Astronomy
&
Astrophysics
A&A 505, 1167–1182 (2009)
DOI: 10.1051/0004-6361/200912397
c ESO 2009
The circumstellar disc in the Bok globule CB 26
Multi-wavelength observations and modelling of the dust disc and envelope
J. Sauter1,2 , S. Wolf1 , R. Launhardt2 , D. L. Padgett3 , K. R. Stapelfeldt4 , C. Pinte5,6 , G. Duchêne7,6 , F. Ménard6 ,
C.-E. McCabe3 , K. Pontoppidan8 , M. Dunham9 , T. L. Bourke10 , and J.-H. Chen9
1
2
3
4
5
6
7
8
9
10
Christian-Albrechts-Universität zu Kiel, Institut für Theoretische Physik und Astrophysik, Leibnizstr. 15, 24098 Kiel, Germany
e-mail: jsauter@mpia.de
Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
California Institute of Technology, 1200 E California Blvd, Mail code 220-6, Pasadena, CA 91125, USA
JPL, 4800 Oak Grove Drive, Mail Stop 183-900, Pasadena, CA 91109, USA
School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
Laboratoire d’Astrophysique de Grenoble, CNRS/UJF UMR 5571, B.P. 53, 38041 Grenoble Cedex 9, France
Astronomy Department, University of California Berkeley, 601 Campbell Hall, Berkeley CA 94720-3411, USA
California Institute of Technology, Division of Geological and Planetary Sciences, MS 150-21, Pasadena, CA 91125, USA
Department of Astronomy, University of Texas at Austin, 1 University Station C1400, Austin, TX 78712, USA
Harvard-Smithonian Center for Astrophysics, 60 Garden St., Cambridge MA02138, USA
Received 27 April 2009 / Accepted 6 July 2009
ABSTRACT
Context. Circumstellar discs are expected to be the nursery of planets. Grain growth within such discs is the first step in the planet
formation process. The Bok globule CB 26 harbours such a young disc.
Aims. We present a detailed model of the edge-on circumstellar disc and its envelope in the Bok globule CB 26.
Methods. The model is based on HST near-infrared maps in the I, J, H, and K bands, OVRO and SMA radio maps at 1.1 mm,
1.3 mm and 2.7 mm, and the spectral energy distribution (SED) from 0.9 µm to 3 mm. New photometric and spectroscopic data from
the Spitzer Space Telescope and the Caltech Submilimeter Observatory are also part of our analysis. Using the self-consistent radiative
transfer code MC3D, the model we construct is able to discriminate between parameter sets and dust properties of both envelope and
disc.
Results. We find that the data are fit by a disc that has an inner hole with a radius of 45 ± 5 AU. Based on a dust model including
silicate and graphite, the maximum grain size needed to reproduce the spectral millimetre index is 2.5 µm. Features seen in the nearinfrared images, dominated by scattered light, can be described as a result of a rotating envelope.
Conclusions. Successful employment of ISM dust in both the disc and envelope hint that grain growth may not yet play a significant
role for the appearance of this system. A large inner hole implies that CB 26 is a circumbinary disc.
Key words. circumstellar matter – planetary systems: protoplanetary disks – radiative transfer – stars: formation –
stars: individual: CB 26
1. Introduction
CB 26 is a small cometary-shaped Bok globule located about
10◦ north of the Taurus/Auriga dark cloud at a distance of
140 pc (Launhardt & Sargent 2001). An IRAS point source
(IRAS 04559+5200) at its southwest rim suggests an embedded
Class I young stellar object (YSO) (Stecklum et al. 2004) source.
Launhardt & Henning (1997) found an unresolved 1.3 mm continuum source associated with the IRAS source.
Interferometric observations by Launhardt & Sargent (2001)
showed that the major fraction of thermal dust emission at millimetre wavelengths has its origin in a young circumstellar disc
with a diameter of about 400 AU and a mass of about 0.1 M⊙ .
This disc is seen almost edge-on, so the central star is not
visible directly. However, the spectral energy distribution suggests a Class I YSO with L ≥ 0.5 L⊙ (Stecklum et al. 2004).
From the 13 CO line emission and the Keplerian rotation curve,
Launhardt & Sargent (2001) derive a central stellar mass of
M∗ = 0.5 ± 0.1 M⊙ . Furthermore, Launhardt et al. (2008) detected a jet-like molecular outflow emanating perpendicular to
the plane of the disc. This outflow seems to be co-rotating with
the disc.
We present new observations and a model for this source that
accounts for spatially resolved data sets over more than 3 orders
of magnitude as well as for the unresolved SED of the object.
Our modelling is based on spatially resolved maps of CB 26
in the millimetre regime from the Sub-millimetre Array (SMA)
and the Owens Valley Radio Observatory (OVRO), high resolution images in the I, J, H, and K bands obtained with the the Near
Infrared Camera and Multi-Object Spectrometer (NICMOS) and
the Advanced Camera for Surveys (ACS) instruments on the
Hubble Space Telescope (HST). The photometric data for the
spectral energy distribution (SED) upon our model is based
are provided by the Multiband Imaging Photometer for Spitzer
(MIPS) and the Infrared Array Camera (IRAC) aboard the
Spitzer Space Telescope (SST) and millimetre photometry. We
also obtained a spectrum with the Infra-Red Spectrograph (IRS)
aboard the SST.
In this paper, we use all available NIR to mm continuum
data on CB 26 to develop a self-consistent model of the source.
Article published by EDP Sciences
1168
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
This model consists of two parts. First, an optically thick dust
disc which accounts for the dark lane seen in images obtained
with the HST of the object and the significantly elongated intensity profiles in the mm range. The second component is an optically thin envelope that reproduces the near-infrared scattered
light nebulosity. While the millimetre observations are sensitive
only to radiation being emitted from dust in the dense region
within the disc, the near-infrared images are dominated by scattered stellar light from dust in the circumstellar envelope and the
disc’s upper optically thin layers, often referred to as the “disc
surface”. These observations trace different physical processes
in different regions of the circumstellar environment, but they
are both strongly related to the dust properties in the system.
Thus, we are in the position not only to model observations
on the common basis of one set of parameters, but we are also
able to investigate whether the dust properties are different in
the disc and the envelope. This has been suggested by investigations of dust evolution in circumstellar discs where dust grain
growth alters the dust grain properties in the circumstellar disc
quite considerably whilst it is of less importance in the lowdensity envelope. Evidence for grain growth has been found, for
instance, for the circumstellar discs IM Lupi (Pinte et al. 2008),
GG Tau (Duchêne et al. 2004; Pinte et al. 2007), HH 30 (Watson
& Stapelfeldt 2004), IRAS 04302+2247 (Wolf et al. 2003), and
VV Serpens (Alonso-Albi et al. 2008).
In order to compare our model with the available observations, we use the self-consistent radiative transfer code MC3D
(Wolf et al. 1999; Wolf 2003b) in a parameter space study on
the free parameters of the model. We aim at finding the best-fit
model, which we define to be the model that reproduces certain
predefined features among the observational data (such as width
of the dark lane; see below for further details) best.
2. Observations and data reduction
In the case of the disc in the Bok Globule CB 26, we are in
the fortunate situation of having a large variety of observational
data at hand. This data includes not only the SED from 0.9 µm
to 2.7 mm, but also resolved maps in the near-infrared and millimetre regimes. We will now briefly discuss those observations
and the data reduction in this section.
2.1. HST imaging
The NICMOS and ACS data were taken by the GEODE1 team.
An overview of the complete program, its objects, and its objectives can be found in Padgett et al. (2009, in preparation).
2.1.1. ACS
CB 26 was observed with the Advanced Camera for Surveys
Wide Field Channel on 2005 September 09. Two 1250 s exposures were made in the F814W filter (λ = 0.80 µm, ∆λ =
0.15 µm), corresponding to Johnson I band. With a pixel scale
of 0.05′′ , the ACS provides a field of view of 201′′ × 100′′ . The
images were reduced, combined to reject cosmic rays, and corrected for geometric distortion by the STScI pipeline. Residual
hot pixels and cosmic rays were manually removed by replacing
the affected pixels by local median values.
1
Group for edge-on disc exploration.
2.1.2. NICMOS
CB 26 was observed using NICMOS on 2005 September 15
with the F110W (λ = 1.12 µm, ∆λ = 0.16 µm ), F160W
(λ = 1.60 µm, ∆λ = 0.12 µm ) and F205W (λ = 2.06 µm,
∆λ = 0.18 µm) filters on the NIC2 array. With a pixel scale of
0.075′′ , the NIC2 array provides a field of view of 19.2′′ on a
side. All data were taken in a MULTIACCUM step = 128 sequence, with total exposure times of 512 s for the F110W data
and 384 s for the F160W and F205W data. The observations
were dithered by 0.75′′ for bad pixel removal.
All three of the NICMOS data sets were taken less than
1900 s after emergence from the South Atlantic Anomaly (SAA)
and therefore suffer from significant cosmic ray persistence. The
data were re-reduced using the most recent calibration files available. The standard STScI CALNICA pipeline was used as a basis for the re-reduction, in addition to which, we employed both
the biaseq and pedsub IRAF routines to remove the pedestal effects visible in each of the quadrants. The biaseq task removes
the time-dependent variations in the bias level for each quadrant,
and the pedsub task then removes the fixed bias offset. After
the data have had the pedestal effect removed, we used the IDL
SAACLEAN program to model and iteratively remove the persistent cosmic rays in the image. After emerging from the SAA,
NICMOS powers back up and takes 2 dark frames. These dark
frames provide the model for the cosmic ray persistence pattern;
SAACLEAN takes this model and iteratively removes it from the
data until the noise in the background reaches a global minimum. Further details on this procedure can be found in Bergeron
& Dickinson (2003) (ISR 2003-010). Following the SAACLEAN
procedure, the data are run through a second round of pedestal
subtraction, have any remaining bad pixels removed, and are
then run through the CALNICB pipeline procedure to generate
the final mosaics.
2.2. Spitzer photometry and spectroscopy
Mid- and far-infrared photometry for CB 26 were retrieved from
the Spitzer Archive. IRAC observations were carried out under GTO program 94 (PI: Charles Lawrence). The data were
taken 2004 February 11, AOR key 4916224 using the high dynamic range mode to obtain 5 dithered exposures of 30 s each.
