Near-infrared Imaging of a Spiral in the CQ Tau Disk

CQ Tau was observed on UT 2018 December 24 (PI: D. Mawet) using the Keck/NIRC2 vortex coronagraph (Mawet et al. 2017; Serabyn et al. 2017; Xuan et al. 2018) combined with ADI. The observation achieved an angular rotation of ∼111°. No standard stars were taken in the same epoch and we did not conduct point-spread function (PSF) subtraction by reference differential imaging (RDI; Ruane et al. 2019) in this study. We measured the off-axis PSF and determined that the FWHM was 9.2 pix (∼00915 with a pixel scale of 9.972 mas pix⁻¹). After a first reduction including flat-fielding, bad-pixel correction, sky-subtraction, and image registration, the data set was processed via the vortex image processing (VIP; Gomez Gonzalez et al. 2017)³⁰ package that applies a principal component analysis (PCA) for the ADI reduction (Amara & Quanz 2012; Soummer et al. 2012).

Figure 1 shows the Keck/NIRC2 ADI-reduced image of CQ Tau overlaid with the ALMA continuum (left) and Subaru/High-Contrast Coronographic Imager for Adaptive Optics (HiCIAO) PI (right; see Section 2.2 for the data). VIP produces a set of different principal components (PCs), results of which are shown in the Appendix. We adopted PC = 8 among these PCs for presenting our result because this image shows an extended object at separations between ∼02 and 04, and position angles (PAs) between ∼45° and 110° with a signal-to-noise ratio (S/N) ∼7–8. The feature appears robust because it survives for a wide range of PC values (see Figure 7). We marginally found some other sources (see Figure 7) in a set of ADI-reduced images, whose S/Ns fall less than 5 at a certain PC and do not discuss other companion candidates. We converted counts into the surface brightness using previous L'-band photometry (2.4 Jy for CQ Tau; McDonald et al. 2017) and the brightest region in this feature has 68 ± 8.5 mJy arcsec⁻². The VIP package enables one to set different fields of view (FoV) and inner working angles (IWA). We adopted IWA = 16 pix so that the asymmetric feature is reproduced with a higher S/N. We reran VIP by setting a smaller IWA to check whether other companion candidates appear at separations smaller than 16 pix and confirmed that only residuals of speckles that vary among different PCs were shown. We first attempted to fit this extended object with a point-source Gaussian, which provided a poor match and thus we concluded that it corresponds to an asymmetric structure in the CQ Tau disk. Figure 2 shows a polar-projected image suggesting that this feature likely corresponds to a spiral. CQ Tau is one of only a few systems that have a spiral detected in the L' band (see Section 1 for the L'-band disks).

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We then compared our results with the ALMA archival data. The spiral overlaps with the ring of the dust continuum, but the ADI-reduced signal experiences self-subtraction by the reduction algorithm as negative regions shown at both sides of the spiral. Centrosymmetric features in the CQ Tau disk are also removed by self-subtraction and thus cannot be seen in the ADI-reduced image (Milli et al. 2012).

Apart from the spiral feature, we did not detect any companion candidates within ∼09 from the central star. The NIRC2 figure with a larger FoV is shown in the Appendix. We then calculated noise profiles as a function of separation relative to the signal from the central star. Figure 3 shows a 5σ detection limit of the NIRC2 data. Although the spiral feature affects the detection limit between 02 and 04, we achieved 2.9 × 10⁻⁵ at 05. Compared with an evolutionary model (COND03; Baraffe et al. 2003) assuming 10 Myr, our contrast limit could constrain down to ∼5 M_J outside the spiral.

