ON THE MORPHOLOGY AND CHEMICAL COMPOSITION OF THE HR 4796A DEBRIS DISK^*

We observed HR 4796A at the Magellan Clay telescope at the Las Campanas Observatory (LCO) in Chile using the Clio-2 1–5 μm camera and MagAO. All Clio-2 observations are summarized in Table 1. We observed the target at 3.8 μm (L') on UT 2013 April 7, at 3.3 μm (hereafter Ls for "Lshort") on UT 2013 April 8, and at 3.1 μm (hereafter Ice band) and 2.15 μm (Ks band) on UT 2013 April 9, all using the narrow camera (plate scale = 001585 per pixel⁹). Due to thermal light leakage in the Ks filter, the Ks band images were contaminated by excess light. This resulted in a Ks band PSF that was much more "blurred" than would have been expected for a normal Ks filter. Therefore we repeated the Ks band observations ∼one year later, on UT 2014 April 10. Henceforth, we use only this latter data set and ignore the original light-leaked images. The observing conditions for all nights were excellent, with seeing values ranging from 05–1'', and the AO corrected 300 modes for all observations. The observing setup and strategy was the same for each night, with the camera rotator off to facilitate angular differential imaging (ADI; Marois et al. 2006), and no coronagraphs were used. We nodded the telescope by several arcseconds vertically along the detector every few minutes and dithered the star horizontally by a fraction of an arcsecond on each nod to mitigate the sky background and bad pixels/detector artifacts. Because MagAO delivers such high Strehl ratios at 1–5 μm, nodding the telescope does not significantly change the PSF, which is critical for the PSF subtraction described in Section 2.1.1. At each nod position unsaturated exposures of the star were taken for photometric references. The longer exposure images were saturated out to ∼01.

After discarding images of poor quality (e.g., from the AO loop being open, PSF blurring due to wind shake, or improper nods), at L' we obtained 455 science exposure images of the target for a total integration of 2.5 hr; at Ls we obtained 120 images for a total integration of 80 minutes; at the Ice band we obtained 349 images for a total integration of 87 minutes; and at Ks band we obtained 240 images for a total integration of 80 minutes. The total parallactic angle rotation was 15073, 935, 1154, and 94° for L', Ls, Ice band, and Ks band, respectively.

We observed HR 4796A at the Magellan Clay telescope using the VisAO camera and MagAO on UT 2013 April 7 (z'; λ_c = 0.91 μm), UT 2013 April 8 (Ys; λ_c = 0.99 μm), and UT 2013 April 9 (i'; λ_c = 0.77 μm), contemporaneously with the Clio-2 observations reported above. All VisAO observations are summarized in Table 1. The VisAO camera has a plate scale of 00079 pixel⁻¹ (Close et al. 2013; Males et al. 2014) and a field of view of 809. No coronagraph was used for any of the observations, resulting in the central 01–05 regions around the star being saturated in the images. The observing strategy was the same as for the observations conducted with Clio-2. After discarding images of poor quality, we obtained 285 images at Ys for a total integration of 95 minutes; at z' we obtained 3030 images for a total of 115 minutes of integration; and at i' we obtained 342 images for a total integration of 114 minutes. The total parallactic angle rotation was 936 at Ys, 967 at z', and 1194 at i'.

All data reduction discussed below was performed using custom scripts in Matlab. The steps described were carried out identically for all four data sets, including the unsaturated photometric data. We divided all the images by the number of coadds, corrected for nonlinearity,¹⁰ and divided by the integration time to obtain units of detector counts s⁻¹. We then subtracted opposite-nod images from each other to remove the nonnegligible sky background and corrected for bad pixels. Next we determined the sub-pixel location of the star in each of the sky-subtracted images by calculating the center of light inside a 05 aperture centered on the star. Based on previous imaging results (Rodigas et al. 2012, 2014b), this is a satisfactory method as long as saturation is limited to <02. The images were then registered so that the star was at the center of each image. During the observing run, bright stars produced ghosts and streaks whose positions varied in unpredictable ways. To remove this unwanted noise, we calculated the standard deviation for each pixel through each star-centered datacube and masked regions where the standard deviation was high (relative to some threshold value). This filtering process significantly improved the quality of our final reduced images.

