Issue |
A&A
Volume 520, September-October 2010
|
|
---|---|---|
Article Number | A18 | |
Number of page(s) | 10 | |
Section | Interstellar and circumstellar matter | |
DOI | https://doi.org/10.1051/0004-6361/200913402 | |
Published online | 23 September 2010 |
Properties of dust in the high-latitude translucent cloud L1780
II. 3D radiative transfer modelling
M. Ridderstad1,2 - M. Juvela1,2
1 - Department of Physics, PO Box 64, 00014 University of Helsinki, Finland
2 -
Observatory, University of Helsinki, Finland
Received 4 October 2010 / Accepted 14 May 2010
Abstract
Context. Lynds 1780 is a high-latitude cloud where, based on 2MASS, the maximum visual extinction is
mag at a resolution of 3
.
In LDN1780, increased far-infrared (FIR) emissivity of dust grains has
been observed, and the infrared emission is found to peak at different
locations at different wavelengths.
Aims. By modelling the FIR observations, we try to quantify
spatial variations of dust properties and to determine to what extent
the observations could be affected by the asymmetry of the heating
radiation field.
Methods. We have constructed a three-dimensional cloud model
and, with the help of radiative transfer calculations, compare its
predictions with the FIR surface brightness measurements of LDN1780
performed with the ISO satellite. The effects of anisotropic radiation,
its attenuation in a diffuse extinction layer around the cloud, and
variations in the dust properties are investigated.
Results. Asymmetry of the radiation field is found to have only
a small effect on the morphology of mid- and far-infrared surface
brightness. The general agreement between observations and the model
predictions is improved by assuming the presence of a low extinction
external layer with
mag.
However, to explain the changes in the relative intensity of mid- and
far-infrared bands, one has to assume strong variations in the relative
abundance of small and large grain components and, at the very centre
of the cloud, enhanced emissivity of large grains.
Conclusions. The separate emission maxima at different
wavelengths in LDN1780 result from real variations in spatial
distributions of dust components. Modifications to standard dust
models, including a 30% increase in the FIR emissivity, are needed to
explain the far-infrared observations towards the centre of LDN1780.
The relative abundances of dust components are found to be very
sensitive to the strength of the external radiation field.
Key words: ISM: clouds - infrared: ISM - ISM: individual objects: L1780 - dust, extinction - radiative transfer
1 Introduction
During the past three decades, the interstellar dust models have gone
through
an intense period of development, beginning from the large, spherical
grains,
and ending up with the latest observational results indicating the
presence of fluffy and/or ice-coated grains with increased emissivity
in the cold cores of molecular clouds (Cambrésy et al. 2001; del Burgo et al. 2003; Stepnik et al. 2003; Kramer et al. 2003). The distribution, dynamics, and evolution of
the interstellar dust in the clouds have become better understood. The first models of the interstellar dust
were based on large grains, assumed to consist mainly of graphite and
silicates (e.g. Mathis et al. 1977; Draine & Lee 1984). However, with the
detection of strong emission in the IRAS 12 m and 25
m bands
(Boulanger et al. 1985), it became clear that a component of very small grains
needs to be included in the models of interstellar medium (ISM) (Weiland et al. 1986). The Infrared Space Observatory (ISO) and the Infrared Telescope in
Space (IRTS) satellites further revealed the presence of the so-called
unidentified infrared bands (UIBs) at 3-12
m, which are now generally
attributed to polycyclic aromatic hydrocarbons (PAHs). A number of models of
interstellar dust, including not only the largest grains but also both very
small grains (VSGs) and PAHs, have been presented (e.g., Désert et al. 1990;
Siebenmorgen & Krügel 1992a,b; Dwek et al. 1997; Draine & Li 2001; and
Li & Draine 2001; Zubko et al. 2004; Draine & Li 2007). For information on
different dust models and their development towards the current models, see,
e.g., Draine & Li (2007); Witt et al. (2000); Li & Draine (2001).
With the development of dust models and methods of continuum radiative
transfer (hereinafter RT), more sophisticated models have been developed for
individual clouds. These take the full grain size distribution into account
and include special treatment for transiently heated grains that includes both
the traditional VSGs and PAHs (see, e.g., Siebenmorgen & Krügel 1992a,b; Bernard et al. 1992, 1993; Verter et al. 2000; Stepnik et al. 2003;
Rawlings et al. 2005). Bernard et al. (1993) used the dust model of Désert
et al. (1990) to compute the emission for three clouds in Chamaeleon and
-Ophiuchi approximated by spherically symmetric homogeneous clouds. They
found that IRAS colours indicate true variations in the distributions of
different dust components. Most notably, the so-called limb-brightening effect
was found to be caused by increased abundance of PAHs in the outer regions of
the clouds. Verter et al. (2000) modelled a sample of eight nearby translucent,
high-latitude clouds using the three-component dust model of Dwek et al.
(1997) that consist of grains of the Mathis-Rumpl-Nordsieck (MRN) model
(Mathis et al. 1977), very small graphite grains, and PAHs.
Their results show that the relative abundance of VSGs and PAHS changes
from cloud to cloud.
Rawlings et al. (2005) compared ISO observations of the Chamaeleon ``Blob''
with theoretical predictions calculated using spherically symmetric cloud
models and variations of the Li & Draine (2001) dust model. Their results
indicate that, even within a single translucent cloud, there are clear
variations in the relative abundances of the dust components of different
sizes. Stepnik et al. (2003), also with the dust model of Désert et al.
