The Shadow Knows: Using Shadows to Investigate the Structure of the Pretransitional Disk of HD 100453

The source HD 100453 was observed with GPI on 2015 April 10–11 UT using polarimetric differential imaging mode in J, Y, and K1 bands. GPI's "direct" mode uses polarization to suppress stellar light, but not a coronagraphic mask, thereby sacrificing contrast in favor of a tighter inner working angle. We used the shortest exposure time (1.49 s) to minimize saturation and coadded 10 frames to increase the signal-to-noise ratio. The half-wave plate angle was rotated from 0° to 675 with 225 steps to obtain linear polarization. This sequence was repeated 41, 35, and 36 times, resulting in total exposure time of 41, 35, and 36 minutes for Y, J, and K1 bands, respectively. The averaged airmass values were 1.21 and 1.19 in the J and K1 bands, respectively.

The data were reduced using the standard polarized data reduction recipe available in GPI pipeline (Maire et al. 2010; Perrin et al. 2014) v. 1.3, with notable customizations. First, microphonics noise was minimized by eye through tuning parameters in the "destripe science image" primitive. Second, the "subtract mean stellar polarization" primitive was added to the standard polarization recipe to remove instrumental polarization (estimated in the region 1 < r < 10 pixels, which shows no significant disk emission). Finally, a custom pipeline fix was implemented to allow image alignment in unblocked mode. GPI image alignment typically relies on well-calibrated satellite spots injected by the GPI apodizers that are not present in unblocked mode, therefore a Gaussian stellar centroid was used instead. Although this alignment method is imperfect due to stellar saturation, it worked well in this case. The resulting images were transformed to "radial" Stokes parameters (Schmid et al. 2006). Images used here represent the Q_R component, which holds all linear polarized flux oriented either parallel (negative) or perpendicular (positive) to the line connecting that pixel to the central star. Positive flux in these images therefore represents singly scattered photons from the circumstellar disk.

The system HIP 56071 was observed as a flux standard, with the same procedures, except without closing the AO loop, thereby avoiding saturation. This allowed us to derive conversion factors between ADU s⁻¹ pixel⁻¹ and mJy asec⁻². Since the K1-band magnitude in HIP 56071 was unavailable, we translated the 2MASS K_s-band magnitude into this band by relating the stellar flux to the Vega flux assuming box passbands in two bands (the GPI K1 band with 1.9–2.19 μm and the 2MASS K_s band with 1.989–2.316 μm) and blackbody radiation with a T_eff of 9200 K for HIP 56071 (A1V) and 9700 K for Vega (A0V). The color correction of ${K}_{{\rm{s}}2\mathrm{MASS}}\mbox{--}K{1}_{\mathrm{GPI}}$ was −0.002; thus, we derived that the K1_GPI magnitude of HIP 56071 is 7.860. We derived that the conversion factors of 1 ADU s⁻¹ pixel⁻¹ are 0.846 and 0.853 mJy asec⁻² in the J and K1 bands, respectively. Note that Y-band flux was not converted into mJy asec⁻² because no literature value for the Y band is available.

We find the projected separation between the image center and the companion to be 105, in agreement with Chen et al. (2006). The region within ∼4 pixels (corresponding to ∼006) from the central star is saturated. We conservatively estimate the features outside 6–7 pixels from the center to be real, while the area interior to this radius is washed out by speckle residuals. We detect the outer disk and spirals, as in Wagner et al. (2015). The total PI within 01 < r < 10 (the inner radius corresponds to 7 pixels) is 13 and 22 mJy for J and K1 bands, respectively.

Wagner et al. (2015) also observed HD 100453 with VLT/SPHERE on 2015 April 10. The observations were carried out in IRDIFS extended mode¹⁹ (Girard et al. 2016) using IRDIS to take dual-band TI images in K1 and K2 bands and simultaneously using the IFS to obtain low-resolution spectra from Y to H bands. Data reduction is described in Wagner et al. (2015). Photometry used in constructing the SED of HD 100453 includes all sources mentioned in Khalafinejad et al. (2016) as well as Herschel PACS data at 70, 100, and 160 μm (Pascual et al. 2015), and 2MASS at J, H, and Ks bands (Cutri et al. 2003).

A radial gap can clearly be seen from 9 ± 2 au, to 18 ± 2 au in the GPI imagery (Figure 1). Inside 9 au the GPI image is saturated, making the inner edge of the gap inaccessible in the image. The outer radius agrees with the Wagner et al. (2015) estimate of ∼19 au using d = 103 ± 3 pc (Gaia Collaboration 2016), and the Khalafinejad et al. (2016) estimate of 20 ± 2 au from SED modeling. We measure a pericenter offset upper limit of 1 ± 1 pixels (0014 ± 0014) (Figure 1).

