Astronomy & Astrophysics
manuscript no. ms
c
©
ESO 2018
July 18, 2018
Planck
2018 results. I.
Overview, and the cosmological legacy of
Planck
Planck Collaboration: Y. Akrami
59
,
61
, F. Arroja
63
, M. Ashdown
69
,
5
, J. Aumont
99
, C. Baccigalupi
81
, M. Ballardini
22
,
42
, A. J. Banday
99
,
8
,
R. B. Barreiro
64
, N. Bartolo
31
,
65
, S. Basak
88
, R. Battye
67
, K. Benabed
57
,
97
, J.-P. Bernard
99
,
8
, M. Bersanelli
34
,
46
, P. Bielewicz
80
,
8
,
81
, J. J. Bock
66
,
10
,
J. R. Bond
7
, J. Borrill
12
,
95
, F. R. Bouchet
57
,
92
∗
, F. Boulanger
71
,
56
,
57
, M. Bucher
2
,
6
, C. Burigana
45
,
32
,
48
, R. C. Butler
42
, E. Calabrese
85
,
J.-F. Cardoso
57
, J. Carron
24
, B. Casaponsa
64
, A. Challinor
60
,
69
,
11
, H. C. Chiang
26
,
6
, L. P. L. Colombo
34
, C. Combet
73
, D. Contreras
21
,
B. P. Crill
66
,
10
, F. Cuttaia
42
, P. de Bernardis
33
, G. de Zotti
43
,
81
, J. Delabrouille
2
, J.-M. Delouis
57
,
97
, F.-X. D
́
esert
98
, E. Di Valentino
67
,
C. Dickinson
67
, J. M. Diego
64
, S. Donzelli
46
,
34
, O. Dor
́
e
66
,
10
, M. Douspis
56
, A. Ducout
57
,
54
, X. Dupac
37
, G. Efstathiou
69
,
60
, F. Elsner
77
,
T. A. Enßlin
77
, H. K. Eriksen
61
, E. Falgarone
70
, Y. Fantaye
3
,
20
, J. Fergusson
11
, R. Fernandez-Cobos
64
, F. Finelli
42
,
48
, F. Forastieri
32
,
49
, M. Frailis
44
,
E. Franceschi
42
, A. Frolov
90
, S. Galeotta
44
, S. Galli
68
, K. Ganga
2
, R. T. G
́
enova-Santos
62
,
15
, M. Gerbino
96
, T. Ghosh
84
,
9
, J. Gonz
́
alez-Nuevo
16
,
K. M. G
́
orski
66
,
101
, S. Gratton
69
,
60
, A. Gruppuso
42
,
48
, J. E. Gudmundsson
96
,
26
, J. Hamann
89
, W. Handley
69
,
5
, F. K. Hansen
61
, G. Helou
10
,
D. Herranz
64
, E. Hivon
57
,
97
, Z. Huang
86
, A. H. Ja
ff
e
54
, W. C. Jones
26
, A. Karakci
61
, E. Keih
̈
anen
25
, R. Keskitalo
12
, K. Kiiveri
25
,
41
, J. Kim
77
,
T. S. Kisner
75
, L. Knox
28
, N. Krachmalnico
ff
81
, M. Kunz
14
,
56
,
3
, H. Kurki-Suonio
25
,
41
, G. Lagache
4
, J.-M. Lamarre
70
, M. Langer
56
, A. Lasenby
5
,
69
,
M. Lattanzi
32
,
49
, C. R. Lawrence
66
, M. Le Jeune
2
, J. P. Leahy
67
, J. Lesgourgues
58
, F. Levrier
70
, A. Lewis
24
, M. Liguori
31
,
65
, P. B. Lilje
61
,
M. Lilley
57
,
92
, V. Lindholm
25
,
41
, M. L
́
opez-Caniego
37
, P. M. Lubin
29
, Y.-Z. Ma
67
,
83
,
79
, J. F. Mac
́
ıas-P
́
erez
73
, G. Maggio
44
, D. Maino
34
,
46
,
50
,
N. Mandolesi
42
,
32
, A. Mangilli
8
, A. Marcos-Caballero
64
, M. Maris
44
, P. G. Martin
7
, E. Mart
́
ınez-Gonz
́
alez
64
, S. Matarrese
31
,
65
,
39
, N. Mauri
48
,
J. D. McEwen
78
, P. D. Meerburg
69
,
11
,
100
, P. R. Meinhold
29
, A. Melchiorri
33
,
51
, A. Mennella
34
,
46
, M. Migliaccio
94
,
52
, M. Millea
28
,
91
,
57
, S. Mitra
53
,
66
,
M.-A. Miville-Desch
ˆ
enes
72
, D. Molinari
32
,
42
,
49
, A. Moneti
57
, L. Montier
99
,
8
, G. Morgante
42
, A. Moss
87
, S. Mottet
57
,
92
, M. M
̈
unchmeyer
57
,
P. Natoli
32
,
94
,
49
, H. U. Nørgaard-Nielsen
13
, C. A. Oxborrow
13
, L. Pagano
56
,
70
, D. Paoletti
42
,
48
, B. Partridge
40
, G. Patanchon
2
, T. J. Pearson
10
,
55
,
M. Peel
17
,
67
, H. V. Peiris
23
, F. Perrotta
81
, V. Pettorino
1
, F. Piacentini
33
, L. Polastri
32
,
49
, G. Polenta
94
, J.-L. Puget
56
,
57
, J. P. Rachen
18
,
M. Reinecke
77
, M. Remazeilles
67
, A. Renzi
65
, G. Rocha
66
,
10
, C. Rosset
2
, G. Roudier
2
,
70
,
66
, J. A. Rubi
̃
no-Mart
́
ın
62
,
15
, B. Ruiz-Granados
62
,
15
,
L. Salvati
56
, M. Sandri
42
, M. Savelainen
25
,
41
,
76
, D. Scott
21
, E. P. S. Shellard
11
, M. Shiraishi
31
,
65
,
19
, C. Sirignano
31
,
65
, G. Sirri
48
, L. D. Spencer
85
,
R. Sunyaev
77
,
93
, A.-S. Suur-Uski
25
,
41
, J. A. Tauber
38
, D. Tavagnacco
44
,
35
, M. Tenti
47
, L. Terenzi
42
, L. To
ff
olatti
16
,
42
, M. Tomasi
34
,
46
,
T. Trombetti
45
,
49
, J. Valiviita
25
,
41
, B. Van Tent
74
, L. Vibert
56
,
57
, P. Vielva
64
, F. Villa
42
, N. Vittorio
36
, B. D. Wandelt
57
,
97
,
30
, I. K. Wehus
66
,
61
,
M. White
27
†
, S. D. M. White
77
, A. Zacchei
44
, and A. Zonca
82
(A
ffi
liations can be found after the references)
July 18, 2018
ABSTRACT
The European Space Agency’s
Planck
satellite, which was dedicated to studying the early Universe and its subsequent evolution, was launched
on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013, producing deep,
high-resolution, all-sky maps in nine frequency bands from 30 to 857 GHz. This paper presents the cosmological legacy of
