Issue |
A&A
Volume 520, September-October 2010
|
|
---|---|---|
Article Number | L8 | |
Number of page(s) | 4 | |
Section | Letters | |
DOI | https://doi.org/10.1051/0004-6361/201015301 | |
Published online | 30 September 2010 |
LETTER TO THE EDITOR
Variations of the spectral index of dust emissivity from Hi-GAL
observations of the Galactic plane![[*]](/icons/foot_motif.png)
D. Paradis1 - M. Veneziani1,2 - A. Noriega-Crespo1 - R. Paladini1 - F. Piacentini2 - J. P. Bernard3,4 - P. de Bernardis2 - L. Calzoletti 5 - F. Faustini5 - P. Martin6 - S. Masi2 - L. Montier3,4 - P. Natoli7 - I. Ristorcelli3,4 - M. A. Thompson8 - A. Traficante7 - S. Molinari9
1 - Spitzer Science Center, California Institute of Technology, Pasadena, CA 91125, USA
2 - Dipartimento di Fisica, Universita di Roma 1 La Sapienza, 00185 Roma, Italy
3 - Université de Toulouse, UPS, CESR, 9 avenue du Colonel Roche, 31028 Toulouse Cedex 4, France
4 - CNRS, UMR 5187, 31028 Toulouse, France
5 - ASI Science Data Center, 00044 Frascati (Rome), Italy
6
- Canadian Institute for Theoretical Astrophysics, University of
Toronto, 60 St. George Street, Toronto, ON M5S 3H8,
Canada
7 - Dipartimento di Fisica, Universita di Roma Tor Vergata, Rome, Italy
8 - Centre for Astrophysics Research, Science & Technology Institute,
University of Hertfordshire, Hatfield, AL10 9AB, UK
9 - INAF - IFSI - via Fosso del Cavaliere 100, Rome, Italy
Received 30 June 2010 / Accepted 13 September 2010
Abstract
Context. Variations in the dust emissivity are critical for
gas mass determinations derived from far-infrared observations, but
also for separating dust foreground emission from the Cosmic Microwave
Background (CMB). Hi-GAL observations allow us for the first time
to study the dust emissivity variations in the inner regions of the
Galactic plane at resolution below 1.
Aims. We present maps of the emissivity spectral index derived from the combined Herschel PACS 160 m, SPIRE 250
m, 350
m, and 500
m data, and the IRIS 100
m
data, and we analyze the spatial variations of the spectral index as a
function of dust temperature and wavelength in the two science
demonstration phase Hi-GAL fields, centered at
and
.
Methods. Applying two different methods, we determine both dust temperature and emissivity spectral index between 100 and 500 m, at an angular resolution (
)
of 4
.
Results. Combining both fields, the results show variations of
the emissivity spectral index in the range 1.8-2.6 for temperatures
between 14 and 23 K. The median values of the spectral index
are similar in both fields, i.e. 2.3 in the range 100-500 m, while the median dust temperatures are equal to 19.1 K and 16.0 K in the
and
field, respectively. Statistically, we do not see any significant
deviations in the spectra from a power law emissivity between 100
and 500
m.
We confirm the existence of an inverse correlation between the
emissivity spectral index and dust temperature, found in previous
analyses.
