SPECKLE SUPPRESSION THROUGH DUAL IMAGING POLARIMETRY, AND A GROUND-BASED IMAGE OF THE HR 4796A CIRCUMSTELLAR DISK

Under very good observing conditions on 2005 January 26 UTC at the 3.63 m Advanced Electro-Optical System (AEOS) telescope in Maui, we obtained three H-band (1.65 μm) coronagraphic polarimetric sequences (+Q, −Q, +U modes) of the star HR 4796A (Table 1). The data were gathered using the Lyot Project coronagraph (Oppenheimer et al. 2003, 2004; Sivaramakrishnan et al. 2007) and the Kermit infrared camera (Perrin et al. 2003). The coronagraph was a diffraction-limited, classical Lyot coronagraph (Lyot 1939; Malbet 1996) with a 455 mas diameter occulting mask and a hard-edged Lyot stop. The AEOS telescope is an altitude–azimuth design, equipped with an AO system using a 941 actuator deformable mirror Roberts & Neyman (2002). The total observing time for this data set was 1080 s, comparable to the 1024 s for the Schneider et al. (1999) F160W Hubble Space Telescope (HST) data. During the observations, the local Fried parameter, r₀, a measure of the strength of turbulence in the atmosphere above the observatory, spanned the range of 15 to 25 cm, indicating nearly ideal conditions for AO observations at AEOS. Over the course of the observations, we obtained only +Q, −Q, and +U images because our retarders did not provide sufficient retardance to obtain a −U image.

The polarimeter implemented in the Lyot Project for the data in this paper was unique in two regards. First, the Wollaston prism was located immediately after the Lyot pupil in the coronagraph. This post-pupil location is the correct location to minimize differential aberrations between the two beams. This setup is an improvement over other polarimeters designed for use in high-contrast imaging, e.g., Perrin et al. (2008). Second, the use of LCVRs as a polarization modulator is relatively rare for night-time polarimetry. The benefits of using LCVRs include a great deal of increased flexibility in modulation, a lack of any image motions induced by rotating optics, and slightly faster modulation (although still not faster than the atmospheric timescales involved). Disadvantages of using retarders of this type include a potentially reduced wavefront quality.

Our goal is to quantify the gain in dynamic range achievable using the dual-imaging polarimetry technique. As a reference, we start by illustrating the dynamic range achieved on our Stokes I images without taking advantage of the polarimetric capabilities. According to a technique we discussed previously (Soummer et al. 2007; Hinkley et al. 2007), we have derived the magnitude difference (dynamic range) between the occulted star and a 5σ point source as a function of position in the Stokes I images. The residual scattered light outside of our coronagraphic mask, usually in the form of highly persistent speckle noise, is the main limiting factor for detection of a point source (See Section 2.3.1). Local evaluation of the amplitude of this noise in turn determines the minimum brightness required for a 5σ point source detection. A radial curve of this sensitivity is shown in Figure 2 and labelled "Stokes-I Dynamic Range."

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All photometric values in this paper were calibrated to unocculted images of HR 4796A, directly prior to the occulted sequences. The raw data images were calibrated through standard dark current subtraction, application of bad pixel maps, and flat fielding. The flat-field images were acquired using incandescent lamps each night. Also, binary star observations with well known orbits were observed to calibrate the pixel scale and image rotation fiducials. Prior to the subtraction, the images are rotated so that north is up in the image, east is to the left, and registered to each other using a cross correlation with subpixel accuracy. The data reduction technique is discussed in greater detail in Soummer et al. (2006) and Appendix A of Oppenheimer et al. (2008)

To actually calculate the polarimetric sensitivity on the image, artificial point sources with varying total brightness and degree of polarization were placed radially into the mutually orthogonal left and right images in the original data. An example of this is shown in Figure 1, which shows an artificial 80% polarized (in the vertical direction) faint point source with a given total brightness. The relative flux for the artificially placed companion in the left and right channels is given by

$$\begin{eqnarray} F_{\updownarrow } &=& \frac{F_{\rm total}}{2}(1 - p\cos {2\theta }) \end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray} F_{\leftrightarrow } &=& \frac{F_{\rm total}}{2}(1 + p\cos {2\theta }), \end{eqnarray} \tag{ 2 }$$

where F_total is the total flux of the object (F_total = F_↕ + F_↔). These images were processed through the normal double differencing process schematically shown in Figure 1, and the total flux of these point sources in the original images were incrementally increased from zero until a 5σ detection was obtained in the double difference images. This threshold total intensity was recorded and is plotted in Figure 2 labelled "100% Polarimetric Dynamic Range (ΔM_polar)."

Figure 2 shows the speckle suppression achieved with the double differencing technique is most effective within 175 and can achieve up to 4 mag of improvement over the Stokes I within 05. This level of polarimetric suppression is comparable to other AO-based polarimeters (Potter et al. 2000; Perrin et al. 2004, 2008), but results using this particular polarimeter on AEOS benefit from the extremely high-order AO system (Roberts & Neyman 2002), and the optimized coronagraph (Sivaramakrishnan et al. 2001) in the beam path before any of the polarimetry optics.

Modelling point sources are especially useful in the context of the data discussed in the next section, since the HR 4796A disk ansae are very near to point sources. Finding the required polarization for detection in our double-difference technique will thus help us to further constrain the value obtained directly (using published NICMOS Stokes I values) described in Section 3. These calculations using point sources can be directly applied to extended objects with resolved surface brightnesses. We have recasted the sensitivity results in terms of surface brightness (mJy arcsec⁻²), and those values are listed on the right-hand side axes of Figure 2. It should be noted, though, that in Figure 2 the brightness difference values (left-hand side axis) indicate the total brightness of a point source, while the surface brightness (mJy arcsec⁻²) values reflect the brightness of the peak intensity of the point source. Nonetheless, our analysis for point sources translates over to extended sources since the key issue is the overall brightness of the source in comparison to the amplitude of the surrounding noise.