Planck
, which currently
provides our strongest constraints on the parameters of the standard cosmological model and some of the tightest limits available on deviations
from that model. The 6-parameter
Λ
CDM model continues to provide an excellent fit to the cosmic microwave background data at high and low
redshift, describing the cosmological information in over a billion map pixels with just six parameters. With 18 peaks in the temperature and
polarization angular power spectra constrained well,
Planck
measures five of the six parameters to better than 1 % (simultaneously), with the
best-determined parameter (
θ
∗
) now known to 0.03 %. We describe the multi-component sky as seen by
Planck
, the success of the
Λ
CDM model,
and the connection to lower-redshift probes of structure formation. We also give a comprehensive summary of the major changes introduced in
this 2018 release. The
Planck
data, alone and in combination with other probes, provide stringent constraints on our models of the early Universe
and the large-scale structure within which all astrophysical objects form and evolve. We discuss some lessons learned from the
Planck
mission,
and highlight areas ripe for further experimental advances.
Key words.
Cosmology: observations – Cosmology: theory – cosmic background radiation – Surveys
Contents
1 Introduction
2
2 The sky according to
Planck
3
2.1
The Solar dipole . . . . . . . . . . . . . . . . . .
3
2.2
Frequency maps and their properties . . . . . . .
7
2.3
Component separation . . . . . . . . . . . . . .
8
2.4
Foregrounds . . . . . . . . . . . . . . . . . . . . 10
2.5
CMB anisotropy maps . . . . . . . . . . . . . . 12
2.6
CMB angular power spectra . . . . . . . . . . . 14
∗
Corresponding author: F. R. Bouchet,
bouchet@iap.fr
.
†
Corresponding author: M. White,
mwhite@berkeley.edu
.
2.6.1
CMB intensity and polarization spectra . 14
2.6.2
CMB lensing spectrum . . . . . . . . . . 16
3 The
Λ
CDM model
18
3.1
Assumptions underlying
Λ
CDM . . . . . . . . . 18
3.2
Planck
’s constraints on
Λ
CDM parameters . . . . 19
3.3
Planck
’s tests of
Λ
CDM assumptions . . . . . . 21
4 Cosmic concordance
24
4.1
The CMB sky . . . . . . . . . . . . . . . . . . . 24
4.2
Large-scale structure . . . . . . . . . . . . . . . 27
4.3
Discord . . . . . . . . . . . . . . . . . . . . . . 29
5
Planck
and fundamental physics
31
1
arXiv:1807.06205v1 [astro-ph.CO] 17 Jul 2018
Planck Collaboration: The cosmological legacy of
Planck
5.1
Large scales and the dipole . . . . . . . . . . . . 31
5.2
Inflation physics and constraints . . . . . . . . . 31
5.3
Neutrino physics and constraints . . . . . . . . . 33
5.4
Dark matter . . . . . . . . . . . . . . . . . . . . 35
5.5
Dark energy and modified gravity . . . . . . . . 35
5.6
Isotropy and statistics; anomalies . . . . . . . . . 36
6
Planck
and structure formation
36
6.1
The normalization and shape of
P
(
k
) . . . . . . . 36
6.2
Lensing cross-correlations . . . . . . . . . . . . 37
6.3
Baryon acoustic oscillations (BAO) . . . . . . . 38
6.4
Clusters and SZ e
ff
ects . . . . . . . . . . . . . . 39
6.5
Cosmic infrared background anisotropies . . . . 42
6.6
Reionization . . . . . . . . . . . . . . . . . . . . 42
7 Post-
Planck
landscape
44
8 Conclusions
44
A The 2018 release
51
A.1 Papers in the 2018 release . . . . . . . . . . . . . 51
A.2 Data products in the 2018 release . . . . . . . . . 51
B Changes for the 2018 release
52
B.1 2018 LFI processing improvements . . . . . . . 52
B.2 2018 HFI processing improvements . . . . . . . 52
B.3 Simulations . . . . . . . . . . . . . . . . . . . . 53
B.4 Map analysis improvements . . . . . . . . . . . 53
B.5 CMB power spectra and likelihood improvements 54
B.5.1
Large-scale
temperature
and
the
Commander
likelihood . . . . . . . . . . 54
B.5.2
Large-scale HFI polarization and the
Simall
likelihood . . . . . . . . . . . . 54
B.5.3
Large-scale LFI polarization and its
likelihood use . . . . . . . . . . . . . . . 55
B.5.4
Small-scale temperature and polariza-
tion HFI likelihood . . . . . . . . . . . . 55
B.5.5
Lensing likelihood . . . . . . . . . . . . 56
C HFI-LFI consistency
56
D Blinding
58
1. Introduction
This paper, one of a set associated with the 2018 release of data
from the
Planck
1
mission, presents the cosmological legacy of
Planck
.