Key words: dust, extinction - infrared: ISM
1 Introduction
The large dust grains (big grain component as defined in Désert et al. 1990) dominate the total dust mass, as well as the
observed emission in the
far-infrared (FIR) domain (Draine & Li 2007). They radiate in thermal equilibrium with
the interstellar radiation field, and their emission spectrum, assuming a fixed dust abundance and a single grain size,
is well approximated by
where






Previous observations in the submillimeter (submm), at arcminute
resolution, such as those by the balloon-borne experiments PRONAOS
(Dupac et al. 2003) and ARCHEOPS (Désert et al. 2008) found evidence of an inverse relationship between
and
in various environments of the
interstellar medium (ISM). In PRONAOS data, variations
of the spectral index were observed in the range 2.4 to 0.8 for
dust temperatures between 11 and 80 K, whereas ARCHEOPS data
showed a more pronounced inverse relationship with
values going from 4 to 1 between 7 and 27 K. Recently Veneziani et al. (2010) highlighted a similar trend analyzing
and
for eight high Galactic
latitude clouds, by combining IRAS, DIRBE, and WMAP data with BOOMERanG
observations. The
values vary from 5 to 1
in the temperature range 7-20 K, with a behavior similar to that
derived from ARCHEOPS data. These variations of
with dust temperature could be owing to intrinsic properties of amorphous dust grains, as
proposed by Mény et al. (2007), but the impact of the noise and the
temperature mixing along the line of sight (LOS) must be
carefully taken into consideration, before a physical interpretation
can be made.Variations of the apparent spectral index in a sample of cores in the Galactic plane have been observed
(Hill et al. 2006) using SCUBA and SIMBA. However, because of the restricted
wavelength range of their observations, these authors could not attribute
them to temperature variations.
Moreover, none of the previous analyses allowed the study of the
correlation at arcminute scales in the inner regions of
the Galactic plane.
Thanks to the Herschel Hi-GAL data (
,
2
maps, centered in the Galactic plane at
and
,
see Molinari et al. 2010a,
b), we can now
extend for the first time this type of analysis to the inner Galactic
plane, and on continuous fields of diffuse emission. An overview of the
Herschel instruments is given in
Pilbratt et al. (2010).
In this paper we analyze emissivity variations between 100 and 500
m. We then derive both the dust temperature and spectral index
from Eq. (1), assuming a single temperature along the LOS. This assumption is relatively correct for the
field, where there is less contamination along the LOS in
comparison with the
field. Indeed, the LOS toward the inner
field crosses several regions with a presumably
wider range of temperatures.
An accurate temperature determination requires sampling both sides of the
emission peak. The 70
m brightness is generally contaminated by
out-of-equilibrium emission from very small grains (VSGs) and cannot
be used to derive thermal dust temperature without an accurate
subtraction of this component. This contribution has been investigated
by Compiegne et al. (2010). Therefore we include the
IRAS data at 100
m in our analysis, for which we estimate an average VSG contamination of less than 10%. This implies
degrading the original resolution of the Hi-GAL data by adopting
the IRAS angular resolution of 4
.
We note, as a
consequence, an averaging effect within the resolution element,
which also needs to be taken into account in the interpretation of the results
of the present analysis.
![]() |
Figure 1:
Left: spectral index in the 100 to 500 |
Open with DEXTER |
One of the key aspects in the analysis of CMB is the ability to separate its emission from the other astrophysical foregrounds (including thermal dust) through multifrequency observations. While it is not easy to achieve successful component separation over the Galactic plane, determining the dust spectral index variations across the sky can efficiently help in reducing the number of unknowns in the problem (Ricciardi et al. 2010).
2 Data
We use the ROMAGAL Herschel PACS and SPIRE maps described in
Traficante et al. (in prep.), combined with the IRIS (Improved Reprocessing
of the IRAS Survey, see Miville-Deschênes & Lagache 2005) 100 m data. Multiplicative factors (0.78,1.02, 1.05 and 0.94 at 160, 250,
350 and 500
m, respectively) have been applied to the data (Swinyard et al. 2010; Griffin et al. 2010; Poglitsch et al. 2010). An absolute calibration accuracy of 20% and 15% for PACS and SPIRE has been adopted. We applied the offsets given in Bernard et al. (2010)
. All maps have been convolved with a Gaussian kernel, with a FWHM of 4
,
i.e. equal to the IRIS 100
m
angular resolution. In addition, the maps have been rebinned on a uniform grid with a pixel size of 1.65
.
The IRIS 100
m calibration uncertainty is taken to be 13.5% (see Miville-Deschênes & Lagache 2005).