(1990), indicate that increased far-infrared emissivity is needed to produce the observed
dust properties inside a cloud filament with a low temperature and
extinction of the order of
.
Ridderstad et al. (2006, hereinafter Paper I) presented ISO far-infrared
(FIR) observations of the cloud Lynds 1780.
LDN1780 is a cometary-shaped, translucent (
mag),
high-latitude cloud. It is one of the few clouds where infrared
emission clearly shows different distributions at different
wavelengths, suggesting the presence of spatially distinct dust
populations (Chlewicki & Laureijs 1987; Laureijs et al. 1995; Paper I and references therein). The FIR emission at 100
m
and 200
m, mainly caused by big grains (BGs), peaks in the westermost part of the cloud, whereas the 60
m
emission, showing the presence of very small grains (VSGs), has its
maximum in the middle of the cloud, eastwards of the 200
m maximum.
The PAH emission is traced by IRAS 12
m
emission, which is strongest towards the east, in the less dense
``tail'' of the cloud. In Paper I, increased emissivity of large
grains and reduced emission of small grains, both of which could be
indicators of grain coagulation, were reported in the centre of
LDN1780. Similar results were, simultaneously and independently,
announced by del Burgo & Cambrésy (2006).
In this paper, we report results from 3D radiative transfer modelling of
LDN1780. We use, in particular, the 100 m and 200
m observations made with the ISOPHOT instrument (Lemke et al. 1996) onboard ESA's ISO satellite. At shorter wavelengths, these are complemented by
surface brightness data from the IRAS satellite. As a starting point, we use
the dust model of Li & Draine (2001).
With the help of the models, we
investigate what dust abundance variations and qualitative changes of
dust
properties are needed so that the observations can be explained. The
effect of
anisotropic radiation field and the role of the possible existence of a
low-extinction layer surrounding LDN1780 are also estimated. Beyond the
study of LDN1780, we wish to demonstrate the usefulness of such
modelling in separating the effects resulting from radiation field,
density
field, and dust properties. Routine 3D modelling can be used for
quantitative
analysis of all these factors.
2 Observations
In Paper I, the maps of 100 m and 200
m emission, observed with
the ISOPHOT instrument onboard the Infrared Space Observatory (ISO) (Kessler et al. 1996), were presented (see also del Burgo & Cambrésy
2006). Maps of FIR colour temperature and 200
m
optical depth were also shown and compared with maps of visual extinction
.
In this paper, those observations are complemented with IRAS
12
m, 25
m, and 60
m data. These and the ISOPHOT
maps were modified to be consistent with the DIRBE surface brightness, as explained in Paper I.
The uncertainty in the relative calibration of the bands is is 20-30% (see, e.g., del Burgo et al. 2003).
The sky background subtraction of the ISOPHOT maps was performed as explained in
Paper I, using the reference area shown in Fig. 1a of that paper. The same
area was used for the background subtraction of the IRAS maps.
In Appendix A, new ISOPHOT photometric observations at the wavelengths
7.3 m, 7.7
m, 10
m, 11.3
m, 12
m, and 20
m are presented. The sky positions of these observations are shown in
Fig. 1. The same positions are used in surface profile plots later in this paper.
![]() |
Figure 1:
Upper frame: the contours show the maxima of the IRAS 12 |
Open with DEXTER |
Table 1: Model parameters.
3 Radiative transfer modelling
In the following, the radiative transfer method used in the modelling, the dust model, and the radiation field used here are described. We present eight cases, denoted by letters A-H and introduced in Table 1.
3.1 Radiative transfer methods
The dust emission was computed using a Monte Carlo radiative transfer program (Juvela & Padoan 2003; Juvela 2005). The program allows us to add a certain number of dust components with distinct spatial distributions. The temperature distributions of transiently heated small grains are solved using the thermal discrete approach of Li & Draine (2001).
The cloud models were discretized into 503 cells. Because direct
calculation of the emission of transiently heated particles is
time-consuming, the so-called library method was used (see Juvela & Padoan
2003). For an individual cell, the emission is obtained by interpolation from
a grid of pre-calculated solutions. In our case, the local radiation field was
characterized using intensity at three wavelengths, 0.36 m, 0.55
m,
and 2.0
m, each discretized into 20 intensity intervals. The accuracy of
this approach was tested with 303 cell models by comparing the results with
direct, more time-consuming calculations. The rms error in the observed
intensity was found to be only of the order of 1%.
The library, i.e., the mapping between the incoming radiation and the
resulting dust emission, is valid only as long as intensities remain in the
range used in the construction of that library. Therefore, when the column
density (or radiation field) in the model was optimized, the library was
re-created from time to time during the iterations. This ensures that the final
result is correct, even when the optimization results in a model that is far
from the initial state.
![]() |
Figure 2:
Differences between the observed surface brightnesses and model predictions at 25 |
Open with DEXTER |
The initial column densities of the cloud model are based on the map of the
200 m optical depth, derived from the 100
m and 200
m ISO
observations (see Paper I). The density distribution along the line-of-sight
is taken to be Gaussian, corresponding to the cloud size in the plane of the
sky. The size of the map area is 1.2 pc, and the FWHM
of the cloud model along the line of sight is 0.26 pc. This
provides the initial cloud model. The dependence of final results on
the original column densities is weak, because they only provide a
starting point for the fitting procedure.
