GHz at low spatial frequencies. At in-
termediate and small angular scales, extragalactic foregrounds,
such as unresolved compact sources, the SZ e
ff
ect from unre-
solved galaxy clusters and di
ff
use hot gas, and the correlated
A1, page 4 of 48
Planck Collaboration:
Planck
2013 results. I.
CIB, become important and cannot be ignored when carrying
out CMB cosmology studies.
Planck
’s all-sky, wide-frequency
coverage is key, allowing it to measure these foregrounds and
remove them to below intrinsic detector noise levels, helped by
higher resolution experiments in characterizing the statistics of
discrete foregrounds.
When detector noise is very low, systematic e
ff
ects that arise
from the instrument, telescope, scanning strategy, or calibration
approach may dominate over noise in specific spatial or fre-
quency ranges. The analysis of redundancy is the main tool used
by
Planck
to understand and quantify the e
ff
ect of systematics.
Redundancy on short timescales comes from the scanning strat-
egy (Sect. 4.1), which has particular advantages in this respect,
especially for the largest scales. When first designed, this strat-
egy was considered ambitious because it required low 1
/
f
noise
near 0.0167 Hz (the spin frequency) and very stable instruments
over the whole mission. Redundancy on long timescales comes
in two versions: 1)
Planck
scans approximately the same circle
on the sky every six months, alternating in the direction of the
scan; and 2)
Planck
scans exactly (within arcminutes) the same
circle on the sky every one year. The ability to compare maps
made in individual all-sky “Surveys” (covering approximately
six month intervals, see Sect. 4.1 and Table 1) and year-by-year
is invaluable in identifying specific systematic e
ff
ects and cali-
bration errors. Although
Planck
was designed to cover the whole
sky twice over, its superb in-flight performance has enabled it to
complete nearly five full-sky maps with the HFI instrument, and
more than eight with the LFI instrument. The redundancy pro-
vided by such a large number of Surveys is a major asset for
Planck
, allowing tests of the overall stability of the instruments
over the mission and sensitive measurements of systematic resid-
uals on the sky.
Redundancy of a di
ff
erent sort is provided by multiple de-
tectors within frequency bands. HFI includes four indepen-
dent pairs of polarization-sensitive detectors in each channel
from 100 to 353 GHz, in addition to the four total intensity
(spider web) detectors at all frequencies except 100 GHz. LFI in-
cludes six independent pairs of polarization-sensitive detectors
at 70 GHz, with three at 44 GHz and two at 30 GHz. The di
ff
erent
technologies used in the two instruments provide an additional
powerful tool to identify and remove systematic e
ff
ects.
Overall, the combination of scanning strategy and instru-
mental redundancy has allowed identification and removal of
most systematic e
ff
ects a
ff
ecting CMB temperature measure-
ments. This can be seen in the fact that additional Surveys have
led to significant improvements, at a rate greater than the square
root of the integration time, in the signal-to-noise ratio (S
/
N)
achieved in the combined maps. Given that the two instruments
have achieved their expected intrinsic sensitivity, and that most
systematics have been brought below the noise (detector or cos-
mic variance) for intensity, it is a fact that cosmological results
derived from the
Planck
temperature data are already being lim-
ited by the foregrounds, fulfilling one of the main objectives of
the mission.
1.3. Status of Planck polarization measurements
The situation for CMB polarization, whose amplitude is typi-
cally 4% of intensity, is less mature. At present,
Planck
’s sensi-
tivity to the CMB polarization power spectrum at low multipoles
(
` <
20) is significantly limited by residual systematics. These
are of a di
ff
erent nature than those of temperature because po-
larization measurement with
Planck
requires di
ff
erencing be-
tween detector pairs. Furthermore, the component separation
problem is di
ff
erent, on the one hand simpler because only three
polarized foregrounds have been identified so far (di
ff
use syn-
chrotron and thermal dust emission, and radio sources), on the
other hand more complicated because the di
ff
use foregrounds
are more highly polarized than the CMB, and therefore more
dominant over a larger fraction of the sky. Moreover, no exter-
nal templates exist for the polarized foregrounds. These factors
are currently restricting
Planck
’s ability to meet its most ambi-
tious goals, e.g., to measure or set stringent upper limits on cos-
mological
B
-mode amplitudes. Although this situation is being
improved at the present time, the possibility remains that these
e
ff
ects will be the final limitation for cosmology using the polar-
ized
Planck
data. The situation is much better at high multipoles,
where the polarization data are already close to being limited by
intrinsic detector noise.
