DISK AND ENVELOPE STRUCTURE IN CLASS 0 PROTOSTARS. I. THE RESOLVED MASSIVE DISK IN SERPENS FIRS 1

Protostars build up their mass by accreting material from a dense protostellar envelope, presumably via a rotationally supported circumprotostellar accretion disk. Disk formation is a natural result of collapse in a rotating core, but it is not known how soon after protostellar formation the disk appears, or how massive it is at early times. Theory suggests that centrifugally supported disks should start out small (radius less than 10 AU), and thus low mass, and grow with time (Terebey et al. 1984). Unstable or magnetically supported disks, however, could be much larger (radii up to 1000 AU in the magnetically supported case; Galli & Shu 1993), and thus more massive at early times.

The remnants of these protostellar accretion disks are easily observed in more evolved phases (e.g., T Tauri stars), but given that the majority of mass is accreted during earlier embedded phases, understanding disks at early times is critical. Directly observing disks during this main accretion phase is quite difficult, however, as they are hidden within dense, extincting protostellar envelopes. The structure of the envelope at small radii is another important characteristic of main accretion phase protostars that is similarly difficult to directly observe. Disk growth or the presence of a binary companion may clear out the inner region of the envelope early on, as inferred for the binary Class 0 source IRAS 16293 − 2422 by Jørgensen et al. (2005b).

There has been a recent push toward detecting disks in more embedded objects, with many now known and roughly characterized in Class I protostars (e.g., Looney et al. 2000; Jørgensen et al. 2005a; Eisner et al. 2005; Andrews & Williams 2007), and a few detected in the earlier Class 0 stage (e.g., Chandler et al. 1995; Harvey et al. 2003; Brown et al. 2000; Looney et al. 2000).⁷ Most previous detailed studies have been limited to the most well known or brightest Class 0 sources, however, due to instrumental limitations and a lack of large unbiased target samples. The ongoing Submillimeter Array survey of low-mass protostars (Jørgensen et al. 2007, 2009) is a notable exception.

With recent large surveys of nearby molecular clouds at mid-infrared and (sub)millimeter wavelengths, it is now possible to define complete samples of Class 0 protostars based on luminosity or envelope mass limits (e.g., Hatchell et al. 2007; Jørgensen et al. 2008; Dunham et al. 2008; Enoch et al. 2009; Evans et al. 2009).

We have recently begun a campaign to characterize disk properties in a large, uniform sample of Class 0 protostars in nearby low mass star-forming regions (M. Enoch et al. 2009, in preparation). Our study is based on the complete (to envelope masses ≳0.1 M_☉) sample of 39 Class 0 protostars in the Serpens, Perseus, and Ophiuchus molecular clouds, identified by Enoch et al. (2009) by comparing large-scale Spitzer IRAC and MIPS and Bolocam 1.1 mm continuum surveys of the three clouds.

Combining Spitzer Infrared Spectrograph (IRS) mid-infrared (MIR) spectra and high-resolution Combined Array for Research in Millimeter-wave Astronomy (CARMA) 230 GHz continuum imaging with radiative transfer modeling of this sample will help to address several fundamental questions about the structure and evolution of the youngest protostars: (1) how soon after the initial collapse of the parent core does a circumprotostellar disk form? (2) What fraction of the total circumprotostellar mass resides in the disk, and does this fraction vary with time? (3) Are large "holes" in the inner envelope, such as that found for IRAS 16293 by Jørgensen et al. (2005b), common at early times?

MIR spectra and millimeter maps provide complementary approaches to these questions. The amount of flux escaping at λ ≲ 50 μm from deeply embedded sources is very sensitive to the opacity close to the protostar, and thus the envelope structure (e.g., Jørgensen et al. 2005b). While the MIR flux is insensitive to disk properties, high-resolution millimeter continuum mapping can directly detect emission from dust grains in the disk. Millimeter observations with excellent uv-coverage, combined with radiative transfer models, can separate the disk from the envelope and constrain the disk mass and size.

Our ultimate goal is to characterize the disk mass, size, and inner envelope structure of typical low-mass Class 0 protostars, and to quantify any trends with evolutionary indicators. In this initial paper, we present results for Serpens FIRS 1, a well-known Class 0 source, which will serve as a test case for the full program.