The column densities and, in the modified dust models, the abundances of the
different dust components are updated pixel by pixel using the ratios of the
observed and the modelled surface brightness values. The column density N is
updated according to 200 m ISO data. Therefore, the resolution of the
modelled density field is effectively 1.5
.
This is twice the cell
size in the model. When computed on the basis of 100
m and 200
m
observations, abundance data share the same resolution. However, when
abundance calculation involves IRAS observations, the resolution of the
corresponding abundance field has a resolution of
.
The
comparison of model surface brightness maps with IRAS is done at the resolution
of 4.5
.
3.2 The dust model
To model interstellar dust emission, we use the dust model of Li & Draine (2001, hereinafter the LD model) as a starting point. This model assumes two main classes of spherical dust grains: amorphous silicate grains and carbonaceous grains, with sizes ranging from 0.35 nm to 350 nm for both types of grains. At very small sizes (a<5 nm), the carbonaceous grains have properties like PAHs and above 5 nm, they have graphitic properties. Therefore, also in our modelling, the carbonaceous grains are divided into these two components, i.e., the carbonaceous grains distribution was divided in two at the grain size 5 nm. Later, in models G and H, we considered modifications to this basic dust model, i.e., changes in the relative abundance of small and large grains and increased emissivity at long wavelengths. Qualitatively, these could correspond to the expected effect of grain coagulation and/or the formation of ice mantles. To create two grain components of different sizes for both types of grains, carbonaceous and silicate, we divided their distributions at 7.5 nm and 5.35 nm, respectively. We then have five different dust grain components: large silicate and large carbonaceous (the big grains component), small silicate and small carbonaceous (the small grain component), and PAHs. In model H, two more large-grain components, carbonaceous and silicate, with increased emissivity (see Sect. 4.3) are added.
3.3 The radiation field
For modelling the local interstellar radiation field (ISRF), we use the
model by Mathis et al. (1983).
However, the ISRF around LDN1780 may not be symmetric, not only because
LDN1780 is situated at a high galactic latitude, but also because the
young OB stars of the Scorpius-Centaurus association, especially the
Upper Scorpius subgroup (USco), are located nearby (de Geus et al.
1989; Tóth et al. 1995).
Because of the stronger radiation coming from the direction of the
galactic plane, we take the radiation intensity incident to LDN1780
from the upper halfspace to be one third of the intensity coming from
the side of the Galactic plane. The scale height of stars responsible
for the ISRF is 100 pc (see,
e.g., Mathis et al. 1983). For a cloud located 100 pc above
the Galactic plane, the geometry implies a
3:1 ratio for radiation
coming from lower and higher Galactic latitudes, respectively. If
interstellar extinction is taken into account, the ratio gets smaller.
However, the scale height of OB stars is much below 100 pc and the
assumed ratio of 3:1 seems a wise approximation, at least for the UV part of the ISRF.
Tóth et al. (1995) calculated that the radiation energy density reaching
LDN1780 from USco is
integrated in the UV (912-1300
). This additional
component is of the same order of magnitude as the ISRF calculated using the model by Mathis et al. (1983),
defined above. Therefore,
when the effect of the OB association is included, the total radiation
incident on LDN1780 is about twice the normal value of the ISRF. The OB
association is in the direction of the Galactic plane, at an angle of
about 15 degrees relative to the Galactic meridian (Tóth
et al. 1995). The radiation,
coming from a narrow solid angle, could affect the location of the IR emission
maxima at different wavelengths. Section 4.2 contains the tests where the effect of the OB association of USco is estimated.
4 Results
We studied eight models listed in Table 1. In
Sect. 4.1 we calculate a baseline model by assuming the Mathis et al. (1983) ISRF model and the LD dust model. In the following
section (Sect. 4.2), we investigate the effects of the external
radiation field by scaling its intensity, by introducing an extinction layer
around the cloud, and by estimating the potential effect of the USco group.
Finally, in Sect. 4.3 we consider what changes in dust properties
are needed to fit all observations from 12 m to
200
m.
4.1 The basic model
We start by studying a model where dust properties follow the LD dust model,
and the intensity of the radiation field is set according to Mathis et al.
(1983). This is our model A (see Table 1).
Although the total ISRF strength is assumed to be normal, its distribution is
anisotropic as described in Sect. 3.3. We fit the model to
the ISO 200 m data, updating the column density N according to the
ratio of modelled and observed surface brightness. After each change in the
column density, the radiative transfer calculations are repeated. The
iterative fitting procedure is continued until the remaining errors at
200
m become less than 0.2 MJy sr-1.
Figure 2 (first row) shows the differences, at different wavelengths,
,
between the observed surface brightness and the predictions of model A.
Because column density is adjusted according to 200
m data and for each
map pixel separately, one may expect that the 200
m fit residuals can be
reduced to zero. This is still not necessarily the case. For example, if the
intensity of the radiation field is severely underestimated, the model might
not be able to produce sufficient surface brightness.
