A&A 641, A1 (2020)
https:
//
doi.org
/
10.1051
/
0004-6361
/
201833880
c
©
ESO 2020
Astronomy
&
Astrophysics
Planck 2018 results
Special issue
Planck
2018 results
I. Overview and the cosmological legacy of
Planck
Planck Collaboration: N. Aghanim
56
, Y. Akrami
59 ,61
, F. Arroja
63
, M. Ashdown
69 ,5
, J. Aumont
98
, C. Baccigalupi
79
, M. Ballardini
22 ,42
,
A. J. Banday
98 ,8
, R. B. Barreiro
64
, N. Bartolo
31 ,65
, S. Basak
86
, R. Battye
67
, K. Benabed
57 ,96
, J.-P. Bernard
98 ,8
, M. Bersanelli
34 ,46
,
P. Bielewicz
78 ,8 ,79
, J. J. Bock
66 ,10
, J. R. Bond
7
, J. Borrill
12 ,94
, F. R. Bouchet
57 ,91,
?
, F. Boulanger
90 ,56 ,57
, M. Bucher
2 ,6
, C. Burigana
45 ,32 ,48
,
R. C. Butler
42
, E. Calabrese
83
, 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
71
, D. Contreras
21
, B. P. Crill
66 ,10
, F. Cuttaia
42
, P. de Bernardis
33
, G. de Zotti
43 ,79
, J. Delabrouille
2
, J.-M. Delouis
57 ,96
, F.-X. Désert
97
,
E. Di Valentino
67
, C. Dickinson
67
, J. M. Diego
64
, S. Donzelli
46 ,34
, O. Doré
66 ,10
, M. Douspis
56
, A. Ducout
70
, X. Dupac
37
, G. Efstathiou
69 ,60
,
F. Elsner
75
, T. A. Enßlin
75
, H. K. Eriksen
61
, E. Falgarone
90
, 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
88
, S. Galeotta
44
, S. Galli
68
, K. Ganga
2
, R. T. Génova-Santos
62 ,15
, M. Gerbino
95
,
T. Ghosh
82 ,9
, J. González-Nuevo
16
, K. M. Górski
66 ,101
, S. Gratton
69 ,60
, A. Gruppuso
42 ,48
, J. E. Gudmundsson
95 ,26
, J. Hamann
87
, W. Handley
69 ,5
,
F. K. Hansen
61
, G. Helou
10
, D. Herranz
64
, S. R. Hildebrandt
66 ,10
, E. Hivon
57 ,96
, Z. Huang
84
, A. H. Ja
ff
e
54
, W. C. Jones
26
, A. Karakci
61
,
E. Keihänen
25
, R. Keskitalo
12
, K. Kiiveri
25 ,41
, J. Kim
75
, T. S. Kisner
73
, L. Knox
28
, N. Krachmalnico
ff
79
, M. Kunz
14 ,56 ,3
, H. Kurki-Suonio
25 ,41
,
G. Lagache
4
, J.-M. Lamarre
90
, 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
90
, A. Lewis
24
, M. Liguori
31 ,65
, P. B. Lilje
61
, M. Lilley
57 ,91
, V. Lindholm
25 ,41
, M. López-Caniego
37
, P. M. Lubin
29
, Y.-Z. Ma
67 ,81 ,77
,
J. F. Macías-Pérez
71
, 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
,
M. Martinelli
99
, E. Martínez-González
64
, S. Matarrese
31 ,65 ,39
, N. Mauri
48
, J. D. McEwen
76
, P. D. Meerburg
69 ,11 ,100
, P. R. Meinhold
29
,
A. Melchiorri
33 ,51
, A. Mennella
34 ,46
, M. Migliaccio
93 ,52
, M. Millea
28 ,89 ,57
, S. Mitra
53 ,66
, M.-A. Miville-Deschênes
1 ,56
, D. Molinari
32 ,42 ,49
,
A. Moneti
57
, L. Montier
98 ,8
, G. Morgante
42
, A. Moss
85
, S. Mottet
57 ,91
, M. Münchmeyer
57
, P. Natoli
32 ,93 ,49
, H. U. Nørgaard-Nielsen
13
,
C. A. Oxborrow
13
, L. Pagano
56 ,90
, 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
79
,
V. Pettorino
1
, F. Piacentini
33
, L. Polastri
32 ,49
, G. Polenta
93
, J.-L. Puget
56 ,57
, J. P. Rachen
18
, M. Reinecke
75
, M. Remazeilles
67
, C. Renault
71
,
A. Renzi
65
, G. Rocha
66 ,10
, C. Rosset
2
, G. Roudier
2 ,90 ,66
, J. A. Rubiño-Martín
62 ,15
, B. Ruiz-Granados
62 ,15
, L. Salvati
56
, M. Sandri
42
,
M. Savelainen
25 ,41 ,74
, D. Scott
21
, E. P. S. Shellard
11
, M. Shiraishi
31 ,65 ,19
, C. Sirignano
31 ,65
, G. Sirri
48
, L. D. Spencer
83
, R. Sunyaev
75 ,92
,
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
72
, L. Vibert
56 ,57
, P. Vielva
64
, F. Villa
42
, N. Vittorio
36
, B. D. Wandelt
57 ,96 ,30
, I. K. Wehus
66 ,61
, M. White
27,
?