FIRS 1 is located at 18^h29^m496 + 01°15'219 (J2000)⁸ in the main core (Cluster A) of the Serpens Molecular Cloud. We adopt a distance of d = 260 ± 10 pc (Straizys et al. 1996), and any quoted literature values are scaled to this distance. It is a well-know Class 0 protostar (e.g., Hurt & Barsony 1996) first noted in the far-infrared by Harvey et al. (1984), and also known by its submillimeter designation Serpens SMM 1 (Casali et al. 1993). There is a narrow λ = 3.6 cm bipolar radio jet at the position of FIRS 1 (Rodríguez et al. 1989; Curiel et al. 1993), indicating a powerful outflow that is also clearly seen in molecular lines (Davis et al. 1999; Curiel et al. 1996).

Figure 1 gives an overview of the FIRS 1 environment with Spitzer 24 μm and Bolocam 1.1 mm continuum maps of the Serpens main core. The nearest known YSO is approximately 25'' away, or 6000 AU in projected distance (Harvey et al. 2007), and the nearest embedded protostar known to have an envelope is 45'' ≈ 11, 000 AU away (Enoch et al. 2009).

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FIRS 1 is referred to as Ser-emb 6 in Enoch et al. (2009), and is associated with the 1.1 mm Bolocam core Ser-Bolo 23 (Enoch et al. 2007). Based on Two Micron All Sky Survey (2MASS), Spitzer, and Bolocam data the bolometric luminosity is 11.0 L_☉,⁹ the bolometric temperature is 56 K, confirming the Class 0 designation, and the total envelope mass is 8.0 M_☉ (Enoch et al. 2009).

Previous high-resolution millimeter observations have placed limits on the mass of a compact disk in FIRS 1. Hogerheijde, van Dishoeck, & Salverda (1999) used observation from the Owens Valley Radio Observatory (OVRO) millimeter interferometer to estimate a total mass (disk plus envelope) within 100 AU of 0.7 M_☉. Brown et al. (2000) place a lower limit on the disk mass of ∼0.1 M_☉ with submillimeter observations (ν ∼ 350 GHz) from the James Clerk Maxwell Telescope–Caltech Submillimeter Observatory (JCMT-CSO) single baseline interferometer.

3.1. Spitzer IRS Spectrum

Mid-infrared spectra were obtained with the IRS on the Spitzer Space Telescope (Werner et al. 2004; Houck et al. 2004) during 2007 October 5 with the Low Res 7.4–14.5 μm (SL1; R ∼ 100), Hi Res 9.9–19.6 μm (SH; R ∼ 600), and Hi Res 18.7–37.2 μm (LH; R ∼ 600) modules. Integration times were 117 s in SL1, 189 s in SH, and 59 s in LH. Off-source or background spectra with the same integration times were also obtained for SH and LH.

Spectra were extracted from the Spitzer Science Center (SSC) pipeline version S16.1.0 BCD images using the reduction pipeline (Lahuis et al. 2006) developed for the "From Molecular Cores to Planet-forming Disks" Spitzer Legacy Program ("Cores to Disks" or c2d; Evans et al. 2003). We use the optimal point-spread function (PSF) extraction method of the pipeline, which is based on fitting the analytical cross dispersion point spread function, plus extended emission, interpolating over bad pixels. The one-dimensional spectra are flux calibrated using a spectral response function derived from a suite of calibrator stars, corrected for instrumental fringe residuals, and an empirical order matching algorithm is applied. PSF extraction was completed for both FIRS 1 and the background field; the final spectrum is the difference between them.

The resulting spectrum from 7.4 to 37.2 μm is shown in Figure 2. Each module is reduced separately, so the degree of agreement gives some idea of the reliability of calibration. Both the full reduced spectra (solid lines), and the average flux in wavelength bins of Δλ ∼ 0.75 μm, 1.5 μm, and 1 μm for SL1, SH, and LH, respectively, are shown. The SH spectrum has the lowest signal to noise, so it is binned on the coarsest grid. Only data with signal to noise greater than one (SL1, SH) or three (LH) are included in the binned points. Binned fluxes are listed in Table 1.

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Table 1. Spitzer IRS and Broadband Spitzer, SHARC-II, and Bolocam Fluxes Used in the SED Fits