However, a good fit is obtained for model A. At 200
m, the
errors are below 0.1 MJy/sr, which is better than the observational accuracy
and small compared to the absolute surface brightness that, after background
subtraction, goes up to
50 MJy/sr.
At other wavelengths, the deviations from the observed surface brightness are
significant. In the densest part of the cloud (i.e., at the location of the
maximum optical extinction and maximum 200 m emission, see Paper I), the
predicted 100
m intensities are up to
3 MJy/sr too high. This
corresponds to
20% of the observed signal. On the other hand, in the
outer parts of the cloud, the predicted intensities are generally too low by
1 MJy/sr and the relative error rises to
30%. This error could
be caused, at least partially, by an inaccuracy in the background
subtraction, and a gradient in the 100
m map relative to the 200
m
map.
In the north, model A shows too much emission both at 25
m and
60
m. On the other hand, towards east and southeast, in the tail of
LDN1780, the observed surface brightness is higher than predicted by the model. At 25
m, the surface brightness is only
40% of the observed. At
60
m, the discrepancy is smaller, some 15% at the centre of the map.
The mass of the model cloud A is 15.3
,
close to the estimate of
18
given in Paper I.
4.2 Models with modified radiation field
Model A could not explain the different locations of the infrared
emission peaks. Therefore, we investigate whether model predictions are
affected by changes in the heating radiation field. In model B, the column densities are again adjusted according to the
200 m observations, but the scaling of the ISRF is added as another free
parameter. The radiation field is adjusted so that the average ratio of
the 100
m and 200
m intensities agrees with the observations. The
comparison is limited to areas where the 200
m surface brightness is
above 10 MJy sr-1 (
960 square arcmin; see
Fig. 1b). This eliminates areas of low signal-to-noise (S/N) and decreases
the sensitivity to possible errors in the sky background subtraction. Within
this area, the average ratio between 100
m and 200
m intensities
becomes equal to the observed value when the intensity of the ISRF is reduced
to
77% of its original value. The cloud mass is correspondingly
increased to 20.6
.
While the previous models are illuminated directly by the full ISRF, the
radiation reaching LDN1780 may be attenuated by diffuse dust layers around the
cloud. The effect could differ from simple scaling of ISRF intensity because
not only the level but also the radiation spectrum is affected. In models C
and D, the ISRF is attenuated by an external dust layer of
or
.
With
(model C), the 100
m emission is generally too low and, at the location of the emission peak, the error is
15% (see
Fig. B.1). Since the 100
m peak intensity in model A is
too high by a similar amount, model D with
is also tested. In
this case, the average level of the 100
m emission fits observations
better and, at the location of the emission maximum, the 100
m error is
only
5%.
The cloud mass of model D is 21.3
.
In model E, the ISRF scaling is optimized like in the case of model B but
using the extinction layer of
around the cloud. The best fit is
obtained when the ISRF level is scaled by 1.01. Therefore, with the assumed
amount of external extinction, the FIR data agree with the
Mathis et al. (1983) ISRF estimates. The cloud mass,
21
,
and the surface brightness maps are almost identical to
those of model B (see Fig. B.1).
![]() |
Figure 3:
Comparison of intensity profiles of models F and A.
Model F includes additional radiation coming from the direction of
the Upper Scorpius OB association. The intensities correspond to the
positions shown in Fig. 1. For plotting, the 100 |
Open with DEXTER |
In models B and E, the ratio of 100 m and 200
m surface
brightness is adjusted by scaling the radiation field. This clearly does not
change the short wavelength emission in the LDN1780 tail. The
asymmetric illumination provided by the USco OB association may be responsible for that.
The exact strength of the radiation from USco is not accurately known (see
Sect. 3.3). In model F, we set the total energy input from
the OB association equal to that of the normal ISRF. The association is
modelled as a distant point source and with the same spectrum as the
ISRF. As shown in Fig. 3, the added radiation increases the
60
m and the 100
m emission far above the observed values.
Nevertheless, the effect on the IR morphology is negligible and, for example,
the location of the 25
m maximum is practically unchanged.
4.3 Models with modified dust properties
In the following, we do not include the OB association as an additional
radiation source. It would not affect the location of mid-infrared maxima and,
as shown by model F, its intensity must be small compared to the normal
ISRF. On the other hand, we keep a thin external extinction layer
corresponding to
even though this will reduce surface
brightness especially at shorter wavelengths. It is clear that the small
volume included in our models (38
on the sky plane) must be surrounded
by some diffuse material.
In model G, the silicate and the carbonaceous grains are divided into two
components, small grains ( nm) and large grains (
nm). The PAH
dust component is left unmodified, leading to a total of five dust components.
However, the abundances of large grains (silicate and carbonaceous) are not
modified, and the same relative abundance is used for both small silicates and
small carbon grains. This results in three free parameters. The column
densities are adjusted according to the 200
m data, while the abundances
of small grains are adjusted according to 60
m data and the abundances
of PAHs according to 12
m data. Each dust component contributes to
emission over a wide range of wavelengths. Nevertheless,
each of these wavelengths is primarily affected by a single dust component and,
with this simple update scheme, the iterative fitting procedure quickly converges to one solution.
![]() |
Figure 4:
Intensity profiles of the cloud in the modified-dust model G,
compared to the results of model A, and the observations. The
intensities correspond to the positions shown in Fig. 1. For plotting, the 100 |
Open with DEXTER |
![]() |
Figure 5:
Spatial distributions of the abundances of the dust components of
model G: PAHs, small grains, and large grains. The abundances are
given relative to the abundance of large grains, which is normalized to
one. Regions of low column density have been masked. The field of view
of the maps is the same as in Fig. 2. The contours correspond to the 200 |
Open with DEXTER |
The results of model G are shown in Figs. 2 and 4. The overall errors are smaller than in previous cases
(models A-E). The 100 m emission is overestimated at the location
of the column density maximum and further in the LDN1780 tail.