Aperture photometry was measured from the Spitzer pipeline
“post-BCD” mosaics (version 11.0.2), using a standard 10 pixel
radius aperture for the source and background annulus with
12–20 pixel radius. MIPS observations were made under GTO
program 53 (PI: George Rieke) on 2005 March 08, AOR key
12020480. A medium scan map covering 0.2◦ × 0.5◦ was performed, providing multiple dithered 4 s exposures and total integration times of 168, 84, and 16 s at 24, 70, and 160 µm, respectively. Spitzer post-BCD pipeline mosaics (version 14.4.0)
were used for aperture photometry. Photometry was measured in
apertures whose radii and background annuli were 7′′ /7′′ −13′′
(24 µm), 35′′ /39′′ −65′′ (70 µm), and 48′′ /64′′ −128′′ (160 µm)
with aperture correction factors as given by Engelbracht et al.
(2007); Gordon et al. (2007); Stansberry et al. (2007).
We carried out our own Spitzer low-resolution spectroscopy
of CB 26 on 2006 October 18 under program 30765, AOR
key 18964992. The ramp duration and number of observing cycles used were 6 × 14 s, 4 × 14 s, 8 × 30 s, and 8 × 30 s for the
SL2, SL1, LL2, and LL1 modules of the IRS (respectively). The
spectra were processed beginning with the intermediate droopres
products from pipeline version 15.3.0. The 2D images were coadded, and the nod pairs subtracted to remove stray light and
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
other additive artifacts, as well as rogue pixels. 1D spectra of
each nodding beam were then extracted using a fixed aperture of
5 pixels. Following Bouwman et al. (2008), the spectra were flux
calibrated using a spectral response function determined by comparing standard star observations with template spectra. These
response functions are also used with the “C2D” Legacy data
set (e.g. Kessler-Silacci et al. 2006). It was not necessary to apply any scaling to match the short-low and long-low modules,
indicating that the source is unresolved at the IRS wavelengths.
2.3. Millimetre and sub-millimetre measurements
2.3.1. SMA
Observations at 270 GHz (1.1 mm) with the Sub-Millimetre
Array (SMA, Ho et al. 2004) were made in December
2006, in two configurations providing baselines in the range
12–62 kλ. Typical system temperatures were 350–500 K. The
quasar 3C279 was used for bandpass calibration, and the quasars
B0355+508 and 3C111 for gain calibration. Uranus was used
for absolute flux calibration, which is accurate to 20–30%. The
data were calibrated using the IDL MIR package (Qi 2005) and
imaged using MIRIRAD Sault et al. (1995). The cleaned and
restored 1.1 mm continuum map was constructed with robust
uv-weighting using line-free channels in both sidebands. Here
we only use the continuum map. The observations together with
the molecular line data are described in more detail in a forthcoming paper (Launhardt et al. in prep.).
2.3.2. OVRO
CB 26 was also observed with the Owens Valley Radio
Observatory (OVRO) between January 2000 and December
2001. Four configurations of the six 10.4 m antennas provided
baselines in the range 6–180 kλ at 2.7 mm (110 GHz) and
12–400 kλ at 1.3 mm (232 GHz). Average SSB system temperatures of the SIS receivers were 300–400 K at 110 GHz
and 300–600 K at 232 GHz. The raw data were calibrated
and edited using the MMA software package (Scoville et al.
1993). Mapping and data analysis were performed with the
MIRIAD toolbox. Observing parameters are described in detail in Launhardt & Sargent (2001). The data presented here include additional observations conducted in 2001. All maps are
generated with robust uv-weighting, cleared, and restored with
a clean beam. Effective synthesised beam sizes of all interferometric millimetre continuum maps used here are summarised in
Table 1.
2.3.3. CSO
Submillimeter observations of CB 26 at 350 µm were obtained
with the Submillimeter High Angular Resolution Camera II
(SHARC-II) at the Caltech Submillimeter Observatory (CSO)
on 2007 October 21. SHARC-II is a 12 × 32 element bolometer
array giving a 2.59′ × 0.97′ field of view (Dowell et al. 2003).
The beam-size at 350 µm is 8.5′′ .
We used the Lissajous observing mode to map a region approximately 1′ × 0.5′ , centred at the position of the source. We
obtained two scans, each 10 mn long, for a total integration time
of 20 min in good weather (τ225 GHz ∼ 0.06). During both scans
the Dish Surface Optimisation System (DSOS)2 was used to
Table 1. Overview of the beam sizes in the millimetre-maps.
Instrument
SMA
OVRO
OVRO
See www.cso.caltech.edu/dsos/DSOS_MLeong.html
λ[mm]
1.1
1.3
2.7
PSF (FWHM) [′′ ]
1.00 × 0.84
0.61 × 0.36
1.21 × 0.87
Orientation
−59.3◦
−53.8◦
−58.3◦
correct the dish surface for gravitational deformations as the dish
moves in elevation.
The raw scans were reduced with version 1.61 of the
Comprehensive Reduction Utility for SHARC-II (CRUSH), a
publicly available3 , Java-based software package. CRUSH iteratively solves a series of models that attempt to reproduce the
observations, taking into account both instrumental and atmospheric effects (Kovács 2006; Kovács et al. 2006; Beelen et al.
2006). Pointing corrections to each scan were applied in reduction based on a publicly available4 model fit to all available
pointing data. Pixels at the edges of the map with a total integration time less than 25% of the maximum were removed to
compensate for the increased noise in these pixels. We then used
Starlink’s stats package to assess the rms noise of the map, calculated using all pixels in the off-source regions. The final map
has a 1σ rms noise of 70 mJy beam−1 .
Photometry was measured in a 20′′ aperture centred at the
peak position of the source. Calibration was performed according to the method used by Shirley et al. (2000); Wu et al. (2007).
This method is based on the requirement that a point source
should have the same flux density in all apertures with diameters
greater than the beam FWHM (8.5′′ for these observations). To
briefly summarise, a flux conversion factor (FCF) is calculated
for a 20′′ aperture by dividing the total flux density of a calibration source in Jy by the calculated flux density in the native
instrument units of µV in a 20′′ aperture. Flux densities of science targets are then derived by multiplying the 20′′ aperture
flux density (in the instrument units) of the source by the FCF.
We measure a 350 µm flux density for CB 26 of 2.8 ± 0.6 Jy.
3. Results from observations – basis for modeling
The focus of this section are the results by the previously described observations. The presented data set forms the basis of
our modeling.
3.1. Images
The maps from the HST in I, J, H, and K bands are shown in
Fig. 1. All all four images have been rotated in order to align the
major axis of the dark lane with the horizontal axis. The emission seen on these maps is scattered light from the central star.
A dark shadowy linear feature that intersects the bipolar structure is present in all images. The dependence of its width on the
wavelength is clearly visible. Since one expects the circumstellar disc to be optically thick at these wavelengths, the dark lane
is interpreted as the disc’s shadow in the encompassing envelope
structure. The bipolar nebula also shows a complex morphology
far above and especially below the disc. For further discussion
we refer the interested reader to Padgett et al. (2009, in preparation).
The interferometric millimetre continuum maps at 1.1 mm,
1.3 mm, and 2.7 mm, together with the dirty beam maps (see
3
2
1169
4
See www.submm.caltech.edu/~sharc/crush/index.htm
See www.submm.caltech.edu/˜sharc/analysis/pmodel/
1170
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
Fig. 1. Inverse HST images obtained with ACS and NICMOS in the
2
I, J, H and K band. The colour scale is ∼S 5 All four images have been
rotated by −30◦ in order to align the major axis of the dark lane with the
horizontal axis. For the image scale a distance to the object of 140 pc
is assumed (100 AU = 0.7′′ ). The image orientation is PA 330◦ up, and
PA 60◦ to the left.
also Table 1), are shown in Fig. 2. For the ease of modelling,
these images have been rotated 30◦ in order to align the major
axis of the elongated structure with the horizontal axis. While the
source is unresolved vertically in all images, it is well-resolved
along its horizontal axis, especially in the highest-resolution map
at 1.3 mm. The 1.3 mm map also recovers some extended emission from the envelope that might be related to a disc wind (see
Launhardt & Sargent 2001). For all images shown, radio and
NIR, North is the same direction.
Figure 3 shows an overlay of a NIR colour-composite image and the 1.3 mm dust continuum emission. The spatial colocation of the millimetre dust emission and the dark lane in
the scattered light images confirms the hypothesis of an edgeon optically thick disc as explanation for the observed features.
However, the HST pointing is only good to about 1 arcsec. Due
to the high extinction in the cloud core and the small NICMOS
field of view, there are no reference stars in the image that could
be used to correct for this pointing uncertainty.
3.2. Spectral energy distribution
The results of photometric measurements are presented in
Table 2 and Fig. 4. The spectrum we obtained from the IRS compliments the photometric points as seen in Fig. 4.
As is evident in this Figure, the 350 µm SHARC-II flux density is lower than expected based on comparison to the complete SED. This discrepancy can be explained by the fact that the
Lissajous observing mode is insensitive to extended emission, as
noted by Wu et al. (2007). This issue will be explored in more
detail by Dunham et al. (2009, in preparation), but preliminary
results suggest that flux densities measured from this particular
observing mode may underestimate the true flux density by up
to a factor of 2, even for relatively compact objects.
Fig. 2. Inverse, reconstructed images from millimetre interferometric
observations (left column) and corresponding dirty beam maps (right
column), linear colour scale. All images have been rotated by −30◦ in
order to align the major axis of the brightness distribution with the horizontal axis. For the image scale a distance to the object of 140 pc is
assumed (100AU = 0.7′′ ). The contour lines are drawn at (from inside
out) 90%, 50%, and 25% of the image maximum flux value. In the dirty
beam images, the 50% contour, marking the FWHM of the Gaussian
clean beam, is marked bold.
4. Model and modeling
In this section, we provide the reader with an introduction to the
concepts and techniques we use.
4.1. The model
First, we discuss the various components of our model, i.e., the
disc and envelope dust density distribution. The employment of
both these parts in the model is readily suggested by the data.
