Combining Radiative Transfer Models of BIMA

1
Combining Radiative Transfer Models of BIMA
SCUBA Continuum Observations

• Yancy L. Shirley1, Lee G. Mundy2, Neal J. Evans
  II3
• 1 Jansky Postdoctoral Fellow at NRAO, 2
  University of Maryland, 3 University of Texas
  at Austin

IV. Radiative Transfer Models The
radiative transfer modeling procedure is the same
procedure used in Shirley et al. (2002) except
that the visibility amplitudes are also simulated
(see flowchart above). By simultaneously
modeling the SED, SCUBA intensity profiles, and
BIMA visibility amplitudes, the shape and scaling
of the density distribution with radius is
constrained. Shirley et al. (2002) found
that a single power-law density distribution,
n(r) 6.5x105 cm-3 ( r /1000 AU)-1.1, fit the
SED (60 mm to 1.3mm) and SCUBA 850 and 450 mm
intensity profiles however, when this model is
observed using the BIMA u,v tracks, the model
does not reproduce the observed visibility
amplitudes. There are two main discrepancies
there is a plateau in the observed visibility
amplitudes at 40 mJy between d of 8,50 kl
indicative of an unresolved compact structure
(e.g., a disk) and the model amplitudes are too
low for the first 2 bins in u,v-distance (green
model in Figure 3). If the unresolved structure
observed in the BIMA amplitude-uv distance plot
is a disk, then there may be an appreciable flux
contribution within the central SCUBA beam.
Pure-envelope radiative transfer models that
ignore this contribution to the flux may
overestimate the slope of a best-fit power law by
up to 0.5 (see Young et al. 2003). Using the
simple disk model of Young et al., we estimate
the flux contribution at 850 mm to be Adding this flux into the models results in a
much flatter best-fit to the SCUBA profiles of
n(r) r-0.6 (blue model). This flatter, single
power-law model also fails to produce enough flux
for the first 2 bins in u,v-distance, but does
fit the 3rd bin. These results suggest that a
broken power-law model with a flatter slope in
the interior may be a good fit to both the SCUBA
and BIMA data while accounting for the flux
contribution from a disk. A
broken power law model adds two additional free
parameters the slope of the inner region and the
break radius. SCUBA observations will be
insensitive to variations in the break radius
within the central beam therefore, we chose a
maximal break radius of 2000 AU. Since the outer
region of the envelope is well fitted by an r-1.1
power law, we keep the slope of the outer profile
constant. A broken power law with r-0.6 in the
inner region and a disk flux of 0.4 Jy at 850 mm
is the best fit to the SCUBA intensity profile
and BIMA visibility amplitudes however, this
model over predicts the flux in a 120 aperture
at 850 mm by a factor of 2. It is not possible
to simultaneously match the 850 mm flux, SCUBA
profile, and BIMA amplitudes. The BIMA
amplitudes require enough mass to always
over-predict the SCUBA 850 mm flux. This may
indicate an opacity change in the inner envelope
the mass opacity for coagulated dust grains
without ics mantle vs. grain with ice mantle is a
factor of 2 at 850 mm (see Ossenkopf Henning
1994). Alternatively, this may be a failure of
the 1D model to properly describe the structure
of the inner envelope.
I. Introduction Current theoretical models
of low-mass (M the evolution of the density, temperature, and
velocity structure within the envelope of the
core. In particular, the density profile as a
function of radius is a strong discriminator
between theories. Submillimeter and millimeter
dust continuum is a powerful probe of the
physical conditions in the envelopes of
star-forming cores since the optically thin
emission is sensitive to the density,
temperature, and opacity structure along the line
of sight. Recent surveys with the single-dish
bolometer camera, SCUBA, have imaged the
continuum emission on large scales (103 to 104
AU) towards more than 50 Pre-protostellar cores,
Class 0, and Class I cores. State-of-the-art
radiative transfer models account for heating
from the interstellar radiation field (ISRF)
and/or an internal source, beam convolution, and
chopping. By simultaneously matching the
observed continuum intensity profile (at multiple
