SPIRAL ARMS IN THE ASYMMETRICALLY ILLUMINATED DISK OF MWC 758 AND CONSTRAINTS ON GIANT PLANETS

MWC 758 was observed in the H-band (λ = 1.635^+0.155_{− 0.145} μm) using the high-contrast imaging instrument HiCIAO (Tamura et al. 2006; Hodapp et al. 2008; Suzuki et al. 2010) on the Subaru Telescope on 2011 December 24 UT as part of the Strategic Exploration of Exoplanets and Disks with Subaru (SEEDS) program (Tamura 2009). The AO 188 adaptive optics system (Minowa et al. 2010) provided a stable stellar point-spread function (PSF; FWHM = 007). We observed with a combined angular differential imaging (ADI; Marois et al. 2006) and polarization differential imaging (PDI) mode with a field of view of 10'' by 20'' and pixel scale of 9.5 mas pixel⁻¹. A 03 diameter circular occulting mask was used to suppress the bright stellar halo. Half-wave plates were placed at four angular positions from 0°, 45°, 225, and 675 in sequence with one 30 s exposure per wave plate position for a total of 15 data sets, and a total integration time for the polarized intensity (PI) image of 1440 s, after removing three low-quality images with FWHM > 01, by careful inspections of the stellar PSF. The field rotation in this data set was 9° on the sky, too small for ADI reduction of the data. While a PSF star was observed immediately following the PDI+ADI image set, the PSF had changed significantly from that observed during the observation of MWC 758, precluding conventional PSF subtraction. H-band photometry for MWC 758, taken with the telescope immediately before the PDI+ADI data set yielded H = 6.48 ± 0.01 mag in the MKO filter system. The polarimetric data were reduced using the procedure described in Hashimoto et al. (2011) using IRAF.⁴³

A second HiCIAO data set was obtained as part of the SEEDS program at K_s (λ = 2.150 ± 0.160 μm) on 2011 December 26 UT, with 17 minutes of integration time in ADI mode. The field of view for this data set was 20'' × 20''. The data were obtained in direct imaging mode, with no coronagraph, but with short 1.5 s frame times to minimize image saturation. Only the peak of the PSF of MWC 758 was saturated in the K_s data. The 1.5 s integrations were co-added into frames of typically 20 integrations, but after culling, some 10-integration frames were also included. After culling of bad frames, 640 s of integration time were available. The data were processed using variants of Locally Optimized Combination of Images (LOCI) in two ways: using aggressive LOCI (na = 300, nfwhm = 0.5) for a companion search and conservative LOCI (na = 10,000, nfwhm = 1.5) to search for structure in the disk. A discussion of these approaches is in Thalmann et al. (2010). Either LOCI variant suppresses azimuthally symmetric or large angle structure, resulting in voids compared to either the PI data or PSF-subtracted imagery.

MWC 758 and a PSF reference star (HD 242067) were imaged on 2011 November 10 with the Subaru Telescope using the Infrared Camera and Spectrograph (IRCS; Tokunaga et al. 1998) and AO188 in natural guide star mode as part of program S11B-012. The data were obtained in the Mauna Kea K' filter (λ = 2.12 μm). The native pixel scale is 20.57 mas pixel⁻¹; we used the 015 diameter coronagraphic mask to reduce light from the PSF core spilling out to angular separations of interest for disk detection. Despite variable weather conditions, AO-188 delivered corrected images with a full-width half-maximum of 007.

Our data consist of co-added 15 s exposures taken in ADI mode (Marois et al. 2006) through transit HA = (−0.6, 0.9) with a total field rotation of 127°. Our cumulative integration time for MWC 758 and HD 242067 is 38 minutes and 10 minutes, respectively. Basic image processing follows steps outlined in Currie et al. (2011a, 2011b) for IRCS, including dark subtraction, flat-fielding, and distortion correction (corrected pixel scale = 20.53 mas pixel⁻¹). We considered all HD 202067 frames to construct a reference PSF.

