THE STRUCTURE OF PRE-TRANSITIONAL PROTOPLANETARY DISKS. II. AZIMUTHAL ASYMMETRIES, DIFFERENT RADIAL DISTRIBUTIONS OF LARGE AND SMALL DUST GRAINS IN PDS 70^*,†

The dust disk structure assumed in this paper follows that from Hashimoto et al. (2012) and Dong et al. (2012a). We synthesize the SED, the NIR polarized intensity image, and the dust continuum at 1.3 mm utilizing an axisymmetric and flared disk model in which the vertical density structure (ρ in cylindrical-polar coordinates {R, z}) in both small and large dust grains is assumed to be Gaussian,

$$\begin{eqnarray} &&\rho (R,z) = \frac{\Sigma (R)}{\sqrt{2\pi }h} \ {\rm exp}\left[-\frac{1}{2}\left(\frac{z}{h}\right)^{2}\right], \end{eqnarray} \tag{ 1 }$$

where Σ is a surface density; h is a scale height varying as a power law with a radius, i.e., h∝R^p. To reduce the number of parameters and simplify, we assume p = 1.25³⁴, i.e., a mid-plane temperature of T ∝ R^−0.5 as approximately estimated by millimeter observations (Beckwith et al. 1990). The scale heights of small and large dust grains are generally different because small dust grains are expected to be coupled well with the gas and might have a similar scale height of the gas whereas large dust grains de-coupled with the gas could be likely to settle in the disk mid-plane due to the stellar gravity. A radial surface density structure (Σ) in dust grains described in the similarity solution for viscous accretion disks (Lynden-Bell & Pringle 1974; Hartmann et al. 1998) is

$$\begin{eqnarray} &&\Sigma (R) = \Sigma _{0} \left(\frac{R}{R_{\rm c}}\right)^{-q}{\rm exp}\left[-\left(\frac{R}{R_{\rm c}}\right)^{2-q}\right], \end{eqnarray} \tag{ 2 }$$

where Σ₀ is a normalized surface density determined by a total disk mass (M_disk); R_c is a characteristic radius; q is a radial gradient parameter. In Whitney's code, in order to generate a gap structure in a central region of a disk, a surface density of a dust disk inside the gap (R_gap) is uniformly scaled down as follows:

$$\begin{eqnarray} \Sigma (R) &=& \delta \ \Sigma _{0} \left(\frac{R}{R_{\rm c}}\right)^{-q}{\rm exp}\left[-\left(\frac{R}{R_{\rm c}}\right)^{2-q}\right],\quad {\rm at} \ R \lesssim R_{\rm gap},\nonumber\\ && \end{eqnarray} \tag{ 3 }$$

where δ is a constant depletion factor. Note that we assume q = 1 as derived in the viscous disk model with T∝R^−0.5 (Hartmann et al. 1998). A radial surface density of small and large dust grains used in our fiducial model is shown in Figure 4.

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Dust properties used in this paper follow Dong et al. (2012a): small dust grains from the standard interstellar-medium dust model (a composition of silicates and graphites; a size distribution of n(s)∝s^−3.5 from s_min = 0.0025 μm to s_max = 0.2 μm) in Kim et al. (1994) and large dust grains (a composition of carbons and silicates; a size distribution of n(s)∝s^−3.5 from s_min = 0.01 μm to s_max = 1000 μm) from Model 2 in Wood et al. (2002). Opacity (κ) of small and large dust grains used in our modeling efforts is shown in Figure 5 (see also Figure 1 in Dong et al. 2012a).

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We have synthesized the NIR polarimetric image, the SED, and the dust continuum of PDS 70 by varying the total mass of the disk (M_disk; assuming gas-to-dust mass ratio of 100), mass fraction (f) of large dust grains in the total mass of dust grains, scale height (h) at 100 AU, depletion factor (δ), size of a gap in large dust grains ($R_{\rm gap}^{\rm l}$), and characteristic radius (R_c). The size of a gap in small dust grains ($R_{\rm gap}^{\rm s}$) is set to 65 AU because NIR imaging constrains this size (Hashimoto et al. 2012; Dong et al. 2012a). Most parameters are similar to those in Hashimoto et al. (2012) and Dong et al. (2012a) except the depletion factor and the characteristic radius. Since the procedure in synthesizing NIR polarimetric images in Hashimoto et al. (2012) and Dong et al. (2012a) did not subtract a "polarized halo (described in Section 2.1 in Hashimoto et al. 2012)", the depletion factor and the characteristic radius in our fiducial models are slightly different from our previous studies. To simplify, we assume the depletion factor and the characteristic radius between small and large dust grains are same. In addition, the scale height inside and outside the gap is also the same. The parameters in the fiducial model and previous model are shown in Table 2.