We then fed the registered, cropped, sky-subtracted images into our custom principal component analysis (PCA; Soummer et al. 2012) pipeline. For the data sets discussed in this work, we found optimal signal-to-noise per resolution element (SNRE¹¹) detections of the disk with "classical" PCA (no small search areas, no rotation requirement). The number of modes that maximized the disk's average SNRE was 28 (out of 455), 13 (out of 120), 21 (out of 349), and 26 (out of 240) for L', Ls, Ice band, and Ks band, respectively. We also tested the LOCI algorithm (Lafrenière et al. 2007) on our data but found better results with PCA, in agreement with previous studies (Meshkat et al. 2014; Rodigas et al. 2014b; Thalmann et al. 2013; Bonnefoy et al. 2013; Boccaletti et al. 2013; Soummer et al. 2012). We de-rotated all the PSF-subtracted images by their parallactic angles + a small offset (−18¹²) to obtain north-up, east-left and combined all the images using a mean with sigma clipping.

Figure 1 shows the final PCA-reduced images at each wavelength, and Figure 2 shows their corresponding SNRE maps. The debris ring is detected at SNRE ∼2–11 at L', ∼2–10.6 at Ls, ∼2–8 at Ice band, and ∼2–16 at Ks band. The ring is detected at high SNRE outside of 04 (in front of and behind the star), allowing accurate characterization of the disk's geometry and morphology.

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We reduced the VisAO Ys, z', and i' data in the same manner as we reduced the Clio-2 data, except for a few differences: for the z' data, we manually coadded the images in sets of 10, resulting in 303 coadded images, to ease the computational effort of the PCA reduction; we did not perform any sky subtraction because the small plate scale of VisAO combined with the faint sky at 0.7–1 μm renders the sky background negligible. Instead, because dark frames were periodically taken throughout the observations, we subtracted from each science image the dark frame taken closest in time to it. We also did not perform any standard deviation filtering because the detector only has one ghost whose position and brightness vary predictably. The number of PCA modes that optimized the SNRE of the disk was 23 (out of 285) at Ys, 28 (out of 303) at z', and 90 (out of 342) at i'. We combined the sets of reduced images using a mean with sigma-clipping and rotated the final images by their parallactic angles + a small offset (−059, from Males et al. 2014) to obtain North-up, East-left. The final PCA-reduced images and their corresponding SNRE maps are shown in Figures 1 and 2. The disk is detected at SNRE ∼2–23 beyond ∼04 at Ys, ∼2–25 beyond ∼04 at z', and at ∼2–17 beyond ∼05 at i'.

We also include here previously unpublished Spitzer/MIPS (Werner et al. 2004; Rieke et al. 2004) data. SED-mode observations (55.0–90.0 μm; λ/Δλ ∼ 20) on HR 4796A (AOR key: 16169984) were obtained on 2016 February 15 using the 196 × 157'' slit/grating and five cycles of 10 s integrations. Each observing cycle consisted of six pairs of 10 s exposures with the slit position alternated between the object and blank sky 1'' away. To remove the background, each sky exposure was subtracted from the immediately preceding frame containing the object. Exposures of an internal calibration source were interspersed within the cycle to track the varying response of the 70 μm detector array. The raw MIPS data were corrected for distortion, registered, mosaicked, and flat-fielded using the MIPS instrument teams data analysis tool (DAT; Gordon et al. 2005). The spectrum was extracted using a 5 pixel extraction aperture and calibrated using the procedure and calibration files described in Lu et al. (2008). The processing steps included applying the dispersion solution, an aperture correction (to account for slit losses), and a flux calibration based on ∼20 infrared standard stars (Gordon et al. 2007). The Spitzer/MIPS photometry is shown in Table 2.

We also compiled literature photometry on HR 4796A at far-infrared (FIR) wavelengths, to be used in Section 4 for the dust grain composition modeling. The data and their references are shown in Table 2. The observations and data reduction for the binned Spitzer/IRS data are described in Chen et al. (2014).