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Subaru/AO188+HiCIAO observed CQ Tau in a combination of PDI and ADI as part of the Strategic Exploration of Exoplanets and Disks with Subaru (SEEDS) project (Tamura 2009). No coronagraph was used in this observation. The total exposure time of the HiCIAO data is only 9 min with FWHM = 5.3 pix (∼50 mas with a pixel scale of 9.5 mas pix⁻¹), which achieved an inner working angle of ∼077 after the ADI reduction and is insufficient for searching planets embedded in the CQ Tau disk (for the ADI result at separations ≥10, see Uyama et al. 2017). In this study, we focus only on the PDI reduction. SEEDS adopted standard PDI (sPDI) and quad PDI, where a different number of Wollaston prisms was used, and sPDI was applied to CQ Tau's observation (for detailed information see Uyama et al. 2017). After the first reduction of destriping the HiCIAO pattern, flat-fielding, distortion correction, and image registration, we reduced the polarimetric data sets by means of an IRAF pipeline,³¹ which was used in previous HiCIAO PDI studies (e.g., Hashimoto et al. 2011, 2012). Figure 4 shows the PI image of CQ Tau overlaid with the ALMA continuum. The whole disk cannot be investigated since there are residual speckles that cannot be removed through post-processing due to short exposure time. We did not detect a gap in the surface of CQ Tau's disk. The PI image shows the spiral feature at the same location as shown in the NIRC2 image. In order to investigate the S/N of the spiral, we used perpendicular regions to the spiral whose PAs range from 125°–165°, 305°–345° for calculating a noise (defined as the standard deviation in the specified area) radial profile. We finally confirmed that the spiral has an S/N ∼5–6 in the PI image. There may be other disk features shown in the PDI-reduced image but below 5σ significance due to speckles in the inner region. An r²-scaled PI image (see Figure 5 for a polar-projected image) clearly shows the spiral feature. There is another extended region at PAs between 10° and 90°, which is perhaps another asymmetric feature and possibly detected in the NIRC2 data with PC = 5, 8, and 10 in Figure 7 with insufficient significance. We discuss this inner feature in Section 2.3. We note that a gap-like feature close to the central star may be affected by r²-scaling because the original HiCIAO data set does not show such a feature (see the left image in Figure 4 for the PI signal and the right image in Figure 1 for the contour).

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In both observations we clearly detected the spiral feature, which overlaps with the ring structure in the millimeter continuum detected by ALMA. The presence of the spiral is consistent with a prediction of a ∼6–9 M_J planet at 20 au (Ubeira Gabellini et al. 2019). However, our observation could not achieve a sufficient contrast limit to detect/constrain such a faint protoplanet. We checked whether a counterpart of the spiral is shown in the ALMA gas data. Tang et al. (2017) reported a pair of spirals for AB Aur at ¹²CO emission that correspond to the PI signal (Hashimoto et al. 2011). However, Ubeira Gabellini et al. (2019) did not show any clear spiral features in the ¹²CO data.

The right panel of Figure 1 compares the NIRC2 and HiCIAO results and these shapes show a good agreement with each other. Polar-projected images (Figures 2 and 5) also clearly show that the spiral feature increases in distance from the central star. We note that the surface brightness in each band shows a different parameter. The NIRC2 and HiCIAO results correspond to the total intensity and polarimetric intensity, respectively. We discuss the difference between these results in Section 3.2. We measured the pitch angle based on the best-fit logarithmic spiral to the trace of the spiral. The trace was identified as radial maxima in azimuthal bins of 1° in the image obtained after deprojection using inclination and PA of the major axis derived by Ubeira Gabellini et al. (2019): i = 35° and PA_a = 55°. Since the spiral feature in the NIRC2 image experiences self-subtraction and is distorted by the reduction algorithm, we used only the HiCIAO data to measure the pitch angle. The PI data corresponds to scattering profiles from the disk surface and does not experience self-subtraction. The fitted result for the spiral (the middle panel in Figure 4) is 34° ± 2°. We also attempted to fit the extended inner region at PAs between 10° and 90°. The result is shown in the right panel of Figure 4 and the pitch angle is measured at 4° ± 3°. In addition to fits to the logarithmic spiral equation, we also fitted the spiral trace to the general Archimedean equation. The result is shown in the Appendix. We note that because scattered light originates from a cone-shape surface instead of a flat plane, when viewed at a finite inclination, different regions in the disk are compressed differently (e.g., Figure 4; Ginski et al. 2016). Because of this, a disk structure in surface density traced by millimeter continuum emission can be projected to a different location in scattered light (e.g., the southern spiral arm in MWC 758; Dong et al. 2018a). Simple deprojection by linearly expanding the disk along the minor axis by a factor of $1/\cos i$ generally does not perfectly restore the face-on view of the disk (Dong et al. 2016). Therefore, our measurements of the arm pitch angles are approximations only. Future modeling work is needed to simultaneously determine the shapes of the disk surface and the spiral arms.

We used both fit results to infer input parameters for the forward modeling of the L'-band feature (for the detailed method for the forward modeling, see Christiaens et al. 2019) to measure a throughput (signal loss due to the ADI reduction); Figure 6 shows our result with injected spirals. We used the off-axis PSF of CQ Tau and injected fake PSFs at several separations and PAs to produce fake spiral features (injected positions are shown in Figure 6). We then measured the ratio between input flux and output flux at the injected locations, which is shown in the right panel of Figure 6. Our forward modeling reproduced the outer spiral with a flux recovered by a throughput of 0.54 at 50 au, which corresponds to 126 mJy arcsec⁻² at the brightest region in the spiral. On the other hand, however, the injected inner spiral is largely affected (a throughput less than 0.3) by not only self-subtraction at small separations but also negative regions produced by the existence of the outer spiral. As the S/Ns of this feature in the practical NIRC2 and HiCIAO data are less than 5, we do not conclude that this inner feature is a spiral.

