NEAR-IR POLARIZED SCATTERED LIGHT IMAGERY OF THE DoAr 28 TRANSITIONAL DISK

The data reduction process we employed for extracting polarized intensity (PI) disk images utilized the double differencing reduction technique described in Hashimoto et al. (2011). To briefly review, the four sub-images of each frame contain two ordinary and two extra-ordinary images, which can be summed and subtracted from their 90° counterparts to create −Q, +Q, −U, and +U images. The Q and U frames were then rotated into a common orientation, corrected for instrumental polarization, and summed to create final Q and U images. Note that as our 2012 epoch imagery were obtained under non-optimal conditions, we only utilized the best 64 of the 76 observed frames for our summed imagery. The final PI images are computed using $\mathrm{PI}=\sqrt{{{\rm{Q}}}^{2}+{{\rm{U}}}^{2}}$. As previously noted by Hashimoto et al. (2012), the PSF convolved by seeing is not perfectly corrected by the AO-188 system, which produces a residual polarized halo. We computed an artificial halo following the procedure outlined in Hashimoto et al. (2012), scaled this to the observed aperture polarization of the system (P = $0.869\%\pm 0.012\%$), and subtracted it from the PI image to create final PI imagery.

We searched for point-source companions to DoAr 28 using the ACORNS-ADI software package (Brandt et al. 2013). We treated each of the four sub-images noted above as its own ADI sequence (Marois et al. 2006) and reduced them using the LOCI algorithm (Lafrenière et al. 2007) with the standard reduction parameters from Brandt et al. (2013). This yielded four residual images, each corrected for partial flux subtraction. We then averaged these PSF-subtracted images to produce a single high-contrast image. We computed the standard deviation in annuli on this combined image to produce a contrast map and searched for 5σ companions. We found one companion candidate as described in Section 3.2; follow-up data showed it to be an unrelated background star.

We observed DoAr 28 with the SMA on 2011 March 16, using the Compact Configuration with six of the 6 m diameter antennas at 230 GHz (1.3 mm) with a full correlator bandwidth of 2 GHz, for a total integration time of 63 minutes. Calibration of the visibility phases and amplitudes was achieved with observations of the quasar 3C 279, at intervals of about 20 minutes. Observations of Titan provided the absolute scale for the flux density calibration. The data were calibrated using the MIR software package.³² We detected DoAr 28 with a flux density of 68.6 ± 1.9 mJy. The double sideband system temperatures were 110–170 K.

DoAr 28 was observed using the ARC Echelle Spectrograph (ARCES; Wang et al. 2003) at the Apache Point Observatory (APO) 3.5 m telescope on 2014 June 19, yielding a R ∼ 31,500 spectrum covering the spectral range of ∼3600–10000 Å. The data were reduced using standard IRAF techniques. We extracted the order containing Hα and continuum normalized these data, enabling us to characterize the line strength discussed in Section 3.3.

Our two epochs of scattered light PI imagery of DoAr 28 are shown in Figure 1. Significant scattered light around the central star is clearly seen in both epochs. The direction and relative intensity of the polarization vectors derived from these data exhibit a clear centrosymmetric behavior around the central star (Figure 2), confirming that this signal arises from scattering off of circumstellar material. These data exhibit less evidence of centro-symmetry about the minor axis, which is much less resolved than the major axis, suggesting that the level of our residual polarized halo correction might be incomplete. Our primary analysis of these data will focus on the measured PI along the major axis of the system.

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Since these data were not observed with a coronagraph, we defined the effective inner working angle as the location where the radial profile measured along the disk major axis (Figure 3) exhibited a clear deviation from the disk dominated scattered light power law behavior seen in the outer disk. Using this criterion, we determined the inner working angle to be 017 (22 AU) for the 2012 epoch data and 010 (13 AU) for the 2014 epoch (Figure 4). The power law that characterizes the radial profile distribution of the scattered light flux along the disk major axis extends out to ∼050 (65 AU), defining the outer edge of the scattered light disk, before becoming clearly dominated by noise. The detected disk appears to be continuous, with no significant gaps or holes clearly visible. The two epochs of imagery appear similar to each other, modulo potential differences arising from the factor of 1.4 better FWHM achieved in the 2014 epoch imagery. For the imagery with a slightly larger FWHM, it is conceivable that a small amount of disk flux could be spread out into the PSF halo, and be subtracted out in the process described in Section 2.1. Nevertheless, the overall surface brightness of the disk is the same at both epochs and the radial surface brightness power law measured along the major axis for both epochs is similar (−2.47 for 2012; −1.84 for 2014). We do note the potential presence of a slight curl in the SW region of the 2014 epoch scattered light disk, and further discuss this feature in Section 4.