The 100
m surface brightness is underestimated over most of the remaining area.
At the centre of the map, the difference is below
2 MJy sr-1, i.e., less than
10% of the 100
m maximum value. The relative error has its maximum
in the west, along the edge of the cloud.
As shown in Fig. 4, the fit to 25
m and 60
m
observations has improved with respect to the previous models. At 25
m,
the predicted intensities are too
high but the error is only
10% over most of the area. At 60
m,
the errors are mostly below 10%. Because the abundances of PAHs are also
free parameters, the errors are negligible at 12
m.
The spatial distributions of the three dust components are shown in
Fig. 5. Because the column density was a separate free
parameter, it is possible to show only relative abundances. In
Fig. 5, these are shown relative to the large grain component,
which, of course, itself might also have significant abundance variations.
Small grains are abundant everywhere in the LDN1780 tail, east of the column
density maximum, i.e., east of the area of the 200
m maximum emission. To produce the observed 60
m surface
brightness, the abundance is increased by one order of magnitude. The PAH
abundance peaks further in the tail and more towards the south. The
displacement towards the south might also indicate of a stronger
radiation field in that direction, which, in the model, is compensated by a
larger PAH abundance.
![]() |
Figure 6:
Intensity profiles of the cloud in the modified-dust model H,
compared to observations and the results of model A. The values at
25, 60, and 100 |
Open with DEXTER |
By merely separating the small and the large grain components, the 100 m
emission in the cold core of LDN1780 can still not be reproduced. In model H,
we introduce an additional large-grain component (consisting of both silicates
and graphite grains) that has an increased FIR emissivity. In this component,
the original emission cross sections of the LD model have been multiplied by
for wavelengths longer than 100
m. The
modification corresponds to the models of Ossenkopf & Henning (1994), where
the FIR/sub-millimetre dust opacity has increased 4-5 times relative to dust
in the diffuse ISM because of coagulation and the presence of dirty ice on the
grains. Model H includes a total of seven grain components: PAHs, very small
silicate grains, very small carbonaceous grains, large silicate grains,
large carbonaceous grains, and large silicate and carbonaceous grains with
increased emissivity. In the fit, there are only four free parameters: PAH
abundance, small grain abundance, the abundance of large grains with increased
emissivity, and the cloud column density.
Although the abundance of large grains is not directly changed, the column
density is again fitted according to the 200
m surface brightness.
Therefore, the errors at 200
m should be zero, while some residuals can
be expected at the other wavelengths. The PAH abundance is again updated
according to the 12
m values and the abundance of small grains according
to 60
m values. The abundance of large grains with increased emissivity
is updated by comparing the modelled ratio of 200
m and 100
m
surface brightness with the observed ratio.
Figure 2 shows that the quality of the fit is for model H mostly similar to
that of model G. The only noticeable difference is that, while model G
overestimates the 100 m intensity by up to
1 MJy sr-1 west
of the density maximum, the error is now close to zero. The overall quality of
the fit is satisfactory and much of remaining deviations can be attributed to
systematic errors and uncertainty in the background subtraction.
Figure 7
shows the relative abundances of the dust components.
The grains with increased emissivity are concentrated in the region of
high density on the western edge of the cloud. There is also an excess
of these grains in the tail, but that is less significant because of
the lower surface brightness of that region. The PAHs and the VSGs are,
respectively, concentrated to the regions of the
IRAS 12
m and 60
m emission maxima. High PAH abundance is also
seen at the southern edge of the cloud.
![]() |
Figure 7:
Spatial distributions of the abundances of the different dust
components of model H: PAHs, small grains, large grains, and large
grains with increased emissivity. The large grains are used as a
reference for the plotted relative abundances. Regions of low column
density have been masked. The field of view of the maps is the same as
in Fig. 2. The contours correspond to the 200 |
Open with DEXTER |
Table 1 shows that the
values given by the models are
higher than those calculated using the 2MASS data for LDN1780 (see Paper I). The
difference between the 2MASS and the model
values are greatest in the densest part of the cloud. When
drops to
3
,
the
difference is reduced to
50%. The 2MASS values might be biased towards
lower values, if the column density increases rapidly in a region that is
small compared to the resolution of the extinction map. The difference between the
values
could mean that the true large grain emissivity is higher than employed in the model; however, the difference could
also be reduced by increasing the radiation field.
5 Discussion
Our first model A assumed normal ISRF and dust properties. The column densities were adjusted according to the observed surface brightness at a single wavelength. This way, one observed map can be fit perfectly while significant residuals remain at other wavelengths. The main advantage of such simple models is that they highlight the differences between observations and the naïve model. This helps to visualize the second-order effects that can be associated with subtle variations in the properties of dust and radiation field. In general, such simple models may already be sufficient to reveal and to quantify such effects or, at least, they will serve as a starting point for more complete modelling.