Planck
was dedicated to studying the early Universe and
its subsequent evolution by mapping the anisotropies in the cos-
mic microwave background (CMB) radiation.
The CMB, discovered in 1965 (Penzias & Wilson 1965;
Dicke et al. 1965), has been a pillar of our cosmological world
view since it was determined to be of cosmological origin.
The CMB spectrum is the best-measured black-body in nature
(Fixsen 2009), and the absence of spectral distortions places very
strong constraints on the amount of energy that could have been
injected into the Universe at epochs later than
z
'
2
×
10
6
(e.g.,
Fixsen et al. 1996; Chluba & Sunyaev 2012), which limits the
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 by a collaboration between ESA and a sci-
entific consortium led and funded by Denmark.
properties of decaying or annihilating particles, primordial black
holes, topological defects, primordial magnetic fields, and other
exotic physics. Perhaps its largest impact, however, has come
from CMB anisotropies, the small deviations in intensity and
polarization from point to point on the sky.
The anisotropies in the CMB, first detected by the COBE
satellite (Smoot et al. 1992), provide numerous, strong tests
of the cosmological paradigm and the current best measure-
ments on most of the parameters of our cosmological model
(Planck Collaboration XVI
2014;
Planck Collaboration XIII
2016; Planck Collaboration VI 2018). The COBE detection ce-
mented the gravitational instability paradigm within a cold dark
matter (CDM) model (Efstathiou et al. 1992). Ground-based
and balloon-borne experiments (e.g., de Bernardis et al. 2000;
Balbi et al. 2000; Miller et al. 2002; Mac
́
ıas-P
́
erez et al. 2007)
established that the Universe has no significant spatial curvature
(Knox & Page 2000a; Pierpaoli et al. 2000). WMAP showed
that the fluctuations are predominantly adiabatic (Kogut et al.
2003; from the phasing of the peaks and polarization) and pro-
vided multiple, simultaneous, tight constraints on cosmological
parameters (Bennett et al. 2003) – a legacy that the
Planck
mission has continued and enriched (Sect. 3.2).
Planck
was the third-generation space mission dedicated to
measurements of CMB anisotropies. It was a tremendous tech-
nical success, operating in a challenging environment without
interruption over three times the initially planned mission dura-
tion, with a performance exceeding expectations. Currently our
best measurements of the anisotropy spectra on the scales most
relevant for cosmology come from
Planck
.
Some milestones in the
Planck
mission are listed in Table 1.
A set of 13 pre-launch papers was published in a special
issue of Astronomy and Astrophysics (Vol. 520, 2010; see
Tauber et al. 2010). For an overview of the scientific operations
of the
Planck
mission see Planck Collaboration I (2014) and the
Explanatory Supplement (Planck Collaboration ES 2015, 2018).
The first set of scientific data, the Early Release Compact
Source Catalogue (ERCSC; Planck Collaboration VII 2011),
was released in January 2011. A set of 26 papers related
to astrophysical foregrounds was published in another spe-
cial issue of Astronomy and Astrophysics (Vol. 536, 2011;
see Planck Collaboration I 2011). The first cosmological results
from
Planck
, based mainly on temperature maps of the whole
sky acquired during the nominal mission duration of 14 months,
were reported in 2013 and the data products made available (as
“PR1”) on the Planck Legacy Archive (PLA
2
). These cosmolog-
ical results were published as a series along with further data-
processing and astrophysics papers in 2014 (A&A Vol. 571,
2014; see Planck Collaboration I 2014). The first results from
the full mission, including some polarization data, were pre-
sented in 2015; for a summary see Planck Collaboration I
(2016). The raw time-ordered observations were released to the
public in their entirety in February 2015, as part of this second
Planck
data release (“PR2”), together with associated frequency
and component sky maps and higher-level science derivatives.
This paper is part of a final series of papers from the
Planck
collaboration, released along with the final data (“PR3”). It
presents an overview of the
Planck
mission and the numerous
contributions
Planck
has made to our understanding of cosmol-
ogy, i.e., we are considering the cosmological legacy of
Planck
.
After a broad overview of the useful products derived from
Planck
data, from the maps at nine frequencies to astrophys-
ical components and their broad characterization (specifics of
2
http://pla.esac.esa.int
2
Planck Collaboration: The cosmological legacy of
Planck
Table 1.
Important milestones in the
Planck
mission.
Date
Milestone
Nov 1992 . . . . . ESA call for M3 (of Horizon 2000 program)
May 1993 . . . . . Proposals for COBRAS and SAMBA submitted
Sep 1993 . . . . . . Selection of COBRAS and SAMBA for assessment
Dec 1994 . . . . . . Selection of COBRAS and SAMBA for Phase A
Jul 1996 . . . . . . (Combined)
Project selection as M3
May 1998 . . . . . Pre-selection of the instrument consortia
Feb 1999 . . . . . . Final approval of scientific payload and consortia
Jan 2001 . . . . . . First meeting of the full Planck Collaboration
Apr 2001 . . . . . . Prime contractor selected.