4.1.1. The disc
The main part of our model for CB 26 is a parametrised disc.
The disc is seen as the radially extended luminous structure in
the millimetre maps. The dark lane in the near-infrared maps is
another indication for a disc as it can be understood as the disc’s
shadow on the surrounding envelope.
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
1171
Fig. 4. Spectral energy distribution. Data with error-bars from Table 2.
The IRS spectrum is the solid line. The dashed-dotted line corresponds
to the best-fit model. The dashed line is the best-fit model with the dust
screen.
Fig. 3. Overlay of the OVRO 1.3 mm continuum map and the
HST NICMOS images. The NICMOS colour image is a 3-colour composite of F205W, F160W, and F110W (in the RGB colour planes, respectively), shown in log stretch. The contour levels are linear, with the
lowest contour at about the 2.5 σ-level, the others at the 6, 10, 14, 22,
and 25 σ-level, respectively.
Table 2. Photometric data points for CB 26.
λ[µm]
0.90
1.25
1.65
2.20
3.6
4.5
5.8
8.0
24
60
70
100
160
350
450
850
1110
1270
1300
2700
Flux [mJy] Aperture [′′ ]
0.062 ± 0.019
24
2.2 ± 0.2
12
8.2 ± 0.8
12
17.1 ± 1.7
12
18.3 ± 0.8
12
17.0 ± 0.8
12
12.5 ± 0.7
12
6.8 ± 0.5
12
160.6 ± 5.2
30
4880 ± 390.4
75
5555 ± 52
120
11 100 ± 1110
125
10 731 ± 69.49
24
2650 ± 850
20
6700 ± 1300
54
600 ± 120
54
225 ± 45
10
240 ± 20
54
190 ± 30
10
20 ± 2
10
Instrument Reference
CAHA 3.5m
(1)
CAHA 3.5m
(1)
CAHA 3.5m
(1)
CAHA 3.5m
(1)
Spitzer IRAC1
Spitzer IRAC2
Spitzer IRAC3
Spitzer IRAC4
Spitzer MIPS1
IRAS PSC
Spitzer MIPS2
IRAS PSC
Spitzer MIPS3
CSO
SCUBA
(2)
SCUBA
(2)
SMA
(2)
IRAM 30m
(2)
OVRO
(3)
OVRO
(3)
References: (1) Stecklum et al. (2004); (2) Launhardt et al., in prep.;
(3) Launhardt & Sargent (2001).
entire disc. R∗ is the stellar radius and h, the vertical scale height,
is a function of rcyl
h(rcyl ) = h0
rcyl
R∗
β
·
(2)
Here the quantities α, β, and h0 in Eq. (2) are geometrical parameters. These parameters allow us to adjust the disc structure and
shape in order to fit the data. This modeling strategy has already
been successfully applied to various other edge-on discs, such as
the Butterfly-Star IRAS 04302+2247 (Wolf et al. 2003), HK Tau
(Stapelfeldt et al. 1998), IM Lupi (Pinte et al. 2008), and HV Tau
(Stapelfeldt et al. 2003).
Integrating Eq. (1) along the z axis yields the surface density
p
R∗
Σ(r) = Σ0
·
(3)
rcyl
Comparison with Eq. (1) yields the following relation between
the exponent of the surface density power law and the geometrical parameters of the ansatz
p = −β + α.
(4)
The radial size of the disc rout is another parameter and is mainly
determined by the size of the elongated structure in the millimetre maps. As Hughes et al. (2008) argues, the millimetre continuum does not trace the outermost region of the disc. However, in
the case of CB 26, the extent of the dark lane is also consistent
with the outer radius estimate we obtain.
4.1.2. The envelope
We employ a parametric approach to such a disc which can
be written as
α
R∗
1 z 2
exp −
ρdisc (r) = ρ0
(1)
rcyl
2 h
where z is the usual cylindrical coordinate with z = 0 corresponding to the disc midplane and rcyl is the radial distance from
this z-axis (see e.g. Wolf et al. 2003; Stapelfeldt et al. 1998).
In our model, the parameter ρ0 is determined by the mass of the
In order to reproduce the pattern of scattered light we see in
the I, J, H, and K observations, we add an envelope-like dust
distribution to the model. The HST optical and NIR data show
while the envelope has a high enough density to produce scattered light, it is orders of magnitude lower than the density of
the circumstellar disc which is optically thick enough to obscure
the central star completely. Further evidence for the low density
in the envelope are the millimetre maps where the envelope cannot be seen.
1172
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
For the model of the envelope structure we follow the ideas
of Ulrich (1976). We thus implement a model for a rotating envelope resulting from infalling matter similar to Whitney et al.
(2003); Eisner et al. (2005):
ρenv =
Ṁ
8π GM∗ r3
µ
1+
µ0
− 12
1 µ
rcf
+ µ20
2 µ0
r
−1
·
(5)
Here Ṁ is the dust infall rate, M∗ the stellar mass, rcf the centrifugal radius and µ = cos θ. The initial infall path of dust particles is given by µ0 as r → ∞.
As this is the only occurrence
of Ṁ and M∗ , the factor Ṁ(8π GM∗ r3 )−1 in Eq. (5) is merely a
coupling constant that scales the mass of the envelope just as ρ0
does in case of Eq. (1).
Hence, we are using Ṁ(8π GM∗ r3 )−1 = ρ̃ as a fitting parameter. To avoid introducing a constant like ρ̃ with no direct
physical interpretation into the discussion later on, we shall in
this work refer to M∗ and Ṁ separately.
As a criterion to decide whether the disc dust distribution or
the envelope dust distribution at a given point should be considered, we compare the two densities and choose the larger value:
ρdisc (r) : ρdisc (r) ≥ ρenv (r)
ρ(r) =
.
(6)
ρenv (r) : ρdisc (r) < ρenv (r)
In this manner, we embed the disc into the envelope and guarantee a smooth transition from the disc to the envelope without the need to alter the density structure of the optically thick,
millimetre-bright part of the object. For the radius of the complete model space we take twice the outer radius of the disc.
Since we do employ a maximum size for the outer disc radius
rout , the remaining space from the disc’s edge to the end of the
model space is readily filled by the envelope. With a computational domain going out to 2rout , we are able to model the scattered light from the envelope.
4.1.3. The dust
Since gas is optically thin5 in the wavelength regime we deal
with, we limit ourselves to radiative transfer through the dust.
For the mass relation of dust and gas we assume the standard
Gas
value of MMDust
= 100 which is in agreement with the findings
of Glauser et al. (2008) in another disc surrounding a low-mass
T Tauri star. Therefore, it is the dust whose density structure
is described by Eqs. (1) and (5) in the disc and the envelope,
respectively. The dust grain properties in our model can be divided in three groups: The shape of the dust grains, their chemical composition, and their size distribution.
Grain shape: We assume the dust grains to be homogeneous
spheres. Real dust grains, of course, are expected to feature
a much more complex and fractal structure. As discussed by
Voshchinnikov (2002), chemical composition, size and shape of
dust grains cannot be determined separately, but only as a combination. We therefore limit our model to the less complex but
also less ambiguous approach of spherical, non-aligned and nonorientated dust grains.
5
This implies that we neglect line emission and absorption by the gas.
We do not aim at modeling those throughout the entire disc since the
dust is by far the dominant coolant of the disc. Hence, thermal equilibrium obtained in radiative transfer calculations based on dust only will
provide a reliable description of the disc’s thermal. structure.
Grain chemistry: For the chemical composition of the dust
grains we employ a model that incorporates both silicate and
graphite material. This grain model has already been used to
model the “Butterfly star” by Wolf et al. (2003). For the optical data, we use the complex refractive indices of “smoothed
astronomical silicate” and graphite as published by Weingartner
& Draine (2001). Since the longest wavelength considered in
our modeling is 2.7mm, we extrapolate the refractive indices to
that wavelength. This is readily done since for this wavelength
regime both the real and the imaginary part of the refractive index show asymptotic behaviour. For graphite we adopt the common “ 13 − 23 ” approximation. That means, if Qext is the extinction
efficiency factor, then
Qext,graph =
1
2
Qext (ǫ ) + Qext (ǫ⊥ ),
3
3
(7)
where ǫ and ǫ⊥ are the graphite dielectric tensor’s components
for the electric field parallel and orthogonal to the crystallographic axis, respectively. As has been shown by Draine &
Malhotra (1993), this graphite model is sufficient for extinction
curve modeling. Applying an abundance ratio from silicate to
graphite of 1 × 10−27 cm3 H−1 : 1.69 × 10−27 cm3 H−1 , we get relative abundances of 62.5% for astronomical silicate and 37.5%
graphite ( 13 ǫ and 23 ǫ⊥ ).
Grain sizes: For the grain size distribution we assume a power
law of the form
n(a)da ∼ a−3.5 da with
amin < a < amax .
(8)
Here, a is the dust grain radius and n(a) the number of dust grains
with a specific radius. For amin = 5nm and amax = 250 nm this
distribution becomes the commonly known MRN distribution of
the interstellar medium by Mathis et al. (1977). We choose those
values as the starting point of the present study.
To model the different grain sizes and chemical populations,
one has to consider an arbitrary number of separate dust grain
sizes within a given interval [amin : amax ]. But, the observables
derived from radiative transfer considering each grain species
separately are close to the observables resulting from radiative
transfer (RT) simulations based on weighted mean dust grain
parameters of the dust grain ensemble (Wolf 2003a). Thus, we
use weighted mean values for the efficiencies factors, cross sections, albedo, and scattering matrix elements. For each dust grain
ensemble, 1000 logarithmically equidistantly distributed grain
sizes within the interval [amin : amax ] have been taken into account for each chemical component in the averaging process.
There are arguments that the grain size can not be governed
by a power law as in Eq. (8). Furthermore, in the complex environment of a circumstellar disc, we expect dust settling and
grain growth to make the grain size distribution quite dependent
on the location within the disc. Unfortunately, a consideration of
grain sizes that takes into account the effects of e.g. dust settling
requires more than just one parameter as Eq. (8) does. Given the
data we have, we are not able to disentangle these parameters
in our study. Therefore, we assume that the power law distribution (8) to be valid in the whole disc and envelope structure and
only use the maximum grain size as a parameter in our modeling
efforts.