![]() |
Figure 2:
Representative SEDs combining IRIS 100 |
Open with DEXTER |
3 Variations of the emissivity spectral index with temperature
We use two different methods for the simultaneous derivation of the dust
temperature and the emissivity spectral index. Both allow us to
fit the data with a modified blackbody function (see Eq. (1)). In
the first method we perform an
minimization, applying the same code as described in
Dupac et al. (2001), using the IDL least-square fit curvefit
function to deduce the
and
parameters, as well as
their 1
uncertainties.
The second method estimates the best-fit parameters by looking for the
maximum likelihood, using a
Monte Carlo Markov Chain (MCMC) algorithm (Lewis & Bridle 2002) and
represents a bayesian approach to parameter
estimation. The posterior distribution for the parameters is sampled
by using the Metropolis-Hastings algorithm, and a maximum likelihood
estimate is derived jointly for
and
.
We chose a
wide flat a priori probablity density of the parameters, i.e. 0 K
K and -
,
in order not to constrain the fit results. A benefit of this
method is that it also recovers the joint posterior distribution of the
two estimated parameters. We make use of this feature to explore the
-
correlation as explained below.
We fit the spectral energy distribution (SED) between 100 and 500 m for each pixel of the maps, using both methods. The color
correction is computed iteratively in all channels. Results of the
-
determination for each field are shown in Fig. 1. Only pixels with a surface brightness at 500
m higher than 105 MJy/sr and 50 MJy/sr for the
and
fields, respectively, have been considered. Both methods show a clear anti-correlation
-
in each field. These two independent methods also highlight a good agreement. The
values range
from
2.6 to
1.9 for temperatures between 17.5-23 K for the
field, and from
2.7 to
1.8, between 14 and 21 K, for the
field.
The assumption made of a single temperature along the LOS
may hold in the
field, but is certainly too simplistic
for the
field, since temperature variations along the LOS
are larger in the inner field (see Bernard et al. 2010). The analysis of the
field
would certainly require an accurate
combination of temperatures and column densities. However, our methods
do not allow the simultaneous fitting of a complex mixture of spectra.
Even if the
field is potentially characterized by several grain temperatures
along the LOS (associated to Sagittarius, Scuttum-Crux and Perseus,
as described in Bernard et al. 2010), and therefore could induce a spurious
-
inverse correlation
(Masi et al. 1995; Shetty et al. 2009), the
field, less contaminated by
various dust mixing effects, still highlights a pronounced behavior in
the
-
parameter space. Both fields, with a different mixture of temperatures,
present a
-
anti-correlation. We therefore interpret
this as an indication that the mixture of temperatures is probably not
the dominant responsible effect for the observed anti-correlation.
The spatial distribution of
is shown in Fig. 1. Warmer regions, which most often correspond to bright
regions, show lower beta values. However,
the
field presents a gradient along the East-West direction,
which is not observed in the PACS or SPIRE surface brightness maps. The stripes visible in the maps are
associated to low-level residual stripes in the IRIS
data. In the
field,
values higher than 2.6 located at
48
,
20
correspond
to one of the less active star-forming regions, although the
PACS 160 data show an artifact at this location, disclosed by a
high
(see Fig. 1). In the same field, the lowest
values
(
1.8) are found for an HII region, with a bright source nearby at
38
,
38
.
Representative
examples of SEDs with a gray-body fit are presented in Fig. 2,
illustrating the agreement between the data and the model.
The two parameters -
are degenerate in the parameter space, creating a spurious inverse relation (Shetty et al. 2009) that has to be considered while investigating if an intrinsic physical correlation indeed exists. In
order to properly estimate the relationship between
and
,
we have to take into account
the correlation that is shown by the spectral shape in
Eq. (1)
and caused by calibration uncertainties. One way to include the effect
of the degeneracy is to estimate this effect not only for the
-
best-fit values but for
points included in the 68% contours of the two-dimensional posterior
probability obtained with the MCMC method. Within the 68% contours
the points are not uniformly distributed, but their density is higher
close to the maximum of the probability, increasing their weight, and lower close to the boundaries. Assuming the model
,
between 100 and 500
m in both fields,
the fit is then performed on all the
-
couples inside
a posteriori probability contour of each pixel, chosen randomly, one for each pixel and weighted as described.