These considerations have led to the strategy adopted by the
Planck
Collaboration for the 2013 release of using only
Planck
temperature data for scientific results. To reduce the uncertainty
on the reionization optical depth,
τ
, we sometimes supplement
the
Planck
temperature data with the WMAP low-
`
polarization
likelihood (the data designation in such cases includes “WP”).
And we give two examples of polarization data at higher multi-
poles to demonstrate the quality already achieved. The first ex-
ample shows that the measured high-
`
EE
spectrum agrees ex-
tremely well with that expected from the best-fit model derived
from temperature data alone (Planck Collaboration XVI 2014).
The second uses stacking techniques on the peaks and troughs
of the CMB intensity (Sect. 9.3), giving a direct and spectacu-
lar visualization of the
E
-mode polarization induced by matter
oscillating in the potential well of dark matter at recombination.
Cosmological analysis using the full 29- and 50-month data
sets, including polarization, will be published with the second
major release of data in 2014. Scientific investigations of di
ff
use
Galactic polarized emissions at frequencies and angular scales
where the polarized emission is strong compared to residual sys-
tematics will be released in the coming months (see Sect. 8.2.3
for a description). The sensitivity and accuracy of
Planck
’s po-
larized maps is already well beyond that of any previous survey
in this frequency range.
2. Data products in the 2013 release
The 2013 distribution of released products (hereafter the “2013
products”), which can be freely accessed via the
Planck
Legacy Archive interface
3
, is based on data acquired by
Planck
during the “nominal mission”, defined as 12 August 2009
to 28 November 2010, and comprises:
–
Maps of the sky at nine frequencies (Sect. 6).
–
Additional products that serve to quantify the characteristics
of the maps to a level adequate for the science results be-
ing presented, such as noise maps, masks, and instrument
characteristics.
–
Four high-resolution maps of the CMB sky and accompa-
nying characterization products (Sect. 7.1). Non-Gaussianity
results are based on one of the maps; the others demonstrate
the robustness of the results and their insensitivity to di
ff
er-
ent methods of analysis.
–
A low-resolution CMB map (Sect. 7.1) used in the low
`
likelihood code, with an associated set of foreground maps
produced in the process of separating the low-resolution
CMB from foregrounds, with accompanying characteriza-
tion products.
3
http://archives.esac.esa.int/pla2
A1, page 5 of 48
A&A 571, A1 (2014)
Table 1.
Planck
Surveys (defined in Sect. 4.1).
Survey
Instrument
Beginning
End
Coverage
a
1 . . . . . . . . . . . . . . . . . .
LFI & HFI
12 Aug. 2009 (14:16:51)
02 Feb. 2010 (20:51:04)
93.1%
2 . . . . . . . . . . . . . . . . . .
LFI & HFI
02 Feb. 2010 (20:54:43)
12 Aug. 2010 (19:27:20)
93.1%
3 . . . . . . . . . . . . . . . . . .
LFI & HFI
12 Aug. 2010 (19:30:44)
08 Feb. 2011 (20:55:55)
93.1%
4 . . . . . . . . . . . . . . . . . .
LFI & HFI
08 Feb. 2011 (20:59:10)
29 Jul. 2011 (17:13:32)
86.6%
5 . . . . . . . . . . . . . . . . . .
LFI & HFI
29 Jul. 2011 (18:04:49)
01 Feb. 2012 (05:25:59)
80.1%
6 . . . . . . . . . . . . . . . . . .