It will turn out that even with these simplifying assumptions
we are able to model observational data of the system, although
different amax in the disc and envelope have been found for other
objects (e.g. Wolf et al. 2003). We assume an average grain mass
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
density of ρgrain = 2.5 g cm−3 . This density does not have any influence on the optical properties of the dust, as they are governed
by the chemical composition and the particle size of the grains.
The average grain mass density merely controls, together with
the disc mass and particle size, the number of dust grains in the
disc.
4.1.4. Heating sources
There are two sources of energy for the disc that need our attention. The disc can be heated by stellar radiation and/or accretion
of in-falling matter.
Accretion heating : Our model involves a parameter with the
dimensionality of an “accretion rate”: Ṁ in Eq. (5) as part of the
description of the envelope structure. However, this quantity is
really an infall rate within the envelope and may not necessarily
describe mass accretion onto the star itself. But it is in general
the latter mass flow that, as e.g. in FU Orionis like objects, accounts for significant contributions to the system’s luminosity.
For a T Tauri like system as CB 26, we thus neglect accretion as
a major source of energy. As our study shows, Ṁ is rather small,
around ∼10−8 M⊙ yr−1 . This is small compared to FU Orionis
objects but average for T Tauri Stars and strongly supports our
ansatz.
Besides matter infall in the envelope, accretion in the disc
might be an important source of energy. As shown by Wolf et al.
(2003), the accretion luminosity from within the disc is about
two of magnitude smaller than the stellar contribution. As the
model setup here is similar, we neglect accretion heating as a
significant source of energy.
Stellar heating : The discussion above leaves the star as the
only primary source of energy in our model. Its radiation heats
the dust which then in turn itself re-emits at longer wavelengths.
In this sense the disc in our model is passive. That is, we neglect accretion or turbulent processes within the disc as a possible other primary energy source.
We do not observe the star directly. This is for the following
two reasons:
1. in the far infrared and at longer wavelengths, where the disc
becomes less opaque with increasing wavelength, the contribution to the spectral energy distribution from the dust is
orders of magnitude larger than that coming from the star;
2. in the optical, near, and mid-infrared bands, the disc becomes
opaque, and the star is shielded from our direct view.
Therefore, we have to assume the stellar parameters (i.e., temperature and luminosity) since we are not able to derive them
directly from observations. Observations only hint at a luminosity being L ≥ 0.5 L⊙ . As a starting point we choose an “average”
T Tauri star as described by Gullbring et al. (1998). This star has
a radius of r = 2 R⊙ and a luminosity of L∗ = 0.92 L⊙ . Assuming
the star to be a black body radiator, this yields an effective surface temperature of T eff = 4000 K.
Both of these parameters have been kept fixed in our parameter study to avoid degeneracies between parameters of the model.
Except for the total flux, this choice has no impact on the nearinfrared images.
As Natta (1993) showed, under certain conditions stellar
light scattered back to the disc can have significant implications
for the thermal structure of the disc. Here, the outer envelope
1173
regions 400 AU ≤ renv ≤ 1000 AU are shown to be of importance. An important assumption in the argument is that the
scattering phase function is independent of the scattering angle.
However, in our modeling framework, the scattering phase function is highly asymmetrical and favours forward scattering by orders of magnitude. Thus, the amount of radiation scattered back
to the disc from the envelope outside our model space, i.e. at
distance larger then 400 AU, can be neglected.
4.2. Means of modeling
In this section we discuss how we proceed with the model. We
discuss the free parameters, their range, and the sampling of the
resulting parameter space. Finally, we review the constraints imposed upon our model by the various observations and give a
criterion for the best-fit model.
4.2.1. Radiative transfer
For our continuum radiative transfer simulations, we made use
of the program MC3D (Wolf et al. 1999; Wolf 2003b). It is based
on the Monte-Carlo method and solves the continuum radiative
transfer problem self-consistently. It estimates the dust temperature distribution taking into account any heating sources, which
in our case is the central star’s radiation. It makes use of the temperature correction technique as described by Bjorkman & Wood
(2001), the absorption concept as introduced by Lucy (1999),
and the enforced scattering scheme as proposed by Cashwell
& Everett (1959). The optical properties of the dust grains
(scattering, extinction and absorption cross sections, scattering
phase function) and their interaction with the radiation field is
calculated using Mie theory. Multiple and anisotropic scattering is considered. The phase function is highly asymmetrical
(e.g. at the peak of stellar emission at λ = 0.7 µm one has
cos(θscatter ) = 0.86), strongly favouring forward-scattering.
In order to derive a spatially resolved dust temperature distribution, the model space has to be subdivided into volume elements inside which a constant temperature is assumed. Both
the symmetry of the density distribution and the density gradient
distribution have to be taken into account. For the present study,
we use a spherical model space, centred on the illuminating star
and an equidistant subdivision of the model in the θ-direction,
whilst a logarithmic radial scale is chosen in order to resolve the
temperature gradient at the very dense inner region of the disc.
The required spatial resolution at the disc inner radius rim of our
model ranges from 10−4 AU up to 10−1 AU, and every grid cell
outwards is 1% larger than its next inner neighbour.
The radiative transfer is simulated at 101 wavelengths. The
first 100 wavelengths are logarithmically distributed in the wavelength range [λmin , λmax−1 ] = [50 nm, 2.0 mm]. The longest
wavelength used is λmax = 2.7 mm.
With MC3D we compute observables from the model. These
observables are then compared to the observed data in the quest
for the best-fit model. Namely, the quantities we derive with
MC3D from the model are:
1. images in the NIR, that is in the I, J, H, and K Band;
2. images in the millimetre regime at 1.1 mm, 1.3 mm and
2.7 mm,
3. 101 points for the SED accordingly to the above wavelength
distribution.
1174
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
4.2.2. Constraints from observations
Given the broad variety of available observational data, there are
primary features are that we want to reproduce with our model.
This also determines the criteria for the best-fit model. The case
is simple for the spectral energy distribution. There, we aim at
reproducing the complete spectrum over three orders of magnitudes from the optical bands down to the millimetre regime. We
can divide the maps of the disc in two major groups: the maps
in the millimetre regime, and the maps in the near-infrared. Both
groups trace different physical processes and different spatial regions of the object.
Millimetre maps: For resolved images, the issue is not as sim-
ple as for the SED. Our model is rotationally symmetric and thus
does not provide for any related asymmetry as seen in observations.
The morphology of the millimetre maps has its origin in the
dust that is heated by the star and re-emits light at those wavelengths. Although the images at 1.1 mm, 1.3 mm and 2.7 mm
are rather simply structured they impose two major features that
constrain our models. These are:
1. the peak flux and;
2. the spatial brightness distribution.
Since in all three maps the beam size is larger or comparable
to the vertical extent of the disc, we can not constrain the flux
distribution on the z-axis, perpendicular to the disc mid plane.
Any feature there is smoothed out by the beam. Therefore, we
focus on reproducing the flux distribution along the midplane of
the disc. All images are fitted in the image plane.
Maps in the near-infrared: The four images in the near-infrared
show more structures and details than the millimetre maps. In
addition to the disc, which appears as a dark lane in the nearinfrared, there is also a complex, wavelength-dependent morphology of the surrounding envelope.
Considering that the circumstellar disc CB 26 is located at
the edge of a Bok globule, one realises that the environment of
the disc can account for the majority of the substructure seen on
these maps; yet the Bok Globule itself is not part of our model.
Hence, we have to restrict ourselves to the following two points
that we want to reproduce with our model:
1. the dependence of the width of the dark dust lane on wavelength and;
2. the relative peak height of the brightness distribution above
and below the dust lane.
We restrict our modeling efforts to a simple envelope structure
and the above two points since it is hard to distinguish whether
the appearance of the object in the observations is due to envelope or environmental structure. We also put no emphasis on
the vertical width of the upper and lower lobe nor on the exact
morphology.
4.2.3. Quality of the fit
For each comparison between model and observation on the
aforesaid points, we get an individual χ2i . The total χ2 of one
model is then just the sum over all the individual χ2 s:
⎛
⎞
⎟⎟⎟
1 ⎜⎜⎜⎜ 2
2
2
2
χtotal = ⎜⎜⎝χSED +
χi +
χ j ⎟⎟⎟⎠ .
(9)
n
mm−maps
NIR−maps
Here, n = 8 as we have one χ2 from the SED, three from the
millimetre maps, and four from the scattered light images.
Based on χ2total we get from Eq. (9), we give our modeling errors as the range where we can alter the parameter values without
changing χ2total more than 10%. This value is rather arbitrary as
there is no mathematical reasoning behind it. Yet, it has proved
within our study to reflect quite well the adjustability of the
model. Allowing for a larger variation of χ2total than 10% gives
generally worse results.
4.2.4. Parameter space study
Based on the model laid out in the previous sections, we are left
with ten adjustable parameters to reproduce the characteristics
as described in the previous section. If not stated otherwise, we
choose the range of a parameter for our study based on modeling
of other similar objects (see e.g. Wolf et al. 2003). Then, we first
sample that range of an individual parameter in four coarse steps,
select the two best values, and go with the same procedure to the
next parameter. Second, we take the results as an indicator how
to refine the stepping in a smaller range. This process is iterated
to reach our final results. As the starting values in our parameter
space study we chose the values obtained for IRAS 04302+2247
which has a similar appearance to CB 26.
In detail, the parameters we use are:
1. the exponents α and β which describe the radial density profile of the disc (see Eq. (1) for details). From D’Alessio et al.