Wavelength (μm)	Flux (Jy)	Uncertainty (Jy)	Aperture (arcsec)	Instrument
3.6	0.00085	0.00016	2.2	IRAC
4.5	0.0026	0.0005	2.2	IRAC
5.8	0.0023	0.0005	2.2	IRAC
7.8	0.004	0.002	3.7	IRS (SL1)
8.5	0.0018	0.0010	3.7	IRS (SL1)
9.1	0.0011	0.0006	3.7	IRS (SL1)
9.7	0.0002	0.0003	3.7	IRS (SL1)
10.3	0.0016	0.0008	3.7	IRS (SL1)
10.9	0.0017	0.0009	3.7	IRS (SL1)
11.5	0.0024	0.0012	3.7	IRS (SL1)
12.1	0.0034	0.0017	3.7	IRS (SL1)
12.7	0.005	0.003	3.7	IRS (SL1)
13.3	0.005	0.002	3.7	IRS (SL1)
13.9	0.006	0.003	3.7	IRS (SL1)
14.5	0.007	0.003	3.7	IRS (SL1)
15.0	0.0019	0.0011	3.7	IRS (SL1)
15.4	0.009	0.006	10.5	IRS (SH)
16.3	0.021	0.008	10.5	IRS (SH)
18.1	0.033	0.010	10.5	IRS (SH)
19.8	0.121	0.017	11.1	IRS (LH)
20.7	0.21	0.04	11.1	IRS (LH)
21.7	0.36	0.04	11.1	IRS (LH)
22.7	0.59	0.07	11.1	IRS (LH)
23.8	1.04	0.11	11.1	IRS (LH)
25.1	2.0	0.2	11.1	IRS (LH)
26.5	3.1	0.3	11.1	IRS (LH)
28.0	4.6	0.5	11.1	IRS (LH)
29.7	6.8	0.7	11.1	IRS (LH)
31.6	9.1	1.0	11.1	IRS (LH)
33.9	11.8	1.3	11.1	IRS (LH)
36.0	13.4	1.5	11.1	IRS (LH)
70	77	41	17	MIPS
350	195	79	40	SHARC II
1100	5.9	1.2	40	Bolocam

Notes. Apertures in which fluxes are calculated correspond to the instrument PSF, with the exception of the SHARC-II and Bolocam fluxes. Calibrated IRS fluxes are averaged in wavelength bins of Δλ ∼ 0.75 μm, 1 μm, and 1.5 μm for SL1, SH, and LH, respectively, as described in Section 3.1. The IRS flux is the mean within a bin, and the instrumental uncertainty is the error in the mean ($\sigma /\sqrt{N}$). All uncertainties include a 10% systematic uncertainty in addition to the instrumental uncertainty.

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In Figure 2, the silicate absorption band at 9.7 μm is clearly visible, and a hint of the CO₂ ice band at 15 μm is also visible. A number of finer features in the LH spectrum are most likely real, but will not be discussed here.

3.2. CARMA 230 GHz Map

Continuum observations at ν = 230 GHz (λ = 1.3 mm) were completed with the CARMA, a 15 element interferometer consisting of nine 6.1 m and six 10.4 m antennas. Data were obtained in the B array (100–1000 m baselines), C array (30–350 m), D array (11–150 m), and E array (8–66 m) configurations between 2007 October 24 and 2008 December 31. These data were combined to provide uv-coverage from 4.5 to 500 kλ. Small seven-pointing mosaics were made in the compact configurations (D and E) in order to mitigate spatial filtering by the interferometer, and to more fully map the spatially extended protostellar envelope.

All three correlator bands were configured for continuum, 468 MHz bandwidth, observations. A bright quasar (1751+096) was observed approximately every 15 minutes to be used for complex gain calibration. Absolute flux calibration was accomplished using 5 minute observations of Uranus, Neptune, or MWC 349. The overall calibration uncertainty is approximately 20%, from the reproducibility of the phase calibrator flux on nearby days. A passband calibrator, typically 3C454.3, was observed for 15 minutes during each set of observations, and radio pointing was performed every two hours. Observations in the most extended B configuration utilized the Paired Antenna Calibration System (PACS) to correct for phase variations on minute timescales (see L. Pérez et al. 2009, in preparation).

Calibration and imaging were accomplished with the MIRIAD data reduction package (Sault et al. 1995). The resulting 230 GHz map of FIRS 1 is shown in Figure 3, with maps made at three resolutions: short baseline data only (D and E configurations), all data, and long baseline data only (B and C configurations). The direction of the 3.6 cm jet (Rodríguez et al. 1989; Curiel et al. 1993) is shown for reference.

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The map including all data was inverted with natural weighting, cleaned with a Steer CLEAN algorithm (Steer et al. 1984), and restored with an 094 × 089 beam. The rms noise level in the central region is 6.7 mJy beam⁻¹, the peak and total flux from a Gaussian fit are 0.42 Jy beam⁻¹ and 1.38 Jy (P.A. = $-4\;\deg$), and the deconvolved FWHM size is 16 × 12. The synthesized beam corresponds to approximately 240 AU, while the longest baselines provide a resolution better than 100 AU (046 × 040). A Gaussian fit to the long baseline data yields P.A. = $25\;\deg$, approximately $75\;\deg$ from the 3.6 cm jet axis (P.A. = $-50\;\deg$).

