OPTICAL IMAGING POLARIMETRY OF THE LkCa 15 PROTOPLANETARY DISK WITH SPHERE ZIMPOL^*

Our RI-band imaging polarimetry of LkCa 15 is shown in Figure 1. Despite the bad PSF quality, the instantaneous nature of dual-beam polarimetry allowed us to remove the starlight effectively and resolve the LkCa 15 disk at high contrast and unprecedented angular resolution.

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The ${Q}_{\phi }$ image reveals a crescent of polarized flux tracing the shape of the near-side edge of the outer disk seen in infrared angular ADI observations (Thalmann et al. 2010, 2014), and a previously unknown bright area of polarized flux surrounding the star at small separations ($\lesssim 0\buildrel{\prime\prime}\over{.} 25$, see panel 1(b)). Both features appear consistently positive in the ${Q}_{\phi }$ image and are significantly brighter than the residuals in the ${U}_{\phi }$ image at similar radii, which identifies them as scattered light from circumstellar material.

Figure 1(c) provides signal-to-noise ratio (S/N) maps produced by dividing the pixel values of star-centered annuli in the ${Q}_{\phi }$ and ${U}_{\phi }$ images by the standard deviation of the ${U}_{\phi }$ image in the same annuli. Both features achieve S/N values above $5\sigma$ over a large number of resolution elements and are therefore detected at high confidence. The inner disk is detected down to a separation of ∼1 FWHM (36 mas).

To estimate the dust distribution from the scattered-light intensity, we compensate for the ${r}^{-2}$ fall-off of the illumination of dust particles with physical distance r from the star. We calculate r for each pixel by deprojecting its apparent distance from the star, assuming its light originates from a plane inclined by $50^\circ$ with its line of nodes at a position angle of $60^\circ$ (cf. Thalmann et al. 2014). Figure 1(d) shows the ${Q}_{\phi }$ and ${U}_{\phi }$ images after multiplying each pixel value with r². The disk gap is visible as an abrupt step in brightness at almost all position angles, including the faint far side that had eluded all previous scattered-light observations. The reduced brightness of the disk surface near the minor axis is likely due to the dependence of scattering polarization on the phase angle. However, we note that phase angles should change by at most ∼6$^\circ$ along radial paths on the visible disk surface; thus, the location of the gap edge should remain largely unaffected.

The eastern ansa appears brighter than the western one on the 1σ level (evaluated in the r²-scaled image in 50 pixel diameter apertures).

ADI observations of circumstellar disks suffer from flux loss and oversubtraction effects (Thalmann et al. 2011, 2013; Milli et al. 2012) and therefore require forward modeling to interpret their results (Thalmann et al. 2014). Imaging polarimetry, on the other hand, yields morphologically sound representations of the disk's appearance in polarized light (e.g., Hashimoto et al. 2011; Garufi et al. 2013; Quanz et al. 2013a, 2013b; Benisty et al. 2015).

We characterize the sharp gap edge in the r²-scaled ${Q}_{\phi }$ image by fitting it with an ellipse using a modified version of the maximum merit method introduced in Thalmann et al. (2011). We generate a number of ellipses with semimajor and semiminor axes a, b displaced from the star's position by offsets x, y along the two axes, respectively. For a parameter set $(a,b,x,y)$, we consider the two concentric elliptical annuli bounded by the triplet of ellipses $(a-\delta ,b-\frac{b}{a}\delta ,x,y)$, $(a,b,x,y)$, and $(a+\delta ,b+\frac{b}{a}\delta ,x,y)$ with an annulus width of $\delta =10$ pixels (=36 mas = 1 FWHM). The merit function $\eta (a,b,x,y)$ is defined as the mean pixel value in the outer annulus of the r²-scaled ${Q}_{\phi }$ image minus the mean value of the inner annulus. The best fit is achieved when the merit function is maximized, i.e., where the mean brightness increase from the inner to the outer annulus is greatest. As a measure of uncertainty, we define the "well-fitting" family of ellipses by a threshold of $\eta \gt {\eta }_{\mathrm{max}}-{\sigma }_{\eta }$, where ${\sigma }_{\eta }$ is the standard deviation of merits of ellipses in the ${U}_{\phi }$ image.

