A&A 576, A104 (2015)
DOI:
10.1051
/
0004-6361
/
201424082
c
ESO 2015
Astronomy
&
Astrophysics
Planck
intermediate results. XIX. An overview of the polarized
thermal emission from Galactic dust
Planck Collaboration: P. A. R. Ade
78
, N. Aghanim
54
, D. Alina
83
,
10
,M.I.R.Alves
54
, C. Armitage-Caplan
81
,M.Arnaud
67
, D. Arzoumanian
54
,
M. Ashdown
64
,
6
, F. Atrio-Barandela
18
, J. Aumont
54
, C. Baccigalupi
77
,A.J.Banday
83
,
10
,R.B.Barreiro
61
, E. Battaner
85
,
86
, K. Benabed
55
,
82
,
A. Benoit-Lévy
24
,
55
,
82
,J.-P.Bernard
83
,
10
,
, M. Bersanelli
33
,
47
, P. Bielewicz
83
,
10
,
77
,J.J.Bock
62
,
11
,J.R.Bond
9
, J. Borrill
13
,
79
, F. R. Bouchet
55
,
82
,
F. Boulanger
54
, A. Bracco
54
,C.Burigana
46
,
31
,R.C.Butler
46
, J.-F. Cardoso
68
,
1
,
55
, A. Catalano
69
,
66
,A.Chamballu
67
,
15
,
54
, R.-R. Chary
53
,
H. C. Chiang
27
,
7
, P. R. Christensen
74
,
36
, S. Colombi
55
,
82
,L.P.L.Colombo
23
,
62
, C. Combet
69
, F. Couchot
65
,A.Coulais
66
,B.P.Crill
62
,
75
,
A. Curto
6
,
61
, F. Cuttaia
46
,L.Danese
77
,R.D.Davies
63
,R.J.Davis
63
,P.deBernardis
32
, E. M. de Gouveia Dal Pino
60
,A.deRosa
46
,
G. de Zotti
43
,
77
, J. Delabrouille
1
, F.-X. Désert
51
, C. Dickinson
63
,J.M.Diego
61
,S.Donzelli
47
,O.Doré
62
,
11
, M. Douspis
54
, J. Dunkley
81
,
X. Dupac
39
, G. Efstathiou
57
,T.A.Enßlin
72
,H.K.Eriksen
58
, E. Falgarone
66
, K. Ferrière
83
,
10
, F. Finelli
46
,
48
, O. Forni
83
,
10
, M. Frailis
45
,
A. A. Fraisse
27
, E. Franceschi
46
,S.Galeotta
45
, K. Ganga
1
, T. Ghosh
54
,M.Giard
85
,
10
, Y. Giraud-Héraud
1
, J. González-Nuevo
61
,
77
,
K. M. Górski
62
,
87
,A.Gregorio
34
,
45
,
50
, A. Gruppuso
46
, V. Guillet
54
,F.K.Hansen
58
,D.L.Harrison
57
,
64
,G.Helou
11
, C. Hernández-Monteagudo
12
,
72
,
S. R. Hildebrandt
11
,E.Hivon
55
,
82
, M. Hobson
6
,W.A.Holmes
62
, A. Hornstrup
16
,K.M.Hu
ff
enberger
25
,A.H.Ja
ff
e
52
,T.R.Ja
ff
e
83
,
10
,
W. C. Jones
27
,M.Juvela
26
,E.Keihänen
26
, R. Keskitalo
13
,T.S.Kisner
71
,R.Kneissl
38
,
8
, J. Knoche
72
, M. Kunz
17
,
54
,
3
, H. Kurki-Suonio
26
,
41
,
G. Lagache
54
, A. Lähteenmäki
2
,
41
, J.-M. Lamarre
66
,A.Lasenby
6
,
64
,C.R.Lawrence
62
, J. P. Leahy
63
,R.Leonardi
39
,F.Levrier
66
, M. Liguori
30
,
P. B. Lilje
58
, M. Linden-Vørnle
16
,M.López-Caniego
61
,P.M.Lubin
28
, J. F. Macías-Pérez
69
,B.Ma
ff
ei
63
, A. M. Magalhães
60
,D.Maino
33
,
47
,
N. Mandolesi
46
,
5
,
31
,M.Maris
45
,D.J.Marshall
67
,P.G.Martin
9
, E. Martínez-González
61
,S.Masi
32
,S.Matarrese
30
, P. Mazzotta
35
,
A. Melchiorri
32
,
49
,L.Mendes
39
,A.Mennella
33
,
47
, M. Migliaccio
57
,
64
, M.-A. Miville-Deschênes
54
,
9
,A.Moneti
55
,L.Montier
83
,
10
, G. Morgante
46
,
D. Mortlock
52
, D. Munshi
78
, J. A. Murphy
73
,P.Naselsky
74
,
36
,F.Nati
32
,P.Natoli
31
,
4
,
46
,C.B.Netterfield
20
, F. Noviello
63
, D. Novikov
52
,
I. Novikov
74
,C.A.Oxborrow
16
,L.Pagano
32
,
49
,F.Pajot
54
,R.Paladini
53
, D. Paoletti
46
,
48
,F.Pasian
45
,T.J.Pearson
11
,
53
, O. Perdereau
65
,
L. Perotto
69
,F.Perrotta
77
, F. Piacentini
32
,M.Piat
1
, D. Pietrobon
62
, S. Plaszczynski
65
, F. Poidevin
24
,
59
,
37
, E. Pointecouteau
83
,
10
,G.Polenta
4
,
44
,
L. Popa
56
,G.W.Pratt
67
,S.Prunet
55
,
82
, J.-L. Puget
54
, J. P. Rachen
21
,
72
, W. T. Reach
84
,R.Rebolo
59
,
14
,
37
, M. Reinecke
72
, M. Remazeilles
63
,
54
,
1
,
C. Renault
69
, S. Ricciardi
46
, T. Riller
72
, I. Ristorcelli
83
,
10
, G. Rocha
62
,
11
, C. Rosset
1
, G. Roudier
1
,
66
,
62
, J. A. Rubiño-Martín
59
,
37
, B. Rusholme
53
,
M. Sandri
46
,G.Savini
76
,D.Scott
22
,L.D.Spencer
78
, V. Stolyarov
6
,
64
,
80
, R. Stompor
1
, R. Sudiwala
78
, D. Sutton
57
,
64
, A.-S. Suur-Uski
26
,
41
,
J.-F. Sygnet
55
,J.A.Tauber
40
, L. Terenzi
46
,L.To
ff
olatti
19
,
61
,M.Tomasi
33
,
47
, M. Tristram
65
, M. Tucci
17
,
65
,G.Umana
42
, L. Valenziano
46
,
J. Valiviita
26
,
41
,B.VanTent
70
, P. Vielva
61
, F. Villa
46
,L.A.Wade
62
,B.D.Wandelt
55
,
82
,
29
, A. Zacchei
45
, and A. Zonca
28
(A
ffi
liations can be found after the references)
Received 28 April 2014
/
Accepted 30 January 2015
ABSTRACT
This paper presents an overview of the polarized sky as seen by
Planck
HFI at 353 GHz, which is the most sensitive
Planck
channel for dust
polarization. We construct and analyse maps of dust polarization fraction and polarization angle at 1
◦
resolution, taking into account noise bias
and possible systematic e
ff
ects. The sensitivity of the
Planck
HFI polarization measurements allows for the first time a mapping of Galactic
dust polarized emission on large scales, including low column density re
gions. We find that the maximum observed dust polarization fraction is
high (
p
max
=
19
.