Disk Imaging. To extract a detection of the MWC 758 disk, we explored two approaches: one using PSF subtraction of MWC 758 frames by a median HD 242067 frame and one leveraging upon an "adaptive" LOCI approach (A-LOCI; Currie et al. 2012) for this subtraction. In both cases, we first identified the highest-quality images of MWC 758. Specifically, we monitored the brightness of a background star 2'' from MWC 758 (∼15 mag) and selected only the frames where the star's brightness is within 20% of the peak brightness of any frame. This selection criterion identified 50 MWC 758 frames (750 s total) to focus on for PSF subtraction. Further reduction steps are as follows.

• 1.  
  Classical PSF Subtraction. Here, we subtract the median-combined HD 242067 image from each MWC 758 image. We choose a weighting that minimizes the residuals between separations of 50 pixels and 150 pixels (∼1''–3''), though weightings over slightly different ranges in angular separations (i.e., 075–25) achieve similar results. We also performed a second subtraction weighting the reference PSF by an additional 10% above the value that minimized the residuals for each MWC 758 image. We then derotated and median-combined each PSF-subtracted MWC 758 image.
• 2.  
  A-LOCI. Here, we treat all HD 242067 images separately as a "reference PSF library." Instead of subtracting each reference image from the MWC 758 image at once, we follow the (A)-LOCI approach, subdividing each science image and reference image into annular sections (see Currie et al. 2012; Lafrenière et al. 2007) and determining coefficients for each reference PSF section that minimize the subtraction residuals within that section for a given science image. To better ensure that any "disk" signal is not instead due to PSF mismatch, we compute the cross-correlation function, r_corr, for each pair of science-reference images and remove poorly correlated image pairs (we find the best results for r_corr > 0.85). We set the optimization area (in units of the image FWHM) over which we define the coefficients to N_A = 3000 and adopt a radial width for the subtraction annulus of dr = 140, equal roughly to the angular extent of the disk as seen in the submillimeter (e.g., Andrews et al. 2011).⁴⁴

A-LOCI Limits on Planetary Companions. To search for companions to MWC 758, we employed much more aggressive PSF subtraction settings using A-LOCI on the full set of images (150 images; 37.5 minutes). We adopted A-LOCI settings of δ = 0.70, N_A = 250, dr = 5, and r_corr = 0.95 (see Currie et al. 2012; Lafrenière et al. 2007). Additionally, we employed a moving-pixel mask over the subtraction zone, using only the pixels outside of this zone to determine the LOCI coefficients to reconstruct a reference PSF annular region. We then quantify and correct for self-subtraction inherent in A-LOCI by comparing the flux of fake point sources prior to and after processing. We use the measured brightness of the star visible at 2'' (K' ∼ 16.93) and assume a brightness for MWC 758 of m(K') = 5.804 for flux calibration and thus to determine the planet-to-star contrast.

MWC 758 was observed in the broadband optical twice by HST/STIS on 2000 January 16 and January 19 as part of HST-GO-8474, with the star placed at a point along the STIS coronagraphic wedge structure (wedgeA1.0) where the wedge occulted the inner 05. The STIS data (observation IDs = O5KQ3010-20 and O5KQ0410-20) were a poor color match to the available library of PSF template data (Grady et al. 2005), yielding disk non-detections with large color mismatch errors. When roll-differenced (Lowrance et al. 2005), a null detection was also seen, indicating either nebulosity that was azimuthally symmetric over 15°, or concentrated within 05 of the star. The STIS data indicate only three point sources in the 25'' × 50'' field other than MWC 758, with the nearest at a separation of 21 at PA = 309°.

MWC 758 was also observed by HST/NICMOS as part of HST-GO-10177 on 2005 January 7. The observations consisted of two independent target acquisitions, short direct images in F171M, the coronagraphic observations at F110W (λ_cent = 1.1 ± 0.3 μm) with the region at r ⩽ 03 occulted, and short direct-light F110W imagery with the star unocculted before rolling HST by 299 and repeating the sequence. The direct-light imagery yielded F110W magnitudes of 7.314 ± 0.014 mag. The observations obtained at a given spacecraft orientation constitute a "visit." The coronagraphic data for each visit were reduced as described in Schneider et al. (2006), and then a suite of PSF template data from the same HST cycle were scaled, registered, and subtracted from the MWC 758 imagery. For the first visit for MWC 758 (visit 31), PSF template data from visits 3D (HD 15745, visit 2), visit 62 and 61(HD 83870), visit 53 (HD 35841 visit 1), visit 41 (HD 22128, visit 1), and 6B (HD 204366, visit 1) provided good color and HST residual matches to MWC 758. For the second visit (visit 32), data from visit 48 (HD 38207 visit 1), 4C (HD 30447, visit 1),4D and 4E (HD 72390, visit 1and 2), 42 (HD 22128 visit 2), 62 (HD 83870 visit 2), 65 and 66 (HD 164249, visits 1 and 2), and 6B (HD 204366, visit 1) provided the best matches. The use of independent target acquisitions and largely independent suites of PSF template data mean that medians of the net images for each visit provide two essentially independent observation sets for MWC 758. Both final images provide no indication of nebulosity for r ⩾ 08, with the bulk of the detected signal within 05 of MWC 758.