Start of phase B
Jun 2001 . . . . . . WMAP blazes the way for
Planck
Sep 2001 . . . . . . System requirements review
Jul–Oct 2002 . . . Preliminary design review
Dec 2002 . . . . . . Science ground segment (SGS) review
Apr–Oct 2004 . . Critical design review
Jan 2005 . . . . . . Delivery of HFI cryo-qualification model to ESA
Aug 2006 . . . . . Calibration of flight instruments at Orsay and Laben
Sep 2006 . . . . . . Delivery of instrument flight models to ESA
Nov 2006 . . . . . HFI and LFI mating at Thales in Cannes
Jan 2007 . . . . . . Integration completed
Mar 2007 . . . . . SGS implementation review
Feb–Apr 2007 . . Qualification review
Jun–Aug 2007 . . Final global test at Centre Spatial de Li
́
eges
Nov 2008 . . . . . Ground segment readiness review
Jan 2009 . . . . . . Flight acceptance review passed
19 Feb 2009 . . . .
Planck
flies to French Guyana
14 May 2009 . . .
Launch
02 Jul 2009 . . . . Injection into
L
2
orbit
20 May 2009 . . . Commissioning begins
13 Aug 2009 . . . Commissioning ends
27 Aug 2009 . . . End of “First light survey”
14 Feb 2010 . . . . Start of second all-sky survey
05 Jul 2010 . . . . First all-sky image released
14 Aug 2010 . . . Start of third all-sky survey
27 Nov 2010 . . .
End of nominal mission
, start of extended mission
14 Feb 2011 . . . . Start of fourth all-sky survey
29 Jul 2011 . . . . Start of fifth all-sky survey
14 Jan 2012 . . . . End of cryogenic mission, start of warm phase
30 Jan 2012 . . . . LFI starts sixth all-sky survey
08 Feb 2012 . . . .
Planck
completes 1000 days in space
14 Aug 2013 . . . Departure manoeuvre executed
04 Oct 2013 . . . . Start of end-of-life operations
09 Oct 2013 . . . . De-orbiting from
L
2
09 Oct 2013 . . . . HFI, LFI, and SCS commanded o
ff
23 Oct 2013 . . . .
Last command
Feb 1996 . . . . . . Publication of the ”Redbook” of
Planck
science
Jan 2005 . . . . . . Bluebook: The Scientific Programme of
Planck
Sep 2009 . . . . . . First light survey press release
Mar 2010 . . . . . First (of 15) internal data releases
Sep 2010 . . . . . . Pre-launch papers, special issue of A&A, Vol. 520
Jan 2011 . . . . . . Early release (compact source catalogue)
Dec 2011 . . . . . . Early results papers, special issue of A&A, Vol. 536
Mar 2013 . . . . .
Nominal mission data release
(temperature, PR1)
Nov 2014 . . . . . 2013 results papers, special issue of A&A, Vol. 571
Feb–Aug 2015 . . Extended mission data release (PR2)
Sep 2016 . . . . . . 2015 results papers, special issue of A&A, Vol. 594
2018 . . . . . . . . This
Legacy data release (PR3)
this release are detailed in Appendix A), we discuss the CMB
anisotropies, which were the main focus of the
Planck
mission.
We then turn to a comparison of our results to theoretical models,
and the way in which the
Planck
data confirm and inform those
models before comparing to a wider range of astrophysical and
cosmological data. A discussion of how
Planck
has placed con-
straints on models of the early and late Universe and the relation-
ship of the
Planck
data to other cosmological probes precedes a
discussion of the post-
Planck
landscape and finally our conclu-
sions. We relegate to appendices some details of this release, and
a more detailed discussion of improvements in the data process-
ing between the 2015 and 2018 releases.
2. The sky according to
Planck
Details of the
Planck
mission, its scientific payload and
performance, have been discussed in previous publications
(Planck Collaboration I 2014, 2016, and references therein).
Planck
was the first submillimetre mission to map the entire
sky to sub-Jansky sensitivity with resolution better than 10
′
.
In this section we describe the calibration and main proper-
ties of the frequency maps, and the methods used to separate
the sky emission into di
ff
erent components. We briefly describe
the main foreground components before discussing the CMB
anisotropies, whose characterization were the main goal of the
Planck
mission.
2.1. The Solar dipole
In the 2015 data release, photometric calibration from 30 to
353 GHz was based on the “orbital dipole,” i.e., the modula-
tion of the Solar dipole induced by the orbital motion of the
satellite around the Solar System barycentre.
3
This allowed us
to
measure
the amplitude and direction of the “Solar dipole”
on the calibrated maps of individual detectors, at frequencies
where the CMB is the dominant signal (70 to 353 GHz). The
dipole parameters measured in 2015 were significantly more
accurate than the previous best measurements provided by
WMAP (see Table 2). However, comparison of individual detec-
tor determinations showed clear indications of the presence of
small residual systematic e
ff
ects (Planck Collaboration II 2016;
Planck Collaboration VIII 2016). The dipole amplitude and di-
rection showed shifts with position in the focal plane for LFI; for
HFI the shifts were associated with frequency, as well as with the
Galactic mask and the component-separation method used, indi-
cating the presence of dipolar and quadrupolar residuals after
removal of the dust and CMB anisotropies.
In 2018, both instruments have achieved a significant reduc-
tion in the levels of residual systematic e
ff
ects (especially at
the largest angular scales where the dipole signals are present)
and in the case of HFI
4
also in the accuracy of photometric
calibration. This has resulted in dramatic improvement in the
determination of the 2018 Solar dipole parameters, which are
presented in Table 2. The independent LFI and HFI measure-
ments are fully consistent with each other and with those of
3
We distinguish between two dipoles related to motion with respect
to the CMB rest frame. The first is the “Solar dipole,” induced by the
motion of the Solar System barycentre with respect to the CMB. The
second is the “orbital dipole,” i.e., the modulation of the Solar dipole
induced by the orbital motion of the satellite around the Solar System
barycentre. The orbital velocity is known exquisitely well, and hence
the induced dipole in
∆
T
/
T
units; this means that the accuracy of the
predicted orbital dipole is ultimately limited by the accuracy with which
we know the temperature of the CMB.
