arXiv:1309.1357v2 [astro-ph.GA] 17 May 2014
Astronomy & Astrophysics
manuscript no. amestudy
c
ESO 2018
November 1, 2018
Planck
intermediate results. XV. A study of anomalous microwave
emission in Galactic clouds
Planck Collaboration: P. A. R. Ade
77
, N. Aghanim
53
, M. I. R. Alves
53
, M. Arnaud
66
, F. Atrio-Barandela
18
, J. Aumont
53
, C. Baccigalupi
76
,
A. J. Banday
82
,
10
, R. B. Barreiro
60
, E. Battaner
83
, K. Benabed
54
,
80
, A. Benoit-L ́evy
24
,
54
,
80
, J.-P. Bernard
82
,
10
, M. Bersanelli
32
,
46
, P. Bielewicz
82
,
10
,
76
,
J. Bobin
66
, A. Bonaldi
62
, J. R. Bond
9
, J. Borrill
13
,
78
, F. R. Bouchet
54
,
80
, F. Boulanger
53
, C. Burigana
45
,
30
, J.-F. Cardoso
67
,
1
,
54
, S. Casassus
81
,
A. Catalano
68
,
65
, A. Chamballu
66
,
15
,
53
, X. Chen
52
, H. C. Chiang
26
,
7
, L.-Y Chiang
56
, P. R. Christensen
73
,
35
, D. L. Clements
51
, S. Colombi
54
,
80
,
L. P. L. Colombo
23
,
61
, F. Couchot
64
, B. P. Crill
61
,
74
, F. Cuttaia
45
, L. Danese
76
, R. D. Davies
62
, R. J. Davis
62
, P. de Bernardis
31
, A. de Rosa
45
, G. de
Zotti
41
,
76
, J. Delabrouille
1
, F.-X. D ́esert
50
, C. Dickinson
62
,
∗
, J. M. Diego
60
, S. Donzelli
46
, O. Dor ́e
61
,
11
, X. Dupac
38
, T. A. Enßlin
70
,
H. K. Eriksen
58
, F. Finelli
45
,
47
, O. Forni
82
,
10
, E. Franceschi
45
, S. Galeotta
43
, K. Ganga
1
, R. T. G ́enova-Santos
59
, T. Ghosh
53
, M. Giard
82
,
10
,
J. Gonz ́alez-Nuevo
60
,
76
, K. M. G ́orski
61
,
84
, A. Gregorio
33
,
43
,
49
, A. Gruppuso
45
, F. K. Hansen
58
, D. L. Harrison
57
,
63
, G. Helou
11
,
C. Hern ́andez-Monteagudo
12
,
70
, S. R. Hildebrandt
11
, E. Hivon
54
,
80
, M. Hobson
6
, A. Hornstrup
16
, A. H. Ja
ff
e
51
, T. R. Ja
ff
e
82
,
10
, W. C. Jones
26
,
E. Keih ̈anen
25
, R. Keskitalo
21
,
13
, R. Kneissl
37
,
8
, J. Knoche
70
, M. Kunz
17
,
53
,
3
, H. Kurki-Suonio
25
,
40
, A. L ̈ahteenm ̈aki
2
,
40
, J.-M. Lamarre
65
,
A. Lasenby
6
,
63
, C. R. Lawrence
61
, R. Leonardi
38
, M. Liguori
29
, P. B. Lilje
58
, M. Linden-Vørnle
16
, M. L ́opez-Caniego
60
, J. F. Mac ́ıas-P ́erez
68
,
B. Ma
ff
ei
62
, D. Maino
32
,
46
, N. Mandolesi
45
,
5
,
30
, D. J. Marshall
66
, P. G. Martin
9
, E. Mart ́ınez-Gonz ́alez
60
, S. Masi
31
, M. Massardi
44
, S. Matarrese
29
,
P. Mazzotta
34
, P. R. Meinhold
27
, A. Melchiorri
31
,
48
, L. Mendes
38
, A. Mennella
32
,
46
, M. Migliaccio
57
,
63
, M.-A. Miville-Deschˆenes
53
,
9
, A. Moneti
54
,
L. Montier
82
,
10
, G. Morgante
45
, D. Mortlock
51
, D. Munshi
77
, P. Naselsky
73
,
35
, F. Nati
31
, P. Natoli
30
,
4
,
45
, H. U. Nørgaard-Nielsen
16
, F. Noviello
62
,
D. Novikov
51
, I. Novikov
73
, C. A. Oxborrow
16
, L. Pagano
31
,
48
, F. Pajot
53
, R. Paladini
52
, D. Paoletti
45
,
47
, G. Patanchon
1
, T. J. Pearson
11
,
52
,
M. Peel
62
, O. Perdereau
64
, F. Perrotta
76
, F. Piacentini
31
, M. Piat
1
, E. Pierpaoli
23
, D. Pietrobon
61
, S. Plaszczynski
64
, E. Pointecouteau
82
,
10
,
G. Polenta
4
,
42
, N. Ponthieu
53
,
50
, L. Popa
55
, G. W. Pratt
66
, S. Prunet
54
,
80
, J.-L. Puget
53
, J. P. Rachen
20
,
70
, R. Rebolo
59
,
14
,
36
, W. Reich
71
,
M. Reinecke
70
, M. Remazeilles
62
,
53
,
1
, C. Renault
68
, S. Ricciardi
45
, T. Riller
70
, I. Ristorcelli
82
,
10
, G. Rocha
61
,
11
, C. Rosset
1
, G. Roudier
1
,
65
,
61
,
J. A. Rubi ̃no-Mart ́ın
59
,
36
, B. Rusholme
52
, M. Sandri
45
, G. Savini
75
, D. Scott
22
, L. D. Spencer
77
, V. Stolyarov
6
,
63
,
79
, D. Sutton
57
,
63
,
A.-S. Suur-Uski
25
,
40
, J.-F. Sygnet
54
, J. A. Tauber
39
, D. Tavagnacco
43
,
33
, L. Terenzi
45
, C. T. Tibbs
52
, L. To
ff
olatti
19
,
60
, M. Tomasi
46
, M. Tristram
64
,
M. Tucci
17
,
64
, L. Valenziano
45
, J. Valiviita
40
,
25
,
58
, B. Van Tent
69
, J. Varis
72
, L. Verstraete
53
, P. Vielva
60
, F. Villa
45
, B. D. Wandelt
54
,
80
,
28
,
R. Watson
62
, A. Wilkinson
62
, N. Ysard
25
, D. Yvon
15
, A. Zacchei
43
, and A. Zonca
27
(A
ffi
liations can be found after the references)
Preprint online version: November 1, 2018
ABSTRACT
Anomalous microwave emission (AME) is believed to be due to e
lectric dipole radiation from small spinning dust grains. T
he aim of this paper is
a statistical study of the basic properties of AME regions an
d the environment in which they emit. We used
WMAP
and
Planck
maps, combined
with ancillary radio and IR data, to construct a sample of 98 c
andidate AME sources, assembling SEDs for each source using
aperture photometry
on 1
◦
-smoothed maps from 0.408 GHz up to 3000 GHz. Each spectrum is
fitted with a simple model of free-free, synchrotron (where n
ecessary),
cosmic microwave background (CMB), thermal dust, and spinn
ing dust components. We find that 42 of the 98 sources have sign
ificant (
>
5
σ
)
excess emission at frequencies between 20 and 60 GHz. An anal
ysis of the potential contribution of optically thick free-
free emission from ultra-
compact H
ii
regions, using IR colour criteria, reduces the significant A
ME sample to 27 regions. The spectrum of the AME is consistent
with
model spectra of spinning dust. Peak frequencies are in the r
ange 20–35 GHz except for the California Nebula (NGC1499), w
hich appears to have
a high spinning dust peak frequency of (50
±
17) GHz. The AME regions tend to be more spatially extended th
an regions with little or no AME.