The HR 4796A debris ring can be described by five sky-projected parameters: the semimajor axis, a, the semiminor axis, b, the position angle measured east of north, P.A., and the ellipse center (ΔR.A., Δdecl.), measured along R.A. and decl., respectively. Once these parameters are measured, we can calculate the true orbital elements of the disk (a, e, ω, i, and Ω, where ω is the longitude of periastron, i is the inclination from face-on viewing, and Ω is the longitude of the ascending node), using the Kowalsky deprojection routine (Smart 1930; Stark et al. 2014). We set out to measure the sky-projected parameters using our high SNRE images of the disk (excluding the Ice band and i' images due to the low SNRE at small inner working angles in both images). This is necessary in order to verify the results of Schneider et al. (2009), Thalmann et al. (2011), and Wahhaj et al. (2014), who all found that the ring is offset from the star by ∼a few AU and thus might indicate the presence of one or more perturbing planetary companions (Wyatt et al. 1999).

We followed the "maximum merit" procedure outlined in Thalmann et al. (2011) and Buenzli et al. (2010) whereby binary images of ellipses described by varying (random) parameters are multiplied with the real images of the disk until a maximum fit is obtained. The parameters were drawn from the following uniform distributions: a ∈ [0.95, 1.2]'', b ∈ [0.2, 0.3]'', P.A. ∈ [24, 28]°, ΔR.A. ∈ [ − 50, 50] mas, and Δdecl. ∈ [ − 50, 50] mas. These limiting values were chosen based on previous fitting results from Schneider et al. (2009), Thalmann et al. (2011), and Wahhaj et al. (2014). The width of the ellipse is an additional free parameter and can significantly alter the fitting results; if the ellipse is too thin, the fitting will naturally prefer the brightest parts of the ring, which may change with wavelength due to the scattering properties of the dust; if the ellipse is too wide, the fitting can be biased by residuals and noise outside the ring. We found that wide ellipses generally offered poorer fits than narrower ellipses, therefore we chose ellipses with a semimajor axis width of 0128 (8 Clio-2 pixels, 16 VisAO pixels) and a semiminor axis width of 0032 (2 Clio-2 pixels, 4 VisAO pixels).

For each image/wavelength, we generated 50,000 binary ellipses and multiplied them with the SNRE images of the disk. As in Thalmann et al. (2011), we computed the merit value, defined as the average SNRE pixel value inside the ellipse, and recorded this value. We then averaged the ring parameters associated with the five highest merit values; the uncertainties on each parameter were computed as the standard deviation of the five values. We also computed the offsets along the major and minor axes, $\Delta \tilde{a}$ and $\Delta \tilde{b}$, by rotating the ΔR.A. and Δdecl. offsets clockwise by the fitted P.A. of the disk at each respective wavelength. The uncertainties in the offsets along the major and minor axes were calculated by propagating the uncertainties in ΔR.A. and Δdecl. Next we determined the debris ring's true orbital elements using the Kowalsky deprojection routine (Smart 1930; Stark et al. 2014). The debris ring's fitted sky-projected and true geometrical parameters are reported in Table 3.

Table 3. Geometrical Parameters of the Ring

	a	e	ω	i	Ω*	ΔR.A.	Δdecl.	$\Delta \tilde{a}$	$\Delta \tilde{b}$
	('')		(°)	(°)	(°)	(mas)	(mas)	(mas)	(mas)
Ys	1.08 ± 0.01	0.06 ± 0.02	101.40 ± 7.00	76.11 ± 0.59	26.70 ± 0.16	−7.56 ± 4.77	−16.86 ± 3.91	−11.67 ± 4.10	14.33 ± 4.61
z'	1.08 ± 0.01	0.04 ± 0.01	135.18 ± 22.88	77.07 ± 0.27	26.22 ± 0.29	5.66 ± 7.81	−27.61 ± 7.08	−27.27 ± 7.23	7.12 ± 7.67
Ks	1.11 ± 0.01	0.08 ± 0.02	108.19 ± 7.91	77.75 ± 0.64	26.72 ± 0.28	−3.92 ± 6.8	−29.61 ± 8.17	−24.69 ± 7.92	16.81 ± 7.10
Ls	1.09 ± 0.01	0.09 ± 0.01	100.70 ± 4.12	78.02 ± 0.64	26.62 ± 0.09	−9.43 ± 3.64	−24.78 ± 6.17	−17.93 ± 5.75	19.53 ± 4.27
L'	1.08 ± 0.01	0.05 ± 0.02	107.58 ± 12.26	77.35 ± 0.24	26.55 ± 0.11	−3.15 ± 6.45	−19.19 ± 11.31	−15.76 ± 10.52	11.39 ± 7.67
Mean	1.09 ± 0.01	0.06 ± 0.02	110.61 ± 12.67	76.47 ± 0.45	26.56 ± 0.20	−3.68 ± 6.08	−23.61 ± 7.72	−19.46 ± 7.42	13.84 ± 6.44

Note. * Errors in Ω are relative in that they do not include the absolute uncertainty in the position of true north on the detector (010 for Clio-2 and 030 for VisAO).