The angular scale of the nebulosity is too small compared with the NICMOS F110W resolution element to assess azimuthal symmetry. We have carried out aperture photometry between 03 < r < 05 for each of the final net visit images. The total brightness in those annuli in instrumental counts s⁻¹ pixel⁻¹ are 5183 for visit 31 and 5419 for visit 32, yielding only a ±2% peak to peak difference about a mean of 5301 counts s⁻¹ pixel⁻¹. Using the NICMOS photometric calibration of 1 counts s⁻¹ pixel⁻¹ = 1.26 × 10⁻⁶ Jy, the total F110W flux density in the measurement annulus is 6.7 mJy. The Two Micron All Sky Survey (2MASS) J magnitude for MWC 758 is 7.22 (2.07Jy), so the total 1.1 μm light scattered by this portion of the disk is 0.32%. The nearby point source noted in the 2000 STIS imagery is recovered at r = 2215, PA = 31086. It is not comoving with MWC 758, and thus is a background object.

NIR aperture photometry and polarimetry was carried out for MWC 758 on 2012 March 8 using SIRPOL (Kandori et al. 2006) at the IRSF. The SIRPOL observations were not accompanied by observation of a polarimetric standard star, so the 2MASS system was used to calibrate the NIR magnitudes of MWC 758 using field stars. We measured J = 7.193 mag, H = 6.560 mag, Ks = 5.804 mag with polarizations of 1.63% at J, 1.60% at H and 0.81% at Ks. The polarization levels are typical of low-inclination young stellar objects (Pereyra et al. 2009).

MWC 758 is a well-studied Herbig Ae star with data from the far-UV through the millimeter. We have assembled a composite SED including International Ultraviolet Explorer spectra SWP 53939 and LWP 30023, optical through M-band photometry (Malfait et al. 1998; Bogaert 1994; de Winter et al. 2001; Beskrovnaya et al. 1999), 2MASS, Midcourse Space Experiment, IRAS, and Infrared Space Observatory SWS data, two epochs of Broadband Array Spectrograph System spectrophotometry (Hackwell et al. 1990), Spitzer IRS data originally published by Juhász et al. (2010), AKARI, and the Wide-field Infrared Survey data (excepting band 2, 4.5 μm). We also include the HST/NICMOS F110W photometry as well as the photometry obtained in tandem with the HiCIAO PDI observation and the SIRPOL data. The data, color-coded by source, are shown in Figure 1, together with a Kurucz T = 8250 K photospheric model, reddened by an R = 3.1 extinction curve with E(B − V) = 0.13. A similarly good fit at short wavelengths can be achieved without foreground reddening and with T_eff = 7580 K, as used by Andrews et al. (2011). This model requires a contribution from UV excess emission (e.g., accretion luminosity) to match the observed FUV flux (Martin-Zaïdi et al. 2008), but is consistent with low line-of-sight extinction (E(B − V) ⩽ 0.1) for the source to be detected by FUSE.

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MWC 758 was observed on 2012 March 11 with VLT/NACO Sparse-Aperture Masking⁴⁵. Observations were taken in the L' band ($\lambda _{{L^{\prime }}}$ = 3.80 ± 0.31 μm) using the "7 holes" aperture mask and the IR wavefront sensor (WFS). A total of 24 data cubes, each one made of 330 frames of 0.12 s integration time were obtained for MWC 758 in L' on the night of 2012-03-12(UT). Observations of two calibrator stars, HR 1921 and HD 246369, were obtained for a total of eight data cubes, interleaved every eight MWC 758 data cubes. The MWC 758 observations were processed with the Observatoire de Paris SAMP pipelines (Lacour et al. 2011a, 2011b).