The AME intensity is strongly correlated with the sub-milli
metre
/
IR flux densities and comparable to previous AME detections i
n the literature.
AME emissivity, defined as the ratio of AME to dust optical dep
th, varies by an order of magnitude for the AME regions. The AM
E regions tend
to be associated with cooler dust in the range 14–20 K and an av
erage emissivity index,
β
d
, of
+
1.8, while the non-AME regions are typically
warmer, at 20–27 K. In agreement with previous studies, the A
ME emissivity appears to decrease with increasing column de
nsity. This supports
the idea of AME originating from small grains that are known t
o be depleted in dense regions, probably due to coagulation o
nto larger grains. We
also find a correlation between the AME emissivity (and to a le
sser degree the spinning dust peak frequency) and the intens
ity of the interstellar
radiation field,
G
0
. Modelling of this trend suggests that both radiative and co
llisional excitation are important for the spinning dust em
ission. The
most significant AME regions tend to have relatively less ion
ized gas (free-free emission), although this could be a sele
ction e
ff
ect. The infrared
excess, a measure of the heating of dust associated with H
ii
regions, is typically
>
4 for AME sources, indicating that the dust is not primarily
heated by hot OB stars. The AME regions are associated with kn
own dark nebulae and have higher 12
μ
m
/
25
μ
m ratios. The emerging picture is
that the bulk of the AME is coming from the polycyclic aromati
c hydrocarbons and small dust grains from the colder neutral
interstellar medium
phase.
Key words.
ISM: H
ii
regions – ISM: general – Radiation mechanisms: general – Rad
io continuum: ISM – Submillimeter: ISM
∗
Corresponding
author:
C.
Dickinson,
clive.dickinson@manchester.ac.uk
1. Introduction
Anomalous microwave emission (AME) has been observed in a
few directions of the Galaxy and is an important foreground f
or
1
Planck Collaboration: P. A. R. Ade et al.: A study of AME in Gal
actic clouds
the cosmic microwave background (CMB) (
Kogut et al. 1996
;
Leitch et al. 1997
;
Finkbeiner et al. 2002
;
Finkbeiner 2004
;
de
Oliveira-Costa et al. 2004
;
Dobler & Finkbeiner 2008
;
Miville-
Deschˆenes et al. 2008
;
Gold et al. 2011
). There is strong evi-
dence, particularly in the Perseus and
ρ
Ophiuchi clouds (
Watson
et al. 2005
;
Casassus et al. 2008
;
Planck Collaboration XX
2011
), that AME is due to electric dipole radiation from small
spinning dust grains. Along these sight lines, there is high
ly sig-
nificant excess emission above free-free, synchrotron, CMB
, and
thermal dust in the frequency range 10–100 GHz. The spectral
energy distributions (SEDs) are peaked at about 30 GHz, and
can be fitted by physically-motivated theoretical models of
spin-
ning dust (
Draine & Lazarian 1998
;
Ali-Ha ̈ımoud et al. 2009
;
Hoang et al. 2010
,
2011
). AME has been detected in H
ii
regions
(
Dickinson et al. 2006
,
2007
,
2009
;
Todorovi ́c et al. 2010
), dust
clouds (
Casassus et al. 2006
,
2008
;
Scaife et al. 2009
), a super-
nova remnant (
Scaife et al. 2007
), and in one external galaxy
(
Murphy et al. 2010a
;
Scaife et al. 2010b
). There is also evi-
dence for AME in the di
ff
use emission at high Galactic latitudes
(
Peel et al. 2012
;
Macellari et al. 2011
;
Ghosh et al. 2012
).
Definitive evidence for spinning dust was provided by
Planck Collaboration XX
(
2011
). Accurate SEDs of the Perseus
and
ρ
Ophiuchi clouds were easily fitted by a physically moti-
vated model for the clouds, including spinning dust compone
nts
associated with the atomic and molecular phases of the inter
-
stellar medium (ISM). The model was found to be an excellent
fit with physical parameters that were reasonable for these r
e-
gions.
Planck Collaboration XXI
(
2011
) applied an inversion
technique to separate the various contributions of the ISM i
n
Galactocentric rings along the Galactic plane and found tha
t
25
±
5 % of the 30 GHz emission comes from AME and was
consistent with spinning dust associated with atomic and mo
lec-
ular gas but not with the ionized phase. Component separatio
n
of the di
ff
use emission at intermediate latitudes in the southern
Gould Belt region (
Planck Collaboration Int. XII 2013
) revealed
an AME component consistent with spinning dust emitting at a
peak frequency of (25
.
5
±
1
.
5) GHz (in flux density units), com-
patible with plausible values for the local density and radi
ation
field.
To date there has been no detailed study of AME in a rea-
sonable sample of sources.
Dickinson et al.
(
2007
) observed
six southern H
ii
regions with the Cosmic Background Imager
at 31 GHz and found tentative evidence for excess emission
from the RCW49 complex.
Scaife et al.