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The CQ Tau disk has a striking similarity with the disk around V1247—both of which show one prominent arm in scattered light and a ringed disk in millimeter continuum emission (Ohta et al. 2016; Kraus et al. 2017). In addition, they share a similar inclination of ∼30°–35°, and the major spiral arm seen is in the direction of the major axis. Simulations have shown that while a massive companion may induce a pair of nearly symmetric spiral arms, when viewed at a modest inclination one of the arms may be compressed more than the other in scattered light, thus falling inside the inner working angle (Dong et al. 2016). Future observations may push for inner separations to look for possible additional arms hidden under the current image mask.

We first investigate whether the L'-band emission can be reproduced by thermal emission from small grains. We assume that the disk is optically thick at the L' band. If the observed emission of 126 mJy arcsec⁻² is entirely due to thermal emission from optically thick dust, the temperature of the grains is expected to be T_grain ∼ 202.5K.

Provided that small grains at the spiral absorb shorter wavelengths of stellar light and emit their heat at ∼3–4 μm, the grain temperature is given by

$$\begin{eqnarray}&&\begin{array}{l}(1-{\omega }_{\nu })\pi {a}_{\mathrm{grain}}^{2}\displaystyle \frac{{L}_{\star }}{{r}_{\mathrm{spiral}}^{2}}\lt {Q}_{\mathrm{abs}}({\lambda }_{\star })\gt \\ \quad =\ 4\pi {a}_{\mathrm{grain}}^{2}\sigma {T}_{\mathrm{grain}}^{4}{Q}_{\mathrm{abs}}({\lambda }_{\mathrm{grain}}),\end{array}\end{eqnarray} \tag{ 1 }$$

where Q_abs(λ) is the absorption efficiency at λ and a_grain is the size of the grain. With this equation, we can derive a set of dust size (a_grain) and albedo (ω_ν) that can reproduce T_grain = 202.5K. Here we assume $\lt {Q}_{\mathrm{abs}}({\lambda }_{\star })\gt =\tfrac{\int {Q}_{\mathrm{abs}}{B}_{\lambda }({T}_{\star })d\lambda }{\int {B}_{\lambda }({T}_{\star })d\lambda }\simeq 1$ for simplicity. This relation is compared with the model of astronomical silicate (Draine & Lee 1984). We find a set of a_grain ∼ 0.8μm and albedo∼0.2 can reproduce T_grain = 202.5 K and is consistent with the astronomical silicate model. The dust opacity (κ) per unit dust mass (assuming that the gas-to-dust ratio is 100) is also estimated to be 3.4 × 10³ cm² g⁻¹ and 1.1 × 10³ cm² g⁻¹ at the H and L' bands, respectively. With the small grain surface density of 0.0375 g cm⁻² of CQ Tau's disk (Ubeira Gabellini et al. 2019), τ_ν is assessed at larger than 30, which corresponds to the optically thick disk. We note that current ALMA observations reported lower κ per unit dust mass (∼100 cm² g⁻¹ at near-IR; Birnstiel et al. 2018). With this value τ_ν is estimated as 3.75 and is enough for the optically thick disk.

With the temperature of 202.5 K, the disk aspect ratio (H/r_spiral) at the location of the spiral structure is estimated to be 0.15. Here, H = c_s/Ω_K is the disk scale height, where c_s and Ω_K are the sound speed and the Keplerian angular velocity, respectively.

We then investigate whether both of the results taken by Subaru/HiCIAO and Keck/NIRC2 can be reproduced by only scattering. As a rough estimate of the surface brightness of the scattered light, we use Equation (9) in Inoue et al. (2008), which is an approximate analytic expression of the scattered light (D'Alessio et al. 1999, 2006). With the modification for inclined disks (see also Jang-Condell & Turner 2013), the observable intensity is given by

$$\begin{eqnarray}&&{I}_{\nu }^{\mathrm{sca}}\simeq \beta {\omega }_{\nu }H(1,{\omega }_{\nu }){B}_{\nu }({T}_{\star })\displaystyle \frac{{{\rm{\Omega }}}_{\star }}{4\pi }\displaystyle \frac{1}{\sin \beta +\cos \eta },\end{eqnarray} \tag{ 2 }$$