Table 2. Parameters in Our Fiducial Model and Previous Model

(Column 1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
Model	Mdisk	f	Rc	$R^{\rm l}_{\rm gap}$	$R^{\rm s}_{\rm gap}$	$h^{\rm l}_{\rm 100\, AU}$	$h^{\rm s}_{\rm 100\,AU}$	p	q	δ
	(MJup)		(AU)	(AU)	(AU)	(AU)	(AU)
This work	4.5	0.9667	20	80	65	2.00	8.00	1.25	1.00	10−4
Previous work	3.0	0.9667	50	65	65	2.00	10.00	1.20	1.00	10−3

Notes. Column 2: total mass of the disk (assuming a gas-to-dust ratio 100). Column 3: mass fraction of big dust in total dust. Column 4: characteristic radius in Equation (2). Columns 5 and 6: gap radius of the disk in large and small dust grains. Superscripts "l" and "s" indicate large and small dust grains, respectively. Columns 7 and 8: scale height at 100 AU. Column 9: power index p in the scale height h∝R^p. Column 10: power index in the surface density in Equation (2). Column 11: depletion factor of the large and small dust disk.

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Figure 6 shows the difference of synthesized NIR images between the fiducial model and the previous model. The SEDs in two models (Figure 6(d)) are consistent, whereas the radial profiles along the major axis are slightly different (Figure 6(e)). After modeling, we subtracted the polarized halo from two synthesized images using IRAF³⁵ as a same manner in Hashimoto et al. (2012). We also added an offset value of 0.14 mJy arcsec⁻² to the synthesized NIR images. Since polarized intensity (PI) is calculated as square-root of sum of squares in Stokes Q and U, i.e., $PI = \sqrt{Q^{2} + U^{2}}$, the noise becomes always positive. The value of 0.14 mJy arcsec⁻² is the averaged noise level in our NIR observations. These two operations, subtracting the polarized halo and adding the offset value of averaged noise, result in the difference of radial profiles of two models.

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As a result of our MCRT modeling with 9 × 10⁸ photons, we found the apparent size of the gap is different (Figure 7): 80 and 65 AU in a radius in large and small dust grains, respectively. We also show the dust continuum images with fiducial parameters in Table 2 with different sizes of a gap in large dust grains ($R_{\rm gap}^{\rm l} =$ 65, 80, and 95 AU) in Figure 7. Dust continuum images are convolved with a 2D elliptical Gaussian function of 097 × 048 at PA = 1233, which is a beam size in our SMA observations. The synthesized dust continuum with a gap radius of 80 AU (Figure 7(b)) is matched well with SMA observations except for the asymmetries due to axisymmetric structures assumed in our modeling efforts. We compare the averaged radial profile of the observed dust continuum with that of synthesized dust continuum (Figure 7(d)). The radial profiles along the apparent major axis at PA of 135° are averaged in the northwest and southeast parts. Though the shapes of the profiles are reproduced well with the synthesized dust continuum with a gap radius of 80 AU, the flux density of the synthesized dust continuum needs to be multiplied by 1.155 in order to obtain the consistent absolute flux density. This result, that the radial profile of the observations is brighter than those of the synthesized dust continuum, implies the flux density may be gathered in the northwest rather than azimuthally symmetric.

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The synthesized SEDs in Figure 7(e) do not differ significantly except around 200 μm. Large dust grains in the disk mid-plane are heated by the emission from the upper layer of the disk (see Figure 1 in D'Alessio et al. 2006). Since the temperature of the upper layer of the disk generally decreases with the distance from a central star, the disk mid-plane irradiated by the upper layer also cools down with the radius. The different gap radius in large dust grains would reflect the amount of thermal emission around 200 μm in the SED. The three synthesized NIR polarimetric images are reasonably consistent with each other (Figure 7(f)). Since the opacity at NIR wavelengths in small dust grains is ∼10 times larger than that in large dust grains (Figure 5); and the disk in large dust grains is located in the midplane, minor geometric differences of the disk in large dust grains do not affect the NIR scattering image.