LFI
01 Feb. 2012 (05:26:29)
03 Aug. 2012 (16:48:51)
79.2%
7 . . . . . . . . . . . . . . . . . .
LFI
03 Aug. 2012 (16:48:53)
31 Jan. 2013 (10:32:08)
73.7%
8 . . . . . . . . . . . . . . . . . .
LFI
31 Jan. 2013 (10:32:10)
03 Aug. 2013 (21:53:37)
70.6%
9 . . . . . . . . . . . . . . . . . .
LFI
03 Aug. 2013 (21:53:39)
03 Oct. 2013 (21:13:38)
21.2%
“Nominal mission” . . . . .
LFI & HFI
12 Aug. 2009 (14:16:51)
28 Nov. 2010 (12:00:53)
...
“0.1-K mission” . . . . . . .
LFI & HFI
12 Aug. 2009 (14:16:51)
13 Jan. 2012 (14:54:07)
...
Notes.
Times are UT.
(
a
)
Fraction of sky covered by all frequencies.
–
Maps of foreground components at high resolution, includ-
ing: thermal dust
+
residual CIB; CO; synchrotron
+
free-
free
+
spinning dust emission; and maps of dust temperature
and opacity (Sect. 8).
–
A likelihood code and data package used for testing cosmo-
logical models against the
Planck
data, including both the
CMB (Sect. 7.3.1) and CMB lensing (Sect. 7.3.2). The CMB
part is based at
` <
50 on the low-resolution CMB map just
described and on the WMAP-9 polarized likelihood (to re-
duce the uncertainty in
τ
), and at
`
≥
50 on cross-power
spectra of individual detector sets. The lensing part is based
on the 143 and 217 GHz maps.
–
The
Planck
Catalogue of Compact Sources (PCCS,
Sect. 8.1), comprising lists of compact sources over the en-
tire sky at the nine
Planck
frequencies. The PCCS super-
sedes the previous Early Release Compact Source Catalogue
(Planck Collaboration XIV 2011).
–
The
Planck
Catalogue of Sunyaev-Zeldovich Sources (PSZ,
Sect. 8.1.2), comprising a list of sources detected by their
SZ distortion of the CMB spectrum. The PSZ supersedes
the previous Early Sunyaev-Zeldovich Catalogue (Planck
Collaboration XXIX 2014).
3. Papers accompanying the 2013 release
The characteristics, processing, and analysis of the
Planck
data
as well as a number of scientific results are described in a series
of papers released simultaneously with the data. The titles of the
papers begin with “
Planck
2013 results.”, followed by the spe-
cific titles below. Figure 2 gives a graphical view of the papers,
divided into product, processing, and scientific result categories.
I. Overview of products and results (
this paper
)
II. Low Frequency Instrument data processing
III. LFI systematic uncertainties
IV. LFI beams and window functions
V. LFI calibration
VI. High Frequency Instrument data processing
VII. HFI time response and beams
VIII. HFI photometric calibration and mapmaking
IX. HFI spectral response
X. HFI energetic particle e
ff
ects: characterization, removal, and
simulation
XI. All-sky model of dust emission based on Planck data
XII. Di
ff
use component separation
XIII. Galactic CO emission
XIV. Zodiacal emission
XV. CMB power spectra and likelihood
XVI. Cosmological parameters
XVII. Gravitational lensing by large-scale structure
XVIII. The gravitational lensing-infrared background
correlation
XIX. The integrated Sachs-Wolfe e
ff
ect
XX. Cosmology from Sunyaev-Zeldovich cluster counts
XXI. Cosmology with the all-sky Compton-parameter power
spectrum
XXII. Constraints on inflation
XXIII. Isotropy and statistics of the CMB
XXIV. Constraints on primordial non-Gaussianity
XXV. Searches for cosmic strings and other topological defects
XXVI. Background geometry and topology of the Universe
XXVII. Doppler boosting of the CMB: Eppur si muove
XXVIII. The
Planck
catalogue of Compact Sources
XXIX. The
Planck
catalogue of Sunyaev-Zeldovich sources
XXX. Cosmic infrared background measurements and
implications for star formation
XXXI. Consistency of the
Planck
data.