2.3.1. Post Speckle Suppression: A Return to the Read Noise Limited Regime

To constrain the nature of the debris disk around HR 4796A, we model optically thin disks assuming a Henyey–Greenstein phase function (Henyey & Greenstein 1941) and a Raleigh-like variation of polarization with scattering angle, which is suitable for disks with small grains or larger grain aggregrates (Kimura et al. 2006). The model is a two-dimensional generalization of the one-dimensional model used in Graham et al. (2007), appropriate for a solar system zodiacal Henyey–Greenstein dust model (Hong 1985; Graham et al. 2007). We have chosen to fit for the Henyey–Greenstein scattering asymmetry paramter g = 〈cos θ〉 and the disk scale height. We fit for these two parameters, since both are intrinsically related to the dust structure in the disk, and can most readily be constrained by the polarimetric data. A sample grid of models with scale heights h₀ = 12 AU, 25 AU, and 50 AU as well as Henyey–Greenstein parameters g = 0.0, 0.3, and 0.6 is shown in Figure 4 to guide the eye. A value g = 0 is completely isotropic scattering, while g = 0.6 signifies moderately strong forward scattering. A value of g = 0.3 is typical of Zodiacal dust and some debris disks. The model assumes a Gaussian vertical density distribution with an adjustable scale height based on the COBE model of zodiacal background light (Kelsall et al. 1998). Using cylindrical coordinates, we adopt the following density structure for the disk,

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$$\begin{equation} n(r,z) = n_0 \left(\frac{r}{r_0} \right)^{\alpha }e^{-\beta (z/h_0)^\gamma }, \end{equation} \tag{ 3 }$$

with α = −1.803, β = 4.973, γ = 1.265 motivated by Kelsall et al. (1998). We have used the inner and outer radii (69 AU and 83 AU, respectively), inclination (1412 from edge on), and position angle (632) from Schneider et al. (2009). Each thumbnail image in Figure 4 was computed using the measured pixel scale of the Lyot Project's infrared camera (13.5 mas pixel⁻¹) and has been convolved with a point-spread function (PSF) for the AEOS telescope at 1.65 μm. This PSF also reflects the reduced effective pupil diameter imposed by the Lyot mask in the Lyot Project coronagraph. During the fits, we also mask out the region covered by our coronagraphic mask. We generated an ensemble of models varying h₀ between 2.5 and 25 AU and g between 0.0 and 0.7.

The χ² fitting procedure was performed on a pixel-by-pixel basis, normalized with the peak brightness in the model matched to the peak brightness in the polarization image. Ideally, such a fit should simultaneously use the polarized intensity and the total intensity of the disk image (Graham et al. 2007) in the fits to avoid degeneracies between dust properties and disk structure (Duchêne et al. 2004; Pinte et al. 2007). Given the relatively low signal-to-noise of this detection, and the lack of a detection in a total intensity image, we chose only to perform a χ² fit to the polarization image. Also, the data showing the fractional polarization may give a better handle on the disk scale height. In addition, the speckle noise pattern in highly corrected AO images can be well modelled with a Rician Probability Distribution Function (Aime & Soummer 2004; Fitzgerald & Graham 2006; Soummer et al. 2007), so a model fit should take this fact into account. However, given that the speckle noise pattern has been significantly subtracted away, as discussed above, a χ² minimization employing a Gaussian noise variance is suitable.

Our best χ² fit (χ² ≃ 1.1) is a model with dust disk scale height of 2.5^+5.0_−1.3 AU and Henyey–Greenstein phase function of 0.20^+.07_−.10. These findings are consistent with several lines of evidence suggesting that HR 4796A is dominated by a micron-sized dust population. Such a value of the asymmetry parameter is similar to models employing interstellar medium (ISM)-type dust grain distributions (Wood et al. 2002; Kim et al. 1994), with the dominant grain size lying between 0.1 and 1 μm. This population is similar that of the (8 ± 2 Myr, A1 V) 49 Cet disk as discussed by Wahhaj et al. (2007), with small (0.1 μm) grains between 30 and 60 AU from the star. On the other extreme, in their analysis of HR 4796A, Debes et al. (2008) suggest that the minimum grain sizes for this disk are between 1 and 5 μm in size, with a dominant population of 1.4 μm grains. Although the Debes et al. (2008) study employed the use of Tholins in their model fits, Köhler et al. (2008) find that the disk spectra can be well fit using less exotic compounds (amorphous silicates, amorphous carbonates, and water ice). In these models, 1 μm grains give the best overall fit. Another powerful diagnostic of the grain size distribution is the level of linear polarization measured in this work (44% ±  5%). Given the efficiency with which small grains can polarize starlight, our results are consistent with a micron-sized dust population leading to this relatively high level of polarization. The age and grain size distribution for HR 4796A support the interpretation of Wahhaj et al. (2007), that it as well as the 49 Cet disk are representative of a class of disks that are "transitional" between the Herbig Ae class and Vega-like stars.

Our best estimate and uncertainties on the disk scale height do not significantly constrain it below 12.5 AU at the 2σ level. Although several authors have measured gas scale heights in disks such as β Pic (Brandeker et al. 2004), to our knowledge this work is one of the only measurements of a dust disk scale height. Kenyon et al. (1999) have simulated the structure of the HR 4796A disk, and predict a scale height between 0.3 and 0.6 AU, nearly consistent with our results. Our value for the phase function is similiar to the phase function values obtained for other disks, including Fomalhaut (Kalas et al. 2005) and HD 141569A (Clampin et al. 2003).