4
Furthermore the dust foreground e
ff
ect was identified with
large-scale (mostly quadrupolar) spectral energy distribution changes.
Correcting these brought full consistency between frequencies, as well
as for detectors within each frequency band.
3
Planck Collaboration: The cosmological legacy of
Planck
Fig. 1.
Fluctuations of the sky emission in each of the nine
Planck
frequency bands, after removal of a common dipole component.
The fluctuations are expressed as equivalent temperature variations at each of the seven lowest frequencies, so that fluctuations with
a thermal spectrum will appear the same in each map (except for the e
ff
ects of the varying resolution of the maps). The highest
frequencies, which monitor the dust emission, are expressed in more conventional units.
4
Planck Collaboration: The cosmological legacy of
Planck
Fig. 2.
The sky polarization in the seven frequency bands of
Planck
. The first two columns show the
Q
and
U
Stokes parameters,
the last column indicates the polarization fraction,
P
=
√
Q
2
+
U
2
(although note that this emphasizes the strength of polarization
in noisy regions). In addition to the rich science that they enable on their own, these maps set the baseline for all future CMB
polarization experiments, for example by defining the most cosmologically challenged areas.
5
Planck Collaboration: The cosmological legacy of
Planck
Table 2.
COBE, WMAP, LFI, HFI, and
Planck
combined measurements of the Solar dipole. Note that the uncertainties are dom-
inated by systematic e
ff
ects, whose assessment is fully discussed in Planck Collaboration II (2018) and Planck Collaboration III
(2018).
G
alactic coordinates
A
mplitude
l
b
E
xperiment
[
μ
K
CMB
]
[deg]
[deg]
COBE
a
. . . . . . . . . . . . . . . . . . .
3358
±
24
264
.
31
±
0
.
20
48
.
05
±
0
.
11
WMAP
b
. . . . . . . . . . . . . . . . . .
3355
±
8
263
.
99
±
0
.
14
48
.
26
±
0
.
03
Planck
2015 nominal
c
. . . . . . . . .
3364
.
5
±
2
.
0
264
.
00
±
0
.
03
48
.
24
±
0
.
02
LFI 2018
d
. . . . . . . . . . . . . . . . .
3364
.
4
±
3
.
1
263
.
998
±
0
.
051
48
.
265
±
0
.
015
HFI 2018
d
. . . . . . . . . . . . . . . . .
3362
.
08
±
0
.
99
264
.
021
±
0
.
011
48
.
253
±
0
.
005
Planck
2018
e
. . . . . . . . . . . . . . .
3362
.
08
±
0
.
99 264
.
021
±
0
.
011 48
.
253
±
0
.
005
a
Kogut et al. (1993); Lineweaver et al. (1996); we have (linearly) added statistical and systematic uncertainty estimates.
b
Hinshaw et al. (2009).
c
The 2015
Planck
“nominal” Solar dipole was chosen as a plausible combination of the LFI and HFI 2015 measurements to subtract the dipole
from the 2018 frequency maps. The di
ff
erence compared with the final determination of the dipole is very small for most purposes.
d
Uncertainties include an estimate of systematic errors. In the case of HFI, we have linearly added statistical and systematic errors.
e
The current best
Planck
determination of the dipole is that of HFI (Planck Collaboration III 2018). The central value for the direction corresponds
to RA
=
167.
◦
942
±
0.
◦
007, Dec
=
−
6.
◦
944
±
0.
◦
007 (J2000). The uncertainties are the (linear) sum of the statistical, and systematic uncertainties
detailed in Planck Collaboration III (2018).The uncertainty on the amplitude does not include the 0.02% uncertainty on the temperature of the
CMB monopole.
WMAP, and, as described in Planck Collaboration II (2018) and
Planck Collaboration III (2018), they are no longer significantly
a
ff
ected by systematic e
ff
ects (in the sense that the results are
consistent between frequencies, sky fractions and component-
separation methods used, although the uncertainties are not
purely statistical). Considering that the uncertainties in the HFI
determination are much lower than those of LFI, we recommend
that users adopt the HFI determination of the Solar dipole as the
most accurate one available from
Planck
.
We note that in all the released 2018 maps, the 2015 “nom-
inal” Solar dipole
5
has been subtracted (which is slightly dif-
ferent than the final best dipole). This was done in order to
produce a consistent data set, which is independent of the best
determination of dipole parameters, made at a later time sep-
arately at each individual frequency. This implies that a very
small residual Solar dipole is present in all the released maps;
this can be removed if desired using the procedure described in
Planck Collaboration III (2018).
It is also useful to note that the Solar dipole can still be mea-
sured with high signal-to-noise ratio at 545 GHz. The 545-GHz
data were not calibrated on the orbital dipole, but instead on
observations of Uranus and Neptune (Planck Collaboration III
2018). Therefore the photometric accuracy of this calibration is
limited by that of the physical emission model of the planets,
to a level of approximately 5 %. However, the dispersion of the
Solar dipole amplitude
measured
in individual 545-GHz detec-
tor maps is within 1 % of that at lower frequencies. This im-
plies that, in actual fact, the planet model can be calibrated on
this measurement more precisely than has been assumed so far
(Planck Collaboration Int. LII 2017). It also means that an im-
proved model can be extended to recalibrate the 857 GHz chan-
nel. These improvements have not been implemented in the 2018
release.