In the next few months additional papers will be released
concentrating on Galactic foregrounds in both temperature and
polarization.
This paper contains an overview of the main aspects of the
Planck
project that have contributed to the 2013 release, and
points to the papers (Fig. 2) that contain full descriptions. It pro-
ceeds as follows:
–
Section 4 summarizes the operations of
Planck
and the per-
formance of the spacecraft and instruments.
–
Sections 5 and 6 describe the processing steps carried out in
the generation of the nine
Planck
frequency maps and their
characteristics.
–
Section 7 describes the
Planck
2013 products related to the
cosmic microwave background, namely the CMB maps, the
lensing products, and the likelihood code.
–
Section 8 describes the
Planck
2013 astrophysical products,
namely catalogues of compact sources and maps of di
ff
use
foreground emission.
A1, page 6 of 48
Planck Collaboration:
Planck
2013 results. I.
–
Section 9 describes the main cosmological science results
based on the 2013 CMB products.
–
Section 10 concludes with a summary and a look towards the
next generation of
Planck
products.
4. The
Planck
mission
Planck
was launched from Kourou, French Guiana, on
14 May 2009 on an Ariane 5 ECA rocket, together with the
Herschel
Space Observatory. After separation from the rocket
and from
Herschel
,
Planck
followed a trajectory to the
L
2
point
of the Sun-Earth system. It was injected into a 6-month Lissajous
orbit around
L
2
in early July 2009 (Fig. 3). Small manoeu-
vres are required at approximately monthly intervals (totalling
around 1 m s
−
1
per year) to keep
Planck
from drifting away
from
L
2
.
The first three months of operations focused on commission-
ing (during which
Planck
cooled down to the operating tem-
peratures of the coolers and the instruments), calibration, and
performance verification. Routine operations and science obser-
vations began 12 August 2009. Detailed information about the
first phases of operations may be found in Planck Collaboration I
(2011) and Planck Collaboration (2013).
4.1. Scanning strategy
Planck
spins at 1 rpm about the symmetry axis of the spacecraft.
The spin axis follows a cycloidal path across the sky in step-
wise displacements of 2
′
(Fig. 4). To maintain a steady advance
of the projected position of the spin axis along the ecliptic plane,
the time interval between two manoeuvres varies between 2360 s
and 3904 s. Details of the scanning strategy are given in Tauber
et al. (2010a) and Planck Collaboration I (2011).
The fraction of time used by the manoeuvres themselves
(typical duration of five minutes) varies between 6% and 12%,
depending on the phase of the cycloid. At present, the recon-
structed position of the spin axis during manoeuvres has not
been determined accurately enough for scientific work (but see
Sect. 4.5), and the data taken during manoeuvres are not used
in the analysis. Over the nominal mission, the total reduction of
scientific data due to manoeuvres was 9.2%.
The boresight of the telescope is 85
◦
from the spin axis. As
Planck
spins, the instrument beams cover nearly great circles in
the sky. The spin axis remains fixed (except for a small drift due
to Solar radiation pressure) for between 39 and 65 spins (corre-
sponding to the dwell times given above), depending on which
part of the cycloid
Planck
is in. To high accuracy, any one beam
covers precisely the same sky between 39 and 65 times. The set
of observations made during a period of fixed spin axis point-
ing is often referred to as a “ring”. This redundancy plays a key
role in the analysis of the data, as will be seen below, and is an
important feature of the scan strategy.