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We find similar values for all parameters to those reported by Schneider et al. (2009), Thalmann et al. (2011), and Wahhaj et al. (2014). In particular, we find that the ring is offset along both the major and minor axes by 2.6σ and 2.15σ, respectively. Within the uncertainties, the center of the ring (along both R.A./decl. and major/minor axis) agrees with previous results (see Figure 3(a)). Most importantly, the physical deprojected center of the ring is offset from the star by a total of 4.76 ± 1.6 AU¹³ (see Figure 3(b)). This corresponds to a physical deprojected eccentricity of 0.06 ± 0.02, which is in general agreement with previously reported values.

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Figure 3(b) shows the rotated, deprojected SNRE map of the disk at L' (since the disk is detected at the smallest inner working angles at L'), with the locations of the star and ring center marked. Based on our geometrical fitting, the star is closer to the western side of the ring.

Several numerical studies have recently shown that planets can create sharp inner and outer ring edges (Chiang et al. 2009; Thebault et al. 2012; Boley et al. 2012). Rodigas et al. (2014a) and Chiang et al. (2009) also showed that a shepherding planet's properties can be constrained by the debris ring's intrinsic width. Schneider et al. (2009) used HST/STIS coronagraphic images to measure the width of the ring near the ansae and found it to be 0184  ±  001. Recently Wahhaj et al. (2014) measured the normalized width of the ring from ground-based AO images obtained by NICI in the J, H, and K bands to be ∼0.10, indicating a much narrower ring. Both of these studies were limited in that the ring was not detected at adequate SNRE at small inner working angles. Our VisAO and Clio-2 images resolve the ring as close as ∼04, which allows us to obtain more accurate measurements of the average ring width. Our VisAO images, in particular, have resolutions of ∼003, lessening the disk-broadening effect of PSF blurring.

To measure the intrinsic ring width, we followed the procedure outlined in Rodigas et al. (2014a). As before, we considered only the Ys, z', Ls, Ks, and L' images, since these have the highest SNRE detections of the ring. First, we rotated each image counter-clockwise by 90°−the best-fit PA (from Table 3) so that the major axis was along the x-axis. Next, using the best-fit inclination, we deprojected the images. We calculated the distance of each deprojected pixel from the star (which was at the center of the images) and stored the squares of these values (for later use). We then shifted the images so that the ring center was at the center of each image. Finally we rotated the images clockwise by the corresponding argument of pericenter so that the true semimajor axis of the ring was along the x-axis.

To compute the radial profiles, we generated ellipses with the same geometry as the ring. The ellipses had semiminor axis widths equal to 1 pixel (00079 for VisAO and 001585 for Clio-2). From 08 to 14, the surface brightness was computed as the median pixel value inside each annulus divided by the respective plate scale squared, and the semimajor axis of each annulus was stored.

Images of point and extended sources obtained using ADI typically suffer from varying degrees of self-subtraction. This can significantly shrink the apparent width of the ring. Indeed negative residuals are evident both inside and outside the ring in Figure 1. These negative residuals are retained in the radial profiles and are generally present within 09. To account for this bias, for each image we subtracted the average negative residual in the 08–09 region from all the values in the radial profiles. The geometric dilution of star light with distance squared was remedied by multiplying the resultant radial profiles by the previously stored squared distance values. Finally, the profiles were normalized by the respective peak surface brightness values. The uncertainties in the profiles at each semimajor axis were computed by repeating the above procedure on the noise maps used to generate the SNRE images at each wavelength. The final radial profiles are shown in Figure 4(a).

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These profiles do not take into account the broadening of the PSF at each wavelength. At <1 μm, where the resolution is ∼003, the broadening is not severe and can be neglected. But at 2–4 μm, this is not the case. We measured the ring broadening effect at Ks, Ls, and L' by repeating the above procedure on a (qualitatively similar) convolved model disk that was inserted 90° away from the real disk into the raw data and then recovered after ADI/PCA data reduction. The observed FWHM values (computed by measuring the distance between the half-peak locations) were compared with the FWHM of the unconvolved noiseless model disk. At Ks, the PSF convolution broadened the disk by a factor of 1.43; at Ls, by a factor of 1.57; and at L', by a factor of 1.74. We then divided the observed FWHM of the real disk at Ks, Ls, and L' by their respective broadening factors.