(1999), we choose for the flaring parameter β = 1.25 and
obtain a corresponding value for α = 2.25 from the relation
α = 3(β − 12 ), which is a result of accretion disc physics (see
e.g. Shakura & Syunyaev 1973). Those values are taken as
a starting point and we then look for agreement between observations and modeling at and beyond those values in steps
of 0.1 and 0.2, respectively;
2. the scale height h0 of the disc at a given radius. In the following, we fix the scale height at a radial distance from the star
of rcyl = 100 AU and consider the cases h0 = 5 AU, 10 AU,
15 AU, 20 AU, and 25 AU;
3. from the density Eq. (5) for the envelope, we have the centrifugal radius rcf and;
4. the coupling constant ρ̃ which is a function of the mass accretion rate Ṁ and the mass of the central star M∗ . For the
centrifugal radius, we probe values in the range 100 AU ≤
rcf ≤ 800 AU. As for ρ̃, we chose for the accretion rate values from the interval Ṁ ∈ [10−5 M⊙ yr−1 ; 10−10 M⊙ yr−1 ]
and calculate ρ̃ under the consideration of the stellar mass
by Launhardt et al. (2008). In this paper a dynamical mass
of M∗ = 0.5 ± 0.1 M⊙ is derived;
5. the inner and outer disc radius. The inner radius was initially
set to 0.1 AU, which is approximately the dust sublimation
radius. However, we do not get good agreement especially
with the 1.3 mm map unless we choose values of ∼45 AU.
For the outer radius, we chose a value of 200 AU but also
considered configurations with 150 AU and 250 AU;
6. the disc mass. We consider 7 different disc dust masses in the
range from 1.0 × 10−5 M⊙ up to 4.5 × 10−3 M⊙ ;
7. the disc’s inclination is such that the system is seen almost
edge-on. We restrict the range for θ to be part of our parameter space to values between 60◦ and 90◦ with a stepping of
1◦ between 80◦ and 90◦ ;
8. the maximum grain size amax . Grain growth is a major issue for protoplanetary discs as it is the first step towards the
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
1175
Table 3. Overview of parameter ranges and best-fit values.
Parameter
α
β
h0 [AU]
rin [AU]
rout [AU]
Dust mass [M⊙ ]
Ṁ[M⊙ yr−1 ]
rcf [AU]
amax [ µm]
θ
Minimum value
2.0
1.0
5
0.1
150
1.0 × 10−5
10−10
100
0.25
60◦
Maximum value
5.0
2.6
25
60
350
5.0 × 10−3
10−5
800
1000
90◦
Best fit value
2.2
1.4
10
45
200
3.0 × 10−3
10−8
460
2.5
85◦
Uncertainty
±0.1
±0.1
±2.5
±5
±25
±0.2 × 10−3
±0.5 × 10−8
±10
±0.3
±5◦
For the definition of the uncertainty see Sect. 3.2.3. The first group of parameters contains purely geometric parameters, the second group physical
parameters and the last group the inclination of the disc as seen by the observer as an observational parameter.
An average dust temperature of T̄ dust = 16 K is obtained
from the temperature distribution by weighting it with the mass
distribution. This goes nicely with Fig. 6 if one bears in mind
that the bulk of the dust is located in the midplane and is well
shielded against stellar radiation by inner parts of the disc. High
temperatures are only reached in a very narrow region at the inner disc rim and in the very low density regions of the disc and,
thus, contributes little to the mass averaged dust temperature.
Since our dust grain model only uses refractive indices, an
effective dust grain opacity can be calculated by re-arranging
Mdust =
Fig. 5. Sketch showing all components of our model and their spatial
arrangement. All sizes are not to scale.
formation of planets from the dust in the interstellar medium.
We allow for a maximum grain size of 1 mm.
For a summary of those ten adjustable parameters of our model
and the range we covered in the study see Table 3. A sketch
showing all components of our model is presented in Fig. 5.
5. Results
The values of the parameters of our best-fit model can be found
in Table 3. Our geometrical parameters α and β of the disc density structure yield with the Eq. (4) a surface density power-law
exponent of p = −0.8.
In Fig. 6 the density and temperature distribution of the bestfit model is shown while in Fig. 7 radial profiles of the density
and temperature distribution in the midplane and 20 AU above
are shown. It is apparent that the high density in the midplane on
the inner rim provides enough opacity so that material behind it
in the midplane is not being heated up directly by the stellar radiation. The highest dust temperature at the inner disc rim amounts
to ≈ 90 K and is reached ∼ 20 AU above the midplane. However,
due to the high density in the midplane, the stellar radiation does
not penetrate deep into the midplane which results in a steep
temperature gradient. In the less dense upper (and lower) layers
of the disc, the stellar radiation also heats more distant parts of
the disc resulting in a less steep temperature gradient.
S ν D2
κν Bν (T̄ dust )
(10)
and assuming gas-to-dust ratio of 100. Here, κν is the wavelength
depended mass absorption coefficient, S ν is the observed flux, D
the distance of the object, and Bν(T̄ dust ) is the Planck-function
at a given temperature. The calculation yields for our model a
dust opacity of κ1.3mm = 0.26 cm2 g−1 . This value is very close
to the ISM dust opacity given by Draine & Lee (1984, 1987).
Compared to opacities for coagulated dust grains and ice-coated
grains Ossenkopf & Henning (1994); Beckwith et al. (1990), our
model yields an effective dust grain opacity at the lower end of
the range of commonly employed opacities.
Figure 4 shows the spectral energy distribution of the best-fit
model in comparison with the spectral data. We achieve quite a
good match to the observational data except for the optical wavelengths. Since the circumstellar disc is embedded in the Bok
globule CB 26 we need to consider the dust outside our model
space as well. Thus, we add a screen that mimics the effect of
foreground extinction between the object and the observer. For
this screen, we assume the extinction properties of interstellar
dust grains. Such a screen is described in detail by Cardelli et al.
(1989). Using AV as a parameter with a minimum value of 2,
we find in our study that a screen with a visual extinction of
AV = 10 can easily account for the missing flux in the optical.
The result is shown in Fig. 4 as the dashed curve, whereas the
dashed-dotted line corresponds to the best-fit model without the
screen.
It needs to be stressed that this screen only applies extinction
law to all observable quantities. It is not subject to any radiative
transfer or thermal re-emission. We estimated the possible contribution to re-emitted radiation of a such a screen with AV = 10
composed of ISM grains at the same distance as CB 26 with a
temperature of 16 K. We found that the screen is clearly optically thin (e.g. τ1.3mm = 8 × 10−5 ) and has only enough mass to
have about ≈1% of the observed flux in the millimetre regime.
1176
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
Fig. 7. Radial profiles of density (upper plot) and temperature (lower
plot) in the midplane along r (solid line) and along z/r = 0.1 (dashed
line). The latter profile is chosen in order to include the scale height h0
at r = 100 AU. The maximum density is normalised to 1 (corresponding
to 0.34 × 10−8 g cm−3 ).
Fig. 6. Upper plot: contours of dust density distribution on a plane perpendicular to the midplane normalised to the peak density of 0.34 ×
10−8 g cm−3 . The contour levels are at 10−7 , 10−3 ,10−2 , 5 × 10−2 , and
2 × 10−1 . Lower plot: contours of the temperature distribution on the
same plane as above. Contour levels are at 20 K, 40 K, 60 K, 70 K, and
80 K. The maximum temperature is 90 K.
Furthermore, the spectral energy distribution of the model
shows that the contribution of the envelope is quite important
for shorter wavelengths. In this regime, the main contribution to
the spectral energy distribution comes from the envelope whilst
in the radio regime the flux comes completely from the dust in
the disc which glows at those wavelengths. Figure 8 illustrates
this.
6. Discussion
6.1. Grain size and growth
It needs to be pointed out that we have found a model capable of explaining all major elements of the observations without the need to increase the maximum grain size in our parameter study significantly. The maximum grain size of our best fit
model is amax = 2.5 µm. While this is a factor ten larger than the
smallest maximum grain size considered in our parameter space,
Fig. 8. Contributions to the spectral energy distribution from disc
(dashed line) and envelope (solid line). The transition from envelope
to disc as the major source of radiation (re-emission and scattering) is
at λ = 217 µm.
the value found is only marginally larger then upper grain sizes
given for the ISM in the literature. In fact, this is only true for
the dust in the the disc component of our model. The maximum
grain size in the envelope is the same as in found in the ISM,
amax = 0.25 µm. If the maximum grain size in the envelope were
bigger, then the short wavelength part of the SED could not be
reproduced.
The disc grain size we determine is certainly smaller by several orders of magnitude than the maximum grain size in other
disc models such as in the work of Pinte et al. (2008). There, a
maximum size of a few millimetres has been found. In contrast,
models in our parameter space featuring values of amax ≈ 1mm
fail to fit the SED in the millimetre regime as the slope of the
model SED is not steep enough. Also, we did not succeed in
reproducing the default value for the maximum grain size of
amax = 250 nm of ISM. In particular, the model would be off
by a factor of ten for the SED data point at 1.3 mm.
One needs to discuss why the change for amax from 250 nm
to 2.5 µm allows for a fit in the millimetre part of the SED
– at wavelengths three orders of magnitude larger than the
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
largest grains in the model. Intuitively, one would expect the
millimetre part of the SED to remain unaltered by a change of
grain size at that level. However, this expectation is based on
the assumption that the absorption efficiency of the grains Cabs
in the millimetre regime is also insensitive to a change in the
grain size at the micrometre level. Yet, this only holds true for
only two of the three dust species in the model. For the astronomical silicate and the graphite component with an alignment
of the crystals’ optical axis perpendicular to the propagation direction of the electromagnetic field Cabs has the same slope in
the millimetre regime for grain size distributions with a maximum grain size of 250 nm and 2.5 µm. But for the third dust
species, namely the graphite component with the crystals’ optical axis aligned with the electromagnetic field, this is different.
Here, the slope of Cabs is significantly larger for amax = 250 nm
than for amax = 2.5 µm. This effect is large enough to dominate
the sensitivity of the SED to changes in the maximum grain size
even at the level discussed despite the fact that the dust species
responsible for this behaviour has only a 12.5% share of the total
dust. This is due to the fact that graphite is a far more effective
absorber than silicate.