,
S. D. M. White
75
, A. Zacchei
44
, and A. Zonca
80
(A
ffi
liations can be found after the references)
Received 16 July 2018
/
Accepted 27 September 2019
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
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
?
Corresponding authors: F. R. Bouchet, e-mail:
bouchet@iap.fr
;
M. White, e-mail:
mwhite@berkeley.edu
1
Planck
(
http://www.esa.int/Planck
) is a project of the Euro-
pean Space Agency (ESA) with instruments provided by two scientific
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 scientific con-
sortium led and funded by Denmark.
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 blackbody 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). This limits the
properties of decaying or annihilating particles, primordial black
holes, topological defects, primordial magnetic fields, and other
Article published by EDP Sciences
A1, page 1 of 56
A&A 641, A1 (2020)
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 Cosmic
Background Explorer (COBE) satellite (Smoot et al. 1992), pro-
vide numerous, strong tests of the cosmological paradigm and
the current best measurements on most of the parameters of our
cosmological model (Planck Collaboration XVI 2014; Planck
Collaboration XIII 2016; Planck Collaboration IV 2020). The
COBE detection cemented 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; Macías-Pérez
et al. 2007) established that the Universe has no significant spa-
tial curvature (Knox & Page 2000; Pierpaoli et al. 2000). The
Wilkinson
Microwave Anisotropy Probe (WMAP) showed that
the fluctuations are predominantly adiabatic (Kogut et al. 2003;
from the phasing of the peaks and polarization) and provided
multiple, simultaneous, tight constraints on cosmological param-
eters (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 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 (see Tauber et al. 2010). For
an overview of the scientific operations of the
Planck
mis-
sion see Planck Collaboration I (2014) and the Explanatory
Supplement (Planck Collaboration 2015, 2018). The first set
of scientific data, the Early Release Compact Source Cata-
logue (ERCSC; Planck Collaboration VII 2011), was released
in January 2011. A set of 26 papers related to astrophysical
foregrounds was published in another special issue of Astron-
omy and Astrophysics (see Planck Collaboration I 2011). The
first cosmological results from
Planck
, based mainly on tem-
perature maps of the whole sky acquired during the nominal
mission duration of 15.5 months, were reported in 2013 and
the data products made available (as “PR1”) on the
Planck
Legacy Archive (PLA
2
). These cosmological results were pub-
lished as a series along with further data-processing and astro-
physics papers in 2014 (see Planck Collaboration I 2014). The
first results from the full mission, including some polariza-
tion data, were presented 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, that is, we consider the cosmological legacy of
Planck
. After
a broad overview of the useful products derived from
Planck
data, from the maps at nine frequencies to astrophysical compo-
nents and their broad characterization (specifics of this release are
detailed in Appendix A), we discuss the CMB anisotropies, which
2
http://pla.esac.esa.int
Table 1.
Important milestones in the
Planck
mission.
Date
Milestone
Nov. 1992 . . . . . . .
ESA call for M3 (of Horizon 2000 programme)
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 Liège
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)
were the main focus of the
Planck
mission. We then turn to a com-
parison of our results to theoretical models, and the way in which
the
Planck
data confirm and inform those models, before com-
paring to a wider range of astrophysical and cosmological data.
A discussion of how
Planck
has placed constraints on models
of the early and late Universe and the relationship of the
Planck
data to other cosmological probes precedes a discussion of the
A1, page 2 of 56
Planck Collaboration:
Planck
2018 results. I.
post-
Planck
landscape, and finally our conclusions. In appen-
dices, we include some details of this release, and a more detailed
discussion of improvements in the data processing between the
2015 and 2018 releases.