The use of the "7 holes" (C7-892, Tuthill et al. 2010) aperture mask transforms the telescope into a Fizeau interferometer. The point spread function is a complex superposition of fringes at given spatial frequencies. In specific cases, pupil-masking can outperform more traditional differential imaging for a number of reasons (Tuthill et al. 2006; Lacour et al. 2011b). First, the masks are designed to have non-redundant array configurations that permit phase deconvolution; slowly moving optical aberrations not corrected by the AO can be accurately calibrated. Second, the mask primarily rejects baselines with low spatial frequency and passes proportionately far more baselines with higher λ/B (where B is baseline length) resolution than does an orthodox fully filled pupil. Third, high-fidelity recovery of phase information allows "super resolution," with a marginal loss of dynamic range up to λ/2D (where D is the mirror diameter). The principal drawback is a loss in throughput so that photon and detector noise can affect the signal-to-noise ratio even where targets are reasonably bright for the AO system. The effective field-of-view of sparse aperature masking (SAM) is determined by the shortest baseline so that the technique is not competitive at separations that are greater than several times the formal diffraction limit. For more details on the SAM mode, see, e.g., Lacour et al. 2011a; Tuthill et al. 2010.

Previous studies of MWC 758 had identified this system as hosting a cavity visible in submillimeter continuum interferometry, but lacking a very conspicuous dip in the IR SED near 10 μm (Isella et al. 2010; Andrews et al. 2011). In contrast, our composite SED based on an assembly of archival photometry and spectrophotometry clearly shows a dip (Figure 1), with indications of mid-IR variability, providing the first independent confirmation that MWC 758 is what has been termed a gapped or "pre-transitional" disk with an inner disk structure (Isella et al. 2008), a wide gap, and an outer disk seen in millimeter data (Isella et al. 2010), and thermal emission (Mariñas et al. 2011). When compared with other transitional disks, the depth of the 10 μm dip is smaller, consistent with the lack of a cavity in our F110W, H, K', and K_s imagery. Modeling of other disks with HiCIAO observations have suggested that the absence of a cavity at H is not atypical of transitional disks, and can be accounted for by grain filtration (Rice et al. 2006), with large mm-sized grains deeply depleted in the cavity region, while smaller grains, which are more tightly coupled to the gas, are less depleted (Dong et al. 2012; Zhu et al. 2012).

The disk of MWC 758 is detected in polarized, scattered light from 02 to 08 (223 AU assuming d = 279 pc or 160 AU assuming d = 200 pc) in polarized intensity at H-band (Figure 2). The disk detection did not require unusually favorable conditions (e.g., MWC 480; Kusakabe et al. 2012): H-band photometry was in the range of previous NIR data for the star (Figure 1). The detected nebulosity is highly asymmetric about the star, with the greatest extent seen to the west of the star at H, while to the east, nebulosity is not detected exterior to 05. To the west of the star, the scattered light disk extends as far as the submillimeter continuum can be traced (Isella et al. 2010; Figures 2(a) and (b)). The disk is also detected at K_s (Figure 2(c)) to within 01 of the star, and in K' (Figure 2(d)) to within 025, and at 1.1 μm (Figure 2(e)). A false-color composite of the H PI (blue) and K' (red) is shown in Figure 2(f). This composite image also allows us to identify a region of reduced polarization intensity along PA = 155° ± 5° and PA = 330° ± 5°, aligned with the projection of the disk semiminor axis. To the east of the star, the H PI surface brightness ∝R^{−5.7 ± 0.1} (Figure 3). To the west of the star, it drops as ∝R^{−2.8 ± 0.1}, consistent with the disk exhibiting some flaring.

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Unlike other protoplanetary (Kusakabe et al. 2012) or transitional disks (Muto et al. 2012) imaged with HiCIAO in H PI, the reflection nebulosity is not aligned with the disk semimajor axis (PA = 65 ± 7°). Moreover, we detect scattered light within the region of partial clearing reported in the submillimeter continuum (Isella et al. 2010), rather than the expected cavity. The PI for r ⩾ 02 is 6.095 ± 0.085 mJy, or 0.09% relative to the star. Between 03 and 05 the PI is 2.72 mJy, or 0.0425% relative to the star, indicating that the region of the arms is providing half of the observed polarized intensity. If we assume neutral scattering, the PI in the arm region 03 ⩽ r ⩽ 05 can be compared with the F110W total intensity of 0.32%, indicating a polarized light fraction of ∼13.3% which is in the range of polarization fractions observed for other Herbig Ae stars.