wavelengths) and the observed spectral energy
distribution, the models constrain the physical
structure of the core. However, the models are
unable to place strong constraints on the
conditions within the central beam, typically on
scales less than 103 AU. Interferometric
continuum imaging is vital for probing the inner
envelope structure and constraining the emission
properties of a disk. We have observed 4
Class 0 cores (L1527, B335, L483, L723) with
BIMA at 2.7 mm in four array configurations
(A,B,C, D). Integrated radiative transfer
models of SCUBA 850 and 450 micron and BIMA 2.7mm
observations of L1527 are presented in this
poster. The combined models probe the physical
structure on scales of 102 to 104 AU.
L1527 is an embedded Class 0 source (IRAS
043682557) associated with a near-infrared
nebula (Eiora et al. 1994) located at a distance
of 140 pc in the Taurus molecular cloud complex.
The submm emission is extended in the NE-SW
direction. The source appears to be a
protobinary on a scale less than 1. A strong
molecular outflow is detected in the E-W
direction (MacLeod et al. 1994, Bontemps et al.
1996). The core is rotating (Goodman et al.
1993) resulting in molecular line radiative
transfer models of rotating collapse
(Terebey-Shu-Cassen infall, Zhou et al. 1996).
Sn(q) In(b) Vn(d)
nd(r)
Radiative Transfer
Simulate Obs.
Td(r)
Gas to Dust
Nearly orthogonal constraints SED Mass x
Opacity I(b), V(d) n(r)
Physical Model n(r), Lint, Iisrf, kn
Iterate
Observations c2r
Figure 1 SCUBA 850 (left) and 450 (middle)
micron images of L1527 (Shirley et al. 2000) and
the VLA 7mm image (right) observed during A
configuration (Loinard et al. 2002).
II. BIMA Observations L1527 was observed and
detected in 4 array configuration of BIMA with
tracks during 8 days between 1997 and 1999. The
digital correlator was setup with two bands of
700 MHz centered at 106 and 109 GHz (2.7 mm).
Mars and quasars were used as absolute flux
calibrators. We estimate a 20 uncertainty in
the final amplitude calbration for each
individual array configuration. The four
configurations were combined into a data set with
252,957 visibility records.
Figure 3 Disk models adapted from Young et al.
(2003) are plotted on the left. The contribution
to the flux at 850 mm is between 0.2 and 0.8 Jy
within the central SCUBA beam. Results of
radiative transfer models are plotted on the
right. The green model is the best-fit r-1.1
power law from Shirley et al. (2002). The blue
model is a r-0.6 power law with a disk flux of
0.8 Jy at 850 mm. The red model is a broken
power law with r-0.6 inside 2000 AU and r-1.1 in
the outer envelope and a disk flux of 0.4 Jy..
Figure 2 u,v tracks for L1527 observations
(left). BIMA images of L1527 with robustness
2, 1, and 0 (left to right).
III. Interpreting Visibilities The specific
intensity of a spherical dust shell at impact
parameter, b, is given by (see Shirley et al.
2000) The observed visibilities, written in
terms of the u,v-distance, d, is the
2-dimensional Fourier transform of the specific
intensity times the interferometric power pattern
(see Looney 1998). If we assume that the source
brightness distribution is smaller than the
interferometers single dish primary beam, the
integration over azimuthal angle results in the
observed visibilities expressed as the Hankel
transform of the specific intensity where J0 is
a zeroth order Bessel function. In general,
these expressions must be solved numerically.
The source structure observed by the
interferometer may be modeled by simulating the
visibility amplitude vs. u,v-distance using the
same u,v tracks as obtained in the observations.
V. Conclusions We are unable to
simultaneously match the SED and the SCUBA
intensity profilesBIMA visibility amplitudes.
This may be indicative of an opacity change in
the inner envelope or the failure of 1D modeling
to account to the physical structure. The
combined modeling of interferometric and
single-dish continuum observations is necessary
to constrain the physical structure throughout
the envelope and to constrain the flux
contribution from a disk. Observations and
modeling at submm wavelengths with the next
generation of interferometers (SMA, CARMA,
ALMA) will provide stronger constraints