(
2008
) observed a sam-
ple of 16 compact H
ii
regions at 15 GHz with the Arcminute
Microkelvin Imager (AMI) and found no evidence for excess
emission; the spectrum was consistent with optically thin f
ree-
free emission from warm ionized gas.
Todorovi ́c et al.
(
2010
)
surveyed the Galactic plane at longitudes 27
◦
≤
l
≤
46
◦
with
the Very Small Array (VSA) at 33 GHz and found statistical evi
-
dence for AME in nine regions, but with an emissivity relativ
e to
100
μ
m brightness that was 30–50 % of the average high latitude
value.
In this paper, we have assembled a sample of 98 Galactic
clouds selected at
Planck
1
frequencies to investigate their SEDs
and constrain the contribution of AME. Due to the large beam
size of the lowest
WMAP
/
Planck
channels and the low frequency
1
Planck
(
http://www.esa.int/Planck
) is a project of the
European Space Agency (ESA) with instruments provided by tw
o 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 ES
A and a sci-
entific consortium led and funded by Denmark.
radio data, there is sometimes a mix of sources within the bea
m.
Many of the sources can be classed as di
ff
use H
ii
regions, al-
though we have found a few AME sources with no obvious
associated H
ii
region and very weak free-free emission. Many
of the regions are in large star-forming complexes, which at
1
◦
resolution contain many individual sources. These are of-
ten located in the vicinity of molecular clouds, which produ
ce
strong thermal dust emission. Nevertheless, combining
Planck
data with ancillary radio and far-infrared data we assemble
their
SEDs from 0.408 GHz to 5000 GHz. We fit the SEDs with a sim-
ple model of free-free, synchrotron (where appropriate), t
hermal
dust, CMB, and AME (spinning dust) components to determine
whether there is evidence for AME at frequencies 20–60 GHz
and if so, if it agrees with spinning dust models. For the most
significant (
≥
5
σ
) AME detections, we investigate the observa-
tional properties of these regions and compare them with eac
h
other and with regions that do not show strong AME. In particu
-
lar, we would like to distinguish AME and “non-AME” regions
using observational and physical properties. This is the fir
st sta-
tistical study of AME regions to date.
In Sect.
2
we describe the
Planck
and ancillary data used in
our analysis. Section
3
describes the sample selection, aperture
photometry, and model-fitting. Section
4
presents the results of
the quantification of AME in these sources. Section
5
investi-
gates the correlation of AME with source properties. Sectio
n
6
gives a brief discussion and conclusions.
2. Data
2.1. Planck data
Planck
(
Tauber et al. 2010
;
Planck Collaboration I 2011
) is the
third generation space mission to measure the anisotropy of
the
CMB. It observes the sky in nine frequency bands covering 30–
857 GHz with high sensitivity and angular resolution from 31
′
to 5
′
. The Low Frequency Instrument (LFI;
Mandolesi et al.
2010
;
Bersanelli et al. 2010
;
Mennella et al. 2011
) covers the
30, 44, and 70 GHz bands with amplifiers cooled to 20 K. The
High Frequency Instrument (HFI;
Lamarre et al. 2010
;
Planck
HFI Core Team 2011a
) covers the 100, 143, 217, 353, 545, and
857 GHz bands with bolometers cooled to 0.1 K. Polarization i
s
measured in all but the highest two bands (
Leahy et al. 2010
;
Rosset et al. 2010
). A combination of radiative cooling and
three mechanical coolers produces the temperatures needed
for
the detectors and optics (
Planck Collaboration II 2011
). Two
data processing centers (DPCs) check and calibrate the data
and
make maps of the sky (
Planck HFI Core Team 2011b
;
Zacchei
et al. 2011
).
Planck
’s sensitivity, angular resolution, and fre-
quency coverage make it a powerful instrument for Galactic
and extragalactic astrophysics as well as cosmology. Early
as-
trophysics results are given in Planck Collaboration VIII–
XXVI
2011, based on data taken between 13 August 2009 and 7 June
2010. Intermediate astrophysics results are now being pres
ented
in a series of papers based on data taken between 13 August
2009 and 27 November 2010.
In this paper we use
Planck
data from the 2013 distribu-
tion of released products (
Planck Collaboration I 2013
), based
on data acquired during the “nominal” operations period fro
m
13 August 2009 to 27 November 2010, and available from the
Planck
Legacy Archive
2
. Specifically, we use the nine tempera-
ture maps summarized in Table
1
. We also use a CMB-subtracted
2
http://www.sciops.esa.int/index.php?
project=planck&page=Planck_Legacy_Archive
2
Planck Collaboration: P. A. R. Ade et al.: A study of AME in Gal
actic clouds
Table 1.
Sources of the datasets used in this paper, as well as centre f
requencies, angular resolutions, and references.
Frequency
Telescope
/
Survey
[GHz]
Resolution
Coverage
Reference
Haslam . . . . . . . . . . . . . . . . . . . . . . . . .
0.408
51.
′
0
Full sky
Haslam et al.
(
1982
)
Reich . . . . . . . . . . . . . . . . . . . . . . . . . .
1.42
35.
′
4
Full sky
Reich
(
1982
);
Reich & Reich
(
1986
);
Reich et al.
(
2001
)
Jonas . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
20.
′
0
Southern sky
Jonas et al.
(
1998
)
WMAP
9-year . . . . . . . . . . . . . . . . . . . .
22.8
51.
′
3
a
Full sky
Bennett et al.
(
2012
)
Planck
. . . . . . . . . . . . . . . . . . . . . . . . . .
28.4
32.
′
3
Full sky
Planck Collaboration I
(
2013
)
WMAP
9-year . . . . . . . . . . . . . . . . . . . .
33.0
39.
′
1
a
Full sky
Bennett et al.
(
2012
)
WMAP
9-year . . . . . . . . . . . . . . . . . . . .
40.7
30.
′
8
a
Full sky
Bennett et al.
(
2012
)
Planck
. . . . . . . . . . . . . . . . . . . . . . . . . .
44.1
27.
′
1
Full sky
Planck Collaboration I
(
2013
)
WMAP
9-year . . . . . . . . . . . . . . . . . . . .
60.7
21.
′
1
a
Full sky
Bennett et al.
(
2012
)
Planck
. . . . . . . . . . . . . . . . . . . . . . . . . .
70.4
13.
′
3
Full sky
Planck Collaboration I
(
2013
)
WMAP
9-year . . . . . . . . . . . . . . . . . . . .