8%), in particular in some regions of moderate hydrogen column density (
N
H
<
2
×
10
21
cm
−
2
). The polarization fraction displays
a large scatter at
N
H
below a few 10
21
cm
−
2
. There is a general decrease in the dust polariza
tion fraction with increasing column density above
N
H
1
×
10
21
cm
−
2
and in particular a sharp drop above
N
H
1
.
5
×
10
22
cm
−
2
. We characterize the spatial structure of the polarization angle using
the angle dispersion function. We find that the polarization angle is ordered over extended areas of several square degrees, separated by filamentary
structures of high angle dispersion function. These appear as interfaces where the sky projection of the magnetic field changes abruptly without
variations in the column density. The polarization fraction is found to be anti-correlated with the dispersion of polarization angles. These result
s
suggest that, at the resolution of 1
◦
, depolarization is due mainly to fluctuations in the magnetic field orientation along the line of sight, rather than
to the loss of grain alignment in shielded regions. We also compare the
polarization of thermal dust emission with that of synchrotron measured
with
Planck
, low-frequency radio data, and Faraday rotation measurements to
ward extragalactic sources. These components bear resemblance
along the Galactic plane and in some regions such as the Fan and North Polar Spur regions. The poor match observed in other regions shows,
however, that dust, cosmic-ray electrons, and thermal electrons generally sample di
ff
erent parts of the line of sight.
Key words.
ISM: general – dust, extinction – ISM: ma
gnetic fields – ISM: cl
ouds – subm
illimeter: ISM
Appendices are available in electronic form at
http://www.aanda.org
Corresponding author: J.-P. Bernard,
e-mail:
Jean-Philippe.Bernard@irap.omp.eu
1. Introduction
Our Galaxy is pervaded by an interstellar magnetic field of a
few microgauss, which fills the entire disk and halo. This mag-
netic field manifests itself in a variety of ways, including Zeeman
splitting of atomic and molecular spectral lines, Faraday rotation
of polarized radio signals, synchrotron emission from relativistic
Article published by EDP Sciences
A104, page 1 of
33
A&A 576, A104 (2015)
electrons, and polarization of starlight and thermal dust emis-
sion. With a pressure larger than the thermal pressure of all
phases and comparable to that of the cosmic rays (
Cox 2005
),
the Galactic magnetic field (GMF) plays a crucial role in the
ecosystem of our Galaxy. In conjunction with gravity, it governs
the structure and the dynamics of the interstellar medium (ISM),
regulates the process of star formation, accelerates cosmic rays,
and channels their trajectories to confine them to the Galaxy. In
addition to a large-scale regul
ar, or coherent, component and a
fluctuating component produced by interstellar turbulence (with
scales up to 100 pc; e.g.,
Gaensler & Johnston 1995
;
Haverkorn
et al. 2008
), the GMF also possesses an ordered random (e.g.,
Beck 2009
;
Ja
ff
e et al. 2010
), or striated random (
Jansson &
Farrar 2012a
), component, whose orientation remains nearly
constant over large scales, but whose strength and sign vary on
small scales. Such fields are probably produced through com-
pression or shearing of isotropic random fields by the Galactic
di
ff
erential rotation, or at large-scale spiral arm shocks, or else
by rising hot plasma bubbles.
Our knowledge and understanding of the GMF has improved
considerably over the past few years, as a result of both progress
in the quality (sensitivity and resolution) of radio observations
and extensive modelling e
ff
orts (e.g.,
Sun et al. 2008
;
Sun &
Reich 2010
;
Ruiz-Granados et al. 2010
;
Ja
ff
e et al. 2010
,
2011
;
Pshirkov et al. 2011
;
Fauvet et al. 2012
,
2013
;
Jansson & Farrar
2012a
,
b
). However, the existing radio observations have inher-
ent limitations, as both Faraday rotation measures (RMs) and
synchrotron (total and polarized) intensities are quantities inte-
grated over the line of sight (LOS), which depend on the poorly
constrained density distributions of thermal and relativistic elec-
trons, respectively. A promising avenue to obtain a more com-
plete and more robust picture of the GMF structure is to comple-
ment the radio data with
Planck
1
measurements of the polarized
thermal emission from interstellar dust, which is independent of
the electron densities.