Our modeling efforts in this paper are relatively simple, and the above fiducial model would not be the best solution. Even so, our disk model with a gap consistently explains the observed images at NIR and millimeter wavelengths and the SEDs. In particular, our modeling suggests different gap radii for small and large grains. Further complicated disk models (e.g., not sharp gap edge) and fitting the visibility profile of the dust continuum will be presented elsewhere.

Figure 1 shows an asymmetric brightness in the dust continuum at 1.3 mm and NIR polarized intensity. Such asymmetries in the dust continuum have been detected in other transitional disks, e.g., LkHα 330 (Brown et al. 2008) and SAO 206462 (Brown et al. 2009). The contrast ratio of the peak emission to the opposite side of the disk is likely to be higher among transitional disks around intermediate mass stars (e.g., ∼30 in HD 142527; Casassus et al. 2013; Fukagawa et al. 2013 and ∼130 in WLY 2-48; van der Marel et al. 2013) than among solar-mass stars (e.g., ∼1.1–1.2 in UX Tau A, DoAr 44, and LkCa 15; Andrews et al. 2011). PDS 70's contrast ratio of 1.4 is similar to 1.3–1.5 in SAO 206462 (Brown et al. 2009; Pérez et al. 2014) and slightly higher than that among solar-mass stars. The physical interpretation of the asymmetries is still under debate: gravitational interaction between planet and disk (e.g., Kley & Nelson 2012), large anticyclonic vortex induced by the Rossby wave instability (e.g., Regály et al. 2012), eccentric disk formed by a massive planet (e.g., Kley & Dirksen 2006), and an azimuthal variance of temperature and opacity. In this subsection, we discuss the potential origin of asymmetric features observed in PDS 70.

Disk–planet interaction. An embedded massive planet with a mass of ≳1 M_Jup could open a gap and excite a spiral density wave in the disk due to tidal interactions, while a less massive planet could only excite a wake because the perturbation is not strong enough (see Papaloizou et al. 2007; Kley & Nelson 2012 for a review). These interactions could also lead to exchange of angular momentum of the gas and dust grains in the disk and are expected to result in asymmetric structures in the disk as well. Actually, previous studies have demonstrated the asymmetries in the surface density of the disk using hydrodynamic simulations (Dodson-Robinson & Salyk 2011; Isella et al. 2013). Though the relationship between disk–planet interaction and asymmetric structures in the disk still remains to be intensively investigated, a single massive planet could tend to induce azimuthally symmetric structures except spirals (Kley & Nelson 2012), whereas multiple massive planets could create azimuthal asymmetries (Dodson-Robinson & Salyk 2011; Isella et al. 2013). Hence, the existence of multiple planets would be one of the key points to explain the observed asymmetries in PDS 70. The possible existence of (unseen) multiple planets opening the gap around PDS 70 has already been argued in Hashimoto et al. (2012) and Dong et al. (2012a) and been supported by following two aspects: the large gas gap around PDS 70 with a radius of ∼65 AU (Figure 1(c)) could be explained by only multiple planets (Zhu et al. 2011; Dodson-Robinson & Salyk 2011); a gap structure (optically thick inner and outer disks separated by an optically thin region) inferred from NIR imaging (Figure 1(c)) and the SED (Figure 7(e)) is most likely due to disk–planet interaction rather than other inside-out scenarios (grain growth; photoevaporation; see Section 1). Furthermore, Hashimoto et al. (2012) put an upper limit of the planetary mass of only ∼2 M_Jup in the gap based on L' band (3.8 μm) imaging, thus being unable to discard the existence of unseen massive planets with a mass of ∼1 M_Jup. Therefore, though further quantitative comparisons between observations and numerical simulations (e.g., comparisons between the observed PDS 70's contrast ratio of 1.4 and simulations) are still necessary, we anticipate the observed asymmetries in the disk of PDS 70 might be induced by interactions between unseen multiple planets and the disk.