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The outer disk is brightest on the southern side in both PI and TI imagery, implying that this is the near side of the disk. However, the northern spiral arm is brighter in PI images while the southern arm is brighter in TI images, indicating possible differences in grain properties. Additionally, there is a dropoff in the spiral arm intensity at longer wavelengths in SPHERE TI images, which suggests that they are made of smaller grains than the outer disk. After absolute flux calibration of the TI images using archival 2MASS photometry (Cutri et al. 2003), we measure the total TI flux between 01 < r < 10 is 49 mJy and 70 mJy in J and H bands, respectively. Using this and the 2MASS flux, we calculate a fractional luminosity for the outer disk $\tfrac{f\mathrm{disk}}{f\mathrm{total}}$ of 0.018 ± 0.001 for J band and 0.025 ± 0.002 for H band, which may suggest that the outer disk is reddish and therefore comprised of large compact grains (Mulders et al. 2013). By contrast, we calculate a fractional luminosity for the spiral arms of 0.0040 ± 0.001 for J band and 0.0045 ± 0.001 for H band, which, although slightly red, is more blue than the rest of the outer disk. This indicates that they may be comprised of smaller grains (Mulders et al. 2013).

Two distinct azimuthally localized dark features are seen at the same position angle (PA) in both TI and PI images, and they are therefore not artifacts of PI imagery. They also have a similar contrast of outer disk to feature in all available bands (Figure 1).

We discuss three possible physical scenarios for the origin of the dark features: a physical gap due to the dynamical clearing of a large body, grain growth and settling, or shadows cast from an inner-disk component.

The SPHERE Y band point-spread funciton (PSF) for HD 100453A has a FWHM of 5 pixels (3.8 au). This suggests that the dark features are resolved and have an azimuthal extent of 14 ± 2 pixels (10 ± 1.5 au) based on the FWHM of the eastern feature in this image. If the dark feature is due to the clearing of a single body's Hill sphere (Hamilton & Burns 1992), it would correspond to an M-type star with a mass of at least 0.4 M_⊙. The M-type companion, HD 100453B, is visible in SPHERE, GPI, and Chandra (Collins et al. 2009) imagery. An M-type star with a mass of 0.4 M_⊙ therefore would certainly be visible in the location of the dark features if it existed. Thus, we reject the hypothesis of local clearing to explain the dark features.

Grain growth and settling has been suggested as a source of dark regions at near-IR (NIR) wavelengths (Dullemond & Dominik 2004a, 2004b; Birnstiel et al. 2012) and should also produce bright rings in the submillimeter. This would require a resolution of at least 003, which is reachable by interferometric telescopes such as ALMA. The differential rotation of the disk would cause the dark features to deform over time, however, which suggests that grain growth and settling is not the cause of the features.

An inner disk would cast two shadows that have a large radial extent and have a similar contrast of the outer disk to the shadow over the wavelength range in which it is optically thick (Stolker et al. 2016), similar to what is seen in the GPI and SPHERE images. We show that shadows cast by an inner disk with a suitable inclination are fully capable of producing such dark features. In the following sections we present a model that is capable of generating the dark features as well as reproducing the observed SED.

3.3.1. Literature Values for the Outer-disk Inclination

3.3.2. Initial Modeling Parameters

In order to reduce the degeneracies in our model, literature values, SPHERE and GPI imagery, and the SED (Figure 2) are used in combination to determine the initial modeling parameters. For the star we used a PHOENIX stellar atmosphere model (Brott & Hauschildt 2005) with T = 7400 K (appropriate for an A9 star) and a distance of 103 pc (Gaia Collaboration 2016). HOCHUNK3D uses the Lucy (1999) method for calculating temperature in our model. Box filters were created in Y-K2 to allow for a direct comparison of the model to data.

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Through SED fitting, Khalafinejad et al. (2016) suggested that the inner disk extends from 0.25 to 1.7 au. Confirmation of the inner edge radius is provided by H-band interferometry with VLTI/PIONIER (Lazareff et al. 2017), which find an upper limit of 0.27 au. The inner disk extends to at least 0.9 ± 0.1 au from the N-band half-light radius of VLTI/MIDI (Menu et al. 2015), updated using d = 103 ± 3 pc (Gaia Collaboration 2016). The long-wavelength slope obtained from the 1.2 mm SIMBA point (Meeus et al. 2002b), the reddish color of the outer disk (Section 3.1), and the lack of a strong silicate peak in the SED (Meeus et al. 2002a) imply that the inner and outer disks are comprised of large compact dust grains (Mulders et al. 2013).