The results for model B (Sect. 4.1) show that the high
200100
m surface brightness ratio in the centre of LDN1780 cannot
be produced simply by treating the intensity of the local ISRF and column
density as free parameters. Model E (Sect. 4.2) shows that, although the
results are improved compared to previous models, the assumption of additional
extinction around LDN1780 does not help in explaining the strong long wavelength
emission in the core of the cloud. Furthermore, models A-F show that the
observed differences in the locations of emission maxima cannot be explained
by a homogeneous distribution of dust. Neither an extra layer of dust around
the cloud, variations in the intensity of the local ISRF, nor increased
radiation from the direction of the OB association changes this conclusion.
The differences in the emission maxima at 12 m, 60
m, and
100-200
m can only be explained by resorting to a dust model, where the
small and large grain populations are concentrated in different parts of the
cloud (model G in Sect. 4.4). The abundance of PAHs must peak on the
eastern side, in the less dense part of the cloud, and the large grains are
concentrated in the dense core of LDN1780. The 60
m emission and,
consequently, the abundance of VSGs peaks in between in the central part of
the mapped area.
Although the ISOPHOT photometric observations at 7.3 m, 7.7
m,
10
m, 11.3
m, and 12
m, presented in Appendix A, do not have
high enough quality to allow a detailed feature-to-feature comparison with the
models, they all show their maxima at the locations of the IRAS 12
m
maximum emission and the maximum abundance of the PAHs in models G and H.
The results of model G confirm that the observed separate emission maxima
result from true variations in the abundances of populations of dust grains of
different sizes in LDN1780.
Table 2: The parameters of the individual ISOPHOT PHT-P observations.
However, even with the ratio of small and large grains as a free parameter,
as we had in model G, the 100 m and 200
m
emission in the densest part of LDN1780 was not perfectly reproduced.
The data could be better fit only with model H, where about 30% of
the large dust grains have the high emissivity that corresponds to
calculations of Ossenkopf & Henning (1994, Fig. 13).
The improved 100 m fit of model H, seen in Fig. 2, is
directly related to the addition of large grains with high emissivity. At
200
m, the emissivity of the new dust component is twice as high as
in the LD model. In Fig. 7, the abundance of the new component
rises up to 30%. Therefore, in the centre of LDN1780, the 200
m
emissivity is effectively higher by
30%.
In model H, as in model G, the abundance of the large grains is highest
in the centre of the cloud, and the distributions of the PAHs and the
VSGs peak at the observed IRAS 12-25 m and 60
m
emission maxima, respectively. The model predicts hardly any PAHs and
VSGs in the dense core of the cometary-shaped cloud. This is in
accordance with the ISOPHOT photometric data presented on
Appendix A, which shows that at the wavelengths between 7.3
m and 20
m, there is little emission in the area of the ISO 100
m emission maximum (see Fig. A.1). This effect can be explained by the depletion of the smaller grains in the coagulation process.
The results of model H agree with our findings in Paper I, which
concluded that the FIR emissivity of large grains has increased in the
cold core of LDN1780, i.e., in the region of 200 m maximum emission and maximum visual extinction. A similar conclusion was reached by del Burgo & Cambrésy (2006)
who, after separating the cloud emission into a warm and a cold
component, could observe a small enhancement in the emissivity of the
cold component. This effect is expected in the presence of grain
coagulation or ice-coated grains (see Cambrésy et al. 2001, and references therein). Such effects have been observed by Stepnik et al. (2003)
in a Taurus filament, which, like LDN1780, also has the maximum visual
extinction of about 4 mag. Del Burgo & Laureijs (2005) found emissivities of large grains increased a few times in another Taurus cloud, TMC-2. However, Nutter et al. (2008),
who modelled a filament in TMC-1, argue that no increased emissivity is
needed to explain the observations in that cloud but, instead, a model
with a layer of extinction corresponding to
was able to explain the observations.
![]() |
Figure 8:
Surface brightness profiles from model H after the external
illumination was increased by 50%. The observed profiles are also
shown. The values at 25, 60, and 100 |
Open with DEXTER |
Our modelling did not provide any strong constraints on the strength of the
external radiation field. If the field is assumed to be too weak, the observed
surface brightness cannot be reproduced even with very high column densities.
The high abundances obtained for the PAH and VSG components indicate that, in
the case of LDN1780, the ISRF by Mathis et al. (1983) is close to the lower limit of
possible values. A strict upper limit is more difficult to derive.
We recalculated model H after increasing the external heating by either 50%
or 100%. With a 50% increase, the quality of the fit was marginally improved
(Fig. 8). At the same time, the peak abundances of PAHs
and VSGs were reduced by one third, while the abundance of large grains with
higher emissivity was increased by a factor of four.
With a 100% increase in the radiation field, the relative abundances of PAHs
and VSGs, relative to the sum of the large grain components, is still
lower. In the tail of the cloud, the abundance ratio is 4 times the
corresponding value in the Li & Draine (2001) model.
However, there is a clear gradient so that, on the NW side of the tail, the
ratio is below 2 but increases to
5 in the SE.
In contrast, the relative VSG abundance peaks in the middle of the tail where
it reaches a value of
6. In the core of LDN1780, the PAH abundance (still
relative to the sum of the large grain components) is close to the Li &
Draine value, while the VSG abundance is reduced almost to zero.
Clearly, the estimates of relative grain abundances are sensitive to the
intensity of the radiation field, which could not be constrained further within the limitations of this model.