A look on the millimetre spectral index of the data yields
αmm = 3.1 ± .27. The corresponding millimetre opacity slope
is βmm = 1.1 ± .27, if the millimetre emission is assumed to be
optically thin. A βmm = 1 and smaller is understood to indicate
dust grain particles larger than in the interstellar medium to be
present. A value of βmm = 2 is expected if only ISM grains were
present in the disc. The latter is true only for grains whose absorption efficiency Cabs behaves like silicate. The value of βmm
we obtain from data and model of CB 26 close to what is expected for large grains despite having still only micrometre sized
grains in the model is due to the unorthodox behaviour of the parallel graphite component on the one hand side and on the other
hand side to the non-vanishing optical depth in the millimetre
regime (e.g. τ1.3mm ∼ 0.6).
Draine (2006) considered also the behaviour of the millimetre opacity slope βmm for dust mixtures of graphite and silicate. There, no dependency of the opacity index as in our work
was found. However, in this analysis not crystalline graphite
was used but the optical properties of amorphous carbonaceous
solids instead.
We summarise that we do not need mm sized grains to model
the circumstellar disc CB 26 but grains with a maximum grain
size still close to what is found in the ISM. This is in contrast
to the modelling of the Butterfly star (see Wolf et al. 2003) as
well as for the circumstellar disc HH 30 (see Wood et al. 2002)
where in both cases the authors found it necessary, to have their
largest grains at least four times larger than the largest grain of
the interstellar matter. Of course, this result is based directly on
the choice of the grain model we made. For another model, especially one without graphite, larger grains might be needed to fit
the observed SED. Yet, due to the poorly constrained dust composition of circumstellar discs – in particular in the disc interior –
this degeneracy between dust model and grain size must remain.
As the dust model used in this work is also used in the context
of other studies of circumstellar discs such as the Butterfly star
(Wolf et al. 2003), it is a reasonable choice as it keeps the models of similar objects comparable as they are built on common
assumptions.
6.2. Inner hole
The most unexpected result of our modeling is the inner disc
radius for the model. In Fig. 9 the solid line shows the flux profile
1177
Fig. 9. Horizontal cut through the spatial brightness distribution at
1.3 mm. The thick solid line represents the OVRO observation, the
dash-dotted lines gives the addition/subtraction of one σ, the dotted
line indicates the 2σ-levels, the dashed line corresponds to our best-fit
model, and the thin solid is the dirty beam of the observation.
along the disc midplane at 1.3 mm as seen by OVRO whilst the
thin solid line is the PSF of the observation. At the centre of the
disc, the profile shows a plateau in the brightness distribution.
There are two possible explanations for this dip.
First, the minimum could indicate that emitting dust in that
region is present but not visible. If the optical depth in the midplane is sufficiently high, the flux contribution from the inner
parts of the disc compared to the contribution of the optically
thin parts on the disc’s surface would be smaller.
A high optical depth can easily be reached in regions of high
dust densities. For a given total disc mass, a disc with small inner radius yields higher densities than the model with the large
inner radius. Hence, the smaller the inner radius in our model,
the more matter we find to be close to the star and thus reaching
higher optical depths in the inner disc regions. However, even
for the smallest inner radius of our parameter space, 0.1 AU we
did not reach an optical depth that obscures enough flux from the
disc centre to reproduce our observations.
This behaviour would also be more obvious when compared
with maps at shorter wavelengths since the optical depth increases with decreasing wavelength. But in the images at 1.1 mm
and 2.7 mm we do not observe a dip at the centre of the disc.
Unfortunately, the other available images do not help us to conclude whether the absence of the dip is really an indicator for
a substantial void in the disc. This is because the point spread
function at those two images is far too large to resolve the feature (see Table 1). Wolf et al. (2008) reasoned this way in the
case of IRAS 04302+2247 where they found a similar dip in the
brightness distribution at λ = 894 µm but not at 1.3 mm.
The second possible cause for the spatial brightness distribution in the 1.3mm map is the actual lack of dust in the inner
region of the disc. Whilst we started with an inner radius in the
order of magnitude of a few tens of the stellar radius, it was not
possible to match the plateau structure of the 1.3 mm map. On
this account, we allow the inner disc radius to be as large as
50 AU. Unfortunately, within our model and parameter framework we are not at liberty to increase the total mass, and hence
the density at the disc centre, because the flux at 2.7 mm already
sets an upper limit for the total disc dust mass. This is because at
1178
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
this wavelength any model is optically thin, so we see the total
matter of the disc.
Another way to think about the issue is to consider the optical depth of the disc at 1.3 mm. We have run one simulation of
the disc with exactly the same parameter values as for our best-fit
model except for the inner radius. For the comparison model we
chose rin = 0.1 AU. For both runs we computed the optical depth
along the line of sight from the observer through the disc. As a
result, for the large inner radius we have τ1.3mm = 0.6, and for
the small inner radius τ1.3mm = 1.9. In the first case we deal with
an optically thin system, while for the second, the optical depth
is borderline. An optical depth of 1.9 means that the initial flux
is reduced by a factor of e−1.9 = 0.15. A much larger value of τ
along the line of sight would be required to hide all emitting dust
in the central region and produce the observed plateau structure.
Thus, in our study, we were not able to fit the millimetre profile
with a small inner radius.
We are therefore forced to conclude that in the millimetre
regime we do see the entire disc. Hence, the plateau structure
rises from the wide spatial separation of the inner rim from the
star, whereas a disc with a small inner radius would have a central peak in the brightness distribution.
Based on this line of arguments, our model provides predictive power for high resolution images at wavelengths longer
than 1.3 mm. Since we conclude that the plateau structure in
the brightness profile is due to lack of dust, it should also be
visible at longer wavelengths. There, the dust becomes more optically thin and thus provides us with literal insight inside the
disc. Now, if the lack of flux in the disc centre is due to an optical depth effect, the central trough should vanish with longer
wavelengths, and the brightness profile should have one central
peak instead of a plateau-structure. Unfortunately, the image at
2.7 mm has a point spread function far too large to allow us to
disentangle between the two possibilities. Future observations of
the disc CB 26 with higher spatial resolution will provide a perfect opportunity to confirm this prediction. Figure 10 shows what
we expect the disc to look like at different wavelengths according to our model with the inner void. With the Atacama Large
Millimeter Array (ALMA) it will be quite easy to confirm our
findings.
It needs to be pointed out that the spectral energy distribution of CB 26 does not hint at the presence of a large inner
hole. Its general shape is similar to SEDs of other edge-on discs.
This is because the inner regions of the disc which completely
dominate the disc emission in the 1–20 micron regime are completely hidden from view in the edge-on configuration. Scattered
starlight from the outer disc and/or the envelope accounts for the
short wavelength bump of the SED, irrespective of the amount
of emission from the disc itself. Only the quality of the OVRO
map at 1.3 mm provides us with the need to postulate about an
inner clearing.
A possible explanation for a large void with 90 AU in diameter is that the disc in the Bok globule CB 26 is actually a
circumbinary disc. Binarity is also a possible explanation for the
rotating molecular outflow described by Launhardt et al. (2008).
However, a detailed dynamical study is not the scope of this
paper.
Of course, another idea might be that the dust in the inner
region has already bean processed to planetesimals, or at least
to bodies that are large enough to decouple from the disc and
its dynamics, and do not contribute to the mm-flux. However, a
first indicator for a low age of the system is the fact that it is still
deeply embedded in its parental cloud. Another indication to the
young age of the system is the absence of dust grains larger than
Fig. 10. Predicted appearance of the inner region of the disc.
found in the interstellar medium. Hence, we do not expect that
we may be dealing with a so called “transitional disc”6 and a
planet population in the centre that has already cleaned up formerly dusty regions.
6.3. Disc mass
Within our model a rather high disc mass is needed to account
for the observed flux in the millimetre regime. With a total of
about 3 × 10−3 M⊙ and dust-to-gas ratio of
MGas
∼ 100,
MDust
(11)
we end up with a total disc mass of ∼0.3 M⊙ which is close to the
star’s mass. Hence, we need to reconsider the mass we computed
for the disc. The derived disc mass essentially builds upon the
assumptions we had to made about the dust grain chemistry and
shape.
6.3.1. The dust grain structure, temperature and density
The radiative transfer in our modeling is performed under the
assumption of spherical dust grains to avoid equivocalities. It
would be possible to have a lower estimate of the dust mass if
we dismiss this assumption. This very much complicates the radiative transfer calculations since we now need to take into account all the possible fractal grain shapes as well as the spatial
orientation of every grain. So far, we do not have the ability to do
such a simulation. But, we can make a gedankenexperiment on
parts of the results. Of course, one expects strong changes in the
scattering behaviour of dust grains with complex shapes. But,
besides that, one also can think of a plenitude of dust grains with
almost the same absorption cross section as spherical dust grains
but with much less mass. Voshchinnikov et al. (2007) discusses
very fluffy particles with a porosity up to 90%.
6
Those discs are considered to be predecessors of evolved debris-type
discs.
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
Fig. 11. Contour lines of the Toomre parameter Q (see Eq. (12)). The
lines, from right to left, are at levels of Q = 0.1, 0.3, 0.5, 0.7.
We furthermore point out that the grain density ρgrain is not
one of the fitting parameters. The disc mass is proportional to
this density and the number of grains. We only can constrain
within our study the disc structure, the grain size, and their number, but not the density of one grain. For our investigation of the
system, we used ρgrain = 2.5 g cm−3 , but it might well be less
than this value. In turn, this will alter our estimate for the disc
mass by the same factor.
6.3.2. The snow line
For the estimation of the total disc mass of gas and dust, we
make use of the canonical relation (11). This relation assumes
that there is some gas and dust of the disc inside the snow line
and some outside. The snow line indicates the largest radius for
which the temperature in the disc is high enough to keep water
from freezing onto the dust grains. This line is usually set at a
radius where the disc temperature drops to 170 K. As reported
above, the maximum temperature we reach within our disc is
about 90 K, and the average is only 16 K. This means, that our
entire disc is outside the snow line. Thus we need to adjust the
dust to gas ratio (11) to about 50 as published by Kokubo & Ida
(2002).
However, the very same dust model we made use of in this
work was also built upon in other modeling projects (e.g. Wolf
et al. 2003). In order to allow comparison of our model for CB 26
with those models, we also give consideration to the disc stability when we keep the dust model.