As the Earth and
Planck
orbit the Sun, the nearly-great cir-
cles that are observed rotate about the ecliptic poles. The ampli-
tude of the spin-axis cycloid is chosen so that all beams of both
instruments cover the entire sky in one year. In e
ff
ect,
Planck
tilts
to cover first one Ecliptic pole, then tilts the other way to cover
the other pole six months later. If the spin axis stayed exactly
on the ecliptic plane, the telescope boresight were perpendicu-
lar to the spin axis, the Earth were in a precisely circular orbit,
and
Planck
had only one detector with a beam aligned precisely
with the telescope boresight, that beam would cover the full sky
in six months. In the next six months, it would cover the same
sky, but with the opposite sense of rotation on a given great cir-
cle. However, since the spin axis is steered in a cycloid, the tele-
scope is 85
◦
to the spin axis, the focal plane is several degrees
wide, and the Earth’s orbit is slightly elliptical, the symmetry
of the scanning is (slightly) broken. Thus the
Planck
beams scan
the entire sky exactly twice in one year, but scan only 93% of the
sky in six months. For convenience, we call an approximately six
month period one “survey”, and use that term as an inexact short-
hand for one coverage of the sky. Nine numbered “Surveys” are
defined precisely in Table 1. It is important to remember that as
long as the phase of the cycloid remains constant, one year cor-
responds to exactly two coverages of the sky, while one Survey
has an exact meaning only as defined in Table 1. Null tests be-
tween 1-year periods with the same cycloid phase are extremely
powerful. Null tests between Surveys are also useful for many
types of tests, particularly in revealing di
ff
erences due to beam
orientation.
4.2. Routine operations
Routine operations started on 12 August 2009. The beginning
and end dates of each Survey are listed in Table 1, which also
shows the fraction of the sky covered by all frequencies. The
fourth Survey was shortened somewhat so that the slightly dif-
ferent scanning strategy adopted for Surveys 5–8 (see below)
could be started before the Crab nebula, an important polariza-
tion calibration source, was observed. The coverage of the fifth
Survey is smaller than the others because several weeks of in-
tegration time were dedicated to “deep rings” (defined below)
covering sources of special importance.
During routine scanning, the
Planck
instruments naturally
observe objects of special interest for calibration. These include
Mars, Jupiter, Saturn, Uranus, Neptune, and the Crab nebula.
Di
ff
erent types of observations of these objects were performed:
–
Normal scans on solar system objects and the Crab nebula.
The complete list of observing dates for these objects can be
found in Planck Collaboration (2013).
–
“Deep rings”. These special scans are performed on obser-
vations of Jupiter and the Crab nebula from January 2012
onward. They comprise deeply and finely sampled (step
size 0.
′
5) observations with the spin axis along the Ecliptic
plane, lasting typically two to three weeks. Since the Crab is
crucial for calibration of both instruments, the average lon-
gitudinal speed of the pointing steps was increased before
scanning the Crab, to improve operational margins and ease
recovery in case of problems.
–
“Drift scans”. These special observations are performed on
Mars, making use of its proper motion. They allow finely-
sampled measurements of the beams, particularly for HFI.
The rarity of Mars observations during the mission gives
them high priority.
The cycloid phase was shifted by 90
◦
for Surveys 5–8 to op-
timize the range of polarization angles on key sources in the
combination of Surveys 1–8, thereby helping in the treatment
of systematic e
ff
ects and improving polarization calibration.
As stated in Sect. 2, the 2013 products are based on the
15.5-month nominal mission, and include data acquired during
Surveys 1, 2, and part of 3.
The scientific lifetime of the HFI bolometers ended on
13 January 2012 when the supply of
3
He needed to cool
them to 0.1 K ran out. LFI continued to operate and ac-
quire scientific data through 3 October 2013.
Planck
operations
ended 23 October 2013. Data from the remaining part of
A1, page 7 of 48
A&A 571, A1 (2014)
Fig. 3.
Trajectory of
Planck
from launch until 13 January 2012, in Earth-centred rotating coordinates (
X
is in the Sun-Earth direction;
Z
points to
the north ecliptic pole). Symbols indicate the start of routine operations (circle), the end of the nominal mission (triangle), and the end of HFI data
acquisition (diamond). The orbital periodicity is 6 months. The distance from the Earth-Moon barycentre is shown in the
bottom right panel
,
together with Survey boundaries.