A glance at the
Planck
all-sky intensity maps (
Planck
Collaboration I 2014
) reveals that, in addition to the mottled
structure of the cosmic microwave background (CMB) at high
Galactic latitudes, the dominant pattern is that of the emission
from our Galaxy. At the lowest frequencies, from the 30 GHz to
70 GHz bands of the
Planck
Low Frequency Instrument (LFI,
Bersanelli et al. 2010
), synchrotron emission dominates; at the
highest frequencies, from the 217 GHz to 857 GHz bands of the
High Frequency Instrument (HFI,
Lamarre et al. 2010
), thermal
emission from interstellar dust is the dominant emission. These
foregrounds have to be understood and taken into account for
detailed CMB studies, but they also provide a unique opportunity
to study the Galaxy’s ISM.
In particular, the thermal dust emission is linearly polar-
ized (e.g.,
Benoît et al. 2004
;
Vaillancourt 2007
). This polarized
emission overpowers any other polarized signal at the higher
Planck
frequencies (e.g.,
Tucci et al. 2005
;
Dunkley et al. 2009
;
Fraisse et al. 2009
). In addition to hindering the detection of
the sought-after, odd-parity,
B
-mode polarization of the CMB
(
Planck Collaboration Int. XXX 2015
), the polarized dust emis-
sion provides, in combination with the emission spectrum itself,
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
scientific consortium led and funded by Denmark.
a powerful constraint on the physical properties of the dust and
on the structure of the magnetic field in the Galaxy.
The linear polarization of the thermal dust emission arises
from a combination of two main factors. Firstly, a fraction of
the dust grain population is non-spherical, and this gives rise to
di
ff
erent emissivities for radiation with the electric vector paral-
lel or orthogonal to a grain’s longest axis. Secondly, the grains
are aligned by the interstellar m
agnetic field because they are
rotating, probably with di
ff
ering e
ffi
ciencies depending on grain
size and composition (
Draine & Fraisse 2009
). While the details
of this process remain unclear (
Lazarian 2003
,
2007
), there is
a consensus that the angular momentum of a grain spun up by
photon-grain interactions (
Dolginov & Mitrofanov 1976
;
Draine
& Weingartner 1996
,
1997
;
Lazarian & Hoang 2007
;
Hoang &
Lazarian 2008
) becomes aligned with the grain’s shortest axis,
and then with the magnetic field via precession (e.g.,
Martin
1971
). The end result is that, if we look across magnetic field
lines, the rotating grain has its long axis orthogonal to the field
lines, and accordingly dust emission is linearly polarized with its
electric vector normal to the sky-projected magnetic field
2
.
A related phenomenon occurs at near-UV
/
optical
/
NIR wave-
lengths (e.g.,
Martin 2007
), where the light from background
sources becomes linearly polarized as a result of dichroic ex-
tinction by the aligned dust grains (
Davis & Greenstein 1951
).
Because extinction is higher for light vibrating parallel to the
grain’s longest axis, i.e., perpendicular to the field lines, the
transmitted light is linearly polarized with its electric vector par-
allel to the sky-projected magnetic field. In fact, historically, the
optical polarization caused by dust extinction led to the predic-
tion that thermal dust emission would be polarized in the mil-
limetre and submillimetre domains (
Stein 1966
). The predicted
orthogonality of the el
ectric vectors in the optical and submil-
limetre on the same line of sight has been demonstrated (
Planck
Collaboration Int. XXI 2015
).
Thus, polarized thermal dust emission carries important in-
formation on the interstellar magnetic field structure, on the
grain alignment mechanisms, and
on the grain geometrical and
physical properties. For example, polarization observations be-
tween 300
μ
m and 3 mm, essentially the domain of the
Planck
HFI instrument, can potentially discriminate between the po-
larizing grain materials, e.g.,
silicate and graphite dust versus
silicate-only grains (
Martin 2007
;
Draine & Fraisse 2009
;
Planck
Collaboration Int. XXI 2015
;
Planck Collaboration Int. XXII
2015
).
The far-IR dust thermal emission being a tracer of the dust
mass along the LOS, sensitivity limits explain why detailed dust
polarized emission was observed mostly in fairly dense, massive
regions of the ISM (
Dotson et al. 2000
;
Curran & Chrysostomou
2007
;
Matthews et al. 2009
;
Dotson et al. 2010
), in general
close to the Galactic plane. Measurements of the more di
ff
use
medium were obtained at relatively low (
2
◦
) angular resolution.
At these large scales, the Archeops balloon experiment (
Benoît
et al. 2004
;
Ponthieu et al. 2005
) detected the thermal dust
emission polarization at 353 GHz. The highest frequency chan-
nel of WMAP (
Page et al. 2007
;
Bennett et al. 2013
), 94 GHz,
picked up the long-wavelength Rayleigh-Jeans tail of the di
ff
use
dust emission and its polarization (in addition to synchrotron
emission).
2
Note that Faraday rotation is unimportant at the frequency consid-
ered here (353 GHz). Even an RM of up to
∼
1000 [rad
/
m
2
] through the
Galactic plane (see, e.g.,
Van Eck et al. 2011
) results in a rotation of the
polarization direction less than a tenth of a degree.
A104, page 2 of
33
Planck Collaboration: The
Planck
dust polarization sky
The
Planck
satellite’s HFI instrument has led to the first all-
sky survey of the polarized submillimetre and millimetre sky,
where thermal dust emission dominates. At 353 GHz, the
Planck
data have an angular resolution of 5
. The polarization sensi-
tivity was expected to be such that, at a resolution of 15
,ISM
structures with
A
V
=
1 mag would be detected with a relative
uncertainty on the polarization fraction of about 40% and an un-
certainty on the polarization angle of about 30
◦
(
Pelkonen et al.