We then take a point within the contour for each pixel of the map and
fit the trend to estimate the A and
parameters. We repeat
this procedure until we obtain a good sampling of the shape of the
distribution of posterior probabilities. This method has been
successfully tested on BOOMERanG data (Veneziani et al. 2010) and allows
us to include the effects of degeneracy in the error bars. The
resulting A and
ditributions are well approximated by Gaussian functions, even if a
slight asymmetry is present. The center of the Gaussian is the more
likely value, while the error is estimated by marginalizing over the
other parameter. The best-fit values so obtained are
![]() |
(2) |
![]() |
(3) |
Figure 3 shows the results of the fitting method over the probability 68% contours with only a few pixels out of



![]() |
Figure 3:
|
Open with DEXTER |








4 Variations of the emissivity spectral index with wavelength
In the previous section we have found evidence of spectral index variations with temperature. As predicted by
Mény et al. (2007), a flattening of the emissivity
spectrum (and so a lower )
is expected for wavelengths longer
than 500
m as a consequence of the internal structure of the
grains. Recently, Gordon et al. (2010) highlighted
an emission excess at 500
m in the Large Magellanic Cloud that could be of the same origin. However, this excess is of about
10%, which is lower than the SPIRE calibration uncertainties of
15%. The Herschel data do not allow us to study emissivity variations at longer wavelengths than 500
m.
Although the SEDs in each field (left and
central panel of Fig. 2) do not provide evidence for any
departures from a power law, we analyze the possibility of an emissivity excess at 500 m. To properly perform this study, the temperature estimates need to be done independently of the 500
m data. Therefore we have redone the
and
determination with the least-square fit method using only data between 100 and 350
m, and we compare the emission at 500
m with the value predicted by extrapolating the emissivity power law between 100 and 350
m. The predicted values are systematically lower than the data at 500
m in both fields, by 16% in
and 13% in
,
which could favor the hypothesis of an emissivity excess at this
wavelength. These values are not significant compared to the
uncertainties on the SPIRE data. Moreover, we suspect that the PACS 160
m data suffer from
calibration issues, as discussed in Bernard et al. (2010). The calibration
uncertainty at 160
m does not impact the results of the
global analysis described above, but here the limitation of the wavelength range (100-350
m)
removes some constraints on the fit, resulting in an overestimate with
respect to the data at 250
m, and an underestimate at 500
m
(see Fig. 2, right panel). However, if we slightly shift down the 160
m data points, the apparent
underestimate at 500
m
would disappear. For this reason, we do not claim that this excess is
real and we think instead that the emissivity spectra are relatively
constantbetween 100 and 500
m with similar median
values in both fields, i.e. 2.3, even if the median temperature is
statistically lower in the
field (
K
for
and
K for
).
5 Conclusions
We investigated variations in the spectral index of the dust
emissivity, with temperature and wavelength, in the inner Galactic
plane, using the new Herschel observations in two Hi-GAL fields, centered at
and
,
acquired during the Herschel Science Demonstration phase, combined with the IRIS 100
m
data. We fitted the
SEDs for each pixel of the two fields with two independent methods,
deriving
simultaneously the emissivity spectral index and the dust temperature
by adjusting a modified blackbody function to the data. The results are
similar with both methods. Using a Monte Carlo Markov Chain algorithm
method we computed the 68% likelihood contours for each point. We
find a
-
inverse correlation, with the local variation
going from 1.8 to 2.6 for temperatures between 14 and 23 K, shown
for the first time in the inner Galactic plane. Moreover, our results
indicate a different trend with respect to previous investigations based on BOOMERanG, ARCHEOPS, and
PRONOAS data, probably because of different dust
properties in the inner Galactic plane compared to other
environments. An extensive follow-up analysis will be required to take
into consideration the mixture of temperatures along the line of
sight. The median value of
is similar in both fields, equal to 2.3, slightly higher than the
usual reference value of 2. We do not favor the hypothesis of an
emissivity excess at 500
m, as suggested for the Large Magellanic Cloud. A complementary forthcoming study will combine Planck with Herschel data to investigate possible changes in the dust emissivity spectrum at wavelengths larger than 500
m, as reported in previous studies of dust emission in our Galaxy.
