ATMOSPHERIC PHASE CORRECTION USING CARMA-PACS: HIGH ANGULAR RESOLUTION OBSERVATIONS OF THE FU ORIONIS STAR PP 13S*

Electromagnetic waves from an astronomical radio source suffer distortion from irregularities in the refractivity of the atmosphere (Thompson et al. 2001). At millimeter and submillimeter wavelengths, the distortions are caused primarily by a turbulent water vapor distribution, though dry air turbulence may also be important under some circumstances (Stirling et al. 2006). The spatial scales of the turbulence extend to kilometer distances with a power-law spectrum (Kolmogorov 1941) that creates atmospheric delay fluctuations on timescales that range from fractions of a second to tens of minutes. The signal degradation is particularly serious for millimeter-wave radio interferometers in extended configurations, where perturbation of phases across the instrument often exceeds many radians. These perturbations can lead to decorrelation (loss of amplitude), distortion of the image, and loss of resolution (Lay 1997a).

Different approaches have been employed to overcome the effect of atmospheric delay fluctuations. A straightforward approach is self-calibration (Schwab 1980), where the visibility phase used to calibrate the data is measured from the actual science target. A model for the source spatial structure is needed and bright sources are required to measure the fringe phase with a high signal-to-noise ratio in a short integration. Two other approaches have been applied to faint targets. In water vapor radiometry (Westwater 1967; Woody et al. 2000), a dedicated radiometer monitors the water vapor emission along the pointing direction of the antenna. In fast position switching (Holdaway et al. 1995), the antennas switch rapidly between the science target and a nearby phase calibrator to capture the atmospheric delay fluctuations on timescales longer than the switching cycle time. Both methods probe the atmosphere close to the line of sight toward the science target, but have limitations in actual applications. Fast position switching reduces the time spent on a source by a factor of ∼2, while water vapor radiometry requires a physical model to relate the water line brightness and the path correction, as well as assuming that refractivity fluctuations are produced only by water vapor.

As an alternative approach, an array of closely paired antennas (Asaki et al. 1996, 1998) continuously monitors the atmospheric phase fluctuations by observing a nearby calibrator. Two arrays of antennas are necessary: antennas belonging to the "science array" observe the science target and phase calibrator, while antennas belonging to the "reference array" simultaneously monitor an atmospheric calibrator. Phase correction on the science target and phase calibrator is accomplished by subtracting the visibility phase measured from the atmospheric calibrator on each baseline. An advantage of the paired antenna technique over water vapor radiometry is that it accounts for atmospheric phase fluctuations due to both water vapor and a dry air component.

Between 2008 November and 2009 February, the Combined Array for Research in Millimeter-wave Astronomy (CARMA) implemented the CARMA Paired Antenna Calibration System (C-PACS) to correct for atmospheric delay fluctuations on the longest baselines of the interferometer (up to 2 km in length). The goal of C-PACS is to enable routine imaging in the most extended CARMA configurations.

In this paper, we describe the C-PACS and apply this calibration technique to observations of the circumstellar dust around PP 13S*.¹⁰ PP 13S* is a young pre-main-sequence star located in the constellation of Perseus and embedded in the L1473 dark cloud at a distance of ∼350 pc (Cohen et al. 1983). This object is thought to have experienced an FU Orionis-type outburst in the past due to a massive accretion episode and is now declining in brightness to a quiescent state (Aspin & Sandell 2001). The FU Orionis nature of PP 13S* has been established based on the highly broadened infrared CO absorption bands (Sandell & Aspin 1998), the jet-like feature seen in [S ii] emission which is a characteristic of Herbig-Haro outflows (Aspin & Reipurth 2000; Aspin & Sandell 2001), and the consistent dimming and morphology changes observed at near-IR and optical wavelengths over several decades (Aspin & Sandell 2001). All of these characteristics are common to FU Orionis objects (Hartmann & Kenyon 1996). The star, with a bolometric luminosity of 30 L_☉ (Cohen et al. 1983), is surrounded by an extended disk and an envelope that contains about 0.6 M_☉ of gas and dust (Sandell & Aspin 1998). The new CARMA observations will help understand the origin of the FU Orionis phenomena in PP 13S* by measuring the distribution of dust continuum emission on spatial scales of ∼50 AU.