2009
). These figures improve significantly at higher
A
V
and
/
or
lower resolution. The polarized
Planck
data bring the first all-
sky fully sampled map of the polarized emission from dust. As
such, they provide unprecedented information on the magnetic
field geometry and the dust polarization properties relevant to the
disk of the Milky Way (MW) and star forming regions, for which
they provide statistical information that is missing in stellar po-
larization extinction data. It should be emphasized, however, that
the dust polarized emission provides information mostly on the
orientation of the sky-projected magnetic field and only very in-
direct indication about the angle of that field with respect to the
plane of the sky, and it is expected to be insensitive to the field
strength.
This paper presents a subset of the
Planck
polarization data
and their large-scale statistical properties. A companion paper
(
Planck Collaboration Int. XX 2015
) analyses the variations
of the polarization fraction and angle described here, in the
framework of simulations of anisotropic magneto-hydrodynamic
(MHD) turbulence. Two other papers provide a detailed analy-
sis of the wavelength dependence of the dust polarization, as
seen by the HFI instrument (
Planck Collaboration Int. XXII
2015
) and a comparison between the dust polarization at visible
and submillimetre wavelengths (
Planck Collaboration Int. XXI
2015
).
In Sect.
2
we describe the data, including discussion of sys-
tematic e
ff
ects and the e
ff
ects of the CMB intensity and polar-
ization. Maps are presented in Sect.
3
, as well as the statistics
of the data. Sect.
4
discusses the implications of the 353 GHz
polarimetry for our understanding of the GMF structure, and
the conclusions are drawn in Sect.
5
. Three appendices discuss
the smoothing of the noise covari
ance matrices, which is needed
when the original data are averaged, the debiasing methods for
obtaining polarization estimates, and tests for the e
ff
ects of sys-
tematic noise bias on the structures that we observe in maps of
the polarization angle dispersion function.
2. Data
The
Planck
mission results are presented in
Planck
Collaboration I
(
2014
) and the in-flight performance of the two
focal plane instruments, the High Frequency Instrument (HFI)
and the Low Frequency Instrument (LFI), are given in
Planck
HFI Core Team
(
2011
)and
Mennella et al.
(
2011
), respectively.
The data processing and calibration of the HFI data used
here are described in
Planck Collaboration VI
(
2014
),
Planck
Collaboration VII
(
2014
),
Planck Collaboration VIII
(
2014
),
Planck Collaboration IX
(
2014
)and
Planck Collaboration X
(
2014
). The data processing and calibration of the LFI data
are described in
Planck Collaboration II
(
2014
),
Planck
Collaboration III
(
2014
),
Planck Collaboration IV
(
2014
), and
Planck Collaboration V
(
2014
).
The
Planck
polarization and total intensity data that we use
in this analysis have been generated in exactly the same man-
ner as the data publicly released in March 2013 and described in
Planck Collaboration I
(
2014
) and associated papers. Note how-
ever that the publicly available data include only temperature
maps based on the first two surveys.
Planck Collaboration XVI
(
2014
) shows the very good consistency of cosmological models
derived solely from total intensity with polarization data at small
scale (high CMB multipoles). However, as detailed in
Planck
Collaboration VI
(
2014
; see their Fig. 27), the 2013 polarization
data are known to be a
ff
ected by systematic e
ff
ects at low multi-
poles which were not yet fully corrected, and thus, not used for
cosmology. We have been careful to check that the Galactic sci-
ence results in this paper are robust with respect to these system-
atics. The error-bars we quote include uncertainties associated
with residual systematics as estimated by repeating the analysis
on di
ff
erent subsets of the data. We have also checked our data
analysis on the latest version of the maps available to the collab-
oration, to check that the results we find are consistent within the
error-bars quoted in this paper.
The maps used include data from five independent consec-
utive sky surveys (called Survey1-Survey5) for HFI, taken six
months apart. Due to the scanning strategy of the
Planck
mis-
sion, surveys taken one year apart (i.e., odd surveys 1 and 3 and
even surveys 2 and 4) share the same observing pattern, which is
di
ff
erent for even and odd surveys. Survey5 had a di
ff
erent scan
pattern from the other odd-numbered surveys, owing to a change
in the precession phase. The products also include data binned
into the first and second halves of the
Planck
stable pointing pe-
riods, or “half-rings” (called HR1 and HR2). Both single-survey
and half-ring data are used for consistency checks and to assess
the level of systematic e
ff
ects. Here, we only analyse the polar-
ization data at 353 GHz, which is the highest frequency
Planck
channel with polarization capabilities and the one with the best
S
/
N for dust polarization. We use the 30 GHz LFI data in our
comparison of the dust emission at 353 GHz with the microwave
and radio synchrotron emission presented in Sect.
4.4
.
In
the
Planck
map-making
process
(
Planck
Collaboration VIII 2014
), measurements from various de-
tectors at the same frequency are combined to obtain the
Stokes parameters (
I
,
Q
,and
U
) at each position on the sky.
The reconstructed polarization is a linear combination of the
weighted di
ff
erences between the signal from pairs of polariza-
tion sensitive bolometers (PSBs) with di
ff
erent orientations on
the sky. The resulting maps of the
Planck
Stokes parameters
Q
and
U
used in this paper are shown in Fig.
1
. The corresponding
map of the observed polarization intensity
P
=
(
Q
2
+
U
2
)
1
/
2
is shown in Fig.
2
. The total intensity map used in this work is
shown in Fig.
5
.
2.1. Conventions and notations
The relations between the observed Stokes parameters (
I
,
Q
,
and
U
) and the polarization fraction (
p
) and polarization an-
gle (
ψ
)aregivenby
p
=
Q
2
+
U
2
I
(1)
and
ψ
=
0
.
5
×
arctan(
U
,
Q
)
,
(2)
where the two arguments function arctan(
Y
,
X
)isusedtocom-
pute
atan
(
Y
/
X
) avoiding the
π
ambiguity, such that
Q
=
p
×
I
×
cos(2
ψ
)
,
U
=
p
×
I
×
sin(2
ψ
)
.