6 Conclusions
Results of 3D radiative transfer modelling of LDN1780 have been presented. Eight cases were studied to find a model that correctly produces the ISOPHOT observations presented in Paper I. We tested the effects of variations in the local interstellar radiation field, the presence of a thin extinction layer around the cloud, and modifications in the dust model of Li & Draine (2001). The results of the modelling lead to the following conclusions.
- -
- Neither the variations of the local radiation field nor a thin layer of diffuse dust around the cloud are sufficient to explain the observed FIR emission of LDN1780.
- -
- Modifications in the properties of the big grains in the standard diffuse dust model are needed to explain the far-infrared emission from the cloud core and the ratio of MIR and FIR intensities elsewhere in the cloud.
- -
- The relative abundances of the dust components were found to be very sensitive to the strength of the external radiation field, which still remains poorly constrained.
- -
- The best fit was obtained by using seven different dust components: PAHs; silicate and carbonaceous very small grains; silicate and carbonaceous large grains; and large grains with increased long wavelength emissivity. In this model, 30% of the large grains in the centre of LDN1780 have their far-infrared emissivities increased corresponding to the values given by Ossenkopf & Henning (1994).
- -
- In our model, the PAHs and
the VSGs are concentrated in the regions of maximum 12
m and 60
m emission of LDN1780, respectively. The ISOPHOT observations at 7.3-20
m show maxima at the location of the maximum concentration of PAHs.
- -
- We conclude that the separate emission maxima at different wavelengths in LDN1780 results from true and significant variation in the distribution of dust grains of different sizes and compositions.
We wish to thank the anonymous referee for hisher comments. The work of M.R. has been supported by the Finnish Academy of Science and Letters (Foundation of Vilho, Yrjö and Kalle Väisälä), the Magnus Ehrnrooth Foundation, and the Finnish Graduate School in Astronomy and Space Physics, which are gratefully acknowledged. We acknowledge the support from the Academy of Finland through grants Nos. 124620, 115056, and 105623.
References
- Bernard, J. P., Boulanger, F., Désert, F. X., & Puget, J. L. 1992, A&A, 263, 258 [NASA ADS] [Google Scholar]
- Bernard, J. P., Boulanger, F., & Puget, J. L. 1993, A&A, 277, 609 [NASA ADS] [Google Scholar]
- Boulanger, F., Baud, B., & van Albada, G. D. 1985, A&A, 144, L9 [NASA ADS] [Google Scholar]
- del Burgo, C., & Laureijs, R. J. 2005, MNRAS, 306, 901 [NASA ADS] [CrossRef] [Google Scholar]
- del Burgo, C., & Cambrésy, L. 2006, MNRAS, 368, 1463 [NASA ADS] [CrossRef] [Google Scholar]
- del Burgo, C., Laureijs, R. J., Ábrahám, P., & Kiss, Cs. 2003, MNRAS, 346, 403 [NASA ADS] [CrossRef] [Google Scholar]
- Cambrésy, L., Boulanger, F., Lagache, G., & Stepnik, B. 2001, A&A, 375, 999 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Chlewicki, G., & Laureijs, R. J. 1987, in Proc. of the NATO Advanced Research and CNRS Workshop, NATO ASI Series 191, ed. A. Leger, L. D. Hendecourt, & N. Boccara (Dordrecht: D. Reidel Publ. Co.), 335 [Google Scholar]
- Désert, F.-X., Boulanger, F., & Puget, J. L. 1990, A&A, 237, 215 [NASA ADS] [Google Scholar]
- Dwek, E., Arendt, R. G., Fixsen, D. J., et al. 1997, ApJ, 475, 565 [NASA ADS] [CrossRef] [Google Scholar]
- Gabriel, C., Acosta-Pulido, J., Heinrichsen, I., et al. 1997, in Proc. of the ADASS VI Conf., ed. G. Hunt, & H. E. Payne, ASP Conf. Ser., 125, 108 [Google Scholar]
- de Geus, E. J., de Zeeuw, P. T., & Lub, J. 1989, A&A, 216, 44 [NASA ADS] [Google Scholar]
- Draine, B. T., & Lee, H. M. 1984, ApJ, 285, 89 [Google Scholar]
- Draine, B. T., & Li, A. 2001, ApJ, 551, 807 [NASA ADS] [CrossRef] [Google Scholar]
- Draine, B. T., & Li, A. 2007, ApJ, 657, 810 [NASA ADS] [CrossRef] [Google Scholar]
- Juvela, M., & Padoan, P. 2003, A&A, 397, 201 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Juvela, M. 2005 A&A, 440, 531 [Google Scholar]
- Kessler, M. F., Steinz, J. A., & Anderegg, M. E. 1996, A&A, 315, L27 [NASA ADS] [Google Scholar]
- Kramer, C., Richer, J., Mookerjea, B., et al. 2003, A&A, 399, 1073 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Lemke, D., Klaas, U., Abolins, J., et al. 1996, A&A, 315, L64 [NASA ADS] [Google Scholar]
- Li, A., & Draine, B. T. 2001, ApJ, 554, 778 [Google Scholar]
- Lopez, B., Mékarnia, D., & Léfevre, J. 1995, A&A, 296, 752 [NASA ADS] [Google Scholar]
- Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425 [NASA ADS] [CrossRef] [Google Scholar]
- Mathis, J. S., Metzger, P. G., & Panagia, N. 1983, A&A, 128, 212 [NASA ADS] [Google Scholar]
- Nutter, D., Kirk, J. M., Stamatellos, D., & Ward-Thompson, D. 2008, MNRAS, 384, 755 [NASA ADS] [CrossRef] [Google Scholar]
- Ossenkopf, V., & Henning, T. 1994, A&A, 291, 943 [NASA ADS] [Google Scholar]
- Rawlings, M. G., Juvela, M., Mattila, K., Lehtinen, K., & Lemke, D. 2005, MNRAS, 356, 810 [NASA ADS] [CrossRef] [Google Scholar]