Survey 3, Surveys 4 and 5 (both LFI and HFI), and Surveys 6–9
(LFI only) will be released in 2014.
Routine operations were significantly modified twice more:
–
The sorption cooler switchover from the nominal to the re-
dundant unit took place on 11 August 2010, leading to an
interruption of acquisition of useful scientific data for about
two days (one for the operation itself, and one for re-tuning
of the cooling chain).
–
The satellite’s rotation speed was increased to 1.4 rpm be-
tween 8 and 16 December 2011 for observations of Mars,
to measure possible systematic e
ff
ects on the scientific data
linked to the spin rate.
Data were acquired in the normal way during the above two
periods, but were not used in the 2013 products.
The distribution of integration time over the sky for the nom-
inal and “0.1-K” (i.e., until the
3
He ran out, see Table 1) mis-
sions is illustrated in Fig. 5 for a representative frequency chan-
nel. More details can be found in the Explanatory Supplement
(Planck Collaboration 2013).
Operations have been extremely smooth throughout the mis-
sion. The total observation time lost due to a few anomalies
is about 5 days, spread over the 15.5 months of the nominal
mission.
4.3. Satellite environment
The thermal and radiation environment of the satellite during
the routine phase is illustrated in Fig. 6. The dominant long-
timescale thermal modulation is driven by variations in Solar
power absorbed by the satellite in its elliptical orbit around Sun.
The thermal environment is sensitive to various satellite opera-
tions. For example, before day 257, the communications trans-
mitter was turned on only during the daily data transmission
period, causing a daily temperature variation clearly visible at
all locations in the Service Module (Fig. 6). Some operational
events
4
had a significant thermal impact as shown in Fig. 6 and
detailed in Planck Collaboration (2013).
The sorption cooler dissipates a large amount of power and
drives temperature variations at multiple levels in the satellite.
The bottom panel of Fig. 6 shows the temperature evolution of
the coldest of the three stacked conical structures or V-grooves
that thermally isolate the warm service module (SVM) from the
cold payload module. Most variations of this structure are due
to quasi-weekly power input adjustments of the sorption cooler,
whose tube-in-tube heat-exchanger supplying high pressure gas
to the 20K Joule-Thomson valve and returning low pressure gas
to the compressor assembly is heat-sunk to it. Many adjustments
4
Most notably: a) the “catbed” event between 110 and 126 days af-
ter launch; b) the “day
Planck
stood still” 191 days after launch; c) the
sorption cooler switchover (OD 460); d) the change in the thermal con-
trol loop (OD 540) of the LFI radiometer electronics assembly box; and
e) the spin-up campaign around OD 950.
A1, page 8 of 48
Planck Collaboration:
Planck
2013 results. I.
Fig. 4.
Top two panels
: path of the spin axis of
Planck
(in ecliptic longitude and latitude) over the period 12 August 2009 (91 days after launch)
to 13 January 2012, the “0.1 K mission” period (Table 1).
Bottom panel
: evolution of the dwell time during the same period. Intervals of accelera-
tion
/
deceleration (e.g., around observations of the Crab) are clearly visible as symmetric temporary increases and reductions of dwell time. Survey
boundaries are indicated by vertical dashed lines in the upper plot. The change in cycloid phase is clearly visible at operational day (OD) 807. The
disturbances around OD 950 are due to the “spin-up campaign”.
are seen in the roughly three months leading up to switchover.
After switchover to the redundant cooler (Sect. 4.4.1), thermal
instabilities were present in the newly operating sorption cooler,
which required frequent adjustment, until they reduced signifi-
cantly around day 750.
Figure 6 also shows the radiation environment history. As
Planck
started operations, Solar activity was extremely low, and
Galactic cosmic rays (which produce sharp “glitches” in the
HFI bolometer signals, see Sect. 4.4.2) were more easily able
to enter the heliosphere and hit the satellite. As Solar activity in-
creased the cosmic ray flux measured by the onboard standard
radiation environment monitor (SREM; Planck Collaboration
2013) decreased correspondingly, but Solar flares increased.