(3)
For the Stokes parameters provided in the
Planck
data, the an-
gle convention above is with respect to Galactic coordinates
A104, page 3 of
33
A&A 576, A104 (2015)
Fig. 1.
Planck
353 GHz polarization maps at 1
◦
resolution.
Upper
:
Q
Stokes parameter map.
Lower
:
U
Stokes parameter map. The maps are shown
with the same colour scale. High values are saturated to enhance mid-latit
ude structures. The values shown have been bias corrected as described in
Sect.
2.3
. These maps, as well as those in following figures, are shown in Galactic coordinates with the Galactic centre in the middle and longitude
increasing to the left. The data are masked as described in Sect.
2.4
.
with
−
90
◦
<ψ<
+
90
◦
,
ψ
=
0
◦
toward Galactic north, and
ψ
be-
coming positive toward Galactic west, the direction of decreas-
ing Galactic longitude (i.e.,
ψ
increases clockwise). Note that
this convention is the one used in the
HEALPix
3
software (
Górski
et al. 2005
), but is di
ff
erent from the IAU convention (
Hamaker
& Bregman 1996
), which is
ψ
=
0
◦
toward Galactic north but
with
ψ
becoming positive toward Galactic east, the direction
3
http://healpix.jpl.nasa.gov
of increasing Galactic longitude (i.e.,
ψ
increases counterclock-
wise). The conversion between
Planck
Stokes parameters and
the IAU convention is given by:
ψ
IAU
=
0
.
5
×
arctan(
−
U
,
Q
)
.
(4)
In this paper, all quoted values of the polarization angle are given
in the IAU convention.
A104, page 4 of
33
Planck Collaboration: The
Planck
dust polarization sky
Fig. 2.
Planck
353 GHz polarized intensity (
P
) map at 1
◦
resolution in log
10
scale. The values shown have been bias corrected as described in
Sect.
2.3
. The same mask as in Fig.
1
is applied.
2.2. Bandpass mismatch leakage correction
Owing to the way the polarization maps are constructed, any
instrumental di
ff
erence between detectors of the same channel
may produce a fake polarization signal, even for unpolarized sky
signal inputs. This is the case for the bandpass mismatch (BPM)
between detectors that a
ff
ects
Planck
polarization maps. In prac-
tice, the e
ff
ect corresponds to a leakage term from total inten-
sity
I
into polarization
Q
and
U
. The BPM polarization leak-
age e
ff
ect is therefore strongest in regions of high intensity, i.e.,
along the Galactic plane, and a
ff
ects both
p
and
ψ
. Because the
353 GHz intensity data used here are calibrated on the CMB
signal, no BPM leakage is produced by the CMB anisotropies.
Other astrophysical emission sources, however, produce BPM
polarization leakage.
Knowing the actual
Planck
sky scanning strategy and the
orientations of the polarization sensitive bolometers in the fo-
cal plane, the BPM polarization l
eakage corrections can be es-
timated from the relative responses of each detector to a given
sky astrophysical emission. The Planck Collaboration is ex-
ploring di
ff
erent methods to compute the relative responses of
detectors, as well as to produce total intensity maps for each
sky emission source. Two methods have been used to deter-
mine the relative responses (
Planck Collaboration IX 2014
).
The first one (method A) involves computing the BPM leak-
age between bolometers using the ground-measured bandpasses
(
Planck Collaboration IX 2014
). The second one (method B) de-
duces the relative detector response on regions of the sky where
we can obtain
I
,
Q
,and
U
maps for each detector individually.
Note that this can only be performed in limited regions of the
sky, outside the Galactic plane, which have been scanned in a
large number of configurations, allowing for the full reconstruc-
tion of
I
,
Q
,and
U
per detector. A comparison between the two
methods is presented in
Planck Collaboration IX
(
2014
).
When folding the above coe
ffi
cients into the
Planck
scanning
strategy, we have chosen to produce template maps
T
X
b
(
ν
)
of the
BPM leakage contribution for each frequency (
ν
) channel, for
each bolometer (
b
(
ν
)) and for each Stokes parameter (
X
being
Q
or
U
). The BPM polarization l
eakage correction is
L
X
ν
=
b
(
ν
)
R
b
(
ν
)
I
ν
T
X
b
(
ν
)
,
(5)
where
R
b
(
ν
)
represents the detector relative responses and
I
ν
is the
sky total intensity. For the purpose of the study presented here
we only take into account BPM leakage from dust thermal emis-
sion, because this is the dominan
t term at 353 GHz. The template
maps in Eq. (
5
) were computed using the
Planck
thermal dust
model described in
Planck Collaboration XI
(
2014
). We used
the standard
Planck
map-making procedure presented in
Planck
Collaboration VIII
(
2014
). Note that the
Planck
353 GHz chan-
nel also includes emission from the CO (
J
=
3
→
2) line (see
Planck Collaboration VI 2014
), which should also in principle be
included in the BPM leakage correction. This, however, is rela-
tively weak with respect to dust thermal emission and the cor-
responding BPM e
ff
ect is expected to be small compared to that
from dust. Because we do not concentrate on regions with strong
molecular emission in this paper, no correction was applied for
the CO emission BPM leakage.
Figure
3
shows the e
ff
ect of the correction for BPM on the
observed distribution of polarization angles toward the plane of
the Milky Way (
|
b
II
|
<
5
◦
) in the four Galactic quadrants (Q1,
Q2, Q3 and Q4, defined by 0
◦
<
II
<
90
◦
,90
◦
<
II
<
180
◦
,
180
◦
<
II
<
270
◦
, and 270
◦
<
II
<
360
◦
, respectively). When
no BPM leakage correction is applied, angles are observed to
be distributed around
+
20
◦
and
−
5
◦
for the inner (Q1 and Q4)
and outer (Q2 and Q3) MW regions, respectively. The di
ff
er-
ence in sign is due to the di
ff
erence in average detector orienta-
tion during Galaxy crossings, resulting from the relative orien-
tation of the scanning strategy and the Galactic plane. Using the
two methods discussed above for the determination of the cou-
pling coe
ffi
cients leads to similar BPM
leakage estimates. Note
A104, page 5 of
33
A&A 576, A104 (2015)
Quadrant Q2
Quadrant Q1
Quadrant Q4
Quadrant Q3
no correction
method A
method B (used)
Fig. 3.