The amplitude of the dipole provides a constraint for build-
ing a picture of the local large-scale structure, through the
expected convergence of bulk-flow measurements for galaxies
5
The induced quadrupole has also been subtracted from the maps.
(e.g., Scrimgeour et al. 2016). The new best-fit dipole ampli-
tude is known more precisely than the CMB monopole, and
even when we fold in an estimate of systematic uncertainties
it is now known to about 0.025 % (essentially the same as the
monopole). The dipole amplitude corresponds to
β
≡
v
/
c
=
(1
.
23357
±
0
.
00036)
×
10
−
3
or
v
=
(369
.
82
±
0
.
11) km s
−
1
,
where we have (linearly) added in the systematic uncertainties.
When giving the amplitude of the dipole in temperature units
one should also include the uncertainty in
T
0
.
The Solar dipole direction lies just inside the little-known
constellation of Crater (near the boundary with Leo). The error
ellipse of
Planck
’s dipole direction (a few arcsec in radius, or
around 30
′′
including systematic uncertainties) is so small that it
is empty in most published astronomical catalogues. We discuss
the cosmological implications of the dipole in Sect. 5.1.
The Sun’s motion in the CMB frame is not the only rela-
tive velocity of interest, and indeed from a cosmological per-
spective more relevant would be the motion of the centre of
our Galaxy relative to the CMB or the motion of our group of
galaxies relative to the CMB. The peculiar motion of the Local
Group is well known to have a
larger
speed than that of the
Sun–CMB, due to the roughly anti-coincident direction of our
rotation around the Galaxy. It is this larger peculiar velocity that
has been the focus of studies to explain the origin of the motion
in the context of structures in our extragalactic neighbourhood
(e.g., Lynden-Bell et al. 1988; Tully et al. 2008). Estimates of
the corrections required to obtain the motion of the Galactic cen-
tre relative to the CMB and the motion of the centre-of-mass of
the Local Group relative to the CMB were given by Kogut et al.
(1993) and have seldom been revisited since then. We summa-
rize more modern determinations in Table 3.
Firstly, we take the estimate of the Sun’s motion relative
to the Local Standard of Rest from Sch
̈
onrich et al. (2010),
which uses nearby stars, and the estimate of the motion of
the LSR around the centre of the Milky Way from McMillan
(2011), which combines studies of larger-scale Galactic dynam-
ics. These can be subtracted from the Solar dipole to give the
6
Planck Collaboration: The cosmological legacy of
Planck
velocity of the Galactic centre relative to the CMB, as presented
in the fourth line of Table 3.
Secondly, we take the estimate of the Sun’s velocity rela-
tive to the centre of the Local Group from Diaz et al. (2014),
found by averaging velocities of members galaxies (as also
performed by several other studies, e.g., Yahil et al. 1977;
Courteau & van den Bergh 1999; Mikulizky 2015). This vector
can be subtracted from the Solar dipole velocity to derive the
velocity of the Local Group relative to the CMB. The value is
(620
±
15) km s
−
1
in a direction (known to about a couple of de-
grees) that lies about 30
◦
above the Galactic plane and is nearly
opposite in latitude to the direction of Galactic rotation. The un-
certainty in the Local Group’s speed relative to the CMB is al-
most entirely due to the uncertainty in the speed of the Sun rela-
tive to the centre-of-mass of the Local Group.
Table 3.
Relative velocities involving the CMB frame, the
Galactic centre, and the Local Group.
Relative
Speed
l
b
velocity
[km s
−
1
]
[deg]
[deg]
Sun–CMB
a
. . . . . 369
.
82
±
0
.
11 264
.
021
±
0
.
011 48
.
253
±
0
.
005
Sun–LSR
b
. . . . . .
17
.
9
±
2
.
0
48
±
7
23
±
4
LSR–GC
c
. . . . . .
239
±
5
90
0
GC–CMB
d
. . . . . .
565
±
5
265
.
76
±
0
.
20
28
.
38
±
0
.
28
Sun–LG
e
. . . . . . .
299
±
15
98
.
4
±
3
.
6
−
5
.
9
±
3
.
0
LG–CMB
d
. . . . . .
620
±
15
271
.
9
±
2
.
0
29
.
6
±
1
.
4
a
Velocity of the Sun relative to the CMB;
Planck
2018.
b
Velocity of the Sun relative to the Local Standard of Rest
from Sch
̈
onrich et al. (2010), adding the statistical and systematic
uncertainties.
c
Rotational velocity of the LSR from McMillan (2011).
d
Resulting velocity, using non-relativistic velocity addition and assum-
ing uncorrelated errors.
e
Velocity of the Sun relative to the Local Group from Diaz et al.
(2014).
2.2. Frequency maps and their properties
The Low and High Frequency Instruments together contained
an array of 74 detectors in nine bands, covering frequencies be-
tween 25 and 1000 GHz, imaging the whole sky twice per year
with angular resolution between 33
′
and 5
′
. Table 4 gives the
main characteristics of the
Planck
frequency maps, including an-
gular resolution and sensitivity.
An extensive series of null tests for the consistency of
the maps is provided in Planck Collaboration XXXI (2014),
Planck Collaboration I (2016), Planck Collaboration II (2018),
and Planck Collaboration III (2018). We find impressive con-
sistency between the maps. Consistency of the absolute cali-
brations across the nine frequency channels is discussed exten-
sively in the same papers, and we discuss inter-instrument con-
sistency in Appendix C. Some considerations about the princi-
ples followed in the
Planck
analysis (including a discussion of
blinding) are given in Appendix D. For the main CMB chan-
nels (70–217 GHz) the inter-calibration is at the level of 0.2 %
(Planck Collaboration I 2016). At 143 GHz the absolute photo-
metric calibration is an astounding 0
.