To match these dust properties, we used Model 2 from Wood et al. (2002) for the settled disk grain opacities. This contains a mixture of amorphous carbon and astronomical silicates, a radial power-law exponent (a) of 3.5 for both grain compositions, no exponential cutoff to the grain size distribution, a maximum particle size ≤1 mm, and a minimum particle size of 0.01 μm. For the less-settled grain opacities we used Model 1 from Wood et al. (2002). Similarly, this contains a mixture of amorphous carbon and astronomical silicates, a power-law size distribution with a = 3.5 and 3.0, respectively, plus an exponential cutoff with a turnover at 50 μm, a maximum particle size ≤1 mm, and a minimum particle size of 0.01 μm.

3.3.3. Inclination of the Outer Disk

After initial modeling of the outer disk, we constructed a more complete disk model to fit the SED (Figure 2). We find that our model closely matches the observed SED, including the NIR region, which was ignored by Bensity et al. (2017), to be discussed later. It consists of an inner disk (∼0.13–1 ± 0.5 au), which reproduces the IR excess of the SED and is in agreement with VLTI/MIDI measurements of 0.9 ± 0.1 au. This is followed by a depleted region to 18 au, and finally, by an outer disk (18–39 au). The inner disk has a vertical inner-edge thickness of 0.11 ± 0.05 au as defined by z = Cr^b, where z is the density scale height (thickness) of the disk, C is a constant, r is the radial distance from the star, and b is the flaring exponent (Whitney et al. 2003). To match mid- to far-IR emission, we find b = 1.28 ± 0.02, which falls within the canonical values of 1.25–1.3 for irradiated disks (Chiang & Goldreich 1997; Hartmann et al. 1998). Changes in the settled disk have little effect on the SED and were not changed appreciably in our modeling. Our final parameters for the settled disk were z = 0.0004 au and b = 1.25. Both the vertical density and the surface density profile are as described in Whitney et al. (2013) for a disk in hydrostatic equilibrium. In particular, we chose density exponents α = 2.30 and α = 2.25 for the less settled and the settled disks, respectively.

3.5.1. Definition of ${\rm{\Delta }}i$

In this section we test the validity of a difference in inclination between the inner and outer disk as the cause of the dark features. We define this difference in inclination as ${\rm{\Delta }}i=i-\beta$, where i is the inclination of the outer disk from face on and β is the inclination of the inner disk from face on. While we define i as positive, β can be positive or negative, depending on the direction of tilt of the inner disk (Figure 3).

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3.5.2. Azimuthal Separation of Dark Features and Comparisonto Model

Model images were produced with the adopted i = 25°, while Δi was varied in 10° increments from 0° to 70° (Figure 4). These were convolved with the PSF of SPHERE J-band images and therefore produced clearer shadows than longer wavelength bands. No azimuthally localized dark features were observed in model images with Δi = 0° despite a good fit to the SED, excluding a coplanar disk system. At Δi = 20°, the inner-disk shadows the northern section of the image and predicts too much flux between 1 and 10 μm because of its nearly face-on orientation with respect to the observer (Figure 4). Moving to Δi = 70°, the shadows narrow and predict too little flux between 1 and 10 μm because the inner disk is nearly edge-on to the observer. We find that Δi = 45° ± 10° matches the general appearance of the imagery, to be quantified below.

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Azimuthal intensity profiles of the GPI images and model imagery were generated for the outer disk (Figure 5) and measure an azimuthal separation of 140° ± 10° for the dark features, which are in the same locations in each band. The additional local minimum in intensity profile plots is due to polarization effects along the minor axis of the outer disk. We find that as Δi is increased, the shadow separation also increases and produces a best fit to the dark features at Δi = 45° ± 10°, which corresponds to β = −20° ± 10°. This deduced inner-disk inclination angle is significantly different from the angle found in Lazareff et al. (2017), β = −48°, using H-band interferometry with VLTI/PIONIER. The main source of uncertainty in our measurement comes from the azimuthal extent of the shadowed region. To match the dark features' azimuthal location, we rotated the inner disk by −40° with respect to the outer disk, which places the major axis of the inner disk at 100° ± 10° east of north. This differs from the PA for the major axis found in Lazareff et al. (2017), 81°, and is discussed later.