1179
Fig. 12. Vertical cuts at the horizontal centre through the near-infrared
scattered light images. The solid line is from observational data, and
the dashed line is from our best-fit model. For an illustration where
those cuts are obtained in the respective maps, see Fig. 13. The plots
are normalised to 1. In case of the I-Band, this corresponds to 1.3 ×
10−7 Jy/beam, 5 × 10−6 Jy/beam in the J-Band, 2 × 10−5 Jy/beam in the
H-Band, and 2.2 × 10−4 Jy/beam (“beam” refers to the FWHM area of
the PSF).
clearly shows, in our model Q < 1 throughout the entire disc by
a factor of two to five.
Yet, the Toomre criterion only can be consistently employed
for a system that is formed by a central star and a surrounding
disc. As discussed above, the inner hole we find in CB 26 can be
an indication for a binary. An example for such a system would
be the young binary system GG Tau. Here, a dusty ring around
the central stars has been observed by Guilloteau et al. (1999)
with a total ring mass of 0.13 M⊙ , which is about a factor of two
smaller than the total mass of CB 26. The discussion of stability of a binary system is quite delicate and not the topic of the
present paper.
However, if one assumes a single central star, there are still
effects that we did not consider in our model but which might be
important for the system’s stability. Following the discussion in
the paper of Gammie (2001), discs violating the Toomre criterion are not stable but nevertheless might be in a steady gravoturbulent state. The paper investigates gravitationally unstable
thin Keplerian discs and concludes that the actual outcome of
the instability depends on the cooling time τc .
However, the parametric model we use does not account for
any dynamical interaction within the dust. Therefore, it would be
interesting to couple our radiative transfer code MC3D with hydrodynamic simulations of circumstellar discs in a future study.
6.3.3. Stability, binarity and dynamics
A criterion for a disc to become unstable was first shown by
Toomre (1964). In order to allow self-gravity of the disc to take
over, it must satisfy
Q=
cs κ
≃1
πGΣ
(12)
where cs is the local sound speed, κ the angular frequency of
the disc, G the gravitational constant and Σ the surface density.
For values of Q smaller then unity, the disc is assumed to be
gravitationally unstable whereas for Q larger unity the disc is
supposed to be stable against gravitational collapse. As Fig. 11
6.4. The width of the dark lane and envelope structure
Another aim of our modeling efforts was to mimic the chromaticity of the dust lane, which narrows with increasing wavelength. Figure 12 shows cuts from north to south through the
centre of the NIR maps from modeling and observations. Our
model of the spherical envelope is quite successful in reproducing the overall flux at each wavelength. Also, the wavelengthdependent width of the dark lane is correctly reproduced.
Figure 13 shows an overlay of the HST/NICMOS H-band
image with the contours given by the best-fit model. The figure
clearly shows that the dark lane is well reproduced. Since our
1180
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
Fig. 14. J Band image from a simulation with a power-law envelope
structure (left) and from rotating envelope (right). See also Fig. 1 for
the observation.
Fig. 13. Inverse H-Band image from HST/NICMOS. The contour lines
are from our best-fit model. From the outer to the inner lines they are
at 27%, 41%, 68% of the peak height. The second dark lane is not reproduced by our modeling as we did not account for envelope asymmetries.
The PSF for those images is rather small ∼7 AU FWHM. The vertical
line illustrates how the cuts were taken in Fig. 12.
envelope model, Eq. (5), is axially symmetric, we cannot expect
the asymmetries of the lower lobe to be modeled as well. Thus,
the model yields the seen discrepancy to the observation.
A second effect of the neglect of asymmetry is that the lower
lobe flux, which in the image is concentrated on the left hand
side, is in the model distributed among the complete lower lobe.
Since both fluxes are equal in magnitude, we end up with a
smaller maximum in the model which also can be seen in Fig. 13.
Fig. 15. Dependency of the brightness distribution along a central cut
on the inclination. All the curves for θ = 90◦ , 85◦ , 80◦ overlay.
6.4.1. Alternative model for the envelope
Besides the rotating, infalling envelope model as described in
Eq. (5), we also tested a spherical symmetric density distribution
as a model for the envelope:
γ
ρenv (r) = ρ0,env rcyl
.
(13)
This brings two parameters into the model, ρ0,env and γ. With
this parameters we are able to model the dependency of the dust
lane wideness on wavelength as well as the overall SED. Yet,
this approach has two major drawbacks:
1. The spatial flux distribution as seen in the I, J, H, and K
images cannot be reproduced. In fact, we obtain a much more
concentrated flux distribution above and below the dark lane
than what we see in Fig. 3. Figure 14 illustrates this.
2. In the SED appears a strong silicate emission feature between 8 µm ≤ λ ≤ 10 µm. We are not able to have the
feature disappearing as required by observations except for
the inclination approaching values 75◦ > θ. But this clearly
contradicts the edge-on nature of the system.
Therefore, we discarded Eq. (13) as a model for the envelope.
6.5. Inclination of the disc
Within our study, we considered two ways to determine disc inclination. The first is to infer it from the millimetre observations,
and the second way is to constrain it from the maps in the nearinfrared.
In Fig. 15, the spatial brightness distribution along a horizontal cut in the 1.3 mm map from the best-fit model at different inclinations is shown. For inclination values in the range of
θ = [80◦ ; 90◦ ] the profile does not change substantially. For inclinations smaller than 80◦ , the profile gets lower. This is because
for an observer the warm inner rim of the disc looks at exactly
90◦ like a line and becomes more and more a circle as one goes
from edge-on to face-on orientation. As long as the complete
rim fits into the size of the point spread function, one cannot distinguish between the different inclinations. But as soon as the
rim gets less ellipsoidal and is no longer within the scope of one
beam, the flux in the centre decreases. This is what can be seen in
Fig. 15. Thus, from the comparison of models at different inclinations with the observations, we can infer an value for theta in
the aforesaid range of θ = [90◦ ; 80◦ ]. Naturally, this way of reasoning is only valid for systems optically thin in the millimetre.
As outlined earlier, this is assumed the case for CB 26.
The second way to determine the disc’s inclination is to compare the relative peak heights from vertical cuts through the
spatial brightness distributions in the near-infrared. Assuming a
symmetric system one expects that both peaks exhibit the same
height if the inclination is exactly edge-on. From an analysis of
the actual peak heights (see Fig. 12) in the HST/NICMOS images we deduce an inclination of θ = 85◦ ± 5◦ which is in good
agreement with the numbers we obtained from the millimetre
maps.
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
6.6. Comparison with similar objects
In general our model has disc and envelope parameters that are
comparable with those of the circumstellar environment of other
young stellar objects. Yet, there are not many edge-on seen circumstellar discs in the sky for which the same richness of observational data is available for modeling as it is for CB 26. Hence,
the number of comparable multi-wavelength studies on edge-on
discs is equally limited. Two objects, HH 30 and the “Butterflystar”, share a large number of features with the disc in CB 26.
All three are seen circumstellar discs seen almost edge-on.
Wolf et al. (2003) has compiled a similar data set for a model
for IRAS 04302+2247, the so called “Butterfly-star”. The data
set includes millimetre maps and high-resolution near-infrared
images obtained with HST/NICMOS. Utilising the same techniques as in this study, the authors’ main result is that the dust
properties must be different in the circumstellar disc and in the
envelope. Whilst a grain size distribution with grain radii up to
100 µm is required to reproduce the millimetre observations of
the disc, the envelope is dominated by smaller grains similar to
those of the interstellar medium. This is quite in contrast to our
model, where we find grains with almost ISM-like properties
are needed in both disc and envelope. However, the original millimetre maps of the model do not suggest any presence of a large
inner void as the spatial resolution is not good enough. In a later
investigation (Wolf et al. 2008) on the “Butterfly-star” with the
Sub-Millimetre Array the authors as well discover a “dip” in the
horizontal brightness distribution. According to the model however, in this case the effect is attributed to an effect of the optical
depth rather than an inner void.
HH 30 was identified as a circumstellar disc with a large
inner void present by HH 30 by Guilloteau et al. (2008). The
authors found a inner hole of radius rin = 40 ± 5 AU and an
outer disc radius of rout = 128 ± 3 AU. At this numbers HH 30
and CB 26 are quite comparable. The separation of two central
stars is postulated to be about 15 AU, so this might also be good
guess for CB 26. Yet, in contrast to our model for CB 26, no
envelope structure is needed to explain the appearance of HH 30
in the near-infrared bands. This suggests that CB 26 is less dynamically evolved than HH 30. Both systems drive a molecular
outflow, but CB 26 shows clear signatures of outflow rotation
(Launhardt et al. 2008), while HH 30 does not (Pety et al. 2006).
The reason for this difference remains unclear, though the early
dynamically state of CB 26 as compared to HH 30 may provide
the key. Yet another difference between HH 30 and our object is
that the presence of cm size grains is needed to model the value
for βmm (Wood et al. 2002). In summary, although all three objects, CB 26, HH 30, and IRAS 04302+2247, feature the same
interior structure, our investigation suggests that the systems are
at different evolutionary states.
1181
then a simple power law distribution. By treating the parameters in this independent and serial manner, the order in which
they are fitted might become an important issue. For instance,
the study could first have focused on the near infrared images
and wideness of the dust lane. As we know from our experience
from modeling other objects this wideness usually requires small
grains at least in the envelope. Modeling the SED in the millimetre regime as a second step would still have lead us to the overall
usage of ISM grains.
This raises the question if our model is really a global minimum in the parameter space or just a local one, and if there
exists in that space a model that reproduces the observations on
CB 26 even better. We exclude this possibility. The model we
obtained exhibits some unexpected features. In the framework of
our model set we thoroughly explored the range of those parameters upon which these features sensitively depend. For example,
we explored the combinations for values of the inner radius and
the scale height and disc mass. If adjusted accordingly, all three
can produce the plateau observed in the 1.3 mm image. However,
only the larger inner radius prevailed. A small scale height might
squeeze the dust tight enough for high optical depth, but clearly
contradicts the wavelength dependence of the dark lane in the
NIR images. The same holds for the maximum grain size. In addition, we do not even have the possibility of mimicking ISM
behaviour by means of disc geometry.
As a remaining issue, we need to consider parameters not
varied at all in our modeling effort. As explained in sections
above, model assumptions such as spherical grains versus fractal grains can hold the key to the mass problem of the disc.