02 %, though it applies only
to the largest angular scales. For the HFI polarization maps, the
largest source of uncertainty is the polarization e
ffi
ciency (Table
4).
The beams are estimated from planetary observations and
the polarized beam models are combined with the specific scan-
ning strategy to generate “e
ff
ective beams,” which describe
the relation of maps to the sky (see Planck Collaboration IV
2016; Planck Collaboration VII 2016). The response in har-
monic space is known as a window function, and both the mean
windows and the major error eigenmodes are provided as part of
the legacy archive (PLA). Typical uncertainties are well below
0.1 % for the main CMB channels.
Figures 1 and 2 show views of the sky as seen by
Planck
in intensity and polarization. Note that
Planck
uses
HEALPix
(G
́
orski et al. 2005) as its pixelization scheme, with resolution
labelled by the
N
side
value.
6
Each panel in Fig. 1 shows the in-
tensity in one of
Planck
’s nine frequency channels, in Galactic
coordinates. In all cases the figures are unable to convey both
the angular resolution and the dynamic range of the
Planck
data.
However, they serve to show the major features of the maps and
the numerous astrophysical components that contribute to the
signal. Similarly, Fig. 2 shows the polarization properties mea-
sured by
Planck
at seven frequencies.
The most prominent feature in the maps is the Galactic plane,
steadily brightening to both higher (where Galactic dust domi-
nates the emission at low latitudes) and lower frequency (where
synchrotron and free-free emission dominate). At high Galactic
latitudes, and over much of the sky between 70 and 217 GHz, the
signal is dominated by the “primary” CMB anisotropies, which
were frozen in at the surface of last scattering and provide the
main information for constraining our cosmological model.
To be more quantitative, it is useful to introduce two-point
statistics, in the form of a two-point angular correlation func-
tion, or its harmonic-space counterpart, the angular power spec-
trum. We follow the usual convention and perform an harmonic
decomposition of the sky maps. If
T
,
Q
, and
U
represent the in-
tensity and polarization
7
Stokes parameters (in thermodynamic
temperature units) then we define
a
`
m
=
∫
d
ˆ
n
Y
∗
`
m
(
ˆ
n
)
T
(
ˆ
n
)
,
(1)
a
E
`
m
±
ia
B
`
m
=
∫
d
ˆ
n
∗
±
2
Y
∗
`
m
(
ˆ
n
)
(
Q
±
iU
)
(
ˆ
n
)
,
(2)
where
±
2
Y
`
m
are the spin-spherical harmonics, which are pro-
portional to Wigner
D
-functions. The polarization is defined
through the scalar
E
and pseudo-scalar
B
fields, which are non-
local, linear combinations of
Q
and
U
(Zaldarriaga & Seljak
1997; Kamionkowski et al. 1997; Hu & White 1997; Dodelson
2003). For small patches of sky
E
and
B
are simply
Q
and
U
in
the coordinate system defined by the Fourier transform coordi-
nate
`
(Seljak 1997). Alternatively, near a maximum of the polar-
ization the direction of greatest change for an
E
mode is parallel
or perpendicular to the polarization direction (see Fig. 7).
When statistical isotropy may be assumed, it demands that
〈
a
∗
`
m
a
`
′
m
′
〉
be diagonal and depend only on
`
. We write
〈
a
T
∗
`
m
a
T
`
′
m
′
〉
=
C
TT
`
δ
`
′
`
δ
m
′
m
(3)
6
In
HEALPix
the sphere is divided into 12
N
2
side
pixels. At
N
side
=
2048, typical of
Planck
maps, their mean spacing is 1.7
′
.
7
Planck
uses the “COSMO” convention for polarization (cor-
responding to the FITS keyword “POLCCONV”), which di
ff
ers
from the IAU convention often adopted for astrophysical data sets
(Planck Collaboration ES 2018).
7
Planck Collaboration: The cosmological legacy of
Planck
Table 4.
Main characteristics of
Planck
frequency maps.
Frequency [GHz]
Property
30
44
70
100
143
217
353
545
857
Frequency [GHz]
a
. . . . . . . . . . . . . . . . . . . . . . .
28.4
44.1
70.4
100
143
217
353
545
857
E
ff
ective beam FWHM [arcmin]
b
. . . . . . . . . . . . . .
32.29
27.94
13.08
9.66
7.22
4.90
4.92
4.67
4.22
Temperature Sensitivity [
μ
K
CMB
deg]
c
. . . . . . . . . . .
2.5
2.7
3.5
1.29
0.55
0.78
2.56
[kJy sr
−
1
deg]
c
. . . . . . . . . .
0.78
0.72
Polarization Sensitivity [
μ
K
CMB
deg]
c
. . . . . . . . . . .
3.5
4.0
5.0
1.96
1.17
1.75
7.31
Dipole-based calibration uncertainty [%]
d
. . . . . . . .
0.17
0.12
0.20
0.008
0.021
0.028
0.024
∼
1
Planet submm inter-calibration accuracy [%]
e
. . . . . .
...
...
...
...
...
...
...
...
∼
3
Temperature transfer function uncertainty [%]
f
. . . . .
0.25
0.11
Ref.
Ref.
0.12
0.36
0.78
4.3
Polarization calibration uncertainty [%]
g
. . . . . . . . .
<
0
.
01 %
<
0
.
01 %
<
0
.
01 %
1.0
1.0
1.0
...
...
...
Zodiacal emission monopole level [
μ
K
CMB
]
h
. . . . . .
0
0
0
0.43
0.94
3.8
34.0
...
...
[MJy sr
−
1
]
h
. . . . .
...
...
...
...
...
...
...