Before presenting the new observations of PP 13S*, we describe the paired antenna calibration system as implemented at CARMA. We first describe the antenna configuration used for the observations, and outline the basic principles of the technique.

2.1. CARMA

CARMA is a heterogeneous interferometer comprising 23 antennas: six 10.4 m telescopes from the California Institute of Technology/Owens Valley Radio Observatory (OVRO), nine 6.1 m telescopes from the Berkeley–Illinois–Maryland Association (BIMA), and eight 3.5 m telescopes from the University of Chicago Sunyaev-Zel'dovich Array (SZA). The two most extended array configurations contain baselines that range in length from 100 m to 1000 m (B configuration) and 250 m to 1900 m (A configuration) to achieve an angular resolution of 03 and 015, respectively, at an observing frequency of 230 GHz.

A schematic of C-PACS is shown in Figure 1. C-PACS pairs the eight 3.5 m antennas with selected 6 m and 10 m antennas, preferentially on the longer baselines. Typically, a 3.5 m antenna is offset by 20–30 m to the west of a larger antenna. This separation is a compromise between the need to put the antennas as close as possible to probe the same atmospheric path and to avoid shadowing between antennas.

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The science array, composed of the 6 m and 10 m antennas, operates in the 1.3 or 3 mm atmospheric windows as requested by the investigator. The reference array, comprising the 3.5 m antennas, operates in the 1 cm window. The observing cycle consists of observations of the science target interleaved with periodic observations of the phase calibrator. Both the science and reference arrays observe the phase calibrator to measure instrumental phases drifts. Subsequently, the science array observes the science target, while the reference array monitors a strong point source (i.e., the "atmospheric" calibrator) close to the science target, to measure the delay introduced by the atmosphere. The atmospheric delay measured by the 3.5 m antennas can then be applied to the science observations.

2.2. Properties of the Atmosphere

2.3. Atmospheric Delay Corrections

Following the discussion in Asaki et al. (1996), consider two pairs of antennas as shown in Figure 1. In the simplest case, we measure the delay difference between the antennas on the reference baseline (i.e., baseline A₃ − A₄ in Figure 1) as a function of time. Assuming a non-dispersive atmosphere, the delay on the science baseline (i.e., baseline A₁ − A₂) is corrected by applying the delay difference on the reference baseline to the visibility measurement.

The reference and science delays are not identical since the two baselines are not exactly co-located. The relevant distances that determine the efficacy of the delay corrections are not the baseline lengths at the ground, but the distances between the radio beams as they traverse the turbulent layer (i.e., A'₁ − A'₃ and A'₂ − A'₄ in Figure 1). The beam separation at the turbulent layer depends upon the relative positions of the target and reference source in the sky, the height of the turbulent layer, and the configuration of the antennas on the ground. The upper limit to the beam separation is given by

$$\begin{equation} d_\mathrm{max} = |A_1-A_2| + \alpha h/\sin (e), \end{equation} \tag{ 1 }$$

where α is the angular separation between the science target and the atmospheric calibrator, h the height of the turbulence, and e is the source elevation. Assuming that the turbulent layer is at a height of 1 km (continuous line) or at 2 km (dashed line), Figure 2 shows the trajectories of the 3.5 m beam locations relative to the 6 m and 10 m beams for an 8 hr observation of PP 13S* centered on transit with 3C111 as the atmospheric calibrator. As shown in this figure, the choice of 3C111 as the atmospheric calibrator is particularly fortuitous for PP 13S* since the science and reference beams for most antennas nearly cross within the turbulent zone.