Anticyclonic vortex. Asymmetric structures in a disk can be explained without any planets. In the last decade, several transitional disks show asymmetric dust continuum emission (Piétu et al. 2005; Brown et al. 2009; Andrews et al. 2011; Pérez et al. 2014) and has been explained with large anticyclonic vortex potentially formed by the Rossby wave instability (RWI; Lovelace et al. 1999; Regály et al. 2012). RWI is excited at steep gas-pressure gradients in an overdense region where is thought to be an outer edge of the "dead zone" (Gammie 1996). The gas in the disk is generally transported from the outer disk through mass accretion, possibly triggered by the magnetorotational instability (MRI; Balbus & Hawley 1991). MRI becomes active when the ionization state of the gas is sufficient, meaning an ionized upper layer of a disk and a less dense outer disk are prone to induce MRI. Conversely, a dense region in the disk mid-plane would have less effective ionization because of gas self-shielding against ionization radiation, resulting in a dead zone where mass accretion by MRI is strongly reduced. As a result, a gas-overdense region is expected to form at the boundaries of the dead zone (Varniére & Tagger 2006; Terquem 2008), leading the RWI to launch anticyclonic vortices. The radius of the outer edge in the dead zone strongly depends on the amount of dust grains (Sano et al. 2000) because degrees of ionization in the gas are suppressed by recombination of ions and electrons at grain surfaces. Assuming the minimum-mass solar nebula (Hayashi et al. 1985), Sano et al. (2000) estimated the dead zone's outer edge is about 20 AU in radius. Since this radius is also a function of the disk's properties (e.g., the vertical magnetic field, density, and temperature of a disk; Okuzumi & Hirose 2011), anticyclonic vortices might take place at a radius of 80 AU in the case of PDS 70. However, this scenario would not explain the gap structure even if it explains asymmetric structures; hence it is unlikely that an anticyclonic vortex induced at the outer edge of the dead zone could be the main scenario.

Steep gas-pressure gradients can also form at the gap edge sculpted by massive planets (Papaloizou et al. 2007; Kley & Nelson 2012), resulting in anticyclonic vortices (e.g., Li et al. 2005; Lin & Papaloizou 2010; Zhu et al. 2014; Zhu & Stone 2014). Coriolis forces in a vortex effectively lead large dust grains into the central vortex (e.g., Figure 1 in Barge & Sommeria 1995), resulting in an increase in the surface density of the large dust grains by more than a factor of 10–100 for fastest drifting particles (Zhu et al. 2014; Zhu & Stone 2014). van der Marel et al. (2013) modeled the asymmetric structures in the dust continuum around WLY 2-48, which has the large contrast ratio of 130, with a vortex-shaped dust trap triggered by a companion. Although PDS 70 has a contrast ratio in flux density of only 1.4, this value may be due to the convolution of the large beam size (∼1'') in our observations. Thus this scenario of the vortex at the planet-induced gap edges would be applied to explain not only the large contrast ratio in HD 142527 and WLY 2-48 with ∼30 and ∼130, respectively, but also the case of PDS 70.

Variance of Temperature and Opacity. When a disk is optically thin, the observed azimuthal flux density F_ν is

$$\begin{eqnarray} &&F_{\nu } \approx \kappa _{\nu } \times M_{d} \times B_{\nu }(T_{d}) \times d^{-2}, \end{eqnarray} \tag{ 4 }$$

where κ_ν and T_d are the opacity and temperature of a disk with a mass of M_d, B_ν is the blackbody intensity, and d is the distance (see Draine 2006). Since the Rayleigh–Jeans limit (hν ≪ kT_d) can be applied at (sub-)millimeter wavelengths (Beckwith et al. 1990; Beckwith & Sargent 1991), F_ν is

$$\begin{eqnarray} &&F_{\nu } \propto \nu ^{2} \times \kappa _{\nu } \times M_{d} \times T_{d}. \end{eqnarray} \tag{ 5 }$$

Hence, assuming the azimuthally symmetric dust opacity κ_ν and mass-distributions of the dust grains, azimuthal distributions of the observed flux density depend on disk temperature. As mentioned in Section 3.2, since the disk mid-plane is heated by the emission from the upper layer of the disk, if the stellar radiation is interrupted by an asymmetric inner disk (e.g., a warp; an asymmetric puffup), a shadow cast from the inner disk might cool down disk temperature in the outer disk. Disk temperature of large dust grains in the mid-plane around r = 80 AU of PDS 70 simulated in our modeling efforts is 23 K, corresponding to the azimuthal temperature variance of 16–23 K using the contrast ratio of the flux density in PDS 70 with 1.4. Thus, we cannot rule out this scenario based on our observations. Although whether this scenario of shadowing can directly affect on (sub-)millimeter radiation and azimuthal redistribution in a (closer to) optically thin environment is still ambiguous, monitoring observations would be useful to test the shadowing scenario because a shadow cast from the inner disk is co-rotating with the inner disk. The Keplerian orbital velocity (ω) of the inner disk at 0.1 AU (where is optically thick in Figure 4) is given by