We computed the normalized FWHM (nFWHM) at each wavelength by dividing the FWHM values by their respective peak semimajor axis values. The uncertainties in the nFWHM values were computed by repeating this procedure on the profiles + and − the errors at each semimajor axis. These values are shown in Figure 4(b). Our measured values are equivalent within the uncertainties and are generally consistent with previous measurements from Schneider et al. (2009), Lagrange et al. (2012), and Wahhaj et al. (2014). Assuming nFWHM is constant with wavelength, we find the combined nFWHM = 0.14$^{+0.03}_{-0.02}$. This corresponds to a physical width of 11.1$^{+2.4}_{-1.6}$ AU.

Inserting the nFWHM value into Equation (5) from Rodigas et al. (2014a), the maximum mass of an interior planet shepherding the ring would be 4.0$^{+3.0}_{-2.5}$ M_J. Using Equation (2) from Rodigas et al. (2014a), the planet would have a minimum semimajor axis in the 48–60 AU range and its eccentricity would be ≈0.06 (the eccentricity of the ring). Assuming the hypothetical planet is apsidally aligned with the ring such that they share the same periastron and apoastron locations (denoted in Figure 3(b)), the planet would spend more time on its orbit closer to apoastron than periastron. Specifically, at any given observation epoch it would be ∼52% more likely to be located in the bottom half of Figure 3(b) than in the top half. If the planet's orbit is more eccentric than the ring, it would be even more likely to be located near apoastron. Unfortunately, a large part of this area is inaccessible in our images (Figure 1). This means it may take several more years before the hypothetical planet is at a more favorable projected separation to be directly imaged.

Our VisAO images (Figure 1) clearly show that excess flux resides beyond the ansae of the disk. These features are detected at SNRE ∼5–10. Their prominence appears to decrease with increasing wavelength; they are brightest at i', fainter at Ys and z', marginally detected at Ks band, and not detected at 3–4 μm. Clearly, the multiple detections of the features over multiple nights at different wavelengths indicates they are not spurious artifacts. Indeed they have been previously detected with several different telescopes/instruments (Thalmann et al. 2011; Wahhaj et al. 2014; Perrin et al. 2014). As originally posited in Thalmann et al. (2011), these features likely arise from the ADI processing of a faint halo of eccentric, small grain dust, which is expected in disks around hot stars (Strubbe & Chiang 2006). We therefore suggest the features be henceforth referred to as the "halo traces." This term effectively conveys that the physical source is a halo, but we are only seeing "traces" of it due to ADI processing.

Reductions of the Ls data set consistently showed residual signal inside the ring consisting of two regions of excess flux (Figure 5). These features, at <05 and at a P.A. consistent with the ring major axis, are detected at marginal SNRE (∼2–3) and thus are not assuredly real astronomical sources. To check whether the features were "carved out" by the outer disk in ADI reduction process, we inserted and recovered an artificial disk 90° away (Figure 5(c)). Residuals are present within the outer artificial disk, but there is no similar symmetric structure as is seen in Figure 5(b). If real, the best explanation for the inner structure would be a ring-like inner disk located at ∼36 AU. As will be discussed in Section 3, the known/outer disk is brightest in scattered light at Ls, so it might make sense that the inner disk would be brightest here as well. Furthermore, the features lie along the same P.A. as the outer disk, which should be the case for an inner disk viewed from Earth around this star. However, it is troublesome that the Gemini Planet Imager (GPI) failed to detect any hint of these features at the Ks band (Perrin et al. 2014), though those observations were limited by <40° of parallactic angle rotation. Furthermore, previous studies have predicted that an inner dust component should reside inside ∼10 AU (Augereau et al. 1999; Wahhaj et al. 2005; Koerner et al. 1998), which is much closer to the star than our observed features. On the other hand, an inner component so close to the star is not required to fully model the SED of the disk (Li & Lunine 2003). Additional imaging at high Strehl ratio and very small inner working angles will be required to determine if the features in our images are spurious residuals or evidence for an inner ring.