93.5
14.
′
8
a
Full sky
Bennett et al.
(
2012
)
Planck
. . . . . . . . . . . . . . . . . . . . . . . . . .
100
9.
′
7
Full sky
Planck Collaboration I
(
2013
)
Planck
. . . . . . . . . . . . . . . . . . . . . . . . . .
143
7.
′
3
Full sky
Planck Collaboration I
(
2013
)
Planck
. . . . . . . . . . . . . . . . . . . . . . . . . .
217
5.
′
0
Full sky
Planck Collaboration I
(
2013
)
Planck
. . . . . . . . . . . . . . . . . . . . . . . . . .
353
4.
′
8
Full sky
Planck Collaboration I
(
2013
)
Planck
. . . . . . . . . . . . . . . . . . . . . . . . . .
545
4.
′
7
Full sky
Planck Collaboration I
(
2013
)
Planck
. . . . . . . . . . . . . . . . . . . . . . . . . .
857
4.
′
3
Full sky
Planck Collaboration I
(
2013
)
COBE
-DIRBE . . . . . . . . . . . . . . . . . . . .
1249
37.
′
1
Full sky
Hauser et al.
(
1998
)
COBE
-DIRBE . . . . . . . . . . . . . . . . . . . .
2141
38.
′
0
Full sky
Hauser et al.
(
1998
)
COBE
-DIRBE . . . . . . . . . . . . . . . . . . . .
2997
38.
′
6
Full sky
Hauser et al.
(
1998
)
IRAS
(IRIS) Band 4 (100
μ
m) . . . . . . . . .
3000
4.
′
7
Near-full sky
Miville-Deschˆenes & Lagache
(
2005
)
IRAS
(IRIS) Band 3 (60
μ
m) . . . . . . . . . .
5000
3.
′
6
Near-full sky
Miville-Deschˆenes & Lagache
(
2005
)
IRAS
(IRIS) Band 2 (25
μ
m) . . . . . . . . . .
12000
3.
′
5
Near-full sky
Miville-Deschˆenes & Lagache
(
2005
)
IRAS
(IRIS) Band 1 (12
μ
m) . . . . . . . . . .
25000
3.
′
5
Near-full sky
Miville-Deschˆenes & Lagache
(
2005
)
Spitzer
IRAC
/
MIPS . . . . . . . . . . . . . . . .
8, 24
μ
m
2
′′
, 6
′′
Partial
Fazio et al.
(
2004
);
Rieke et al.
(
2004
)
a
We use the symmeterized, 1
◦
-smoothed version.
version for testing the robustness of the detections, using
the
SMICA
CMB map (
Planck Collaboration XII 2013
). We use
the standard conversion factors from CMB to Rayleigh-Jeans
(RJ) units and updated colour corrections described in
Planck
Collaboration I
(
2013
). The
Planck
bands centred at 100 and
217 GHz are known to be contaminated by CO lines. We cor-
rected these channels using the
Dame et al.
(
2001
) integrated
CO map smoothed to 1
◦
resolution and scaled with the con-
version factors described in
Planck Collaboration XIII
(
2013
);
however, for some sources, we still see discrepancies with t
he
spectral model at the
>
10 % level. We therefore did not include
these two channels in our fitting of the spectral model. The CO
contamination in the 353 GHz channel is small, typically
<
1 %
(
Planck Collaboration XIII 2013
), and we do not see significant
deviations in our SEDs. Therefore, no correction was made fo
r
CO lines in the 353 GHz band.
Although we limit ourselves to bright Galactic regions with
typical flux densities at 30 GHz far greater than 10 Jy, at 1
◦
angular scales the integrated flux density of CMB fluctuation
s
can be 10 Jy or more at 100 GHz, a significant fraction of
the total flux density of some of the sources in our sample.
CMB-subtracted maps would, in principle, be most appropria
te
for our analysis. However, in bright regions near the Galact
ic
plane, significant foreground residuals remain in the CMB ma
ps
produced by the
Planck
component separation codes in 2013
(
Planck Collaboration XII 2013
), which used only
Planck
data
and frequencies for separation. These regions can be masked
for
cosmological work, but they are precisely the regions that w
e
need here. Investigations comparing CMB-subtracted with n
on-
CMB-subtracted maps revealed biases in the plane at the leve
l
of 10–15 %. Furthermore, incorrect subtraction, particula
rly at
frequencies near 100 GHz, resulted in high
χ
2
values for some
SEDs, and poorly fitted thermal dust components. We therefor
e
use the CMB-subtracted maps only for finding regions of AME,
and use non-CMB-subtracted maps for the photometric analy-
sis, where we fit for a CMB component in the spectrum of each
source, using the full data available in Table
1
(see Sect.
2.2
). In
this way we do not bias the flux densities (due to the component
separation process), and more importantly, we can characte
rize
and propagate the uncertainty due to the CMB fluctuation. The
AME amplitudes from both datasets agree within a fraction of
the uncertainty for the majority of sources. In the future,
Planck
component separation will also make use of many of the extern
al
datasets listed in Table
1
, and it may be possible to subtract the
CMB directly.
2.2. Ancillary data
We use a range of ancillary data to allow the SEDs to be
determined from radio (around 1 GHz) to far-infrared (aroun
d
3000 GHz). All ancillary data are summarized, along with the
Planck
data, in Table
1
. These data have been smoothed to a
common resolution of 1
◦
since some of the maps have only
slightly higher resolution than this. The smoothing also re
duces
the e
ff
ects of any residual beam asymmetry in some cases, e.g.,
WMAP
and
Planck
, where non-circular beams vary across the
map.
We analysed the northern sky survey at 12–18 GHz from
the COSMOSOMAS experiments (
Gallegos et al. 2001
); how-
ever, due to the filtering of emission on large angular scales
and large intrinsic beam width, the majority of the sources
were strongly a
ff
ected by negative filtering artefacts from neigh-
bouring bright sources. The exceptions were G160.26
−
18.62
and G173.6
+
2.8, which were previously reported by
Planck
3
Planck Collaboration: P. A. R. Ade et al.: A study of AME in Gal
actic clouds
Collaboration XX
(
2011
). We therefore did not consider further
the COSMOSOMAS data in our analysis.
In the following sections, we describe the ancillary data in
more detail.