As demonstrated in Figure 2(a), the best-fit ellipse matches the visual locus of the gap edge convincingly. Its numerical parameters and uncertainties are provided in Table 1. Figure 2(b) compares this fit to a second ellipse obtained by applying the maximum merit method to the best-fit model from our ADI forward-modeling analysis in Thalmann et al. (2014). The two ellipses share similar sizes, aspect ratios, and significant minor-axis offsets y. However, while we found a marginal major-axis offset x toward the west in Thalmann et al. (2014), our present data are consistent with x = 0.

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Table 1.  Numerical Results

In (mas) In Proj. (AU) Fit Ellipse to the Disk Gap Edge in${Q}_{\phi }$

Semimajor axis a	338	(+11, −18)	47.4	(+1.5, −2.5)
Semiminor axis b	245	(+21, −11)	34.3	(+3.0, −1.5)
Major-axis offset x	−3	(+11, −14)	−0.5	(+1.5, −2.0)
Minor-axis offset y	−79	(+11, −18)	−11.1	(+1.5, −2.5)
	In (mas)		In Proj. (AU)
Characteristic Length Scales of the Inner Scattering Component
Major axis (east) lE	69	(+15, −11)	9.7	(+2.1, −1.5)
Major axis (west) lW	74	(+11, −9)	10.4	(+1.6, −1.2)
Minor axis (north) lN	51	(+6, −5)	7.2	(+0.9, −0.7)
Minor axis (south) lS	38	(+10, −6)	5.3	(+1.6, −0.9)

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Figure 2(c) shows the ellipse fit to the reconstructed 7 mm emission images reported in Isella et al. (2014) superimposed on our fit. Their ellipse is centered on the star, which results in a significant mismatch with our off-centered ellipse. While the two ellipses can be brought to coincide well with each other by translating one of them by $y\approx 80$ mas (Figure 2(d)), this offset is highly significant compared to the astrometric accuracy of the 7 mm interferometry (10 mas, Isella et al. 2014) and of the ZIMPOL data ($\lt 10$ mas) and must therefore be physical.

Figures 3(a) and (b) plot the surface brightness profiles in the ${Q}_{\phi }$ image (without r² scaling) along the major and the minor axis, respectively. The plotted values are pixel values as a function of separation averaged over a width of 21 pixels (=76 mas) and 81 pixels (=292 mas), respectively, and normalized by the brightest pixel value of the star's intensity PSF. Since some exposures in the data are saturated, the normalization is only approximate.

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The new inner disk component appears as a roughly exponential rise of surface brightness within a radius of ∼025. We fit each side of the structure in each of the two profiles as proportional to $\mathrm{exp}(-\theta /l)$, with θ the angular separation from the star and l a characteristic length scale, using least-squares fitting. These fits are listed in Table 1 and illustrated in Figure 3.

To gauge the uncertainty of these results, we extract a number of surface brightness profiles from the noise-like ${U}_{\phi }$ image at various position angles, add each of them to the science profiles from the ${Q}_{\phi }$ image, and recalculate the exponential fits. The standard deviations of these "disturbed" l values are then adopted as the error bars for the table values of l. The disturbed surface brightness profiles are shown in gray in Figure 3.

The polarized intensity is likely underestimated at the innermost separations due to overlapping PSF wings in the Q and U images (Avenhaus et al. 2014a).