Histograms of the observed polarized angle at the full data resolution toward the Galactic plane (
|
b
II
|
<
5
◦
) for the four Galactic quadrants.
The various curves show data uncorrected for bandpass mismatch (red), and corrected using sky coupling coe
ffi
cients derived either from ground
(method A: green) or sky measurements (method B: dark blue). The vertical dashed lines show the peak value obtained from fitting the histograms
with a Gaussian.
also that because the magnetic fie
ld is expected to be statisti-
cally aligned with the Galactic plane (see, e.g.,
Ferrière 2011
)
we expect the polarization dir
ection toward the plane to be on
average around
ψ
=
0
◦
. The fact that both correction methods
bring the peak of the histograms toward this value confirms the
validity of the BPM correction method used here. In the follow-
ing, we adopted the coe
ffi
cients from method B. We note, how-
ever, that although the situation is clearly improved by the BPM
leakage correction, the average observed angle distributions still
peak a few degrees away from
ψ
=
0
◦
, with the same sign pat-
tern as for the uncorrected data. This could in principle be due
to incomplete correction. However, preliminary tests have shown
that the remaining correction could be due to non-linearity in the
analogue-to-digital conversion (ADC) of the signal, which pro-
duces an additional correction with the same sign as observed
here and roughly the right amplitude.
We do not attempt here to fully assess the quality of the dif-
ferent corrections, but simply use them to estimate where on
the sky the uncertainties in the corrections are small enough
to be unimportant for this study. A plot of the BPM-leakage-
corrected polarization angle versu
s the uncorrected polarization
angle shows the magnitude of the correction, while the corre-
lation coe
ffi
cient gives a quantitative measure. For the di
ff
er-
ent corrections considered above, the correlation coe
ffi
cient is
over 0.95 for most regions of the sky at
|
b
II
|
>
5
◦
.Above
|
b
II
|
=
10
◦
, the correlation coe
ffi
cients are above 0.98, implying
that the correction becomes very small. This is a natural result
of the fact that the intensity that is leaking into polarization is
brightest toward the Galactic
plane. As measured from the dif-
ference between method A and B, the corresponding uncertain-
ties on the polarization angle
ψ
and fraction
p
are
|
Δ
ψ
|
<
10
◦
and
Δ
p
<
1%, respectively, toward the inner Galactic plane. These
uncertainties become less than the random errors away from the
plane. However, BPM leakage corrections are probably not the
dominant uncertainty at high Galactic latitudes and very low sig-
nal levels, where other systematic e
ff
ects remaining in the data
become more important (see Sect.
2.4
). For this reason, we do
not discuss specifically the polarization properties in the lowest
brightness sky area in this paper and defer this discussion to fu-
ture papers.
The above discussion applies to the HFI data, but we will
also compare the thermal dust emission at 353 GHz to the
30 GHz emission from LFI, which has a similar bandpass leak-
age issue. The LFI BPM co
rrection is discussed in
Planck
Collaboration II
(
2014
), where the principle di
ff
erence is the
presence of multiple astrophysical foregrounds, with di
ff
erent
spatial and spectral distributions. The component separation
products are therefore used in the LFI BPM correction. From
a comparison of the di
ff
erent surveys, we estimate that the un-
certainties are of the order 10
μ
K in the polarized intensity and
dominated by the noise rather th
an the leakage except in the in-
nermost plane (
|
II
|
<
30
◦
and
|
b
II
|
<
3
◦
), where the e
ff
ect is only
slightly above the noise level. For the polarization angle, we esti-
mate the uncertainties as roughly 15
◦
in the plane (
|
b
II
|
<
5
◦
)and
35
◦
away. Again the uncertainty appears dominated by noise,
with no obvious structure related to the bandpass leakage or scan
pattern. We have also cross-checked with WMAP 23 GHz data
and verified that th
e results in Sect.
4.4
are very similar.
2.3. Deriving polarization parameters
The polarization parameters
I
,
p
,and
ψ
are derived from the ob-
served Stokes parameters
I
,
Q
,and
U
using the Bayesian method
described in
Montier et al.
(
2015a
). This method extends that
described in
Quinn
(
2012
) by using the full 3
×
3 noise co-
variance matrix of each pixel. The e
ff
ective ellipticity, as de-
fined in
Montier et al.
(
2015a
), characterizes the shape of the
noise covariance matrix and couples all the terms in
Q
and
U
.
e
ff
=
1 corresponds to the case described in
Quinn
(
2012
),
whereas
e
ff
>
1 means that the relation between
C
QQ
,
C
QU
,
C
UU
is not trivial, and there are asymmetries in the noise covariance
matrix. We calculated
e
ff
for the
Planck
data used here. At 1
◦
resolution it is normally distributed with a mean value of 1.12
and a standard deviation of 0.04. At the full
Planck
resolution,
the distribution of
e
ff
is a bit wider (standard deviation of 0
.
05),
but the mean value does not change. Thus, although they are not
very strong, the asymmetries of the noise covariance matrix can-
not be neglected, and the Bayesian method is well suited for the
analysis of the data.