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We first considered compositional model fits to the scattered light data alone. These data come from HST/STIS, HST/NICMOS, and MagAO/Clio-2, and are shown in Figure 6. We considered only the porous two-component mixtures, since these resulted in predominantly better fits to the data than the simpler models. The lowest reduced chi-square value achieved was 0.89, indicating a very good fit (with perhaps overestimated errorbars). However, there were more than 1000 fits with reduced chi-square values ⩽2. This means that there are many reasonably good fits to the available scattered light data (see Figure 8(a)). Therefore to assess which root compositions were most often favored in the fits, we weighted each root composition at a given volumetric fraction in all 6705 fits by the inverse of the corresponding reduced chi-square values, 1/$\chi _{\nu }^2$, then computed the weighted average probabilities and normalized all of these values by the highest single probability. For example, in Figure 9, compositions with values close to 1 were favored more often in good fits than compositions with values close to 0.

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From Figure 9(a), we can immediately distinguish the compositions that were least favored: water ice, organics (Henning), tholins, iron, and troilite. The compositions that were most often favored are the olivines and pyroxenes (i.e., silicates), amorphous carbon, and organics (Li). The discrepancy between Henning and Li's organics likely arises from their differing optical constants.

Regarding porosity, we found that there was a slight preference for porosity = 30%, but this was only marginally favored over the others (Figure 10). The size distribution power-laws for each family were generally shallow, varying slightly around −3, and the minimum and maximum grain size were ∼2 μm and 500 μm, respectively. The absence of very small grains and the shallow power law suggest that large grains are required to reproduce the red slope of the scattered light photometry. This is comparable to the results of Köhler et al. (2008) and Li & Lunine (2003).

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Before proceeding to fitting the disk's thermal emission alone, we examined how well the good fits to the scattered light data reproduced the disk's thermal emission. Figure 8(b) shows that three good fits to the scattered light data shown in Figure 8(a) are poor fits to the thermal data. This suggests that caution should be exercised when interpreting models of a disk's scattered light data alone.

We next fit the disk's thermal emission alone.²⁰ We excluded emission at λ < 13 μm to ensure the models were testing predominantly the outer (known) disk alone. We found that the best fit composition had a reduced chi-square of 1.83, indicating a marginally good fit. Whereas there were ∼1000 fits with reduced chi-square values <2 for the scattered light data, there were only 8 such fits for the thermal data. Nonetheless, it is still instructive to gauge which root compositions were the most frequently preferred. Therefore we calculated the relative probabilities for each root composition's fractional abundance in all 6705 porous two-component fits, as before for the scattered light case.

Figure 9(a) shows that amorphous carbon and astrosilicates were the most frequently preferred root compositions. The least preferred were the water ices, iron, troilite, and crystalline olivine. It is not surprising that crystalline olivine was not preferred because its optical constants have very narrow features in the thermal infrared. To detect such features, high-resolution spectra are required (e.g., de Vries et al. 2012).

The preferred fractional porosity was 70% (Figure 10), marginally favored over the others. The average power law for the thermal fits was ∼−3.4, with the best-fitting models using ∼−4. The minimum and maximum grain sizes were ∼3.5 μm and 600 μm, similar to the large grains preferred in fits to the scattered light data alone.

As was the case for the scattered light models, the best fitting thermal emission model failed to reproduce the scattered light data (Figures 8(d) and (c)). This once again shows that when fitting just the scattered light alone or just the thermal data alone, the preferred model fails to reproduce both data sets simultaneously.

Can any compositional mixture reproduce the entire SED (both scattered light and thermal emission) of the HR 4796A debris disk? To test this, we repeated the model fitting process using both the scattered light and thermal emission data simultaneously. The best-fitting model had a reduced chi-square value of 2.14, indicating a mediocre fit (Figures 8(e) and (f)). As before, we computed the relative probability of each root composition's fractional abundance. Figure 9(a) shows that the results are similar to the previous cases, with silicates and organics being the most frequently preferred and water ice, iron, and cyrstalline olivine being the least preferred.

Lower porosities were preferred more than higher porosities (Figure 10). The average size distribution power law was ∼−3.4, with the power-law being ∼−2.5 for the best-fitting mixtures. The minimum and maximum grain sizes were ∼3 μm and 500 μm, similar to the previous cases.