2. The sky according to
Planck
Details about the
Planck
mission and its scientific payload
and performance have been discussed in previous publications
(Planck Collaboration I 2014; Planck Collaboration I 2016, and
references therein).
Planck
was the first submillimetre mission
to map the entire sky to sub-Jansky sensitivity with angular res-
olution better than 10
′
. In this section we describe the calibration
and main properties of the frequency maps (Figs. 1 and 2), and
the methods used to separate the sky emission into di
ff
erent com-
ponents. We briefly describe the main foreground components
before discussing the CMB anisotropies, whose characterization
was the main goal of the
Planck
mission.
2.1. The Solar dipole
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”, that
is, 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 pre-
dicted orbital dipole is ultimately limited by the accuracy with
which we know the temperature of the CMB. In the 2015 data
release, photometric calibration from 30 to 353 GHz was based
on the “orbital dipole”. This allowed us to measure the ampli-
tude 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 mea-
sured in 2015 were significantly more accurate than the previous
best measurements provided by WMAP (see Table 2). However,
comparison of individual detector 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 direction showed shifts with posi-
tion in the focal plane for LFI; for HFI the shifts were associ-
ated with frequency, as well as with the Galactic mask and the
component-separation method used, indicating 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 also in the accuracy of photometric calibra-
tion. Furthermore, the HFI dust foreground e
ff
ect was identified
with large-scale (mostly quadrupolar) spectral energy distribu-
tion changes. Correcting these brought full consistency between
frequencies, as well as for detectors within each frequency band.
This has resulted in dramatic improvement in the determina-
tion of the 2018 Solar dipole parameters, which are presented
in Table 2. The independent LFI and HFI measurements are
fully consistent with each other and with those of WMAP,
and, as described in Planck Collaboration II (2020) and Planck
Collaboration III (2020), 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 statis-
tical). Considering that the uncertainties in the HFI determina-
tion are much lower than those of LFI, we recommend that users
adopt the HFI determination of the Solar dipole as the most accu-
rate one available from
Planck
.
In the 2018 maps, the 2015 “nominal” Solar dipole, which
is slightly di
ff
erent than the final best dipole, has been sub-
tracted. (The induced quadrupole has also been subtracted from
the maps.) This was done in order to produce a consistent data
set that is independent of the best determination of the dipole
parameters, which was made at a later time separately at each
individual frequency. This implies that a very small, residual
Solar dipole is present in all released maps. This can be removed
if desired using the procedure described in Planck Collaboration
III (2020).
The Solar dipole can still be measured with high signal-
to-noise ratio at 545 GHz. The 545 GHz data were not calibrated
on the orbital dipole, however, but instead on observations of
Uranus and Neptune (Planck Collaboration III 2020). Therefore
the photometric accuracy of this calibration is limited by that of
the physical emission model of the planets, to a level of approx-
imately 5%. However, the dispersion of the Solar dipole ampli-
tude measured in individual 545 GHz detector maps is within 1%
of that at lower frequencies. This implies that, in actual fact, the
planet model can be calibrated on this measurement more pre-
cisely than has been assumed so far (Planck Collaboration Int.
LII 2017). It also means that an improved model can be extended
to recalibrate the 857 GHz channel. 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
(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 added in the systematic uncertainties linearly.
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
relative to the CMB, due to the roughly anti-coincident direc-
tion 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 centre 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 summarize more modern determinations in Table 3.
Firstly, we take the estimate of the Sun’s motion relative
to the Local Standard of Rest from Schönrich et al. (2010),
A1, page 3 of 56
A&A 641, A1 (2020)
Fig. 1.
Fluctuations of sky emission in each of 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.
A1, page 4 of 56
Planck Collaboration:
Planck
2018 results. I.
Fig. 2.
Sky polarization in seven polarized frequency bands of
Planck
. The
first two columns
show the
Q
and
U
Stokes parameters; the
last column
indicates the polarized intensity,
P
=
√
Q
2
+
U
2
(although 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.
A1, page 5 of 56
A&A 641, A1 (2020)
Table 2.
COBE, WMAP, LFI, HFI, and combined
Planck
measurements of the Solar dipole.
Galactic coordinates
Experiment
Amplitude [
μ
K
CMB
]
l
[deg]
b
[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
Notes.
The uncertainties are dominated by systematic e
ff
ects, whose assessment is discussed in Planck Collaboration II (2020) and Planck
Collaboration III (2020).