We use a flat prior on all three parameters
p
,
ψ
,and
I
over a
range centred on the conventional value given by Eqs. (
1
)and(
2
)
for
p
and
ψ
and the observed value for
I
, and a width correspond-
ing to 20
σ
,where
σ
is the conventional estimate for the uncer-
tainties (see Appendix
B.1
). The range on
p
and
ψ
is further
limited to
−
1
<
p
<
1and
−
90
◦
<ψ<
90
◦
, respectively, allow-
ing negative values of
p
in order to reduce bias in the posterior
probability. We compute the 3D posterior probability distribu-
tion function (PDF) using 2
7
values on each axis over the pa-
rameter range. The values of the polarization parameters are ob-
tained using the mean posterior (MP) estimator on the posterior
A104, page 6 of
33
Planck Collaboration: The
Planck
dust polarization sky
3D PDF. A comparison between th
e polarization parameters and
uncertainties obtained with this method and using the conven-
tional approach described in Appendix
B.1
isshowninFig.
B.1
for the
Planck
data at 1
◦
resolution.
When spatial smoothing is applied to the polarization data,
Stokes parameter maps are convolved with a Gaussian kernel of
the appropriate width using the dedicated smoothing software
part of the
HEALPix
library, which guarantees proper transport
of
Q
and
U
. The maps are then resampled to larger pixel size
(asspecifiedbythe
HEALPix
N
side
parameter) so as to preserve
full sampling of the data (pixel size smaller than 1
/
2.4 times
the data FWHM resolution). The corresponding smoothing of
data covariances was performed using the method described in
Appendix
A
. The corresponding smoothed maps of
p
and
ψ
are
then computed as described above
. The statistical uncertainties
in
p
and
ψ
(
σ
stat
p
and
σ
stat
ψ
, respectively) have been estimated as
described in Appendix
B.3
.
2.4. Impact of systematic effects, CIB, ZL, and CMB
We assessed the level of contamination by systematic e
ff
ects by
comparing the maps of
p
and
ψ
obtained at 1
◦
resolution for
the full
Planck
data with those obtained for the various individ-
ual
Planck
surveys (see introduction to Sect.
2
). We constructed
maps of systematic uncertainties on
p
and
ψ
(
σ
sys
p
and
σ
sys
ψ
,re-
spectively) by averaging these di
ff
erences over the
Planck
indi-
vidual surveys. These were added to the statistical uncertainty
maps
σ
stat
p
and
σ
stat
ψ
, to obtain the total uncertainty maps used in
the rest of the analysis.
In this paper we only show the
Planck
polarization data
and derived quantities where the systematic uncertainties are
small and where the dust signal dominates total emission. For
this purpose we defined a mask such that
σ
sys
p
<
3% and
I
353
>
0
.
1 MJy sr
−
1
. We defined the mask at a resolution of 1
◦
and smoothed it to 3
◦
resolution to avoid complex edges. As a
result, the maps shown exclude 21% of the sky. Note that a di
ff
er-
ent mask is used for the polarization angle dispersion function,
as defined in Sect.
3.3
.
The cosmic infrared background (CIB) is due to emission
from a large number of distant galaxies with random orienta-
tions and is expected to be, on average, unpolarized. However, it
can contribute non-negligible emission at 353 GHz in low bright-
ness regions of the sky and hence reduces the apparent degree
of dust polarization. The zero level of the 353 GHz total inten-
sity map has been established by correlation with Galactic H
i
,
using the method described in
Planck Collaboration XI
(
2014
),
as was done for the publicly released 2013 maps. This o
ff
set
is 0
.
0887 MJy sr
−
1
(uncertainty 0
.
0068 MJy sr
−
1
) and was sub-
tracted from the total intensity map we use, which therefore does
not contain the CIB monopole. We added the corresponding un-
certainty in quadrature with the uncertainty of the total intensity,
so that the statistical uncertainties on
p
include the uncertainty
on the CIB subtraction.
The zodiacal light (ZL) has a smooth distribution on the
sky. From the model constrained by its detection in the
Planck
bands (
Planck Collaboration XIV 2014
), its median total inten-
sity at 353 GHz is 1
.
9
×
10
−
2
MJy sr
−
1
over the sky area stud-
ied here, and reaches
4
.
3
×
10
−
2
MJy sr
−
1
in dust lanes near
the ecliptic plane. Its polarization in the submillimetre is cur-
rently unconstrained observationally. Because this intensity is
subdominant over most of the sky fraction and the polarization
level of ZL is currently unknown, we apply no correction for the
possible contribution of ZL. We note that, if ZL was assumed
unpolarized, subtracting its intensity would raise the observed
polarization levels by about 0.5% of the observed polarization
fraction, on average over the sky region studied here, and would
not change the observed polarization angles. We have checked
that no noticeable systematic vari
ation of the polarization frac-
tion is detected in our maps along zodiacal dust lanes.
CMB fluctuations are polarized at a level of 0.56 mK (
Kovac
et al. 2002
) at a resolution of about 1
◦
, which corresponds to
1
.
6
×
10
−
4
MJy sr
−
1
at 353 GHz. In the mask we use here, the
e
ff
ect of CMB polarized fluctuations
is therefore negligible and
we did not attempt to correct for those fluctuations.
No additional correction was applied to the data.
2.5. External data
In Sect.
4.4
, we compare the
Planck
HFI polarization maps with
low-frequency radio and microwave observations that are dom-
inated by synchrotron emission over most of the sky. These
include:
–
the 408 MHz total intensity map of
Haslam et al.
(
1982
) from
the LAMBDA
4
site;
–
the 1.4 GHz total intensity map of the northern (
Reich 1982
;
Reich & Reich 1986
) and southern (
Reich et al. 2001
)sky;
–
the 1.4 GHz polarized intensity maps of the northern
(
Wolleben et al. 2006
) and southern (
Testori et al. 2008
)sky.
For the analysis in Sect.
4.4
,the
Planck
HFIandLFImapsare
smoothed to 1
◦
FWHM resolution to match these radio data and
downgraded to
N
side
=
256. Most of the 1.4 GHz maps are avail-
able on the Bonn survey site
5
as FITS images in Cartesian co-
ordinates. They are converted into
HEALPix
using the procedure
described in
Paradis et al.