However, this would not alter the model we have at hand or provide a hint to the “real” global χ2 -minimum if one thinks the
model is trapped in a local minimum.
Degeneracy might also be an issue for the stellar parameters.
Varying the luminosity and effective temperature of the embedded T Tauri star in general changes the total energy throughput
in the radiative transfer and the location of the peak of the stellar
spectrum in the wavelength space. Deviations from our assumed
“typical” T Tauri star of course will affect the numbers of our
best-fit model. For instance, the total mass critically depends on
the flux in the millimetre regime and this flux on the total energy provided by the central star. Also, the screen introduced to
mimic interstellar extinction is affected by the choice of surface
temperature. However, no choice of stellar parameters is able to
affect the main conclusions of our model. These are the presence
of ISM grains in the disc and the disc inner hole.
Despite the discussed caveats, the fact we actually found a
good model suggest that we do not need to introduce more complex physics, such as grain growth or dust settling. The data do
not require this.
6.7. Errors and caveats
7. Summary
A matter that has not been touched so far is the uniqueness of our
model. Despite the simplifications we applied, the volume of the
parameter space is still too vast to be completely scanned in a
single study. We therefore employed the above described stepby-step technique for the parameters to find our best-fit model.
For instance, we began by modeling the millimetre maps as
for those the envelope structure is not a dominant contribution.
Thus, we obtained information about the disc total mass as well
as its inner and outer radius and the apparent absence of large
dust grains. The exploration of the near infrared images then
showed the requirement for a rotational envelope structure rather
For a large span of wavelengths, we have compiled a high quality
data set for the circumstellar disc in the Bok globule CB 26. We
obtained images in the near infrared and in the millimetre regime
as well as photometric data and spectra. Together with literature
values, we have constructed a detailed model that allows interpretation of observations with one single set of parameters. The
conclusions we obtained are as follows:
1. In order to account for the brightness distribution in the
1.3 mm map we needed to include an inner hole with
a radius of 45 AU. Future observations, especially in the
1182
J. Sauter et al.: The circumstellar disc in the Bok globule CB 26
sub-millimetre regime, are required to confirm our interpretation of a low optical depth along the line of site at 1.3 mm.
2. Our model very nicely reproduces the prominent chromaticity of the dark lane as seen in the near infrared images.
3. Based on the chosen dust composition (astronomical silicate,
graphite) and the resulting opacity structure of the best-fit
disc model, we find that the millimetre SED indicates that the
grains feature the same grain size distribution and almost the
same upper limit to the grain size as the interstellar medium.
4. The disc is massive with a total dust and gas mass of
0.3 M⊙ under the assumption of spherical grains and ρgrain =
2.5 g cm−3 , compared to a mass of the central T Tauri star
with 0.5 M⊙ , and therefore is possibly, but not inevitably,
unstable. We discussed that, due to possible grain fractal
structure and other effects, the real disc mass may be small
enough to have a stable system.
Acknowledgements. The authors thank all members of the GEODE-team for
their help in this project. J. Sauter thanks Owen Matthews, Jens Rodmann,
and Arjan Bik for enlightening discussions. This work is supported by the
DFG through the research group 759 “The Formation of Planets: The Critical
First Growth Phase”. F. Menard thanks financial support from Programme national de Physique Stellaire (PNPS) of CNRS/INSU, France and from Agence
Nationale pour la Recherche of France under contract ANR-07-BLAN-0221.
This work has been supported by NASA funding from the Space Telescope
Science Institute, HST general observer program 10603; and by NASA funding from the Jet Propulsion Laboratory, under Spitzer general observer program
30765. C. Pinte acknowledges the funding from the European Commission’s
Seventh Framework Program as a Marie Curie Intra-European Fellow (PIEFGA-2008-220891). The Submillimeter Array is a joint project between the
Smithsonian Astrophysical Observatory and the Academia Sinica Institute of
Astronomy and Astrophysics and is funded by the Smithsonian Institution and
the Academia Sinica.
References
Alonso-Albi, T., Fuente, A., Bachiller, R., et al. 2008, ApJ, 680, 1289
Beckwith, S. V. W., Sargent, A. I., Chini, R. S., et al. 1990, AJ, 99, 924
Beelen, A., Cox, P., Benford, D. J., et al. 2006, ApJ, 642, 694
Bergeron, L. E., & Dickinson, M. E. 2003, Instrument Science Report NICMOS
2003-010 (Baltimore: STScI)
Bjorkman, J. E., & Wood, K. 2001, ApJ, 554, 615
Bouwman, J., Henning, T., Hillenbrand, L. A., et al. 2008, ArXiv e-prints, 802
Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245
Cashwell, E. D., & Everett, C. J. 1959, A practical manual on the Monte Carlo
Method for random walk problems (Pergamon)
D’Alessio, P., Cantó, J., Hartmann, L., Calvet, N., & Lizano, S. 1999, ApJ, 511,
896
Dowell, C. D., Allen, C. A., Babu, R. S., et al. 2003, in SPIE Conf. Ser. 4855,
ed. T. G. Phillips, & J. Zmuidzinas, 73
Draine, B. T. 2006, ApJ, 636, 1114
Draine, B. T., & Lee, H. M. 1984, ApJ, 285, 89
Draine, B. T., & Lee, H. M. 1987, ApJ, 318, 485
Draine, B. T., & Malhotra, S. 1993, ApJ, 414, 632
Duchêne, G., McCabe, C., Ghez, A. M., et al. 2004, ApJ, 606, 969
Eisner, J. A., Hillenbrand, L. A., Carpenter, J. M., et al. 2005, ApJ, 635, 396
Engelbracht, C. W., Blaylock, M., Su, K. Y. L., et al. 2007, PASP, 119, 994
Gammie, C. F. 2001, ApJ, 553, 174
Glauser, A. M., Ménard, F., Pinte, C., et al. 2008, A&A, 485, 531
Gordon, K. D., Engelbracht, C. W., Fadda, D., et al. 2007, PASP, 119, 1019
Guilloteau, S., Dutrey, A., Pety, J., et al. 2008, A&A, 478, L31
Guilloteau, S., Dutrey, A., & Simon, M. 1999, A&A, 348, 570
Gullbring, E., Hartmann, L., Briceno, C., et al. 1998, ApJ, 492, 323
Ho, P. T. P., Moran, J. M., & Lo, K. Y. 2004, ApJ, 616, L1
Hughes, A. M., Wilner, D. J., Kamp, I., et al. 2008, ApJ, 681, 626
Kessler-Silacci, J., Augereau, J.-C., Dullemond, C. P., et al. 2006, ApJ, 639, 275
Kokubo, E., & Ida, S. 2002, ApJ, 581, 666
Kovács, A. 2006, Ph.D. Thesis, AA(Caltech), attila@submm.caltech.edu
Kovács, A., Chapman, S. C., Dowell, C. D., et al. 2006, ApJ, 650, 592
Launhardt, R., & Henning, T. 1997, A&A, 326, 329
Launhardt, R., & Sargent, A. I. 2001, ApJ, 562, L173
Launhardt, R., Pavlyuchenkov, Y., Gueth, F., et al. 2008, VizieR Online Data
Catalog, 34940147
Lucy, L. B. 1999, A&A, 344, 282
Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, ApJ, 217, 425
Natta, A. 1993, ApJ, 412, 761
Ossenkopf, V., & Henning, T. 1994, A&A, 291, 943
Pety, J., Gueth, F., Guilloteau, S., et al. 2006, A&A, 458, 841
Pinte, C., Fouchet, L., Ménard, F., Gonzalez, J.-F., & Duchêne, G. 2007, A&A,
469, 963
Pinte, C., Padgett, D. L., Menard, F., et al. 2008, ArXiv e-prints, 808
Sault, R. J., Teuben, P. J., & Wright, M. C. H. 1995, in Astronomical Data
Analysis Software and Systems IV, ed. R. A. Shaw, H. E. Payne, & J. J. E.
Hayes, ASP Conf. Ser., 77, 433
Scoville, N. Z., Carlstrom, J. E., Chandler, C. J., et al. 1993, PASP, 105, 1482
Shakura, N. I., & Syunyaev, R. A. 1973, A&A, 24, 337
Shirley, Y. L., Evans, II, N. J., Rawlings, J. M. C., et al. 2000, ApJS, 131, 249
Stansberry, J. A., Gordon, K. D., Bhattacharya, B., et al. 2007, PASP, 119, 1038
Stapelfeldt, K. R., Krist, J. E., Menard, F., et al. 1998, ApJ, 502, L65
Stapelfeldt, K. R., Ménard, F., Watson, A. M., et al. 2003, ApJ, 589, 410
Stecklum, B., Launhardt, R., Fischer, O., et al. 2004, ApJ, 617, 418
Toomre, A. 1964, ApJ, 139, 1217
Ulrich, R. K. 1976, ApJ, 210, 377
Voshchinnikov, N. V. 2002, in Optics of Cosmic Dust, ed. G. Videen, &
M. Kocifaj, 1
Voshchinnikov, N. V., Videen, G., & Henning, T. 2007, Appl. Opt., 46, 4065
Watson, A. M., & Stapelfeldt, K. R. 2004, ApJ, 602, 860
Weingartner, J. C., & Draine, B. T. 2001, ApJ, 548, 296
Whitney, B. A., Wood, K., Bjorkman, J. E., et al. 2003, ApJ, 591, 1049
Wolf, S. 2003a, ApJ, 582, 859
Wolf, S. 2003b, Comp. Phys. Commun., 150, 99
Wolf, S., Henning, T., & Stecklum, B. 1999, A&A, 349, 839
Wolf, S., Padgett, D. L., & Stapelfeldt, K. R. 2003, ApJ, 588, 373
Wolf, S., Schegerer, A., Beuther, H., Padgett, D. L., & Stapelfeldt, K. R. 2008,
ApJ, 674, L101
Wood, K., Wolff, M. J., Bjorkman, J. E., et al. 2002, ApJ, 564, 887
Wu, J., Dunham, M. M., Evans, II, N. J., Bourke, T. L., & Young, C. H. 2007,
AJ, 133, 1560