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We determine the inclination of the disk to be ∼50° (Table 1). This was found by subtracting a suite of disk models for a range of inclination angles, described in Section 3.3, and identifying the inclination which yielded the smallest residuals (Figure 5). Note that this residual image (Figure 5) exhibits clear deviations from axisymmetry, with a deficit of scattered light present along the northern side of the major axis. We will be further discuss this non-axisymmetric structure in Section 4.

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Table 1.  Disk Model Parameters

Variable	Model	Low Bound	Upper Bound
Teff (K)	4375	...	...
${R}_{\odot }$	1.6	1.5	1.6
Disk Mass (${M}_{\odot }$)	0.01	0.005	0.05
Max Disk Radius (AU)	250	200	500
Fraction of Mass	0.8	0.7	0.99
Inner Gap Radius (AU)	0	...	...
Outer Gap Radius (AU)	8	7	9
Wall height (AU)	0.5	0.5	0.5
Wall length (AU)	0.5	0.5	1.1
Zscale Disk 1	1.7	...	...
Zscale Disk 2	1.7	1.7	1.9
α	2.0	1.9	2.1
β	1.0	0.99	1.01
Accretion (${\dot{M}}_{\odot }$)	4.0E-9	...	...
Gap Density	5E-6	5E-7	5E-7
Inclination (i)	50°	40°	65°

Note. A summary of the lower and upper acceptable bounds of key HOCHUNK3D parameters that yield a fit consistent with our observations, along with the "best" values that were adopted for our final model. The "fraction of mass" parameter represents the fraction of the mass located in the large dust grain disk; the rest of the disk mass is located in the small dust grain disk. The parameter "zscale" represents the scale height parameter. The "gap density" is the ratio of the dust density inside the gap relative to the density of dust at the inner edge of the disk. The "Zscale Disk" is the scale hight of disks 1 and 2 where disk 1 is large grain dust and disk 2 is small grain dust. Parameters α and β describe the density profile of the disk defined in Equation (1).

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We identified a candidate point source companion $1.^{\prime\prime} 08$ northwest of DoAr 28, with an H-band contrast of 9.5 mag, in our July 2012 data. Our second epoch images from 2014 June indicate that this object is almost certainly a background star. DoAr 28 was too faint for a proper motion from the Tycho satellite, but is part of to the same star forming region as ρ Oph. We assume that it shares ρ Oph's proper motion of $(-5.5\pm 0.9,\;-21.7\pm 0.9)$ mas yr⁻¹ in R.A. and decl. (van Leeuwen 2007). At a distance of ∼140 pc, 1 mas yr⁻¹ corresponds to ∼0.7 km s⁻¹, similar to the velocity dispersions of the Hyades, Pleiades, and TW Hya (Jones 1970; Perryman et al. 1998; Makarov & Fabricius 2001), and somewhat less than the ∼2–3 km s⁻¹ of Orion (Jones & Walker 1988; Fűrész et al. 2008). Figure 6 shows that the companion candidate follows the expected background track assuming common proper motion with ρ Oph. If the point source were co-located with DoAr 28, their relative velocity would be at least 17 km s⁻¹, much too high for the system to be bound at its observed location.

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Figure 7 shows our sensitivity limits, assuming a distance of ∼140 pc and converting contrast to absolute magnitude, and neglecting extinction (estimated to be ∼0.4 mag at H-band, using A(v) = 2.3 (McClure et al. 2010), R_v = 3.1, and the Cardelli et al. (1989) extinction relations), making these sensitivity estimates slightly optimistic. It is more difficult to interpret these results as mass limits, given DoAr 28's extreme youth and uncertainties about the luminosities of very young planets (Marley et al. 2007; Fortney et al. 2008; Allard et al. 2011; Spiegel & Burrows 2012). Our SEEDS observations reach a limiting H-band absolute magnitude of ∼13.5 at a projected separation of 100 AU. At an age of 5 Myr, this corresponds to ∼4 ${M}_{\mathrm{Jup}}$ in the BT-Settl models, but anywhere from ∼4 ${M}_{\mathrm{Jup}}$ up to the deuterium-burning limit of ∼13 ${M}_{\mathrm{Jup}}$ in the Spiegel & Burrows (2012) models (SB12), depending on the initial entropy. We note that the high-mass end of this range requires a very cold start. Assuming an initial entropy midway between the minimum and maximum values of the SB12 models, the SB12 mass limits are only slightly higher than the BT-Settl limits.

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There are theoretical reasons arguing against the formation of substellar companions below ∼5 ${M}_{\mathrm{Jup}}$ by direct gravitational collapse (Low & Lynden-Bell 1976; Bate et al. 2003; Bate 2009). Our SEEDS imagery rule out such a companion, which would necessarily form hot and beyond ∼80 AU. While a less massive core-accretion planet is unlikely to form at such a wide separation (DoAr 28's disk only extends to 70 AU), our data cannot rule out a Jovian planet scattered into a wide or unbound orbit.