$$\begin{eqnarray} &&\omega \approx 27 \left(\frac{M}{0.8\, {M}_{\odot }}\right)^{\frac{1}{2}} \left(\frac{r_{{\rm d}}}{0.1\, {\rm AU}} \right)^{-\frac{3}{2}} \ {\rm [deg\, day^{-1}]}, \end{eqnarray} \tag{ 6 }$$

where M is the mass of the central star and r_d is the orbital radius of the inner disk. Such rotation could be observed within a few months. Furthermore, a non-axisymmetric illumination from the central star (Takami et al. 2014) possibly causes asymmetric distributions of the disk temperature. Assuming PDS 70 has the rotational velocity of ∼10 km s⁻¹ and a radius of 1.39 R_☉ (Gregorio-Hetem & Hetem 2002), the rotation period is ∼50 days. Such a periodic fluctuation could be also observable within a few months.

Note that although above discussions are based on the azimuthally symmetric dust opacity, asymmetrically distributed dust opacity could also affect the flux density. If the dust opacity κ_ν is assumed to have a power-law dependence on frequency, κ_ν∝ν^β (Beckwith et al. 1990; Beckwith & Sargent 1991), the observed azimuthal flux density in Equation (5) becomes F_ν∝ν^α (where α = β + 2) assuming azimuthally symmetric disk temperature and mass distributions of the dust grains. A power-law index β is known to strongly depend on size distributions and maximum sizes of dust grains (Draine 2006). For instance, interstellar medium (ISM) dust mainly consisting of sub-μm size grains that are less than (sub-)millimeter emitters shows β ≈ 1.7 (e.g., Li & Draine 2001), while circumstellar disks consisting of both small and large dust grains show β ∼ 0 (e.g., Andrews & Williams 2007). Thus, if grain growth locally takes place in the disk due to, for example, anticyclonic vortices, asymmetric dust continuum emission could be observed. The parameter β in κ_ν of large dust grains in our modeling is ∼0.6 (Figure 5), and β changing with δβ ∼ 0.017 reproduces the contrast ratio of 1.4 of PDS 70 at 1.3 mm. When dust grains grow into larger dust grains in the disk, this change in β would be reasonable. Hence, though we cannot exclude this scenario based on our single-wavelength observations, future high-resolution multi-color radio interferometric observations with ALMA could reveal azimuthal β distributions, allowing the investigation of whether dust grains locally evolve in the disk.

Eccentricity. Numerical calculations expect that when a massive planet with a stellar-to-planet mass ratio of q ≳ 3–5 × 10⁻³ is embedded in the disk, an eccentric disk can form at the gap edge (eccentricity of up to ∼0.25; Kley & Dirksen 2006; Ataiee et al. 2013; Regály et al. 2014). Keplerian orbital velocity at the apocenter of the elliptic orbits is slower than at the pericenter, resulting in a possible enhancement of disk materials at the apocenter of the disk. This scenario makes a "traffic jam" instead of a dust trap, suggesting a lower azimuthal contrast than that in the vortex. According to Ataiee et al. (2013), the contrast ratio of the disk mass between the apocenter and the pericenter is ∼1.5 (see Figure 3 in Ataiee et al. 2013). This value is consistent with that of PDS 70. However, the minimum planetary mass necessary to induce an eccentric disk around PDS 70 would be ∼2–4 M_Jup; such planetary-mass objects in the gap should be detected in our previous observations (see Figure 2(f) in Hashimoto et al. 2012). One of the differences in this scenario compared to the above is that the asymmetries in an eccentric disk are fixed at the same position instead of co-moving with planets or vortices; hence future follow-up observations could confirm whether an eccentric disk forms around PDS 70.