0.04
0.12
LFI zero level uncertainty [
μ
K
CMB
]
i
. . . . . . . . . . . .
±
0
.
7
±
0
.
7
±
0
.
6
...
...
...
...
...
...
HFI Galactic emission zero level uncertainty [MJy sr
−
1
]
j
...
...
...
±
0
.
0008
±
0
.
0010
±
0
.
0024
±
0
.
0067
±
0
.
0165
±
0
.
0147
HFI CIB monopole assumption [MJy sr
−
1
]
k
. . . . . . .
0
.
0030
0
.
0079
0.033
0.13
0.35
0.64
HFI CIB zero level uncertainty [MJy sr
−
1
]
l
. . . . . . . .
...
...
...
±
0
.
0031
±
0
.
0057
±
0
.
016
±
0
.
038
±
0
.
066
±
0
.
077
a
For LFI channels (30–70 GHz) this is the centre frequency. For HFI channels (100–857 GHz), it is a reference (identifier) frequency.
b
Mean FWHM of the elliptical Gaussian fit of the e
ff
ective beam.
c
Estimate of the noise in intensity or polarization scaled to 1
◦
assuming that the noise is white. These levels are unchanged from 2015.
d
Absolute calibration accuracy obtained using the measurement of the Solar dipole at
`
=
1.
e
The 857-GHz channel retains the 2015 planet calibration, and the accuracy is calculated a posteriori using a model of planet emission (Planck Collaboration LII
2017) and the 545-GHz data.
f
For LFI this is the ratio of 30- and 44-GHz half-ring cross-spectra in the range
`
'
50–850 to that of the 70-GHz cross-spectrum. For HFI it is the upper limit
derived from the levels of the first three CMB acoustic peaks (
`
'
15–1000), relative to the 100 GHz channel.
g
Additional calibration uncertainty applicable to
Q
and
U
only. For LFI, the additional uncertainty (based on simulations) is negligible. For HFI, the dominant
inaccuracy is the knowledge of the polarization e
ffi
ciency, which is currently derived from the relative levels of the first three CMB acoustic peaks (
`
'
15–1000),
in combination with a prediction of the best-fit
TT
-based cosmology. The best estimates (Planck Collaboration III 2018) indicate that a bias should be applied to
the maps of 0.7,
−
1.7, and 1.9 %, at 100, 143, and 217 GHz, respectively, with an uncertainty as indicated in this table.
h
Average contribution of the zodiacal emission to the monopole. As the level of this emission is dependent on the time of observation, it has been removed from the
frequency maps during processing.
i
Estimated uncertainty in the zero levels that are associated with Galactic emission. The zero levels were set by fitting a a model of Galactic emission that varies as
the cosecant of the latitude to the maps after CMB subtraction. The levels subtracted were 11.9,
−
15.4, and
−
35.7
μ
K
CMB
at 30, 44, and 70 GHz, respectively.
j
The zero levels of the HFI maps are set by correlating the Galactic emission component to a map of the di
ff
use H
i
column density, as in Planck Collaboration VIII
(2014). The uncertainties in the estimated zero levels are unchanged since 2013.
k
Once the Galactic zero level has been set, the monopole of the B
́
ethermin et al (2012) CIB model has been added to the frequency maps.
l
The estimated uncertainty of the CIB monopole that has been added to the maps.
and similarly for
TE
,
EE
,
BB
, etc. We will find it convenient to
define
D
XY
`
=
`
(
`
+
1)
C
XY
`
2
π
,
(4)
which we will often refer to as the angular power spectrum. It is
useful to note that an auto-spectrum,
D
XX
`
indicates the approxi-
mate contribution per logarithmic interval of multipoles centred
on
`
to the variance of the fluctuation, i.e., the 2-point correlation
function at zero lag. It thus captures the relative importance of
various contributions to the signal as a function of scale.
Figure 3 shows the estimated levels of CMB and residual
systematics in frequency maps as a function of scale. The plots
show the
E
-mode power spectra,
D
EE
`
, for all core CMB chan-
nels at 70, 100, 143, and 217 GHz, and at the adjacent 30- and
350-GHz channels, which are of particular use for understand-
ing foregrounds. At the largest scales, the residual systematics
are comparable to the noise level, which is itself close to the
low level of the reionization bump determined by
Planck
(see
Sect. 6.6). This points to the great challenge of this measure-
ment. At small scales, residual systematic e
ff
ects are signifi-
cantly smaller than the signal and the noise in the main CMB
channels. This figure is actually the summary of most of the
data-processing work by the
Planck
collaboration, in the sense
that it embodies the final quantitative understanding of the mea-
surements and their processing. This determines what has to be
included in faithful end-to-end simulations.
The all-sky, fully calibrated maps of sky intensity and polar-
ization, shown in Figs. 1 and 2, together with their detailed in-
strumental characterization and simulations, are the main legacy
of the
Planck
mission and will be a resource to multiple commu-
nities for addressing numerous science questions in decades to
come. In the next few sections we discuss the separation of the
maps into their physical components and then the cosmological
consequences that can be derived from the CMB anisotropies.
2.3. Component separation
In addition to the primary anisotropies that are the main focus
of the
Planck
mission, the sky emission contains many other
astrophysical components, which di
ff
er by their dependence on
frequency as well as their spatial properties. By making mea-
surements at multiple frequencies, spanning the peak of the
CMB black-body spectrum, we are able to characterize the fore-
grounds and reduce their contamination of the primary CMB
anisotropies to unprecedented levels.
In order to separate the maps into their contributing sig-
nals and to clean the CMB map from foregrounds, we have
used four di
ff
erent approaches, as we did in earlier re-
leases (Planck Collaboration XII 2014; Planck Collaboration IX
8