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Using phase closure (Jennison 1958), the difference (Δτ) between the actual delay for the target beams A'₁ − A'₂ and the atmospheric reference beams A'₃ − A'₄ is given by Δτ = τ(A'₁ − A'₂) − τ(A'₃ − A'₄) = τ(A'₁ − A'₃) − τ(A'₂ − A'₄). In a favorable configuration, the beam separations A'₁ − A'₃ and A'₂ − A'₄ will be much less than either the target beam separation A'₁ − A'₂ or the reference beam separation A'₃ − A'₄. The RMS of the corrected visibilities will be $\sqrt{2}$ worse than for an array with the beam separation A'₁ − A'₃, which implies that C-PACS will have a performance equivalent to an array that has baseline lengths ∼20%–70% larger than the A'₁ − A'₃ beam separation, depending on the structure function exponent. The complete analysis contains additional correlation terms and added uncertainties caused by the finite signal-to-noise ratio for the atmospheric calibrator observations.

2.4. Atmospheric Calibrators

The ability of C-PACS to correct the atmospheric delays is limited by the delays from the short beam spacings A'₁ − A'₃ and A'₂ − A'₄ (see Figure 1), instrumental phase drifts on the reference array, and the radiometer noise. The delay errors caused by differences in the beam spacings between the science and reference arrays are given statistically by the structure function R(|A'_i − A'_j|). The instrumental errors can be removed by removing a box-car average over the length of the observation, and will contribute negligible delay errors as long as the timescale for the instrumental drifts is large compared to the box-car width. The delay errors due to the radiometric phase noise depend on the strength of the source being observed, the receiver properties, and the atmospheric characteristics (Thompson et al. 2001). The uncertainty in the measured phase from the radiometer noise is given by

$$\begin{eqnarray} &&\Delta \phi = \frac{\sqrt{2}k_{\mathrm{B}}T_{\mathrm{sys}}}{\eta _Q A_{\mathrm{eff}} S \sqrt{B t}}, \end{eqnarray} \tag{ 2 }$$

where k_B is Boltzmann's constant, T_sys is the system temperature, η_Q is the correlator quantization efficiency, A_eff is the effective collecting area of the antennas, S is the flux density of the atmospheric calibrator, B is the bandwidth of the observations, and t is the integration time. The measurement uncertainty in the delay is then Δϕ/(2πν). The net variance in the delay after applying C-PACS is given by

$$\begin{equation} \Delta \tau ^2 \approx R(|A_1^{\prime }-A_3^{\prime }|) + R(|A_2^{\prime }-A_4^{\prime }|) + \Bigl ({k_B T_\mathrm{sys} \over \eta _Q A_\mathrm{eff} S \pi \nu \sqrt{2 B t}}\Bigr)^2. \end{equation} \tag{ 3 }$$

The structure function is generally described by a power law with exponents varying from 5/3 to 2/3 depending upon the spacing and thickness of the turbulent layer. The scaling coefficient of the power law also varies depending upon the weather conditions. In order for C-PACS to improve the image quality, the target and reference beams must be close at the turbulent layer such that R(|A'₁ − A'₃|) +  R(|A'₂ − A'₄|) ≪ λ². This requires angular separations ≲5° for the A- and B-configuration C-PACS pairings and typical winter weather conditions at the CARMA site. A future publication will use actual measurements to quantify how the quality of the C-PACS correction varies with the angular separation between the science target and the atmospheric calibrator (B. A. Zauderer et al. 2010, in preparation).

The radiometer noise should also contribute much less than a wavelength of delay error for the C-PACS corrections to be successful. For the characteristics of the 3.5 m telescopes and the 1 cm receivers, the radiometer delay error is given by

$$\begin{equation} \Delta \tau _\mathrm{radiometer} = 1.3 \;\mathrm{mm} \,\Bigl ({S_\nu \over \mathrm{1 \;Jy}}\Bigr)^{-1} \,\Bigl ({t \over \mathrm{1 \;s}}\Bigr)^{-1/2}. \end{equation} \tag{ 4 }$$

Thus, 1.3 mm observations with the integration times of t = 4 s (short enough to measure and correct most of the atmosphere fluctuations) require a reference source brighter than S ∼ 1 Jy in the 1 cm band. When several atmospheric calibrators are available, the optimum choice between calibrator separation and brightness can be found by minimizing Equation (3) for the expected weather conditions.

