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 m to 1.3mm) and SCUBA 850 and 450 m 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 of [8,50] k 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 m to be < 0.8 Jy. 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 m 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 m by a factor of 2. It is not possible to simultaneously match the 850 m 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 < few Msun) star formation predict 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 04368+2557) 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).

Combining Radiative Transfer Models of BIMA & SCUBA Continuum ObservationsYancy 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

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.

nd(r) Td(r)SI(b)V()

Nearly orthogonal constraints:Nearly orthogonal constraints:SEDSED Mass x Opacity Mass x OpacityI(b), V(I(b), V()) n(r)n(r)

IterateIteratePhysical Model

n(r), Lint, Iisrf, Observations

2r

Gas to

Dust

Radiative

Transfer

Simulate

Obs.

V. Conclusions We are unable to simultaneously match the SED and the SCUBA intensity profiles+BIMA 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

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, , 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 interferometer’s 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.

Figure 3: Disk models adapted from Young et al. (2003) are plotted on the left. The contribution to the flux at 850 m 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 m. 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).

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).