The extended, complex nature of the source is apparent, thanks to the excellent uv-coverage achieved with multiple configurations. Although it is difficult to see the more extended envelope even in the short baseline map, it is clearly visible as an amplitude peak at uv-distances <20 kλ in a plot of amplitude versus uv-distance (Figure 4). Note that the interferometer does filter out flux at uv-distances less than 4 kλ, corresponding to the separation of the closest antenna pairs. Figure 4 shows that most of the source flux is concentrated at low and intermediate uv-distances (extended structure), but the source is clearly detected at uv-distances greater than 200 kλ, indicating an unresolved or marginally resolved compact (<1'') component. Values of the 230 GHz flux as a function of uv-distance are given in Table 2.

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Table 2. CARMA 230 GHz Visibilities

uv-distance (kλ)	Flux (Jy)	Uncertainty (Jy)
4.50	2.45	0.12
7.50	2.05	0.07
10.5	1.96	0.07
13.5	1.70	0.06
16.5	1.60	0.06
19.5	1.38	0.05
22.5	1.31	0.05
25.5	1.17	0.04
28.5	1.10	0.04
31.5	1.07	0.04

Notes. Visibilities and uncertainties used in the model fits. The amplitude bias, or expected value for zero signal, has been subtracted from the data.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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3.3. Spitzer, Bolocam, and SHARC-II Broadband Data

To model the observed emission from FIRS 1, we use the two-dimensional Monte Carlo radiative transfer code RADMC of Dullemond & Dominik (2004). RADMC performs both Monte Carlo radiative transfer to derive the temperature distribution from an input density distribution, and ray tracing to produce images and photometry in specified apertures. We adopt a density profile very similar to that of Crapsi et al. (2008), which includes three components: the envelope, the outflow cavity, and the disk. For both the envelope and disk, we use the dust opacities from Table 1, Column 5 of Ossenkopf & Henning (1994) for dust grains with thin ice mantles, including scattering, interpolated onto the necessary wavelength grid. We note that although this is a young source, there could be significant difference in the dust properties of the disk and envelope, as have been demonstrated in some Class I sources (Wolf et al. 2003).

The envelope density profile is that of a rotating, collapsing sphere (Ulrich et al. 1967),

$$\begin{equation} \rho _{\rm env}(r,\theta) = \rho _0 \left(\frac{r}{R_c}\right)^{-1.5} \left(1+\frac{\mu }{\mu _0}\right)^{-0.5} \left(\frac{\mu }{\mu _0}+2\mu _0^2 \frac{R_c}{r}\right)^{-1}, \end{equation} \tag{ 1 }$$

where μ = cos θ, R_c = R_cent is the centrifugal radius, and ρ₀ is the density at (r, θ) = (R_c, 0), which is set by the total envelope mass M_env = 8 M_☉. A gas-to-dust mass ratio of 100 and mean molecular weight of 2.33 are included. Here, μ₀ = cos θ₀ is the solution of the parabolic motion of an infalling particle, given by

$$\begin{equation} \left(\frac{r}{\mbox{$R_{\rm cent}$}}\right) \left(\frac{\mu _0 - \mu }{\mu _0 \sin ^2\mu _0}\right) = 1. \end{equation} \tag{ 2 }$$

The model has no time dependence; R_cent is not a true centrifugal radius defined by the conservation of angular momentum during collapse, but simply a set radius where the density peaks, and inward of which the density drops to very low values. The envelope outer radius R_out is the maximum value of the radial grid, so the envelope density is zero for r > R_out. The outflow cavity is defined by setting the density to zero in the region where cos θ₀ > cos(Ang/2). This results in a funnel-shaped cavity, which is conical only at large scales where Ang is the full opening angle.

The disk density is given by a power-law dependence in radius and a Gaussian dependence in height:

$$\begin{equation} \rho _{\rm disk}(r,\theta) = \frac{\Sigma _0}{\sqrt{2\pi } H(r)} \left(\frac{r}{\mbox{$R_{\rm disk}$}}\right)^{p1} \exp \left[-\frac{1}{2}\left(\frac{r \mu }{H(r)}\right)^2\right], \end{equation} \tag{ 3 }$$

where Σ₀ is set by the input disk mass M_disk. At R_disk, p1 changes from −1 to −12, effectively setting the disk radius. The scale-height variation (flaring) is given by H(r) = r(H₀/R_disk)(r/R_disk)^p2. We set p2 = 2/7, corresponding to the self-irradiated passive disk of Chiang & Goldreich (1997). Given that the disk is in large part hidden by the envelope, a much simpler description would likely work just as well, but we choose to follow the setup of Crapsi et al. (2008) here. Most of the disk parameters are held fixed for the main model grid, with only M_disk and R_disk varying.