We combined the SZA 30 GHz calibrator list, the NRAO VLA Sky Survey (NVSS) pointing catalog at 1.4 and 5.0 GHz (Condon & Yin 2001), and the WMAP point-source catalog (Wright et al. 2009) to estimate the density of potential C-PACS calibrators. For each source in the GBT catalog, we extrapolated the flux density from 5.0 GHz to 30 GHz by measuring the spectral index α between 1.4 and 5.0 GHz (S_ν ∝ ν^α). We find that 50% of the sky is within 5° of a point source with flux density greater than 1 Jy at 30 GHz. The number of suitable C-PACS calibrators could be expanded by increasing the sensitivity of the reference array, which would allow us to employ fainter atmospheric calibrators. This could be accomplished by increasing the correlator bandwidth or improving the receiver sensitivity.

PP 13S* is particularly well suited for C-PACS observations since the nearest atmospheric calibrator (3C111) is bright (∼4 Jy at 1.3 mm at the time of the observations) and separated by 15 from PP 13S*. Thus, the calibrator satisfies the basic criteria needed for the successful C-PACS corrections (see Section 2.4). In this section, we describe the CARMA observations and data reduction of PP 13S*.

3.1. CARMA 1.3 mm Wavelength Observations

3.2. CARMA 1 cm Wavelength Observations

3.3. Applying 1 cm Delays to the 1.3 mm Data

The effect of the C-PACS on the calibrated phases can be analyzed in several stages. We first compare the phase fluctuations measured toward 3C111 at wavelengths of 1 cm and 1.3 mm to demonstrate that the reference and science arrays are tracing the same atmospheric fluctuations. We then demonstrate that the C-PACS yields quantitative improvement in the quality of the PP 13S* star image. Throughout this section, no absolute flux scale or amplitude calibration are applied to the data in order to evaluate how the C-PACS improves the phase stability on the phase calibrator (Section 4.1) and PP 13S* (Section 4.2).

4.1. 3C111

Figure 3 shows the measured fringe phase toward 3C111 for one paired baseline in the B configuration to illustrate the correlation that exists between the phases measured at wavelengths of 1.3 mm and 1 cm. For this figure, the phases measured on the reference array were scaled by the ratio of the observed frequencies (227 GHz/30.4 GHz = 7.5). The correlation between the 1 cm and 1.3 mm phases is evident over the nearly 8 hr time period and is present for all paired baselines. In addition, the phases are tracked between the two arrays even though the science array is switching between two sources. These results demonstrate that (1) the 1 cm phases can be used to track the delay fluctuations at higher frequencies, (2) the atmosphere is non-dispersive at these wavelengths such that a linear scale with frequency can be used to predict the phases fluctuations at other wavelengths, and (3) C-PACS can correct the science observations while preserving the link to the phase calibrator observations in the science array.

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The observed phases at 227 GHz toward 3C111 on all paired baselines in the A and B configurations are shown as a function of uv-distance¹² in Figure 4. The upper panels show the visibility phases measured in 4 s integrations before applying C-PACS corrections, and the middle panels show the visibility phases after applying the corrections. The RMS scatter on the visibility phase before correction is between 33° (at short uv-distances) and 53° (at long uv-distances) for the B configuration and between 26° and 48° for the A configuration. After applying the C-PACS correction, the phase scatter is reduced to 15°–18° for correction across all uv-distances in both configurations.

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Another way to grasp the effect of the C-PACS corrections can be seen in the bottom panels in Figure 4, where the coherence value ($e^{-\phi _{\rm RMS}^2/2}$) is measured over uv-distance bins of width 130 kλ. Before applying the C-PACS corrections, the coherence decreases with increasing baseline length since the longer baselines have larger atmospheric fluctuations. After applying the C-PACS corrections, the coherence is uniform with baseline length at a value of ∼95%. The coherence becomes nearly constant with baseline length since the C-PACS converts the 200–1800 m baselines into ∼30–50 m effective baselines for all paired antennas. While the results shown in Figure 4 emphasize the improvement in coherence, the C-PACS also improves the visibility phases, which results in higher image fidelity.

4.2. PP 13S*

After applying the C-PACS atmospheric delay corrections to the 1.3 mm data, we removed the instrumental delay drifts by phase referencing to the 3C111 observations. Figure 5 shows the resulting maps before and after applying the C-PACS corrections for the A and B configurations separately and the combined data sets.