Given the structure seen in the H-band PI imagery, it is natural to explore what we would have expected to have seen based on combined modeling of the submillimeter data and the IR SED. To address this goal, we carried out Monte Carlo radiative transfer modeling using the code developed by Whitney et al. (2003a, 2003b; B. A. Whitney et al. 2013, in preparation), with modifications as described in Dong et al. (2012). In particular, we adopt a disk outer radius of 200 AU, viewed at i = 23°, and assume an accretion rate of $\dot{M}=10^{-8}\,M_\odot$ yr⁻¹ (Andrews et al. 2011). We model the entire disk with two components: a thick disk with small grains (∼μm-sized and smaller), which represents the pristine dust grains from the star forming environment, and a thin disk with large grains (up to ∼mm-sized), which is the result of dust growth and settling toward the disk mid plane. We adopt the interstellar medium dust model in Kim et al. (1994) for our small-grain dust, and the dust model 2 from Wood et al. (2002) for our large-grain dust, which has a power law size distribution up to 1 mm (with power law index 3.5). The large-to-small-dust mass ratio is assumed to be 0.85/0.15 as in Dong et al. (2012). The properties of the grains can be found in Wood et al. (2002).

With these assumptions, the total dust mass of the disk is 0.067 M_J. The radial surface density distribution of both dust grain populations is assumed to have the following profile

$$\begin{equation} \Sigma (R)=\Sigma _{\rm 0}\left(\frac{\rm 1\, AU}{R}\right)^\alpha, \end{equation} \tag{ 1 }$$

where Σ₀ is the normalization factor, R is radius, and α is the power law index. In the vertical direction, we assume

$$\begin{equation} \rho (R,z)=\frac{\Sigma (R)}{\sqrt{2\pi }H} e^{-z^2/2H^2}, \end{equation} \tag{ 2 }$$

where ρ(R, z) is the local volume density, z is the vertical dimension, and H is the scale height (input parameters in the code). Radially, both scale heights for the small and large dust vary with radius as

$$\begin{equation} H\propto R^\beta, \end{equation} \tag{ 3 }$$

where β is a constant power law index, assumed to be 1.08 in this work. The scale height, h, of the small dust is assumed to be 15 AU at 100 AU, while that for the large dust is assumed to be 1/5 of the h for the small dust, to reflect the fact that big grains tend to settle to the disk mid-plane, while small grains tend to be well coupled with the gas and have a much larger vertical extension (Dullemond & Dominik 2004, 2005; D'Alessio et al. 2006).

Our disk model has a gap structure located from 0.5 AU to 73 AU. Inside the gap there are no large dust grains, as suggested by the spatially resolved submillimeter array observations, which revealed a clear cavity 73 AU in radius at 880 μm (Andrews et al. 2011). However, the H-band PI data demonstrate that there is a significant amount of scattered light within this radius, indicating the presence of starlight-scattering small dust grains. We set α = 1 for both dust populations in the outer disk, and α = −3 for the small dust inside the gap, with a continuous surface density distribution across the gap edge. As discussed in detail in Dong et al. (2012), this kind of surface density distribution of the small dust results in a heavy depletion at the inner disk, producing the IR excess depression around 10 μm on the SED seen in transitional disks, but a smooth NIR scattered light image with no breaks or discontinuities of the surface brightness radial profile at the inner edge of the outer disk. MWC 758 has an NIR excess (Figure 1), and VLTI/AMBER data (Isella et al. 2008) indicating a small amount of hot, small dust grains at the innermost radii. To reproduce these features, we put a inner rim located at 0.33–0.5 AU. The surface density of the rim is ∼0.002 g cm⁻².