2.2.1. Radio surveys
Data at low frequencies (around 1 GHz) are important for ex-
cluding regions with synchrotron emission, and for estimat
ing
the level of free-free emission. Ideally, we would have seve
ral
frequency channels in the range 1–10 GHz; however, no large
area surveys exist above 2.3 GHz, except for higher resoluti
on
surveys that do not retain large-angular-scale informatio
n. We
therefore use the three well-known surveys at 0.408, 1.42, a
nd
2.326 GHz.
The all-sky survey of
Haslam et al.
(
1982
) at 0.408 GHz is
widely used as a tracer of synchrotron emission at high Galac
tic
latitudes; however, it also contains strong free-free radi
ation
from the Galactic plane and from H
ii
regions, where the free-
free typically dominates over synchrotron emission even at
these
lower frequencies.
A number of di
ff
erent versions of the 0.408 GHz map are
available. The most widely used is the NCSA
3
destriped and
desourced version available on the LAMBDA website
4
at an
angular resolution of 1
◦
. This map has been Fourier filtered to
remove large-scale striations, and bright sources have bee
n sub-
tracted, including many of the bright H
ii
regions. Since we want
to retain all the sources for this work, we use a less-process
ed
version of the map
5
at 51
′
resolution that was originally sam-
pled in a 2-D Cartesian projection with 0.
◦
33
×
0.
◦
33 square pixels
and B1950 coordinate frame. This version retains all the bri
ght
compact sources, although striations are much more visible
by
eye. However, at low latitudes and in bright regions, the str
ia-
tions are negligible compared to the sky signal. This map was
regridded into the
HEALPix
format (
G ́orski et al. 2005
) using a
procedure that computes the surface intersection between i
ndi-
vidual pixels of the survey with the intersecting
HEALPix
pixels
(see Appendix A of
Paradis et al. 2012a
). After smoothing the
resulting map with a 31.
′
6 FWHM Gaussian kernel to bring it to
1
◦
resolution, this new map gave results more consistent with t
he
1.42 and 2.326 GHz maps.
The Reich et al. full-sky 1.42 GHz map (
Reich 1982
;
Reich
& Reich 1986
;
Reich et al. 2001
) has 36
′
resolution, and the
Jonas et al.
(
1998
) 2.326 GHz map of the southern hemisphere
has 20
′
resolution. These have been destriped but not source-
subtracted. Although the 2.326 GHz map covers up to
+
15
◦
, we
do not use declinations
>
+
10
◦
because the smoothing operation
a
ff
ects the edges of the map.
The 0.408 GHz map is formally calibrated on angular scales
of 5
◦
by comparison with the 404 MHz survey of
Pauliny-Toth
& Shakeshaft
(
1962
), while the 1.42 GHz and 2.326 GHz maps
are tied to absolute sky horn measurements by
Webster
(
1974
)
and
Bersanelli et al.
(
1994
), respectively. Our study is at 1
◦
reso-
lution, with some regions being extended to 2–3
◦
. Therefore one
would expect the brightness temperature (and thus flux densi
ty)
to be under-estimated for many of our sources. The maximum
correction factor is given by the full-beam to main-beam rat
io,
3
National Center for Supercomputing Applications (NCSA), l
ocated
at the University of Illinois at Urbana-Champaign;
http://www.ncsa.
illinois.edu
4
http://lambda.gsfc.nasa.gov/
5
Available from the Bonn Survey Sampler webpage
http://www.
mpifr-bonn.mpg.de/survey.html
which quantifies the power in the full beam (including sidelo
bes)
compared to the main beam. The largest correction factor we a
p-
plied is 1.55 for the Reich et al. 1.42 GHz survey, based on com
-
parisons with bright calibrator sources. We did not make any
corrections to the 0.408 and 2.326 GHz maps, since they were
found to be consistent to within 10 % of the 1.4 GHz data for the
majority of the sources in our sample and for bright extragal
ac-
tic sources. We also note that the positional accuracy of the
se
maps, particularly the 0.408 GHz map, is not particularly go
od.
Visual inspection of the maps suggests inconsistencies of b
right
sources at the level of up to 15
′
at 0.408 GHz. For our analysis,
however, this is not likely to be a major source of error, sinc
e our
integration aperture has a diameter of 2
◦
.
We assumed a 10 % uncertainty in the radio data at all three
frequencies. For the 408 MHz map, which has striations, we
added an additional 3.8 Jy uncertainty corresponding to the
base-
line uncertainty of
±
3 K (
Haslam et al. 1982
) at 1
◦
angular
scales. This is required to bring the
χ
2
value to within acceptable
levels for some sources. This additional uncertainty is not
always
required for sources in our sample, and we find, in fact, that w
e
overestimated our uncertainties in many cases (see Sect.
4.4
).
2.2.2. WMAP
WMAP
9-year data are included in our analysis (
Bennett et al.
2012
). The data span 23 to 94 GHz and thus complement
Planck
data, particularly the K-band (22.8 GHz) channel. The
1
◦
-smoothed maps available from the LAMBDA website are
used. We apply colour corrections to the central frequencie
s us-
ing the recipe described by
Bennett et al.
(
2012
); the local spec-
tral index across each band is calculated using the best-fitt
ing
model (see Sect.
3.5
). This does not exactly take into account
curvature of the spectrum, but is a good approximation given
that the colour corrections are typically a few percent. For
the
majority of sources studied in this paper we are not limited b
y
instrumental noise and we assume a 3 % overall calibration un
-
certainty.
2.2.3. Submm/infrared data
To sample the peak of the blackbody curve for temperatures
greater than 15 K, we include the
COBE
-DIRBE data at 240
μ
m
(1249 GHz), 140
μ
m (2141 GHz), and 100
μ
m (2997 GHz). The
DIRBE data are the Zodi-Subtracted Mission Average (ZSMA)
maps (
Hauser et al. 1998
) regridded into the
HEALPix
format us-
ing the same procedure as used for the 408 MHz map described
in Sect.
2.2.1
. Colour corrections are applied as described in
the DIRBE explanatory supplement version 2.3. Data at highe
r
frequencies are not included in the spectral fits, since they
are
dominated by transiently heated grains not in thermal equil
ib-
rium with the interstellar radiation field and therefore not
easily
modelled by a single modified blackbody curve. Furthermore,
at wavelengths
.