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C-PACS improved the image quality for both the A- and B-configuration maps as measured by the increase in the peak flux, the reduction in the noise level, and the decrease in the observed source size. The improved image quality resulted from correcting the phase fluctuations in the 1.3 mm data. The increase in the source flux and the decrease in the source size are also illustrated in Figure 6, which shows radial profile plots across the 1.3 mm emission toward PP 13S* along right ascension and declination. In the combined A+B configuration map, the peak flux measured toward PP 13S* increased from 42.4 mJy to 67.8 mJy (a factor of 1.6) after applying the C-PACS correction. The noise level decreased from σ = 1.5 mJy beam⁻¹ to σ = 1.1 mJy beam⁻¹, which corresponds to a 36% improvement. The observed full width at half-maximum (FWHM) source size diminished from 041 × 027 to 027 × 026 or a 52% decrease in the size of the major axis of the 1.3 mm emission.

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Before proceeding to analyze the properties of the dust surrounding PP 13S*, we must flux-calibrate the C-PACS data. The absolute flux calibration was set from observations of Uranus in the B configuration and 3C84 in the A configuration. The flux density of Uranus was inferred from a planet model, while the flux density of 3C84 was obtained from CARMA observations on a different day when both 3C84 and Uranus were observed. The uncertainty on this calibration is estimated to be 20% due to uncertainties in the planetary model and the bootstrapped flux for 3C84. The antenna gains as a function of time were then determined from the 3C111 observations.

Figure 7 shows the calibrated visibility amplitude observed toward PP 13S* as a function of baseline length. An unresolved source will have a constant flux density with baseline length. By contrast, the visibility amplitude toward PP 13S* decreases with increasing baseline length, which suggests that the source is resolved. While the decline in amplitude with baseline length could be explained by a coherence as low as ∼0.2 on ≳1 km baselines, the minimum measured coherence on 3C111 at any uv-distance was 0.65 even before applying the C-PACS correction (see Figure 4). A similar decline in the visibility amplitude for PP 13S* with baseline length can be seen as well when only a fraction of the data are averaged together (for example, using 1 hr of data at a time), indicating that atmospheric decorrelation over long timescales is not giving rise to the amplitude drop at long baselines. Thus, the primary cause of the decrease in amplitudes with increasing baseline length is that the source is resolved.

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The FWHM of the 1.3 mm continuum emission toward PP 13S* is 022 × 021, which was obtained by fitting a two-dimensional Gaussian to the surface brightness distribution in the combined A+B configuration image after applying the C-PACS corrections and deconvolving the synthesized FWHM beam size of 015 × 014. The integrated flux density of PP 13S* in the C-PACS corrected image after flux and the amplitude calibration is 241 ± 48 mJy, measured by integrating over an aperture of radius R_disk ∼ 1.4 × FWHM ∼ 036, where R_disk is defined to encompass 95% of the emission. The flux observed with CARMA corresponds to about half of the emission measured by single-disk observations (450 mJy at 1.3 mm with a beam size of 195; Sandell & Aspin 1998). The remaining 1.3 mm flux is presumably contained in an extended envelope larger than 16, which is the largest angular scale probed by the CARMA data.

The presence of a circumstellar disk in PP 13S* has been previously inferred from several lines of evidence: (1) reflected light along the outflow axis is observed despite the fact that the central object is heavily obscured in the optical (A_V ∼ 30–50; Cohen et al. 1983), which indicates that the circumstellar material is not spherically symmetric; (2) infrared absorption bands at 3 μm and 10 μm indicate substantial quantities of cold dust, probably present in an obscured inclined disk (Cohen et al. 1983; Smith 1993); and (3) the broad 2.2μm CO overtone absorption feature present in the PP 13S* spectra (Sandell & Aspin 1998; Aspin & Sandell 2001) can be explained by the presence of a massive accreting circumstellar disk (Hartmann & Kenyon 1996). Nonetheless, without observations of the gas kinematics, we cannot determine if the dust emission detected by CARMA originates from the central cusp of an envelope or from the circumstellar disk that surrounds PP 13S*. Since the presence of a massive accretion disk has been invoked to explain several characteristics of FU Orionis objects, we assume that the millimeter continuum emission around PP 13S* observed by CARMA originates primarily from a circumstellar disk.