Our observations and modeling efforts suggest that the disk around PDS 70 has different radial structures in large and small dust grains: a gap of r = 80 AU for large dust grains and 65 AU for small dust grains (Section 3.2; Figure 7). In Section 1, we mentioned grain growth and photoevaporation as potential scenarios to explain the properties of transitional disks (e.g., Clarke et al. 2001; Dullemond & Dominik 2005). As discussed by other authors (e.g., Espaillat et al. 2014), these two scenarios are expected to result in inside-out disk dispersal. Since PDS 70 has an optically thick inner disk at ∼0.1 AU (Figure 4; Hashimoto et al. 2012), these two would be less dominant in PDS 70. Another possible scenario is disk–planet interaction (e.g., Kley & Nelson 2012). However, only gravitational interaction between the disk and planet might result in similar radial structures in three disk components (the gas and the large and small dust grains), i.e., no radial difference; thus only disk–planet interaction would also be less likely in PDS 70. Other scenarios mentioned in Section 1 (dust filtration and radiation pressure) need planet(s) in the gap. In this subsection, we briefly review and discuss the combinations of scenarios: disk–planet interaction with dust filtration and/or radiation pressure.

Dust filtration (Rice et al. 2006; Zhu et al. 2012; Pinilla et al. 2012; de Juan Ovelar et al. 2013; Owen 2014) is induced at the outer edge of the gap. Dust filtration has been originally suggested to explain apparently contradictory transitional disk properties: a T-Tauri-star-like moderate mass accretion rate ($\dot{M} \sim$10⁻⁸ to 10⁻⁹  M_☉ yr⁻¹; Najita et al. 2007) with an optically thin or empty inner hole. Since the disk materials in the inner disk are resupplied from the outer disk through mass accretion, moderate mass accretion and an inner hole are apparently inconsistent. To interpret these transitional disk properties, theorists make use of a physical consequence that dust particles are trapped at gas-pressure maxima. When a dust particle embeds in a gaseous disk where the pressure has a radially negative gradient, since the gas rotates with the sub-Keplerian velocity, a dust particle feels a headwind and loses angular momentum. On the other hand, when a gaseous disk's pressure has a radially positive gradient, for example, at the outer edge of the gap, since the gas rotates with the super-Keplerian velocity, a dust particle feels a tailwind and gains angular momentum. Eventually, dust particles are led into gas-pressure maxima. The gas can still accrete onto the central star through the gap (Lubow & D'Angelo 2006) even there are multiple planets in the gap (Dodson-Robinson & Salyk 2011; Zhu et al. 2011). That is how large dust grains are distributed at gas-pressure maxima, whereas moderate mass accretion is still observable.

Zhu et al. (2012) demonstrated that though dust filtration with a single or multiple planets affects (sub-)millimeter dust particles, which possibly accounts for (sub-)millimeter observations of large gapped (r ≳ 20 AU) transitional disks with moderate mass accretion of ≳10⁻⁸ to 10⁻⁹  M_☉ yr⁻¹, the filtration process hardly affects (sub-)micron sized dust particles since small dust grains are generally coupled well with the gas. This can nicely explain the missing gaps in NIR scattered light images of some transitional disks (Dong et al. 2012b), such as SR 21 (Follette et al. 2013), SAO 206462 (Muto et al. 2012), and MWC 758 (Grady et al. 2013). Subsequent studies in dust filtration (Pinilla et al. 2012) calculated the position of gas pressure maxima depends on disk viscosity, the planetary mass, and location (e.g., a gas pressure maximum at 30 and 50 AU when 1 and 9 M_Jup at 20 AU, respectively, in Figure 1 in Pinilla et al. 2012); de Juan Ovelar et al. (2013) showed observed radii of the gap in the NIR and sub-millimeter wavelengths could also depend on the planetary mass and location (e.g., gap radii in the NIR and submillimeter wavelengths are 20 and 30 AU, respectively, when a planet with 1 M_Jup at 20 AU in Figure 2 in de Juan Ovelar et al. 2013). The radius of the gap in the NIR wavelengths could reflect the scattered position at the outer gap edge of the disk in small dust grains carved by a planetary perturbation, while the radius in the (sub)-millimeter wavelength reflects the peak position of the dust surface density (i.e., gas pressure maximum, which slightly locates at the far side; see Figure 7 in de Juan Ovelar et al. 2013). The dependence of the dust–gas coupling on the size of the dust grains leads to different gap radii at different wavelength, as seen in PDS 70. Such disk systems have been reported in SAO 206462 (Garufi et al. 2013; Pérez et al. 2014), HD 100546 (Avenhaus et al. 2014; Pineda et al. 2014), and Sz 91 (Tsukagoshi et al. 2014); thus PDS 70 is not unique.