40
μ
m the spectrum contains many emis-
sion
/
absorption lines, which complicates the modelling. For the
statistical comparison, we also include the shorter wavele
ngths
of DIRBE band 7 (4995 GHz) and the
IRAS
12
μ
m (25000 GHz)
and 25
μ
m (12000 GHz) bands. We use the IRIS maps of
Miville-
Deschˆenes & Lagache
(
2005
), which have had bright sources
and a model of zodiacal light removed. Residuals from zodiac
al-
light subtraction are known to be an issue at wavelengths sho
rter
than about 25
μ
m, but are not expected to be significant for the
bright regions in this study because the zodiacal light is re
la-
tively smooth spatially except for a narrow band at low eclip
-
4
Planck Collaboration: P. A. R. Ade et al.: A study of AME in Gal
actic clouds
tic latitudes. We test this assumption by comparing the flux
densities from improved zodiacal-light-subtracted maps (
Marc-
Antoine Miville-Deschenes, private comm.) where the resid
uals
are clearly much smaller. We obtained consistent results wi
thin
a fraction of the errors; the scatter is less than 5 % at the wor
st
band (12
μ
m). Sources were not removed for
|
b
|
>
5
◦
and there-
fore do not a
ff
ect the majority of the sources in our sample.
We use
Spitzer
data where available at 8 and 24
μ
m as a dust
diagnostic for the polycyclic aromatic hydrocarbons (PAHs
) and
very small grains (VSGs), respectively. The
Spitzer
data are ob-
tained from the
Spitzer
data archive,
6
and are reprocessed for the
purposes of this paper in order to mitigate possible systema
tics.
An extended emission correction is applied to the 8
μ
m data, and
the zodiacal light contribution is subtracted from both the
8 and
24
μ
m data. Bright point sources are extracted from both bands
to enable us to investigate the extended emission, and an ove
r-
lap correction is applied to ensure a consistent background
level.
Finally, all the reprocessed data are combined to produce th
e fi-
nal maps used in this analysis; see
Tibbs et al.
(
2011
) for more
details. We are able to measure flux densities for 24 regions.
3. Sample selection and SED fitting
In this section we cover the methods we use to create the
sample of sources. Section
3.1
describes the source detection
method that forms the main sample. Section
3.2
describes the
component subtraction method for detecting potential AME r
e-
gions. Section
3.3
summarizes the final sample of 98 sources.
Section
3.4
describes the aperture photometry method used to
extract the flux densities of the sources. Section
3.5
describes the
model-fitting that is adopted to quantify the various compon
ents
and to assess the contribution of AME. Section
3.6
presents ex-
ample SEDs
7
and a summary of what is observed in our sample.
3.1. Detection of bright sources
At high radio frequencies (30–70 GHz), synchrotron and ther
-
mal dust emission are expected to be relatively faint. The do
mi-
nant emission mechanism is thought to be optically thin free
-free
emission (
α
≈−
0
.
14, where
S
∝
ν
α
), with a possible contribu-
tion from AME. Free-free emission is expected to be particul
arly
strong near the Galactic plane due to the presence of H
ii
regions
and ionized gas near OB stars. This allows H
ii
regions to be de-
tected by simply searching for bright sources in individual
fre-
quency maps. However, in this paper we are mainly interested
in
constructing accurate SEDs across the radio
/
submillimetre
/
far-
infrared wavelength range, which requires the detection of
the
brightest clouds at
all WMAP
/
Planck
frequencies. We used the
SExtractor
software (
Bertin & Arnouts 1996
), which was used
in the “Sextra” pipeline for the Planck Early Release Compac
t
Source Catalogue (
Planck Collaboration VII 2011
), to detect
bright sources at each
Planck
frequency of the CMB-subtracted
maps.
We begin with a
SExtractor
catalogue of 1194 sources de-
tected at 70 GHz. To increase reliability and to ensure the re
-
gion is bright at all
Planck
frequencies, this catalogue is fur-
ther cross-matched with the 28.4 and 100 GHz catalogues, us-
ing a matching radius of the largest beam FWHM (16.
′
38). This
6
http://sha.ipac.caltech.edu/applications/Spitzer/
SHA/
7
Strictly speaking, the SED is frequency multiplied by the flu
x den-
sity (with units W m
−
2
). Here we use the term for the flux density spec-
trum (units W m
−
2
Hz
−
1
).
results in 462 sources that are well-detected across the 30–
100 GHz range. We remove extragalactic sources by searching
the NASA Extragalactic Database (NED
8
) for radio galaxies.
Approximately half of all detected sources, and a majority a
t
|
b
|
&
5
◦
, are found to be extragalactic, most of which are likely
blazars. We also remove a small number of sources associated
with known bright supernova remnants (
Green 2009
) and plan-
etary nebulae (
Acker et al. 1992
). The SIMBAD
9
database is
found to be useful for confirming that a region is dominated by
Galactic emission and that many of our sources are in fact lar
ge
H
ii
complexes or parts of molecular clouds. These regions often
contain several individual sources.
The final stage of catalogue trimming is made by visual in-
spection of the maps and preliminary SEDs made by aperture
photometry (Sects
3.4
,
3.5
, and
3.6
). We make visual inspec-
tion at this resolution, since the final SEDs are to be constru
cted
using 1
◦
-smoothed maps (to ensure that the response to di
ff
use
emission is the same at all frequencies). To ensure a robust s
am-
ple, sources that are not well-defined after smoothing to 1
◦
(i.e.,
do not show a definite peak of emission on scales of
.
2
◦
), or
are relatively faint (
≪
10 Jy at a frequency of 30 GHz), are dis-
carded, except for a few cases at several degrees distance fr
om
the Galactic plane. We find a few sources whose positions are n
ot
exactly centred on the peak of the emission at frequencies of
20–
60 GHz, with o
ff
sets as large as 10–20
′
. This can occur because
of the complexity of the Galactic plane, which after filterin
g can
produce multiple peaks in close proximity to each other. In t
hese
cases, we manually shift the position to the approximate cen
tre
of the hotspot. Since we are using a large 1
◦
radius aperture (see
Sect.
3.4
), this makes little di
ff
erence to the SEDs. We identify
94 candidate AME sources using this technique.
3.2. Detection of AME regions by component subtraction
We use a simple CMB
/
foreground subtraction method to iso-
late AME from the other di
ff
use components. This method is
essentially the same as was used by
Planck Collaboration XX
(
2011
), where potential AME regions were located by a sim-
ple subtraction of the non-AME components from the 28.4 GHz
Planck
CMB-subtracted map. The one di
ff
erence is that here
we only use the 0.408 GHz map to trace the synchrotron emis-
sion, which is extrapolated with a single power law and a spec
-
tral index
β
=
−
3
.