Table 3 lists the range of input values for the model input parameters, some of which are held fixed. The internal luminosity is set by the bolometric luminosity; it is input to the model as the stellar luminosity, although most likely a majority of the luminosity is due to accretion. We do not include an interstellar radiation field here, as the luminosity of any reasonable field is negligible compared to the internal luminosity of FIRS 1, and has only a negligible effect on the long-wavelength SED.

Small single parameter grids were run to test that "fixed" parameters have no significant affect on the model SED or millimeter visibilities. The scale height (H₀) and flaring (p1) of the disk do affect the 3–20 μm fluxes, although only for $\mbox{Incl}<10 \;\deg$, where there is too much NIR flux to match the data regardless of the value of these parameters. A very puffy disk (H₀ ≳ 0.5R_disk) produces more emission in this range, while a very thin disk (H₀ ≲ 0.1R_disk) produces less emission. Similarly, a flared disk produces more MIR emission than one with no flaring.

To determine the best-fit envelope parameters we run a grid of models varying R_out, R_cent, Ang, and Incl. This results in a total of 588 envelope models, each observed at 13 inclination angles. A nominal disk of M_disk = 0.01 M_☉, R_disk = 150 AU is used for all envelope models. A separate grid varying M_disk and R_disk with fixed envelope parameters includes 140 models. Our tests show that the disk has little effect on the SED for this source, making separate grids feasible.

The model grids are compared to the SED and 230 GHz visibilities with an χ² analysis using data from Tables 1 and 2. Contour plots of the resulting reduced χ² ($\tilde{\chi }^2$) are shown in Figure 5, where contours for both the SED and 230 GHz visibilities are plotted. The model and data visibilities are calculated by the same method, using vector averaging in radial annuli.

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The best-fitting model (R_out = 5000 AU, R_cent = 600 AU, $\mbox{Ang}=20\;\deg$, $\mbox{Incl}=15\;\deg$, M_disk = 1.0 M_☉, R_disk = 300 AU) is compared to the data in Figure 6. The same envelope model with no disk is also shown for reference, as is an envelope model with no inner envelope hole (R_cent = 20 AU; dotted line). Determination of the best-fit model from Figure 5 is described in Sections 5.1 and 5.2. Due to the small uncertainties and the limited number of models, the reduced χ² values for even the best-fit model are still fairly high ($\tilde{\chi }^2\sim 13$ and 5 for the SED and visibilities, respectively). The bolometric temperature and luminosity of the best-fit model are 35.3 K and 17.3 L_☉. The bolometric luminosity differs from the input stellar luminosity due to inclination effects.

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While we only show the best-fit model here, there is a range of values for each parameter that can reasonably fit the data, as determined by eye from χ² plots and visual inspection of the SED fits. We find that the envelope parameters have the following reasonable ranges: R_out ∼ 5000–7000 AU, R_cent ∼ 400–600 AU, $\mbox{Ang}\sim 10\hbox{--}30\;\deg$, and $\mbox{Incl}\sim 10\hbox{--}25\;\deg$. Reasonable disk parameters are M_disk ∼ 0.7–1.5 M_☉, and R_disk ∼ 200–500 AU.

Literature fluxes are shown in comparison to our data and the best-fit model SED in Figure 7. Shown are IRAS HIRES 25, 60, and 100 μm from Hurt & Barsony (1996), SCUBA 450 and 850 μm peak fluxes from Davis et al. (1999), JCMT 800, 1100, 1300, and 2000 μm fluxes from Casali et al. (1993), and the OVRO 3 mm flux from Testi & Sargent (1998). They cannot be compared directly to the model SED because many of them are peak fluxes calculated in small apertures; circles show the corresponding model values computed in similar apertures. While there is not perfect agreement, the model is roughly consistent with the literature values, with the exception of IRAS fluxes. The IRAS observations are lower resolution than the Spitzer maps, and FIRS 1 may be confused with nearby protostars (24''–45'' away). Literature fluxes are not included in the $\tilde{\chi }^2$ fitting.

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5.1. Envelope Structure

5.2. Disk Structure

5.3. Other Models

Here, we compare our models to other disk and envelope models. This serves both as a check on our derived envelope and disk parameters by indicating which conclusions are dependent on the density model, and a test that our models give the most reasonable fit to the data.