(
a
)
Kogut et al. (1993), Lineweaver et al. (1996); we have added statistical and systematic uncertainty estimates
linearly.
(
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 added statistical and systematic
errors linearly.
(
e
)
The current best
Planck
determination of the dipole is that of HFI (Planck Collaboration III 2020). 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 (2020). The uncertainty on the amplitude does not include the 0.02% uncertainty on
the temperature of the CMB monopole.
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
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 relative
to the centre of the Local Group from Diaz et al. (2014), found
by averaging velocities of members galaxies (as also perfor-
med by several other studies, e.g., Yahil et al. 1977; Courteau &
van den Bergh 1999; Mikulizky 2015). This vector can be sub-
tracted 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 degrees) that lies about
30
◦
above the Galactic plane and is nearly opposite in latitude to
the direction of Galactic rotation. The uncertainty in the Local
Group’s speed relative to the CMB is almost entirely due to the
uncertainty in the speed of the Sun relative to the centre-of-mass
of the Local Group.
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
between 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
angular 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 (2020),
and Planck Collaboration III (2020). We find impressive con-
sistency between the maps. Consistency of absolute calibration
across the nine frequency channels is discussed extensively in
the same papers, and we discuss inter-instrument consistency
in Appendix C. Some considerations about the principles fol-
lowed in the
Planck
analysis (including a discussion of blind-
ing) are given in Appendix D. For the main CMB channels
(70–217 GHz) the inter-calibration is at the level of 0.2% (Planck
Collaboration I 2016). At 100 GHz, the absolute photometric
calibration on large scales is an astounding 0
.
008%. For the HFI
Table 3.
Relative velocities involving the CMB frame, the Galactic cen-
tre, 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
Notes.
(
a
)
Velocity of the Sun relative to the CMB;
Planck
2018.
(
b
)
Velocity of the Sun relative to the Local Standard of Rest from
Schönrich et al. (2010), adding statistical and systematic uncertainties.
(
c
)
Rotational velocity of the LSR from McMillan (2011).
(
d
)
Resulting
velocity, using non-relativistic velocity addition and assuming uncorre-
lated errors.
(
e
)
Velocity of the Sun relative to the Local Group from Diaz
et al. (2014).
polarization maps, the largest source of uncertainty is the polar-
ization 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 harmonic space
is known as a window function, and both the mean windows and
the major error eigenmodes are provided in the 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.
Planck
uses
HEALPix
(Górski et al.
2005) as its pixelization scheme, with resolution labelled by the
N
side
value. In
HEALPix
the sphere is divided into 12
N
2
side
pix-
els. At
N
side
=
2048, typical of
Planck
maps, their mean spacing
is 1
′
.
7. Each panel in Fig. 1 shows the intensity 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
A1, page 6 of 56
Planck Collaboration:
Planck
2018 results. I.
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 noise level [
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 noise level [
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
Notes.
(
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
)
Estimates of noise in intensity and 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 Int. 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
T T
-based cosmology. The best
estimates (Planck Collaboration III 2020) 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 associated with Galactic emission. The zero levels were set by fitting 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 Béthermin 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.
the major features of the maps and the numerous astrophysi-
cal components that contribute to the signal. Similarly, Fig. 2
shows the polarization properties measured by
Planck
at seven
frequencies. The CMB component of the maps has a 6% linear
polarization, though the foregrounds exhibit di
ff
ering polariza-
tion levels as a function of frequency.
The most prominent feature in the maps is the Galactic plane,
steadily brightening to both higher (where Galactic dust dom-
inates the emission) and lower (where synchrotron and free-
free emission dominate) frequencies. 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 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
intensity and polarization
3
Stokes parameters (in thermody-
namic temperature units), then we define
a
`
m
=
∫
d
ˆ
n
Y
∗
`
m
(
ˆ
n
)
T
(
ˆ
n
)
,
(1)
3
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 2018).
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
4
. 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
T T
`
δ
`
′
`
δ
m
′
m
,
(3)
and similarly for
T E
,
EE
,
BB
, etc. We find it convenient to define
D
XY
`
=
`
(
`
+
1)
C
XY
`
2
π
,
(4)
which we will often refer to as the angular power spectrum. An
auto-spectrum,
D
XX
`
indicates the approximate contribution per
logarithmic interval of multipoles centred on
`
to the variance
of the fluctuation, that is, the 2-point correlation function at zero
lag. It thus captures the relative importance of various contribu-
tions to the signal as a function of scale.
4
See e.g.,
Wikipedia
.
A1, page 7 of 56