4.4. Instrument environment, operations, and performance
4.4.1. LFI
The front-end of the LFI array is cooled to 20 K by a sorp-
tion cooler system, which included a nominal and a redundant
unit (Planck Collaboration II 2011). In early August of 2010,
the gas-gap heat switch of one compressor element on the ac-
tive cooler reached the end of its life. Although the cooler
5
http://www.sidc.be/sunspot-data/
can operate with as few as four (out of six) compressor el-
ements, it was decided to switch operation to the redundant
cooler. On 11 August at 17:30 GMT the working cooler was
switched o
ff
, and the redundant one was switched on. Following
this operation, an increase of temperature fluctuations in the
20 K stage was observed. The cause has been ascribed to the
influence of liquid hydrogen remaining in the cold end of the
inactive (previously operating) cooler. These thermal fluctua-
tions produced a measurable e
ff
ect in the LFI data, but they
propagate to the power spectrum at a level more than four or-
ders of magnitude below the CMB temperature signal (Planck
Collaboration III 2014) and have a negligible e
ff
ect on the sci-
ence data. Furthermore, in February 2011 these fluctuations were
reduced to a much lower level and have remained low ever since.
The 22 LFI radiometers have been extremely stable since the
beginning of the observations (Planck Collaboration III 2014),
with 1
/
f
knee frequencies of order 50 mHz and white noise lev-
els unchanging within a few percent. After optimization during
the calibration and performance verification phase, no changes
to the bias of the front-end HEMT low-noise amplifiers and
phase switches were required throughout the nominal mission.
The main disturbance to LFI data acquisition has been an
occasional bit-flip change in the gain-setting circuit of the data
acquisition electronics, probably due to cosmic ray hits (Planck
Collaboration II 2014). Each of these events leads to the loss of
A1, page 9 of 48
A&A 571, A1 (2014)
Fig. 5.
Survey coverage for the nominal (
top
) and 0.1 K (
bottom
) missions (see Table 1). The colour scale represents total integration time (varying
between 50 and 8000 s deg
−
2
) for the 353 GHz channel. The maps are at
N
side
=
1024.
a fraction of a single ring for the a
ff
ected detector. The total level
of data loss was extremely low, less than 0.12% over the whole
mission.
4.4.2. HFI
HFI operations were extremely smooth. The instrument param-
eters were not changed after being set during the calibration and
performance verification phase.
The satellite thermal environment had no major impact on
HFI. A drift of the temperature of the service vehicle module
(SVM) due to the eccentricity of the Earth’s orbit (Fig. 6) in-
duced negligible changes of temperature of the HFI electronic
chain. Induced gain variations are of order 10
−
4
per degree K.
The HFI dilution cooler (Planck Collaboration II 2011) oper-
ated at the lowest available gas flow rate, giving a lifetime twice
the 15.5 months of the nominal mission. This was predicted to
be possible following ground tests, and demonstrates how repre-
sentative of the flight environment these di
ffi
cult tests were.
The HFI cryogenic system remained impressively stable
over the whole cryogenic mission. Figure 7 shows the temper-
ature of the three cold stages of the
4
He-JT and dilution cool-
ers. The temperature stability of the 1.6 K and 4 K plates, which
support the feed horns, couple detectors to the telescope, and
support the filters, was well within specifications and produced
negligible e
ff
ects on the scientific signals. The dilution cooler
showed the secular evolution of heat lift expected from the small
drifts of the
3
He and
4
He flows as the pressure in the tanks
decreased. The proportional-integral-di
ff
erential (PID) temper-
ature regulation of the bolometer plate had a long time con-
stant to avoid transferring cosmic-ray-induced glitches on the
PID thermometers to the plate. The main driver of the bolome-
ter plate temperature drifts was the long-term change in the
cosmic ray hit rate modulated by the Solar cycle, as described
in Planck Collaboration II (2011; see also Fig. 7). These very
A1, page 10 of 48