Hogerheijde et al. (1999) observed FIRS 1 with the OVRO interferometer at 3.4, 2.7, and 1.4 mm. They used a power-law envelope model plus a point source, with the dust temperature power-law set at −0.4 and fixed inner and outer envelope radii of 100 and 8000 AU. These millimeter data were best fit by an envelope with mass 6 M_☉ and density power law −2.0, plus an unresolved point source of approximately 0.7 M_☉. Hogerheijde et al. (1999) note that they are unable to separate the inner envelope from any disk emission, and thus cannot place a meaningful limit on the disk itself. Compared to the Hogerheijde et al. (1999) uv-coverage, 10–180 kλ at 1.4 mm, our CARMA observations trace much more of the envelope (down to 4.5 kλ), allowing us to separately model and remove the envelope contribution. Our data also have much higher signal to noise on long baselines (uv-distances >100 kλ).

In addition to the rotating, collapsing spheroid (or "Ulrich") envelope models described in Section 4, we also ran a small grid of models with a simple power-law envelope density profile (ρ ∝ r^−p), plus a conical cavity. A steep power law, ρ ∝ r⁻², provides a reasonable fit to the visibilities without requiring a massive disk or large inner envelope hole. The best fit is for M_disk = 0.1 M_☉, R_disk = 100 AU, and R_cent = 100 AU, as shown in Figure 8. Here, the emission at intermediate uv-distances is filled in by the envelope, which reaches high densities close to the protostar, thus requiring less disk emission. But, only a special combination of outflow opening angle and inclination can come close to matching the SED ($\mbox{Ang}=40\;\deg$, $\mbox{Incl}=25\;\deg,$ or $\mbox{Ang}=60\;\deg$, $\mbox{Incl}=30\;\deg$; looking down the edge of a wide outflow cavity), and even the best-fit model gives a much poorer fit to the SED than the Ulrich models. In general, the power-law models seem unable to reasonably fit the NIR and MIR emission, although only p = −2 and −1.5 have been tested here.

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The ability of the power-law envelope model to fit the visibilities without a large disk is consistent with some previous studies that have found that disks are often not required to millimeter data of Class 0 and Class I sources (e.g., Looney et al. 2000). The results here demonstrate that it is necessary to include both spectral and visibility data in order to fit a consistent disk and envelope model.

We use the online SED fitting tool of Robitaille et al. (2007) as another estimate of the envelope parameters, although the 230 GHz visibilities cannot be included in the fit. Robitaille et al. (2007) use an envelope setup similar to ours, with the envelope infall rate $\dot{M}_{\rm env}$ setting the fiducial density ρ₀ (rather than M_env as used here). The best-fit model corresponds to a protostar with age t = 2 × 10⁵ yr, M_* = 1.8 M_☉, R_* = 7 R_☉, T_* = 4400 K, envelope infall rate $\dot{M}_{\rm env}=10^{-4} \,M_\odot$ yr⁻¹, R_out = 11, 000 AU, $\mbox{Ang}=27\;\deg$, and $\mbox{Incl}=75\;\deg$. The total luminosity and envelope mass of this best-fit model are consistent with our values (18.4 L_☉ and 7.4 M_☉).

Looking at the 10 best-fitting models, only the age (t < 2 × 10⁵ yr), protostellar mass (M_* < 2 M_☉), temperature (T_* = 3000–4500 K), and envelope infall rate ($\dot{M}_{\rm env}=10^{-5}\hbox{--}10^{-4} \,M_\odot$ yr⁻¹) are reasonably well constrained, while the other parameters cover a large range. We do not attempt to constrain the disk properties as the SED is relatively insensitive to the disk in embedded sources. In addition, we cannot use the online grid to constrain the envelope inner radius, because it is fixed to the disk inner radius and very few models with both large envelope mass (>1 M_☉) and large inner envelope radius (≳10 AU) are included in the grid. This difference in the inner envelope behavior likely accounts for the large outer radius and inclination required by the Robitaille et al. (2007) models.

Given our limited exploration of various models, we feel that the Ulrich envelope model provides the best description of the observed SED. While the derived disk parameters do depend on the input envelope density profile, even in the most conservative case M_disk ≳ 0.1 M_☉.

Our derived disk mass of M_disk ∼ 1.0 M_☉ within a radius of 300 AU is consistent with the Brown et al. (2000) limit of M_disk > 0.1 M_☉, as well as the Hogerheijde et al. (1999) limit of 0.7 M_☉ on the unresolved mass within a radius of 100 AU. The early evolutionary state of FIRS 1 is confirmed by the low bolometric temperature (T_bol ∼ 56 K) and the small disk-to-envelope mass ratio (M_disk/M_env ∼ 0.1) despite the high disk mass. Thus, our results suggest that large disks can accumulate very early in the protostellar collapse process.