Figure 4 shows the model SED and H-band polarized light image from the modeling, with the disk major axis horizontal, and the near side of the disk in the bottom half of the image. The model images show both the PI as modeled, and after convolution with an observed HiCIAO PSF (see Dong et al. 2012 for details). The model reproduces the extent of the polarized intensity to the west of the star, but, as expected, predicts a similar extent of the scattered-light disk to the east of the star, beyond 05. The model predicts a bright arc on the near-side of the image, which is not seen in the data. The raw model imagery predicts a cavity visible at H in the immediate vicinity of the star, which is not conspicuous after convolution with the PSF, and which is in the region occulted by the coronagraph in our H-band data. Higher Strehl ratio and smaller inner working angle imagery, such as can be provided by extreme AO systems, will be required to test these predictions of the model.

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The most distinctive features in the NIR images that are not captured in the model imagery are a spiral feature on the east side of the star, wrapping toward the south, which we term the southeast (SE) arm, and a similar feature originating in the NW and wrapping to the north, which we term the northwest (NW) arm. The spiral arms are most clearly detected interior to 05 (100 AU for d = 200 pc, or 140 AU for d = 279 pc). Our data for MWC 758 therefore demonstrate that SAO 206462 (Muto et al. 2012) is not unique in hosting spiral arms straddling the region of the partially cleared millimeter cavity. Moreover, like SAO 206462, and unlike HD 142527 (Casassus et al. 2012; Rameau et al. 2012) there is no indication of a cleared zone at H-band for r ⩾ 02 (40 AU for d = 200 pc, 56 AU for d = 279 AU).

The spiral arms in the disk of MWC 758 are detected as a contrast in surface brightness. The drop in polarized surface brightness immediately exterior to the SE arm is consistent with that arm fully shadowing the outer disk. Shadowing by the NW arm is less complete: Some signal is seen beyond the arm in our 2011 data. We measure the SB contrast of the arm features by measuring the amplitude at the SE arm at PA = 90° and the corresponding surface brightness the same distance from the star at PA = 270°. For the SE arm we find a ratio of 50% ± 20%. The angular extent of the NW arm is sufficiently small that to confidently measure the amplitude and fit the pattern we will require data obtained with a combination of higher Strehl ratio, and a coronagraph with smaller inner working angle, such as may be provided by SCExAO in tandem with AO188+HiCIAO on Subaru (Martinache et al. 2011, 2012). We therefore restrict all but qualitative discussion of the arms to the SE arm.

Both of the arms have the same rotation sense. If they are trailing structures, as expected for spiral density waves, the rotation of the disk, and any companions associated with the arms, is clockwise. Comparison with the millimeter data (Isella et al. 2010), then indicates that the northwest side of the disk is the near side of the disk. Our PI image is fully consistent with the disk being viewed at a low inclination from face-on, since it lacks the compression of the PI toward the disk semimajor axis, which is conspicuous at i ⩾ 38° (Kusakabe et al. 2012). Given the asymmetric illumination of the disk, we adopt the millimeter disk inclination i = 21 ± 2° (Isella et al. 2010).

To be correctly interpreted as spiral density waves, the spiral arms should be recovered in observations made at different wavelengths and with different instruments. The IRCS K' data detect the disk in scattered light to at least 05 from the star, and recover both spiral arms using either classical PSF subtraction and using A-LOCI as long as we set dr to be larger than the size of the disk gap (dr > 25). The K_s data sample the disk less completely, due to the very short integration times for each individual exposure. However, they recover the inner portions of the arms, in the conservative LOCI processing of the data, to an inner working angle of 01 but suppress them in aggressive LOCI processing.

The brightest portion of the disk as seen at 1.1 μm is the region occupied by the spiral arms, between 03 and 05. The HST/NICMOS data from 2005 provide no indication of the asymmetric illumination seen in the 2011 data: This may either be due to changes in illumination over time, or to contrast limits of the HST/NICMOS data. However, we note that asymmetric illumination of the disk was not seen in the HST/STIS data from 2000. Additional observations will be required to establish whether the illumination of the outer disk changes with time. The locations of the arms coincide with the brightest 12 μm signal from the MWC 758 disk (Mariñas et al. 2011). The coincidence of structural features in scattered light, polarized scattered light, and in thermal emission indicate that the spiral arms are density features, and not merely distortions of the disk surface. The rapid drop in surface brightness seen in the H-band PI data to the east of the spiral arms (Figure 3) further indicates that the arm is optically thick and extends sufficiently far above the undistorted disk surface to cast a long shadow. The region of the NW arm near PA = 340° coincides with the clump in continuum emission noted by Isella et al. (2010), although with a synthesized beam size of 076 × 056, the available submillimeter continuum interferometry lacks the angular resolution to directly detect the arms. As the angular resolution of submillimeter interferometry improves, we expect that these features should be detectable in continuum and gas observations, such as can be provided once ALMA reaches its full extent.