0 (
T
∝
ν
β
). This is a typical value of the
slope between 408 MHz and
WMAP
/
Planck
frequencies (
Davies
et al. 2006
;
Gold et al. 2011
). The combination of the 1.4 GHz
and 2.3 GHz maps is not used, as it creates large-scale arte-
facts. Although there is some evidence of flattening (
β
≈−
2
.
7)
of the synchrotron index at low Galactic latitudes (e.g.,
Gold
et al. 2009
), we use the typical high latitude value. For most
sources on the Galactic plane, the synchrotron emission is a
mi-
nor component at frequencies above 23 GHz. For the free-free
component we use the dust-corrected H
α
map of
Dickinson et al.
(
2003
). For thermal dust, we use model 8 of
Finkbeiner et al.
(
1999
). Both are calculated at a frequency of 28.4 GHz.
We smooth the
Planck
CMB-subtracted maps to a reso-
lution of 1
◦
and subtract the non-AME components from the
Planck
28.4 GHz map to create a map of residuals. A 5
◦
-
smoothed version is also created and subtracted from the 1
◦
map
to remove large-scale emission and highlight the compact re
-
gions most suited for this analysis. The di
ff
use emission re-
moved here will be the focus of future papers.
8
http://ned.ipac.caltech.edu/
9
http://simbad.u-strasbg.fr/simbad/
5
Planck Collaboration: P. A. R. Ade et al.: A study of AME in Gal
actic clouds
Fig. 1.
Map of residuals at 28.4 GHz after subtracting o
ff
syn-
chrotron, free-free, thermal dust, and CMB components (see
text), in mK (R-J) units. A 5
◦
-smoothed version of the map is
subtracted to remove extended di
ff
use emission to more easily
identify bright, relatively compact sources. This map is sh
own
in the Mollweide projection, with
l
=
0
◦
in the centre and in-
creasing to the left.
The resulting map of residuals at 28.4 GHz is shown in
Fig.
1
. The large-scale features, including negative artefacts,
are not of concern here. Instead, we used this map as a “find-
ing chart” to identify new regions that emit detectable leve
ls of
AME. Approximately 100 bright well-defined sources are lo-
cated by eye and a spectrum is produced for each one using
aperture photometry (see Sect.
3.4
). The well-known AME re-
gions in Ophiuchus and Perseus stand out in this map. Lots
of free-free emission (usually because it can be self-absor
bed
at lower frequencies) and synchrotron point sources (with a
flatter spectral index than
β
=
−
3
.
0, and hence not removed
completely by extrapolating the synchrotron map assuming a
steep spectrum) can be found in this residual map. Most of
the 100 AME candidates are H
ii
regions; 20 sources show ev-
idence for excess emission at 30 GHz based on an initial spec-
tral fit, out of which 16 have already been identified using the
source-detection method (Sect.
3.1
). The four additional sources
found using this technique are G037.79
−
00.11, G293.35
−
24.47,
G317.51
−
00.11, and G344.75
+
23.97.
3.3. Final sample
The final sample contains 98 sources, listed in Table
3
. The
superscript letter after the name indicates which method th
e
source is chosen from. Most of the sources are located using
the
SExtractor
detection technique, with a few of the AME-
dominated sources being detected using the component sub-
traction method. We also indicate if a source is already know
n
from previous AME studies. A few previously identified AME
candidates are not on this list because they are not detected
at
high significance in the
Planck
data, mostly due to the lim-
ited angular resolution of this study. These include RCW175
(
Dickinson et al. 2009
), LDN1621 (
Dickinson et al. 2010
), M78
(
Castellanos et al. 2011
), LDN1780 (
Vidal et al. 2011
), and
LDN1111
/
675
/
1246 (
Scaife et al. 2009
,
2010a
). Associations
with known objects are listed in the notes column of Table
3
.
The
Planck
CMB-subtracted map with the locations of the
sources is shown in Fig.
2
. Most of the sources lie within a few
degrees of the Galactic plane. A few sources are in the well-
known regions of Ophiuchus (
l
=
0
◦
), Perseus (
l
=
160
◦
), Orion
(
l
=
200
◦
), and the Gum nebula (
l
=
260
◦
). The most signifi-
cant (
σ
AME
>
5 and
f
UCH
ii
max
<
0
.
25; see Sect.
4
) AME sources
are shown as thick squares; sources that have excess emissio
n
(
σ
AME
>
5) but have a potentially large contribution of opti-
cally thick free-free emission from ultra-compact H
ii
(UCH
ii
)
regions (
f
UCH
ii
max
>
0
.
25) are shown as stars. It is interesting to
see that these AME-bright sources appear to cluster in certa
in
regions, particularly along the local Gould Belt region (
Planck
Collaboration Int. XII 2013
). There seem to be no bright AME
regions along the lines-of-sight to the local spiral arm at
l
=
90
◦
and
l
=
270
◦
. In general, few of the most significant AME
sources lie on the plane. This is partly explained by the remo
val
of AME sources that have a potential UCH
ii
contribution, based
on infrared sources (see Sect.
4.2
), which preferentially lie in
the Galactic plane. In addition, there is a selection e
ff
ect, since
the high free-free brightness temperatures and overall con
fusion
in the plane make it more di
ffi
cult to identify individual AME-
bright objects. It may also be that these sight-lines contai
n a
strong component of free-free emission from warm ionized ga
s,
which is thought to exhibit less AME than cold neutral medium
(CNM) or molecular clouds (
Planck Collaboration XXI 2011
).
With our incomplete sample, such claims cannot be confirmed
in this study.
3.4. Aperture photometry
We use the
HEALPix
aperture photometry code developed for
Planck Collaboration XX
(
2011
) to extract the flux densities of
the regions from the maps. This software has also been used
to investigate at the polarization of AME from
ρ
Ophiuchi
in
Dickinson et al.
(
2011
). After converting from CMB ther-
modynamic units (K
CMB
) to RJ units (K
RJ
) at the central fre-
quency, the maps are converted to units of Jy pixel
−
1
using
S
=
2
kT
RJ
Ω
ν
2
/
c
2
, where
Ω
is the
HEALPix
pixel solid angle.