As pointed out by Zhu et al. (2012), one problem in dust filtration is that it is difficult to account for the low NIR excess generally seen in transitional disks. In addition to dust filtration, to reduce the NIR excess generated from small dust grains, "a planetary accretion luminosity" was proposed by Owen (2014) in which small dust grains are expected to push back by radiation pressure from an accreting planet, resulting in allowing the dust-free gas to accrete onto the central star (Owen 2014). This scenario would be useful to explain the properties of general transitional disks with the reduced NIR excess and moderate mass accretion. However, in contrast to general transitional disks, weak-line T Tauri star PDS 70 should have low mass accretion (a Hα equivalent width of 2.0 Å; Gregorio-Hetem & Hetem 2002).

Though we have discussed the possible scenarios to explain the asymmetries in PDS 70, all proposed scenarios except eccentricity are hardly excluded based on our single epoch and single wavelength observations with SMA (Section 4.1). On the other hand, we found disk–planet interaction + dust filtration could account for different radial structures in small and large grains (Section 4.2). In this subsection, we discuss whether disk–planet interaction + dust filtration is potentially responsible for the complicated structures of the disk around PDS 70.

Planet(s) in the gap could reduce mass accretion and might explain the low mass accretion of PDS 70. Though mass accretion onto a planet is not conclusively understood, in general, a more massive planet (e.g., 10 M_Jup) or multiple planets (e.g., 1 M_Jup) could reduce mass accretion onto the central star. Since the existence of such a single 10 M_Jup planet was already ruled out in our previous studies (Hashimoto et al. 2012), accreting multiple planets remain as a possible scenario. If a single planet with ∼1 M_Jup can be assumed to have sufficient mass accretion onto the planet itself and induce dust filtration, this planet might be responsible for the large-gapped disk structure in the dust continuum (Pinilla et al. 2012) and low accretion rate of PDS 70. However, a single planet would likely induce a relatively symmetric structure in the disk (Kley & Nelson 2012) and thus be inconsistent with the asymmetries observed in PDS 70. Meanwhile, a single planet with ∼1 M_Jup could create the asymmetries in the disk if vortices take place at the gap edge sculpted by this single planet. However, a single planet is expected to create a narrow gap in the gas and small dust grains (i.e., r ≲ 15 AU; Zhu et al. 2011; Dodson-Robinson & Salyk 2011); hence a single accreting planet inducing vortices would be ruled out as the origin of the large NIR gap around PDS 70. Remaining accreting multiple planets could explain both of low mass accretion and the asymmetries of the large gapped-disk in PDS 70. These combinations could also induce dust filtration at the gap edge and are likely to account for the different gap radii in the NIR and millimeter wavelengths.

To summarize, accreting multiple planets inducing dust filtration at the outer gap edge could explain all observed properties of PDS 70: different observed radii of the gap in the different wavelengths, low mass accretion onto the central star, a depletion of disk components inside the gap except the optically think inner disk, and no very massive planets in the gap. However, direct observational evidence of dust filtration has not been detected in any disk system. One conclusive observational proof of dust filtration would be "a gap in the gas" (see, e.g., Figure 7 in de Juan Ovelar et al. 2013). As mentioned, in the outside of the planetary orbit, a combination of positive and negative gas-pressure gradients is critical to trap large dust grains at gas-pressure maxima. Inside the planetary orbit, gas pressure would have only negative gradients, resulting in the depletion of large dust grains. Future ALMA observations with high resolution and high sensitivity will enable the detection of a gas gap. Furthermore, detecting any planets in the gap would be important to verify whether planets form gap structures in the dust grains and induce dust filtration. A hint to enhance the detectability of planets in the optical/NIR wavelength may be the planetary accretion luminosity (Owen 2014). Though a low-mass binary, a companion in the gap of HD 142527 (a mass of 2.2 M_☉; a distance of 145 pc; an age of 5 Myr; Verhoeff et al. 2011) exhibits an accretion luminosity and was detected in the narrowband of Hα (Close et al. 2014). Therefore, combining integral field spectroscopy with angular differential imaging (ADI; Marois et al. 2006) or spectral differential imaging (SDI; Racine et al. 1999) with ADI focusing on accretion-sensitive lines such as Hα (0.656 μm); Paβ (1.282 μm); Brγ (2.166 μm); H₂ v = 1–0 S(1) (2.122 μm) may increase the detectability and allow discovery of accreting planets in the gap.