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A recent study by Bensity et al. (2017) also proposed a misaligned inner disk as the cause of the outer disk shadowing in HD 100453. The authors generate a model to test this hypothesis using measurements from Lazareff et al. (2017). In order to test the validity of their model, we generated our own using their value for the outer-disk inclination, i = 38°, and their quoted Δi of 72°. This model does not produce shadows in the same locations as in the data (Figure 6), however, similar to what was found earlier in this section.

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In our modeling we find that the inclination of the outer disk had little effect on the separation of the shadows on its own, unless the near side of the outer disk is reversed. We also find that the separation of the shadows is smaller than 180° on the side of the outer disk, which corresponds to the near side of the inner disk. Essentially, the inner-disk major axis divides the outer disk into two semicircles. The 180° constraint implies that the centers of the shadows cannot exist in separate semicircles, and this strongly constrains the orientation of the inner disk. In Figure 6 we see that the quoted orientation of the inner-disk major axis places the shadows in separate semicircles in the GPI image, which cannot occur if the inner disk is the source of the shadows. In addition, the gap has a visibly more strongly elliptical structure in the Bensity et al. (2017) model than in the data, which is most likely due to the thickness of the outer disk, as discussed in Section 3.4, as well as to the larger inclination of the outer disk. It is important to note that this Δi corresponds to β = −34° instead of the inner-disk inclination proposed separately in Bensity et al. (2017) of β = −48°. Additionally, in our modeling we find that the NIR region of the SED is fairly sensitive to the inclination of the inner disk (Figure 4). Because Bensity et al. (2017) did not fit the NIR excess of the SED, the Bensity et al. (2017) model is not as tightly constrained as our simultaneous image and SED fitting. We found the inclination of the inner disk proposed by Benisty et al. (2017) did not produce a good match to the 1–10 micron SED nor the constraints on the shadows that we found (Figure 7). Differences in the inner disk orientation which produce shadows along an axis other than the major axis may be possible, though we did not observe this in the parameter space of our modeling.

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To examine how the inner-disk thickness affects the morphology of the shadows, we generated model images at inner-edge inner-disk thicknesses from 0.07 to 0.14 au in increments of 0.014 au without fitting the SED. We find that as the thickness increases, the width of the shadows increases with no change in the location of the shadows. (Figure 8). The differences in width become small at smaller thicknesses, however, suggesting that shadows can act as an upper constraint of the inner-disk thickness.

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Model images were also generated at flaring exponents (Section 3.4) of 1.00, 1.20, and 1.40 (Figure 9) in order to examine the effect of the outer-disk structure on shadow morphology, also without fitting the SED. We find that the width of the shadows' inner edge decreases with increasing b, while the outer edge remains largely unaffected. In addition, we observe that the flaring of the disk causes the outer disk to appear thicker on the far side, as seen in Figure 9, where the SW side is the near side of the outer disk. This effect is most prevalent in the rightmost panel, where the SW side of the disk is approximately half the thickness of the NE side. In the case of HD 100453, the SW side of the outer disk is narrower in GPI images (Figure 1), indicating that this is the near side. The ratio of thicknesses between the near and far side of the disk, coupled with the inclination of the outer disk, could allow us to quantitatively describe the degree of flaring of the outer disk. When taken in conjunction with the inner-disk thickness, this should allow us to strongly constrain the disk's physical structure.

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As a result of the thickness of the outer disk, we find that any ${\rm{\Delta }}i\ne | 90^\circ |$ will offset the apparent location of the shadows on the outer disk in the direction of the tilt of the inner disk (Figure 10). The shadows are cast along the major axis of the inner disk and create a shadow, which is not coplanar with the outer disk, on the inner edge of the outer disk. The shadow will therefore be shifted by an amount that depends both on the thickness of the outer disk and on the value of Δi. This suggests that the separation of shadows must be smaller than 180° on the side of the outer disk, which corresponds to the near side of the inner disk, as seen in Figure 10. Examination of the shadow location therefore allows for a simple effective method of determining the near side of the inner disk. In the case of HD 100453, it is clear that the northern side of the inner disk is the near side because the shadow separation is smaller than 180° on that side. In contrast, it is much more difficult to discern the near side of the outer disk via examination of the shadows because this depends on both the tilt of the outer disk and Δi. In this case, because we know Δi = 45°, the inclination of the outer disk is $| 25^\circ |$ from Section 3.3.3, and from the NIR portion of the SED we are not looking along the edge of the inner disk, the SW side of the disk must be the near side.