The pixels are then summed in a circular aperture of 60
′
to ob-
tain an integrated flux density. An estimate of the backgroun
d is
subtracted using a median estimator of pixels lying at radii
be-
tween 80
′
and 100
′
. By using Monte Carlo injection of sources,
we find that this choice of aperture and annulus size provides
the least scatter in recovered flux densities, and is a reason
able
balance for obtaining an appropriate background level with
out
subtracting appreciable flux density from the source itself
.
The flux density uncertainties are estimated from the rms
of the values in the background annulus and added in quadra-
ture to the absolute calibration uncertainties for each map
(see
Sect.
2.2
). Simulations of injected point-like sources show that
the flux density estimates are unbiased and that the uncertai
nties
are reasonable; however, the exact value of flux density unce
r-
tainty for each source is di
ffi
cult to quantify, since it depends
very strongly not only on the brightness of the source and bac
k-
ground, but also on the morphology of the emission in the vici
n-
ity of the source. This will be discussed further in Sect.
4.4
.
Colour corrections, based on the local spectral index acros
s each
band, are applied during the model-fitting, as described in t
he
next section.
3.5. Model fitting
We take the flux density
S
for each source from the aperture
photometry and fit a simple model of free-free, synchrotron
(where appropriate), CMB, thermal dust, and spinning dust c
om-
ponents:
6
Planck Collaboration: P. A. R. Ade et al.: A study of AME in Gal
actic clouds
Fig. 2.
CMB-subtracted
Planck
28.4 GHz map covering the entire Galactic plane and latitude
s
|
b
|
<
30
◦
. The colour scale has a
logarithmic stretch. Regions with the most significant AME a
re highlighted as thick squares while the rest of the sample a
re shown
as circles. Regions with significant excess emission but wit
h a potential UCH
ii
contribution (
f
UCH
ii
max
>
0
.
25) are shown as star
symbols (see Sect.
4.2
).
S
=
S
ff
+
S
sync
+
S
td
+
S
CMB
+
S
sp
.
(1)
The free-free flux density
S
ff
is calculated from the brightness
temperature
T
ff
, based on the optical depth
τ
ff
, using the standard
formula
S
ff
=
2
k T
ff
Ω
ν
2
c
2
,
(2)
where
k
is the Boltzmann constant,
Ω
is the solid angle of the
aperture, and
ν
is the frequency, with
T
ff
=
T
e
(1
−
e
−
τ
ff
)
,
(3)
and the optical depth
τ
ff
is given by
τ
ff
=
5
.
468
×
10
−
2
T
−
1
.
5
e
ν
−
2
EM
g
ff
,
(4)
in which the Gaunt factor can be approximated
10
by
g
ff
=
ln
exp
5
.
960
−
√
3
π
ln(
Z
i
ν
9
T
−
3
/
2
4
)
+
2
.
71828
.
(5)
For the analysis of AME, we assume a fixed electron temperatur
e
of 8000 K for
T
e
for all regions, fitting only for the emission
measure (EM). Note that this is not the true EM, but an e
ff
ective
EM over the 1
◦
radius aperture. For compact sources, the quoted
EM will be underestimated.
For six sources, we also include a synchrotron component
modelled as a power law with amplitude
A
sync
and variable flux
density spectral index
α
,
S
sync
=
A
sync
ν
GHz
α
.
(6)
The thermal dust is fitted using a modified blackbody model,
S
td
=
2
h
ν
3
c
2
1
e
h
ν/
kT
d
−
1
τ
250
(
ν/
1
.
2 THz)
β
d
Ω
,
(7)
fitting for the optical depth
τ
250
, the dust temperature
T
d
, and the
emissivity index
β
d
. The CMB is fitted using the di
ff
erential of a
blackbody at
T
CMB
=
2
.
7255 K (
Fixsen 2009
)
S
CMB
=
2
k
Ω
ν
2
c
2
!
∆
T
CMB
.
(8)
10
Here we use the approximation given by
Draine
(
2011
), which is ac-
curate to better than 1 % even up to frequencies of 100 GHz and h
igher.
Here
∆
T
CMB
is the CMB fluctuation temperature in thermody-
namic units. The spinning dust is fitted using
S
sp
=
A
sp
j
(
ν
+
ν
shift
)
Ω
,
(9)
where we use a model for
j
ν
calculated using the
SPDUST
(v2)
code (
Ali-Ha ̈ımoud et al. 2009
;
Silsbee et al. 2011
). We choose a
model corresponding to the warm ionized medium (WIM) with a
peak at 28.1 GHz to give the generic shape, and allow for a shif
t
of this model with frequency. We therefore fit for two parame-
ters corresponding to the AME amplitude
A
sp
, and a frequency
shift
ν
shift
. Note that the units of
A
sp
are formally of column den-
sity (cm
−
2
). If the spinning dust model was appropriate for the
line-of-sight, and no frequency shift was applied, then thi
s would
indeed be the column density
N
H
; however, since this quantity is
model-dependent and there is potentially a shift in frequen
cy, we
do not take this to be a reliable estimate of
N
H
. Similarly, in this
paper we do not attempt to fit specific spinning dust models to
each source, hence the derived column density is not necessa
rily
physical;
A
sp
is essentially the flux density at the peak normal-
ized to the spinning dust model. Given the large uncertainti
es
and di
ffi
culty in separating the various spectral components, we
have not attempted to look for deviations from the basic spin
ning
dust model (
Hoang et al. 2011
).
The least-squares fit is calculated using the
MPFIT
11
(
Markwardt 2009
) package written in IDL, with starting val-
ues estimated from the data and with amplitude parameters co
n-
strained to be positive except for the CMB, which is allowed
to go negative.
MPFIT
also provides estimates of the 1
σ
uncer-
tainties for each parameter, taken as the square root of the d
i-
agonal elements of the parameter covariance matrix. We note
four special cases in Table
3
(G068.16
+
01.02, G076.38–00.62,
G118.09
+
04.96 and G289.80–01.15) where the fitting returned
A
sp
=
0
.
0
±
0
.
0. These could be mitigated by removing the posi-
tivity prior, with best-fitting negative values still being
consistent
with zero. Instead, for these special cases, we fixed
A
sp
to zero
to make the fits more physically meaningful, since the spinni
ng
dust spectrum should not go negative.
3.6. Example SEDs
Some example SEDs for regions with weak AME are shown in
Fig.
3
; see Sect.
4.3
and Fig.
8
for SEDs with significant AME.
11
http://purl.com/net/mpfit
7