We modeled the DoAr28 system with the HOCHUNK3D Monte Carlo Radiative Transfer (MCRT) code as described in Whitney et al. (2013). HOCHUNK3D is similar to other codes (Wolf & Hillenbrand 2003; Dullemond & Dominik 2004a; D'Alessio et al. 2006; Pinte et al. 2006; Min et al. 2009; Robitaille 2011) and has a long history of being used to constrain the dust distribution in protoplanetary systems. The latest version of HOCHUNK3D decouples the small and large dust grain distributions, allowing settling of dust to be incorporated. This implementation can be thought of as utilizing overlapping disks with different dust grain size distributions. Dust density distributions in HOCHUNK3D are adopted from Shakura & Sunyaev (1973) and are characterized by a radial power law (α), and a vertical gaussian distribution (β), as given by Equation (1), where r is the radial component in cylindrical coordinates and z is the height of the disk from the mid-plane. h is the scale height defined in Equation (2), which is normalized at a defined radius of 100 AU. Deviations in the dust density distribution, such as gaps, spiral arms, and warped disks, can also be fully parameterized with HOCHUNK3D.

$$\begin{eqnarray}&&\rho \propto {r}^{-\alpha }\mathrm{exp}\{{[\displaystyle \frac{z}{h}]}^{2}\}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&h\propto {r}^{-\beta }.\end{eqnarray} \tag{ 2 }$$

Whitney et al. (2013) and references therein describe the full radiative transfer of the HOCHUNK3D code. To briefly summarize, the code uses a Henyey–Greenstein scattering phase function and includes parameters for forward-scattering and albedo calculated from the adopted dust grain model. The dust models we used are described below. Temperature corrections utilized the Lucy method with a maximum number of six iterations (Lucy 1999). We utilized 5*10⁶ photons for our broad exploration of MCRT parameter space, and 5*10⁷ photons for each of our runs where we compared both the observed SED and PI imagery against the models.

As is true with many MCRT codes, the large number of free parameters exceed the number of data points leading to model degeneracies. Since we lacked spatially resolved sub-millimeter observations that trace the radial distributions of large grains we assumed that the small and large grain disks had the same α and β. We included a wall along the disk edge, as walls are thought to be common in transitional disks (Calvet et al. 2005; Espaillat et al. 2007a). We also assumed that there was a negligible envelope, no warping of the disk, and that the disk was azimuthally symmetric. We adopted dust parameters from Wood et al. dust model 1 (2002) for our large dust grains, which are composed of amorphous carbon and silicon ranging in sizes up to 1 millimeter. The small dust grain model we adopted was the average galactic ISM model from Kim et al. (1994). We generated a grid of 270 models and identified a broad range of parameters consistent with the observed SED in Table 1.

Our model SED is consistent with the observed photometry of DoAr 28, as shown in Figure 8, with the new SMA data point helping to constrain the large dust grain disk. We explored a range of gap sizes and how these influenced the resultant SED and images, and demonstrate below that a gap size of ∼8 AU best represents our data. We also found that the accretion rate and the gap density parameter had similar effects on the SED (Table 1). We adopted the accretion rate quoted by Keane et al. (2014), $4.0\;\ast \;{10}^{-9}$ ${M}_{\odot }\;{\mathrm{yr}}^{-1}$, which led us assume a gap density parameter of 5 ∗ 10⁻⁶ (Table 1). Note however that our analysis of our new spectroscopic observations of DoAr 28 revealed a H-alpha equivalent width ($30\pm 0.1\;\mathring{\rm A}$) that was different than the 36 Å reported in Keane et al. (2014). This suggests that the system likely exhibits a variable accretion rate. Thus, the upper and lower bound values of the gap density shown in Table 1 are more representative of the system.

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After using the observational SED of DoAr 28 to constrain our MCRT model parameters, we next used the observed surface brightness of our PI imagery to further constrain these parameters. Specifically, we measured the surface brightness of our PI imagery using a 4-pixel wide aperture along the major axis of the disk, and compared this to the H-band PI surface brightness predicted by our models (Figure 4). This iterative process enabled us to arrive at our final adopted model parameters listed in Table 1, including the adoption of the gap size at ∼8 AU. We used the model image subtracted from the PI images to find the inclination of 50°. To search for potential deviations from axi-symmetry in our data, we subtracted our (axi-symmetric) model, scaled to the peak intensity of the observed PI disk, from our observations. This process revealed evidence that the northern side of the disk exhibits a deficit of polarized flux near the inner working angle of our data as compared to the southern side of the disk (Figure 5). We discuss the potential origin of this asymmetry in the discussion section.