We follow the approach given in Muto et al. (2012) to fit the spiral arms. Our initial fits have been restricted to the H-band PI data. Given the nearly face-on system inclination, we have not de-projected the data to compensate for the non-zero inclination, but have compensated for the r⁻² drop in illumination of the disk (Figure 5). From the data, we have looked for the local maxima of the surface brightness × r² profile for each radial profile both for the SE spiral and the NW spiral. If the features are a part of a ring, the points would lie horizontally in a polar coordinate plot of the intensity. The SE spiral is clearly non-axisymmetric, but only a small angular extent of the NW arm is non-axisymmetric, given the inner working angle of our data. For the remainder of this study we restrict our attention to the SE spiral.

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Assuming i = 21° and PA = 65° for the disk major axis, the fitting function for the spiral is

$$\begin{eqnarray} \theta (r) &=& \theta _0 + {\displaystyle \frac{\mathrm{sgn}(r-r_{\rm c})}{h_{\rm c}}} \nonumber \\ && \times \bigg[ \left({\displaystyle \frac{r}{r_{\rm c}}} \right)^{1+\delta } \left\lbrace {\displaystyle \frac{1}{1+\delta }} - {\displaystyle \frac{1}{1-\gamma +\delta }} \left({\displaystyle \frac{r}{r_{\rm c}}} \right)^{-\gamma } \right\rbrace \nonumber \\ && - \left({\displaystyle \frac{1}{1+\delta }} - {\displaystyle \frac{1}{1-\gamma +\delta }} \right) \bigg]. \end{eqnarray} \tag{ 4 }$$

Here, as in SAO 206462 paper, The corotation point (∼launching point of the spiral) is at (r_c, θ₀). The disk rotation profile is Ω(r)∝r^−γ and the disk sound speed profile is c(r)∝r^−δ. The disk aspect ratio (H/R) at the corotation radius is h_c. Note that assuming H = c/Ω, β that appears in Equation (3) is related to γ and δ by β = γ − δ. We also note that if the disk temperature varies as T∝r^−q, q and δ are related by δ = q/2 since temperature is proportional to the square of the sound speed and the disk sound speed profile is c(r)∝r^−δ.

Note that the sign after the first θ₀ in the right hand side of Equation (4) is different from that in Muto et al. (2012), due to the counter clockwise rotation of the SAO 206462 disk.

There are five fitting parameters: (r_c, θ₀, h_c, γ, δ). Among them, three (h_c, γ, δ) are determined by the disk structure and the two (r_c, θ₀) determine the location of the spiral feature. Assuming Keplerian rotation, γ = 1.5. In our study of SAO 206462 (Muto et al. 2012), the sound speed profile δ was fixed, but we have varied this parameter as well. There is a range of values related to δ in the literature, ranging between 0.45 (the ψ parameter in Andrews et al. 2011), 0.19 (q in Chapillon et al. 2008), and 0.05 (the ζ parameter in Isella et al. 2010). We note that for δ = 0.5, the opening angle of the disk is almost constant, in disagreement with our radial SB profile. We looked for the best-fit parameters in the least χ² sense by dividing the (r_c, θ₀) space in 128 × 128 cells and (h_c, δ) space in 100 × 100 cells with equal spacing in the linear scale. The parameter space explored, and best-fit parameters, are shown in Table 1. Our value for h_c is similar to that derived by Andrews et al. (2011). The external perturber fit resulted in a reduced χ² of 0.68.

Table 1. Spiral Arm Fitting

Parameter	Search Range	Best-fit External Perturber
rc	005 ⩽ rc ⩽ 155	rc = 155
θ	0 ⩽ θ0 ⩽ 2π	θ0 = 1.72[rad] a
hc	0.05 ⩽ hc ⩽ 0.25	hc = 0.182
δ	−0.1 ⩽ δ ⩽ 0.6	δ = 0.6

Note. ^aMeasured from PA = 90°.