To determine the disk properties, we assumed that the radial surface density [Σ(R)] can be described by the similarity solution for a viscous accretion disk given by

$$\begin{eqnarray} &&\Sigma (R,t) = \Sigma _t \left(\frac{R_t}{R} \right)^{\gamma } \exp \left[ -\frac{1}{2(2-\gamma)} \left[ \left(\frac{R}{R_t} \right)^{2-\gamma } -1 \right] \right], \;\;\;\; \end{eqnarray} \tag{ 5 }$$

where γ is the slope of the disk viscosity (ν(R) ∝ R^γ) and Σ_t is the surface density at R_t (Isella et al. 2009). The transition radius is the radius at which the mass flow is zero, such that for R < R_t the mass flow goes inward and mass is accreted into the disk, and for R > R_t the mass flow goes outward as the disk expands to conserve angular momentum.

We assume that the central star has a bolometric luminosity of L_bol = 30 L_☉ (Cohen et al. 1983) and a mass of M_* = 1 M_☉. The dust opacity, assumed to be constant throughout the disk, is calculated using compact non-porous spherical grains with fractional abundances from Pollack et al. (1994): 12% silicates, 27% carbonaceous materials, and 61% ices. The grain-size distribution is assumed to be a power law (n(a) ∝ a^−q), with slope q = 3.5 and minimum grain size a_min = 0.05 μm. We adopt a dust emissivity index of β = 1.23 (derived from a gray-body fit to the spectral energy distribution; Sandell & Aspin 1998), and a dust-to-gas ratio of 0.01. For these assumed parameters, the implied maximum grain size of the distribution is a_max = 0.1 cm and the mass opacity corresponds to κ_ν = 0.1 cm² g⁻¹ at 1.3 mm.

The dust surface density defined in Equation (5) was fitted to the observed visibilities using the procedure described in Isella et al. (2009). Figure 7 compares the observed and modeled visibility profile for PP 13S*. The model provides a reasonable fit to the data, although the observed visibility amplitudes are larger than the model for baselines longer than ∼1 km. A map of the model was created and subtracted from the observed PP 13S* map, but no significant residuals (>3σ) were found.

The best-fit disk model has a disk inclination of 15° (where 90° is defined as an edge-on disk), R_t = 13 AU, Σ_t = 145 g cm⁻², γ = 0.95, M_disk = 0.06 M_☉, and R_disk = 128 AU. The mass estimate is larger than the median mass of a Class II circumstellar disk (Andrews & Williams 2005), and is in agreement with the measured masses around other FU Orionis objects. For example, Sandell & Weintraub (2001) estimated circumstellar masses (disk and envelope) between 0.02 M_☉ to a few solar masses for a sample of 16 FU Orionis objects.

Figure 8 shows the surface density distribution (Σ) and the optical depth (τ) as a function of the disk radius. The vertical line marks the separation between the optically thin and thick regimes. We find that the disk becomes optically thick inward of ∼48 AU given the assumptions in the model. We caution that the surface density distribution within this region is poorly constrained not only because of the high optical depth, but because the disk is unresolved for a radius less than 26 AU. The radius where the dust becomes optically thick is large compared to what is found in disks around classical T Tauri stars, where only the inner few astronomical units are opaque at such long wavelength. Furthermore, the transition radius we find for PP 13S* is smaller than any of the pre-main-sequence circumstellar disks studied by Isella et al. (2009). Thus, the circumstellar disk of PP 13S* is more concentrated than the disks around classical T Tauri stars.

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Gravitational instabilities in the disk might be responsible for the enhanced accretion episodes seen in FU Orionis objects (Armitage et al. 2001). To investigate if the disk around PP 13S* is gravitationally unstable, we computed Toomre's Q parameter:

$$\begin{eqnarray} &&Q = \frac{c_s \kappa }{\pi G \Sigma (R)}, \end{eqnarray} \tag{ 6 }$$

where c_s is the sound speed and κ is the epicyclic frequency (which is equal to the angular velocity for a Keplerian disk). A disk becomes gravitationally unstable if Q ≲ 1.5, as spiral waves develop and mass is transported inward and momentum is transported outward (Lodato & Rice 2004).