- Ridderstad, M., Juvela, M., Lehtinen, K., Lemke, D., & Liljeström, T. 2006, A&A, 451, 961 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Siebenmorgen, R., & Krügel, E. 1992a, A&A, 259, 614 [NASA ADS] [Google Scholar]
- Siebenmorgen, R., & Krügel, E. 1992b, A&A, 266, 501 [NASA ADS] [Google Scholar]
- Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 [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]
- Tóth, L. V., Haikala, L. K., Liljeström, T., & Mattila, K. 1995, A&A, 295, 755 [NASA ADS] [Google Scholar]
- Verter, F., Magnani, L., Dwek, E., & Rickard, L. J. 2000, ApJ, 536, 831 [NASA ADS] [CrossRef] [Google Scholar]
- Weiland, J. L., Blitz, L., Dwek, E., et al. 1986, ApJ, 306, L101 [Google Scholar]
- Witt, A. N. 2000, in Astrochemistry: From Molecular Clouds to Planetary Systems, ed. Y. C. Minh, & E. F. van Dishoeck, Proc. IAU Symp., 197, 317 [Google Scholar]
- Zubko, V., Dwek, E., & Arendt, R. G. 2004, ApJS, 152, 211 [NASA ADS] [CrossRef] [Google Scholar]
Appendix A: New ISOPHOT observations at 7.3-20
m
We present additional photometric observations at the wavelengths 7.3 m,
7.7
m, 10
m, 11.3
m, 12
m, and 20
m. The observations
were made with the ISOPHOT instrument aboard ISO, using the PHT03 detector
(Lemke et al. 1996).
The sky positions of the photometric measurements are the same as for
the raster scan measurements shown in Fig. 1. The data reduction was
performed using PIA (ISOPHOT Interactive Analysis) V10.0
(Gabriel et al. 1997). The data reduction steps have been explained in Paper I.
The details for the observations are listed in Table 2.
![]() |
Figure A.1:
The ISOPHOT photometric observations of LDN1780 at 7.3 |
Open with DEXTER |
Most of the PHT03 measurements showed detector response drifts,
especially in the beginning of an observing sequence.
We modelled and subtracted the drift assuming it follows an
exponential drift curve. Finally, we fitted a linear baseline
to the measurements indicated with squares in Fig. A.1.
The figure shows the PHT observations after these corrections.
The intensities from the narrow bandpass
P11.3 filter are higher than those from the much wider P11.5 filter. This suggests
that the main contribution in the P11.5 filter, which corresponds to
the IRAS 12 m filter, comes from the most prominent feature in this wavelength
region, the 11.3
m emission peak, which is generally attributed to PAHs.
Appendix B: Surface brightness maps of the models
In Sect. 4 maps of surface brightness error were shown for models A, E, G, and H. For completeness, the error maps for the remaining models B, C, D, and F are shown here.
![]() |
Figure B.1:
Surface brightness error,
|
Open with DEXTER |
All Tables
Table 1: Model parameters.
Table 2: The parameters of the individual ISOPHOT PHT-P observations.
All Figures
![]() |
Figure 1:
Upper frame: the contours show the maxima of the IRAS 12 |
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Differences between the observed surface brightnesses and model predictions at 25 |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Comparison of intensity profiles of models F and A.
Model F includes additional radiation coming from the direction of
the Upper Scorpius OB association. The intensities correspond to the
positions shown in Fig. 1. For plotting, the 100 |
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Intensity profiles of the cloud in the modified-dust model G,
compared to the results of model A, and the observations. The
intensities correspond to the positions shown in Fig. 1. For plotting, the 100 |
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Spatial distributions of the abundances of the dust components of
model G: PAHs, small grains, and large grains. The abundances are
given relative to the abundance of large grains, which is normalized to
one. Regions of low column density have been masked. The field of view
of the maps is the same as in Fig. 2. The contours correspond to the 200 |
Open with DEXTER | |
In the text |
![]() |
Figure 6:
Intensity profiles of the cloud in the modified-dust model H,
compared to observations and the results of model A. The values at
25, 60, and 100 |
Open with DEXTER | |
In the text |
![]() |
Figure 7:
Spatial distributions of the abundances of the different dust
components of model H: PAHs, small grains, large grains, and large
grains with increased emissivity. The large grains are used as a
reference for the plotted relative abundances. Regions of low column
density have been masked. The field of view of the maps is the same as
in Fig. 2. The contours correspond to the 200 |
Open with DEXTER | |
In the text |
![]() |
Figure 8:
Surface brightness profiles from model H after the external
illumination was increased by 50%. The observed profiles are also
shown. The values at 25, 60, and 100 |
Open with DEXTER | |
In the text |
![]() |
Figure A.1:
The ISOPHOT photometric observations of LDN1780 at 7.3 |
Open with DEXTER | |
In the text |
![]() |
Figure B.1:
Surface brightness error,
|
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.