(
2012
) and are made available in this
form on the CADE site
6
. The resolution of the observations is
roughly 1
◦
, and so no additional smoothing is applied to the
radio data. The total intensity map at 1.4 GHz is estimated to
have an o
ff
set of 2.8 K (
Reich et al. 2004
) due to the combina-
tion of zero-level calibration uncertainty, unresolved extragalac-
tic sources, and the CMB, and so this was subtracted from the
data.
The total intensity data include thermal bremsstrahlung
(free-free) emission, particularly in the plane. This is not neg-
ligible at 408 MHz or 1.4 GHz. We use the WMAP MEM free-
free solution (
Gold et al. 2011
) to subtract it. We note that this
free-free template likely includes anomalous dust emission, and
there are indications that it is an overestimate by roughly 20 to
30% (
Alves et al. 2010
;
Ja
ff
e et al. 2011
). Because synchrotron
dominates over free-free emission at low radio frequencies, even
on the Galactic plane, the uncertainties on the free-free correc-
tion are not expected to a
ff
ect the qualitative comparison with
dust emission in this paper. But the MEM template is not suf-
ficiently accurate to correct for free-free when the synchrotron
is subdominant at 30 GHz. Furthermore, the 30 GHz total inten-
sity also includes anomalous dust emission for which we have
no correction. We therefore do not use 30 GHz in total intensity,
but only in polarization.
4
http://lambda.gsfc.nasa.gov
5
http://www.mpifr-bonn.mpg.de/survey.html
. The southern
part of the 1.4 GHz total intensity data was provided by Reich
(priv. comm.).
6
Analysis Center for Extended Data,
http://cade.irap.omp.eu
A104, page 7 of
33
A&A 576, A104 (2015)
Fig. 4.
Upper
: map of the 353 GHz polarization fraction
p
at 1
◦
resolution. The colour scale is linear and ranges from 0% to 20%.
Lower
:map
of the 353 GHz polarization fraction uncertainty,
σ
p
,at1
◦
resolution in log
10
scale. The colour scale is from
σ
p
=
0
.
1% to
σ
p
=
10%. The data
are not shown in the grey areas where the dust emission is not dominant or where residuals were identified comparing individual surveys (see
Sect.
2.4
). The polarization fraction is obtained using the Bayesian method with a mean posterior estimator (see Sect.
2.3
). The uncertainty map
includes statistical and systematic contributions. The same mask as in Fig.
1
is applied.
3. Description of the
Planck
polarization maps
Figure
4
shows the maps of the polarization fraction (
p
)at
a resolution of 1
◦
.ThemapinFig.
5
is based on the polar-
ization direction, also at a resolution of 1
◦
. Both figures also
show the corresponding map of the total uncertainty, which
includes the contribution from statistical and systematic un-
certainty estimates, as described in Sect.
2.4
. The maps were
masked as described in Sect.
2.4
in regions where large residual
systematic uncertainties were evident or where the total inten-
sity at 353 GHz is not dominated by dust emission. Figures
4
and
5
were constructed using the Bayesian method described in
Sect.
2.3
,
Montier et al.
(
2015a
), and Appendix
B.3
, in partic-
ular the Mean Posterior Bay
esian estimator defined in
Montier
et al.
(
2015b
). These figures are discussed in Sects.
3.1
and
3.2
.
In Fig.
6
we highlight several regions of interest that we will
discuss below; parameters of t
hese regions are given in Table
1
.
3.1. Polarization fraction
As seen from Fig.
4
, the measured polarization fraction shows
significant variations on the sky. One of the aims of this paper
is to characterize those variations as a step toward understand-
ing their origin. These characteristics are compared to those of
polarized emission maps computed in simulations of anisotropic
MHD turbulence in a companion paper (
Planck Collaboration
Int. XX 2015
).
Figure
4
shows that the polarization fraction of the thermal
dust emission can reach up to about 20% in several large-scale
A104, page 8 of
33
Planck Collaboration: The
Planck
dust polarization sky
Fig. 5.
Upper
: map of the apparent magnetic field (
B
⊥
) orientation. The polarization segments from the measured 353 GHz polarization, having
been rotated by 90
◦
, show the orientation of the apparent magnetic field, but their length is constant, not reflecting the changing polarization
fraction. The colour map shows the 353 GHz emission in log
10
scale and ranges from 10
−
2
to 10 MJy sr
−
1
.
Lower
: map of the 353 GHz polarization
angle uncertainty (
σ
ψ
)at1
◦
resolution. The scale is linear from
σ
ψ
=
0
◦
to
σ
ψ
=
52
.
3
◦
. The polarization angle is obtained using the Bayesian
method with a mean posterior estimator (see Sect.
2.3
). The uncertainty map includes statistical and systematic contributions. The same mask as
in Fig.
1
is applied.
regions of the sky. This is particularly the case in the sec-
ond Galactic quadrant (
II
145
◦
,
b
II
0
◦
, including a re-
gion at low latitude known as “the Fan”
7
), the Perseus area
7
The term “the Fan” generally refers to an area extending over roughly
120
◦
II
160
◦
and 0
◦
b
II
20
◦
seen in the earliest maps of
Galactic polarized radio emission in the 1960s. The region is one of
the brightest features of the polarized radio sky and has a distinctive
(
II
143
◦
,
b
II
−
25
◦
), the Loop I area (
II
40
◦
,
b
II
+
45
◦
)
and a region in Microscopium (
II
15
◦
,
b
II
−
40
◦
). The
fan-like appearance of the polarization vectors at low radio frequencies.
The “fanning” of these vectors disappears at higher frequencies where
Faraday rotation is weak, leaving a large region with coherent polar-
ization that as yet has no definitive explanation. See, e.g.,
van de Hulst
(
1967
)and
Wolleben et al.
(
2006
).
A104, page 9 of
33