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Now we consider the degeneracy of the parameter space. The degeneracy of parameters of the spiral position (r_c, θ₀) and those of the disk parameter (h_c, δ) are investigated separately. The left panel of Figure 6 shows the degeneracy of (r_c, θ₀). The best fit to the SE spiral arm places the launching point of the spiral outside of both where we detect the spiral arm, and at a radius exterior to the dust disk as seen in the submillimeter. It might worth pointing out that there is a range of parameters where the corotation radius r_c is inside the spiral arms and where the values of δχ² becomes small, although these parameters are outside the range of 99% confidence.

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In the right panel of Figure 6, we show the degeneracy in the (h_c, δ) parameter space. For each fixed values of (h_c, δ), we looked for the set of (r_c, θ₀), which gives the minimum δχ² value. Note that δ = 0 is a constant temperature, flared disk and δ = 0.5 is the constant opening angle disk. Although the degeneracy is significant, we favor a disk with a rather flat, constant opening angle geometry. In this case, the spiral can cast a long shadow over the outer disk rather easily, if the spiral has sufficient amplitude, as is observed in the H-band PI imagery. We also note that the parameters for a warmer disk (h_c ⩾ 0.1) are favored.

If we assume that a perturbing body excites the spiral arm, the mass of the perturber launching the spiral density waves can be estimated independent of knowledge of where it might be located, if there are data indicating the relative disk scale height (h_c), the mass of the star, and the amplitude of the spiral pattern as follows:

$$\begin{equation*} {M_p/M_*} = {\rm (Pattern\; Amplitude)}\, {(h_{\rm c})^{3}}. \end{equation*}$$

Adopting 1.8 ± 0.2 M_☉ for the stellar mass, h_c = 0.18 from the pattern fitting for the SE spiral, and a pattern amplitude of 0.5 ± 0.2 from the surface brightness contrast for the SE arm, we find a perturber mass for the SE pattern of ∼5⁺³_{− 4} M_J, consistent with the perturber being a giant planet, but excluding stellar or brown dwarf mass objects. This mass estimate is also consistent with accretion continuing onto the star.

The 5σ contrast map from our SAM NACO observations is presented in Figure 7(a). At L' band, SAM is sensitive to companions at separations ⩽300 mas from the primary. Attained contrasts range from Δmag(L) = −4 to Δmag(L) = −8. Contrasts were converted to minimum detectable companion mass using the models of Baraffe et al. (1998, 2002), and adopting an age of 3.7 Myr and a distance of 279 pc. Similar limits are achieved for 5 Myr and a distance of 200 pc. With these assumptions, minimum detectable mass images are shown in Figure 7(b). Our SAM observations are sensitive down to very low mass stellar companions (∼80 M_J): we conclude that MWC 758 is a single star. Thus, our limits for companions within the region occulted in the HiCIAO H-band PI data are at the low end of the stellar/high end of the brown dwarf range.

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Figure 8(a) shows S/N maps for the K_s and K' data sets. Within 3'' of the star, the only point-source object is the K = 16.98 mag background star, which was detected at 37σ at K_s. K-band 5σ contrast limits for the K_s data (from 01–025) and the K' data (r ⩾ 025) are shown in Figure 9. The deepest imagery in our set of observations is the IRCS K' data which provide 5σ contrasts of 1.4 × 10⁻⁴ at 025, 2.1 × 10⁻⁵ at 05, 3.3 × 10⁻⁶ at 1'', and 1.12 × 10⁻⁶ at 155 (see Figure 8).

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Adopting an age of 5 Myr and the COND models (Baraffe et al. 2003), these contrasts correspond to 5 σ detection limits of 15–20 M_J at 025, 8–10 M_J at 05, and 3–4 M_J at 1'', and near 2 M_J at 155 for distances of 200 and 279 pc respectively. These data exclude brown dwarf-mass companions exterior to 05 and are in general agreement with the mass estimates based on the spiral arm fitting. Interior to 05, our upper limits are consistent with at most low-mass brown dwarf close companions to MWC 758. Our mass limits are consistent with accretion continuing onto the star, as observed, and as predicted for disks with Jovian-mass companions (Rice et al. 2006; Lubow & D'Angelo 2006).