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We observed a dropoff in spiral arm intensity at longer wavelengths in SPHERE TI imagery, most prevalent in K1 (Figure 1), which suggests that they consist of small compact grains. Although the gas-to-dust ratio in the disk of HD 100453 is low (Kama et al. 2016), no tail dominated by small dust grains is detected by HST ACS (Collins et al. 2009). The lack of a tail, as seen in HD 141569 (Konishi et al. 2016) and young debris disks, suggests that the gas-to-dust ratio is not low enough for radiation pressure to dominate. If gravitational interactions with the M-type companion are the source of the spiral arms, the small grains, which are more tightly coupled to the gas than the large grains, would be pulled more easily along with the gas and may lie in a slightly different plane than the rest of the disk. This could explain why the arms are bluer than the rest of the outer disk and why, according to Fung & Dong (2015), they appear to be almost face on. When coupled with the difference in optical depth between the arms and the ring of the outer disk, this suggests that there is a gradient in the particle size distribution of the disk.

A coplanar inner and outer disk cannot reproduce the shadows seen in the SPHERE and GPI data. From the shadow separation and comparison of model images to data we find a misaligned inner disk with Δi = 45° ± 10° and a rotation of the inner-disk major axis of −40° ± 10° with respect to the outer disk or 100° ± 10° east of north. This disagrees with Lazareff et al. (2017), however, who find a major axis PA for the inner edge of the inner disk of 81° ± 1° east of north. This measurement was found using simplified ellipse and ring models of the inner disk based on VLTI/PIONIER H-band data taken from 2012 December 19 to 2013 February 20.

At this time, there has been no observed change in the shadow pattern over the ∼11.5 months spanned by the SPHERE data taken by Wagner et al. (2015) and Bensity et al. (2017). There is the possibility, however, of a 19° change in major axis position angle between the measurements of Lazareff et al. (2017) and Wagner et al. (2015) that spans ∼25–27 months. If this is a change in the major axis, it could be due to precession of the inner disk, orbital motion of material in the inner disk, or the discrepancy could be a warp between the shadowing structure and the inner region of the inner disk.

Although the cause of the misalignment between the inner and outer disk is unknown, it has been shown in β Pic (Lagrange et al. 2010) that a planet can warp the inner disk. If a planet did cause the misalignment of the inner disk in HD 100453, as suggested above, it would likely cause precession of the inner disk, and by extension, precession of the shadows. However, this precession would occur on a timescale on the order of 10³ times the orbital timescale expected from Newtonian dynamics (Rawiraswattana et al. 2016). This suggests that we should not observe a change in the location of the shadows as a result of precession for timescales shorter than a decade. A change of 19° ± 10° in ∼25–27 months ($\sim 16^\circ \,{\mathrm{yr}}^{-1}$) is too large to be accounted for with precession and is therefore not the cause of the discrepancy.

The orbital radius of an object with this orbital motion would be ∼10 au. This is much larger than the proposed outer radius of the inner disk and just outside the region excluded by speckle residuals in GPI data. The large radius and lack of any disk detection in GPI data suggest that this is also most likely not the cause of the discrepancy between major axis PAs.

This leaves us with a warp between the inner region of the inner disk (traced by VLTI/PIONIER) and a shadowing region farther out. Although this cannot be ruled out using existing GPI or SPHERE data, N-band measurements using VLTI/MATISSE would allow for the angular resolution necessary to detect any difference in the inner and outer portions of the inner disk.

To date, 3 of the 14, that is ∼21%, transitional disks with published images have exhibited these shadows, which suggests that the shadows are not uncommon. The origin of the shadows is still under debate, however. Suggested causes include stellar magnetic activity (Pffeifer & Dong 2004), perturbation by the binary companion (Martin et al. 2014), and an unseen planet on an inclined orbit (Mouillet et al. 1997). However, magnetic field strengths in Herbig stars like HD 100453A are smaller, ∼100 G (Hubrig et al. 2015), than the magnetic fields required for disk misalignment, ∼10³ G (Pffeifer & Dong 2004). A close binary system can cause a misaligned inner disk, but Collins et al. (2009) did not observe a strong X-ray source at the location of HD 100453A, which would be indicative of another M-type companion, and brighter stars would be visible in the SED. Alternatively, a wide binary system, where the companion lies outside of circumstellar disk (as in the case of HD 100453), can also cause misaligned disks. However, this causes a high outer-disk eccentricity at higher misinclinations (Martin et al. 2014), which is not seen here. The possibility of an unseen planet, however, makes HD 100453 a promising candidate for future planet searches (Gratia & Fabrycky 2016). To date, no radial velocity measurements have been taken for the star with the intent of planet detection, however. In addition, this system resembles β Pic in having a two-belt architecture and a misaligned inner disk, indicating that the similar structure in young debris disks is most likely inherited from the transitional disk phase.