where β, ω_ν, ${{\rm{\Omega }}}_{\star }=\pi \tfrac{{R}_{\star }^{2}}{{r}_{\mathrm{spiral}}^{2}}$, and T_⋆ are a grazing angle, albedo, a solid angle of the stellar photosphere from the spiral, and effective temperature of CQ Tau, respectively. η is defined as the sum of the inclination and $\arctan (\tfrac{{dH}(r)}{{dr}})\sim H/r$. $H(1,{\omega }_{\nu })$ represents the law of diffuse reflection (Chandrasekhar 1960) and ${B}_{\nu }({T}_{\star })$ is Planck's law. Here, we assume $H(1,{\omega }_{\nu })=1$ (single scattering) for simplicity.³²

To estimate the surface brightness of the scattered light from the spiral region, we used the disk and dust parameters estimated in Section 3.1. With this dust model, the albedo is about 0.4 at the H band. The grazing angle ($\beta ={dH}/{dr}-\arctan (H/r)=f\,\times \,H/r$, where f is a flaring index defined by $H(r)\propto {r}^{(1+f)}$) is assumed to be β ≲ H/r = 0.15 (f ≲ 1). R_⋆ was derived from the Stefan–Boltzmann law with T_⋆ = 6900 K and L_⋆ = 10L_⊙ (Testi et al. 2001; Ubeira Gabellini et al. 2019). We used 50 au as a typical value for r_spiral and i = 35° for the disk's inclination (Ubeira Gabellini et al. 2019). We finally assessed the expected scattered brightness as 62 and 8.5 mJy arcsec⁻² at the H and L' band, respectively. Note that we do not take into account of polarization degree in the H-band calculation. In the HiCIAO result, the spiral has a surface brightness of ∼30–40 mJy arcsec⁻² and does not show a large disagreement with the estimate. The NIRC2 result, however, is much brighter than the expected brightness in the L' band.

We note that CQ Tau has IR excess in its spectral energy distribution (Ubeira Gabellini et al. 2019). The inner disk with an effective temperature of ∼1000 K may behave as another source of heating and scattering mechanisms at the L' band. Assuming that the inner disk contributes as the light source of the scattering more than the central star by an order of magnitude, the expected L'-band brightness of the spiral is ∼90 mJy arcsec⁻² and is comparable to the NIRC2 result. Therefore, both thermal emission and scattering may equally contribute to the spiral feature at the L' band, if the disk is heated up to ∼200 K at ∼50 au and the inner part of the disk contributes as a light source of scattering. Detailed discussions using radiative transfer modeling will help to have better understandings of the spiral feature.

We have seen that the disk temperature at ∼50 au can be ∼200 K, indicating that the disk aspect ratio is ∼0.15. The pitch angle of the spiral feature (in radian) is comparable with the disk aspect ratio if the spiral feature is due to the spiral density wave in a differentially rotating disk (e.g., Rafikov 2002; Bae & Zhu 2018). However, the fitted pitch angle of the spiral from the r²-scaled HiCIAO image (34° ± 2°) is much larger than the expected H/r_spiral = 0.15. Tang et al. (2017) reported a large pitch angle in the AB Aur disk, which is similar to the CQ Tau case, and they predicted an unseen gaseous planet that coincides with the large pitch angle. As mentioned in Section 1, a high-mass planet can induce shocks and heat the spiral enough to be detected in the L' band (Lyra et al. 2016). The heating of the spiral arms driven by a massive companion may occur due to shock heating (≤15°–20°; Dong et al. 2015b; Zhu et al. 2015). In this sense the prediction of Ubeira Gabellini et al. (2019) of an unseen protoplanet is consistent with a heated spiral scenario.

Several other mechanisms can induce a large pitch angle: gravitational instability (≤15°–20°; Dong et al. 2015a) or shadow casting (≤20°–25°; Montesinos et al. 2016; Montesinos & Cuello 2018). Note that these studies, in many cases, assume a vertically isothermal disk temperature profile. Juhász & Rosotti (2018) performed another simulation by assuming that the disk surface is hotter than the midplane and showed that the spiral pitch angle near the surface can be more open compared to that at disk midplane. As we mentioned in Section 2.2, our fitted result of the pitch angle can be distorted by the inclination effect and we do not identify the mechanism to make a wide-open spiral. Combining gas observations of different emission lines enables to estimate the vertical temperature profile of the disk (Akiyama et al. 2011, 2013) and such future observations will help to understand the thermal structure of the spiral. Since the NIRC2 observation did not detect any companion candidates, follow-up observations to search for planets within 30 au are required to further investigate this scenario.