The FIRS 1 disk is likely too small to be considered a magnetically supported "pseudo-disk." Given the expected young age of FIRS 1, however, both the mass and radius derived here are much larger than expected for disk formation via gravitational collapse of a rotating core. Terebey et al. (1984) predict that the disk radius, where centrifugal balance is achieved, should depend on the initial rotation Ω and isothermal sound speed c_s in the core as

$$\begin{equation} R_d = 7\left(\frac{c_s}{0.35\;\mathrm{km\;s}^{-1}}\right) \left(\frac{\Omega }{4\times 10^{-14}\;\mathrm{s}^{-1}}\right)^2 \left(\frac{t}{10^5\;\mathrm{yr}}\right)^3\;\mathrm{AU}. \end{equation} \tag{ 4 }$$

Based on the statistical relationship between T_bol and time derived in Enoch et al. (2009; T_bol ∝ t^1.8), the bolometric temperature of FIRS 1 suggests that it has an age of (0.7–0.8) × 10⁵ yr. For a reasonable sound speed, c_s ∼ 0.23 km s⁻¹ (T ∼ 15 K), this age and R_disk = 300 AU requires an initial rotation rate of approximately 5 × 10⁻¹³ s⁻¹. This value is higher than typical dense cores, which have Ω ∼ 10⁻¹³–10⁻¹⁴ s⁻¹ (Goodman et al. 1993). Alternatively, if the age of the source is actually closer to 3 × 10⁵ yr, a more typical rotation rate would be sufficient for growing a 300 AU disk.

Similarly, we can estimate how long it would take for the disk to build up 1 M_☉ via infall from the envelope. For an infall rate of $\dot{M}_{\rm env} \sim c_s^3/G \sim 10^{-5} \,M_\odot$ yr⁻¹, and conservatively assuming that all of the infalling material falls onto the disk rather than directly onto the protostar, accumulating 1 M_☉ would take 10⁵ yr. Although this is probably close to the age of FIRS 1, a disk of 1 M_☉ requires that little of the infalling material be accreted from the disk onto the star. Below we mention a few plausible methods for building up a large circumprotostellar disk in this object.

A Class 0 lifetime longer than a few times 10⁵ yr, i.e., longer than the estimated timescale for Class 0 sources in nearby low-mass star-forming regions (Enoch et al. 2009; Evans et al. 2009), would allow larger disks to grow before the end of the Class 0 phase.

FIRS 1 may have a higher envelope infall rate than average, allowing the disk to quickly accumulate mass. The bolometric luminosity of FIRS 1 is quite large compared to the typical luminosity of YSOs in nearby low-mass star-forming regions (≲1 L_☉; Dunham et al. 2008; Enoch et al. 2009). A luminosity of 11 L_☉ implies an accretion rate onto the protostar of at least 2 × 10⁻⁵ M_☉ yr⁻¹ (for $\dot{M}_{*} \sim R_*L_{\rm bol}/GM_*$, R_* ∼ 5 R_☉ and M_* ∼ 1 M_☉). If this corresponds to an even higher envelope infall rate, M_disk ∼ 1 M_☉ could easily be achieved in (0.7–0.8) × 10⁵ yr.

If the FIRS 1 disk has very low viscosity, mass may build up in the disk with very little accreting onto the protostar (although this is at odds with the high luminosity). Brown et al. (2000) suggest that early disk formation and similar disk masses in the Class 0 and Class I phases could be achieved with a time-dependent viscosity, low at early times and higher by Class I.

Perhaps more likely, this source could have recently entered a period of relatively rapid accretion, as expected in the episodic accretion scenario (e.g., Hartmann & Kenyon 1985; Enoch et al. 2009; Evans et al. 2009). Such a high mask disk around a presumably low protostar mass should be unstable, and undergoing rapid accretion, explaining the high luminosity. In this picture, the current high accretion phase would have been preceded by a period of low accretion onto the protostar while material built up in the disk (assuming infall from the envelope onto the disk is steady).

A larger sample is certainly needed to determine if such large, high mass disks are typical in the Class 0 phase. The recent Jørgensen et al. (2009) study of 20 Class 0 and Class I sources finds disks masses in Class 0 from 0.01–0.5 M_☉, and M_disk/M_env ratios of 1%–10%. If we calculate our disk mass by the same method as Jørgensen et al. (2009), which uses the flux at 50 kλ and assumes an optically thin, unresolved disk, we get M_disk = 0.6 M_☉. While this is at the high end of the Jørgensen et al. (2009) disk sample, the disk-to-envelope mass ratio (∼8% when using M_disk = 0.6 M_☉) is consistent with their results, as is the idea that disks are already well established in the Class 0 stage.