The newly discovered inner disk component, detected from ∼30 AU down to the inner limit of ∼7 AU (Figure 3), overlaps with the location of the protoplanet candidate at ∼16–21 AU derived from SAM observations (Kraus & Ireland 2012). As with the outer disk, we expect anisotropic scattering to produce a distinct full-intensity forward-scattering maximum on the near side, which coincides with the position angle of the protoplanet candidate. Taken together with the forward-scattering maximum of the outer disk edge (Thalmann et al. 2014), these disk features likely interfere with the reconstruction of SAM data, as in the case of T Cha (Olofsson et al. 2013). However, given the recent Hα detection (K. Follette 2015, private communication), a protoplanet embedded in the inner disk similar to HD100546 b (Quanz et al. 2013a) remains the most plausible interpretation.

The inner disk component also sheds light on the extent of the gap as inferred from previous non-resolved observations. Espaillat et al. (2007) proposed a three-component structure with an outer disk at ∼50 AU consistent with the millimeter cavity, an inner disk starting at the dust sublimation radius to explain the near-infrared flux, and an optically thin component out to ∼5 AU to explain the prominent silicate emission feature. Our detection of scattered light between 7–30 AU shows illuminated dust is present at these locations above the disk mid plane. An extrapolation of the gap wall temperature ($T\approx 100$ K $/\sqrt{a/{a}_{\mathrm{wall}}}$) yields a temperature of 150–250 K, consistent with the presence of the 10 and 20 μm silicate emission feature in the SED. We hypothesize that this new scattering structure represents the optically thin part of the inner disk extending out to at least 30 AU. A quick adaptation of the disk model from Mulders et al. (2010) indicates that this can be reconciled with the SED, since the contribution of the optically thin part to the SED is minor. This geometry (narrow gap, depleted inner disk, millimeter cavity) qualitatively matches the imprint of a single planet on a disk (e.g., Jang-Condell & Turner 2012; Zhu et al. 2012).

Our RI-band polarimetry confirms the prediction from K-band ADI forward-modeling (Thalmann et al. 2014) that the outer boundary of the gap in the LkCa 15 disk appears off-centered in reflected light, with a highly significant offset of $y\approx 80$ mas (a third of the gap's projected radius) between the star and the gap's apparent center. While disk gaps are known to vary in size as a function of observed wavelength in systems with planet-induced dust filtering (de Juan Ovelar et al. 2013), a lateral displacement of the gap is more difficult to justify and has not been predicted by numerical simulations.

The outer disk's vertical structure cannot account for this displacement since the gap wall profile is tapered ("round") rather than vertical (Thalmann et al. 2014). This is qualitatively confirmed by the wide, homogeneous distribution of scattered light in Figure 1(d).

Another explanation is provided by shadowing. Espaillat et al. (2007) originally proposed an inner disk coplanar with the outer disk, casting a shadow onto the outer disk's inner wall Mulders et al. (2010). Our forward modeling in Thalmann et al. (2014) achieved significantly better fits with an unshadowed gap wall, which led us to speculate that the inner disk—and its shadow—were tilted out of the outer disk's plane. On the other hand, this arrangement should result in dark lanes cutting across the outer disk where the shadow plane intersects it, as seen in HD 142527 (Marino et al. 2015). No such lanes are apparent in the LkCa 15 imagery.

This conundrum can be resolved if the inner disk has a slightly higher inclination than the outer disk (Figure 4). The near-side disk rim as observed from Earth would then be fully exposed to stellar irradiation, whereas the far-side disk surface would be obscured at the rim and only become visible further out where the disk surface flares out of the shadow. This would create an off-centered apparent gap in reflected light even with a symmetric physical disk gap. For the disk architecture in Thalmann et al. (2014), the requisite differential tilt would be of order $1^\circ$, which could be induced by a planet on a tilted orbit (cf. Mouillet et al. 1997; Augereau et al. 2001; Lagrange et al. 2012).

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A similar effect could be caused by a shadowing structure vertically extending from an otherwise coplanar inner disk (Espaillat et al. 2011), though this would imply dramatic variability on the timescale from days to years. While we cannot exclude this possibility, we find no significant variability in our observations (Thalmann et al. 2014; this work).