Data processing and maps production have been possible thanks to ASI generous support via contract I/038/080/0. M.V. is grateful to Davide Pietrobon for software support.
References
- Bernard, J.-P., Paradis, D., Marshall, D., et al. 2010, A&A, 518, L88 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Compiegne, M., Flagey, N., Noriega-Crespo, et al. 2010, ApJ, submitted [Google Scholar]
- Désert, F.-X., Boulanger, F., & Puget, J. L. 1990, A&A, 237, 215 [NASA ADS] [Google Scholar]
- Désert, F.-X., Macías-Pérez, J. F., Mayet, F., et al. 2008, A&A, 481, 411 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Draine, B. T., & Li, A. 2007, ApJ, 657, 810 [NASA ADS] [CrossRef] [Google Scholar]
- Dupac, X., Giard, M., Bernard, J.-Ph., et al. 2001, ApJ, 553, 604 [Google Scholar]
- Dupac, X., Bernard, J.-Ph., Boudet, N., et al. 2003, A&A, 404, L11 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Gordon, K., Galliano, F., Hony, S., et al. 2010, A&A, 518, 89 [Google Scholar]
- Griffin, M. J., Abergel, A., Abreu, A., et al. 2010, A&A, 518, L3 [Google Scholar]
- Hill, T., Thompson, M. A., Burton, M. G., et al. 2006, MNRAS, 368, 1223 [NASA ADS] [CrossRef] [Google Scholar]
- Lewis, A., & Bridle, S. 2002, Phys. Rev., 66, 103511 [Google Scholar]
- Masi, S., Aquilini, E., Boscaleri, A., et al. 1995, ApJ, 452, 253 [NASA ADS] [CrossRef] [Google Scholar]
- Mathis, J. S., Mezger, P. G., & Panagia, N. 1983, A&A, 128, 212 [NASA ADS] [Google Scholar]
- Mény, C., Gromov, V., Boudet, N., et al. 2007, A&A, 468, 171 [Google Scholar]
- Miville-Deschênes, M. A., & Lagache, G. 2005, ApJS, 157, 302 [NASA ADS] [CrossRef] [Google Scholar]
- Molinari, S., Swinyard, B., Bally, J., et al. 2010a, PASP, 122, 314 [NASA ADS] [CrossRef] [Google Scholar]
- Molinari, S, Swinyard, B., Bally, J., et al. 2010b, A&A, 518, L100 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Pilbratt, G. L., Riedinger, J. R., Passvogel, T., et al. 2010, A&A, 518, L1 [CrossRef] [EDP Sciences] [Google Scholar]
- Poglitsch, A., Waelkens, A., Geis, N., et al. 2010, A&A, 518, L2 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Ricciardi, S., Bonaldi, A., Natoli, P. et al. 2010, MNRAS, 406, 1644 [NASA ADS] [Google Scholar]
- Shetty, R., Kauffmann, J., Schnee, S., et al. 2009, ApJ, 696, 2234 [NASA ADS] [CrossRef] [Google Scholar]
- Stepnik, B., Abergel, A., Bernard, J. P., et al. 2003, A&A, 398, 551 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Swinyard, B. M., Ade, P., Baluteau, J. P., et al. 2010, A&A, 518, L4 [Google Scholar]
- Veneziani, M., Ade, P. A. R., Bock, J. J., et al. ApJ, 2010, 713, 959 [Google Scholar]
Footnotes
- ... plane
- Herschel is an ESA space observatory with science instruments provided by European-led Principal investigator consortia and with important participation from NASA.
- ...Bernard et al. (2010)
- See their Table 1
All Figures
![]() |
Figure 1:
Left: spectral index in the 100 to 500 |
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Representative SEDs combining IRIS 100 |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
|
Open with DEXTER | |
In the text |
Copyright ESO 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.