Regarding the envelope structure, it is important to keep in mind that while we refer to R_cent as the centrifugal radius, our model is not dynamical, and there is no dependence on rotation rate. Thus the sharp drop in density inside of this radius could have any number of causes, including a companion that has cleared out material, as well as rotational collapse onto a disk. Any binary companion with a disk mass larger than 0.1 M_☉ should have been detected. There is a tentative second detection 500 AU to the northwest of FIRS 1 (see Figure 3(C)); the peak of approximately 55 mJy would correspond to a disk mass of ∼0.06 M_☉, but this may just be a "clumpy" feature in the envelope. The more likely explanation is that the inner envelope cavity is a result of collapse in a rotating core, and creation of the 300 AU radius disk. Alternatively, a clumpy envelope could cause a similar decrease in MIR opacity and might alleviate the need for an inner envelope hole (Indebetouw et al. 2006).

If the disk and envelope are physically connected, with both the disk and inner envelope hole governed by rotation in the collapsing core, we might expect R_disk ≈ R_cent. Although the best-fit R_cent is a factor of 2 larger than R_disk here, the range of reasonable values allow for R_cent to be as small as 400 AU and R_disk to be as large as 500 AU. Thus, a physical continuity between the disk and envelope is certainly plausible.

We utilize Spitzer IRS spectra, high-resolution CARMA 230 GHz continuum data, and broadband photometry together with a grid of radiative transfer models to characterize the disk and envelope structure of the Class 0 protostar Serpens FIRS 1. Our conclusions are the following.

• 1.  
  Radiative transfer models combined with mid-infrared spectra and millimeter data with excellent uv-coverage can reasonably constrain envelope parameters, including the inner (centrifugal) radius, outer radius, and outflow opening angle. In all cases, there is a range of parameter values able to reasonably fit the data. Once the envelope parameters have been determined, the mass and radius of the disk are robustly constrained by millimeter interferometry data with uv-coverage from <5 to >300 kλ.
• 2.  
  We find a centrifugal radius for FIRS 1 in the range 400–700 AU, indicating a large "hole" in the inner envelope, similar to IRAS 16293 (Jørgensen et al. 2005b). Unlike IRAS 16293, however, there is no strong evidence for a binary companion that might have cleared out the inner envelope. Other explanations for such a large R_cent in this source are: (1) collapse of the inner envelope onto the disk due to the conservation of angular momentum in a rotating, collapsing core; or (2) the R_cent does not indicate a true inner radius, but rather a "clumpy" envelope with much lower opacity in the MIR than a smooth envelope density profile.
• 3.  
  Using envelope parameters set by the SED, the CARMA 230 GHz visibilities require a quite massive, resolved disk. The best-fitting disk has a mass of 1 M_☉, and a radius of approximately 300 AU. While this mass is consistent with previous limits (Hogerheijde et al. 1999; Brown et al. 2000), it also indicates that protostars can accumulate relatively massive disks at very early times. This is somewhat at odds with theoretical expectations that disks start small and grow with time (Terebey et al. 1984). The range of reasonable disk and envelope parameters does allow for a physical continuity between the disk and inner envelope.
• 4.  
  Our results for FIRS 1 demonstrate the feasibility of using this method to characterize the disk and envelope structure in a larger sample of Class 0 sources. Similar modeling for an unbiased sample will allow us to characterize the typical disk mass, size, and inner envelope structure during the Class 0 phase.

The authors thank the referee T. Bourke, and N. Evans for comments and suggestions that improved this manuscript. We are also grateful to C. Dullemond for the use of his RADMC radiative transfer code and helpful discussions, and to A. Crapsi for providing his model setup. Support for this work was provided by NASA through the Spitzer Space Telescope Fellowship Program, through a contract issued by the Jet Propulsion Laboratory (JPL), California Institute of Technology, under a contract with NASA. Support for CARMA construction was derived from the states of California, Illinois, and Maryland, the Gordon and Betty Moore Foundation, the Kenneth T. and Eileen L. Norris Foundation, the Associates of the California Institute of Technology, and the National Science Foundation. Ongoing CARMA development and operations are supported by the National Science Foundation under a cooperative agreement, and by the CARMA partner universities. Support for c2d, a Spitzer Legacy Science Program, was provided by NASA through contracts 1224608 and 1230782 issued by JPL, California Institute of Technology, under NASA contract 1407. The development of Bolocam was provided by NSF grants AST-9980846 and AST-0206158.