As shown in Figure 9, the PP 13* disk is gravitationally stable to axisymmetric perturbations across all radii for the inferred surface density. The disk surface density would need to be increased by more than an order of magnitude (see the dashed line of Figure 9) for the disk to develop a gravitational instability. The inferred disk surface density can vary widely depending on the adopted dust properties, as composition, the grain-size distribution (q, a_min, a_max), emissivity index (β) and dust-to-gas ratio, all affect the resulting opacity. For example, κ_ν diminishes by 20%–30% if ices are ignored from the dust composition, increasing the surface density by the same percentage. Also, flattening the grain distribution slope to q = 3.0 gives a 30% increase in the disk mass. Furthermore, we adopted a fixed power law (β) of the dust opacity law. If β decreases toward the center of the system (as observed in Class 0 sources; Kwon et al. 2009), we can expect to have larger grains in the circumstellar disk that will reduce the mass opacity and increase the surface density. Despite the uncertainties in the dust properties, it will be difficult to increase the surface density by more than an order of magnitude at a radius >48 AU where the disk is optically thin, unless the dust properties of PP 13S* are extraordinarily different from what are found in typical disks (Andrews & Williams 2007a, 2007b; Isella et al. 2009).

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We have described C-PACS, which uses paired antennas as a means to calibrate the atmospheric phase fluctuations on long interferometric baselines. Specifically, while the 6 m and 10 m CARMA antennas observe a science source in the 3 mm or 1 mm atmospheric windows, the 3.5 m CARMA antennas simultaneously observe a nearby atmospheric calibrator in the 1 cm band. The 3.5 m antennas are placed within 30 m of the larger antennas to sample similar atmospheric delay fluctuations. We have applied the calibration technique to CARMA observations of the circumstellar material around the FU Orionis object PP 13S*. C-PACS yields quantitative improvement in the image quality of PP 13S*: the observed peak flux increased by a factor of 1.6, the image noise level decreased by 36%, and the FWHM of the major axis decreased by 52%.

The improvement in the phase error and amplitude coherence provided by the paired antennas technique is a function of the projected beam separation of the antenna pairs at the height of the turbulent layer, and the radiometric noise introduced from the reference array to the science array. Thus, the brightness of the atmospheric calibrator and the angular separation between the atmospheric calibrator and the science target are the main restrictions to the application of this technique for general science observations. Our current estimate requires a calibrator closer than 5° to the science target and brighter than 1 Jy at 30 GHz to correct 1.3 mm observations. Based on existing radio catalogs, we estimate that there are 420 sources that have S_ν > 1 Jy, such that 50% of the sky can be observed with a suitable calibrator.

With C-PACS, we have obtained 015 resolution images of the circumstellar material around PP 13S* at an observing frequency of 227 GHz. We measure an integrated flux density of 241 mJy at 227 GHz, which is about half of the extended emission detected in a 195 beam (Sandell & Aspin 1998). We constrain the surface density profile of PP 13S* using a self-consistent disk model. The main difference in the inferred disk properties compared to disks around other pre-main-sequence circumstellar disks is that the dust is more centrally concentrated and there is a larger region that is optically thick at millimeter wavelengths. From analysis of the Toomre Q parameter, we find that the disk is gravitationally stable over all disk radii unless the disk surface density is underestimated by an order of magnitude or more.

Support for CARMA construction was derived from the Gordon and Betty Moore Foundation, the Kenneth T. and Eileen L. Norris Foundation, the James S. McDonnell Foundation, the Associates of the California Institute of Technology, the University of Chicago, the states of California, Illinois, and Maryland, and the National Science Foundation. Ongoing CARMA development and operations are supported by the National Science Foundation under a cooperative agreement (grant AST 08-38260), and by the CARMA partner universities. L.M.P. acknowledges support for graduate studies through a Fulbright-CONICYT scholarship. S.M. acknowledges support from an NSF Astronomy and Astrophysics Fellowship.