Up to this point, we have tried to fit the scattered light and thermal emission of the HR 4796A debris disk using porous two-composition mixtures with few fitting constraints. For example, we tested a wide range of size distribution power-law exponents, and we used the phase function generated by Mie theory. Which compositions are preferred if these two constraints are varied?

To test this, first we refit the data (scattered light and thermal simultaneously) while enforcing a Dohnanyi size distribution (power-law exponent = −3.5). Second, we refit the data while ignoring the phase function predicted by Mie theory. Specifically, we fit the thermal data, and then arbitrarily scaled the model disk until it best matched the scattered light data. Finally, we repeated these same fits while also enforcing a Dohnanyi size distribution.

Figure 9(b) shows that for a Dohnanyi size distribution, silicates and organics were the predominantly preferred compositions and the best overall fit (Figures 11(a) and (b)) had a reduced chi-square of 2.68, indicating a poor fit. If we ignored the Mie phase function and relaxed the Dohnanyi constraint, organics and silicates were the most preferred compositions and the best overall fit (Figures 11(c) and (d)) had a reduced chi-square of 2.08, indicating a mediocre fit. If we ignored the Mie phase function and also enforced a Dohnanyi size distribution, organics and silicates were the most often preferred and the best overall fit (Figures 11(e) and (f)) had a reduced chi-square of 2.64, indicating a poor fit. These results are similar to our findings in the previous fitting cases, with slight variations.

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The silicate compositions (amorphous olivine, iron-poor/nominal iron/iron-rich olivine, astrosilicates, and the pyroxenes) were always generally preferred over the other compositions (Figure 9). Furthermore, these compositions were favored at higher fractional abundances (i.e., >50%). Therefore we consider it likely that the HR 4796A dust contains silicates.

Crystalline olivine was only favored in the scattered light case. However, because we did not have high-resolution thermal spectra (near 69 μm in particular; de Vries et al. 2012), its unique spectral features would not have been detected even if it was abundant. On the other hand, Kessler-Silacci et al. (2005) found no spectral features indicative of crystalline silicates at 8–13 μm. Therefore we conclude that if crystalline olivine is present, it is likely at low fractional abundance.

The water ice compositions (Li/Warren/Henning water ice) were generally not preferred. Furthermore, good fits containing water ice seemed to require smaller fractional abundances (i.e., the most probable volumetric fractions were usually <50%). Therefore we conclude that water ice must either be at very low abundance or not present at all in the HR 4796A dust. The lack of water ice may not be surprising, since for stars earlier than M type, UV sputtering has been predicted to remove icy grains on very short timescales (Grigorieva et al. 2007). If the collisional timescale for the dust around HR 4796A is much longer than the photosputtering timescale, grains will be ice-poor for most of their lives, potentially explaining our findings. Interestingly, the lack of water ice in the dust around HR 4796A is counter to a few other debris disks that have been found to require more water ice (Donaldson et al. 2013; Lebreton et al. 2012; Chen et al. 2008). This could point to real differences in dust compositions, though resolved scattered light at multiple wavelengths from 1 to 4 μm is still absent for these disks.

Compositions containing carbon (amorphous carbon, Li/Henning organics, Titan tholins) were generally favored, and at high volumetric fractions. Therefore we consider it likely that the HR 4796A dust contains organics. The specific "type" of organics is still not certain, given the discrepancies between the root compositions (e.g., the Li and Henning organics), which most likely arise due to their differing optical constants. The tholins that were proposed in Debes et al. (2008a) were favored less often than the other organics, suggesting that any complex organics are unlikely to be the dominant constituent of the dust. Nonetheless organics in general being favored suggests that at least some of the base building blocks of Earth-like life, which are also found in interstellar dust (Zubko et al. 2014) and solar system comets (e.g., Protopapa et al. 2014; Zubko et al. 2014), may be present around HR 4796A.

Troilite was generally infrequently preferred and there was no discernible trend in volumetric fraction. Therefore we consider troilite to be unlikely to comprise the dust around HR 4796A.

Iron was generally not frequently preferred, other than an apparently special case involving 30% fractional abundance (Figure 9). However, the iron-rich and nominal iron compositions of the olivines and orthopyroxenes were generally favored over the iron-poor cases. This might suggest that more iron is required in the silicates. Therefore we consider iron to be a plausible constituent of the dust around HR 4796A.