HD 104860 and HD 192758: Two Debris Disks Newly Imaged in Scattered Light with the Hubble Space Telescope

The data on HD 104860 and HD 192758 were obtained as part of two surveys with the near-IR NICMOS instrument on HST that aimed to resolve a selection of debris disks identified from their infrared excess with the Spitzer Space Telescope (HST-GO-10527, PI: D. Hines) and with IRAS/Hipparcos (HST-GO-11157, PI: J. Rhee), respectively. The data were all obtained with the intermediate-sampling camera NIC2 (007565 pixel⁻¹) and with its coronagraphic mode featuring a 03 radius occulting mask.

HD 104860 was observed in two telescope orientations, with the spacecraft rolled by 30° to enable the subtraction of the coronagraphic point-spread function (PSF) through roll differential imaging (Lowrance et al. 1999). HD 192758 was also observed in two 30° different rolls on 2007 July 03, then again in two other rolls about a year later (UT 2008 June 04). However, the guide star acquisition failed during one roll of the later observing sequence, and none of the integrations within this roll were acquired with the star centered on the occulting spot. We only used exposures from the three successful roll acquisitions in our study, and we combined data from both epochs to maximize the signal-to-noise ratio (S/N) on the detection, as we do not expect significant temporal variations in the disk morphology and photometry.

HD 104860 was observed with the NICMOS F110W filter, and HD 192758 with both the F110W and F160W filters. These two wideband filters were the most commonly used for NICMOS coronagraphic observations, which facilitated assembling large and homogeneous PSF libraries for advanced post-processing (Hagan et al. 2018). The F160W NICMOS filter (pivot wavelength 1.600 μm, 98% integrated bandwidth 0.410 μm) is comparable to the ground-based H bandpass, while the NICMOS F110W filter (pivot wavelength 1.116 μm, 98% integrated bandwidth 0.584 μm) is twice as extended toward shorter wavelengths as the J band.

The observing parameters and instrument characteristics of the three data sets (HD 104860 (F110W), HD 192758 (F110W), and HD 192758 (F160W)) are summarized in Table 1.

To detect the signal of the disks, which is fainter compared to the star, we used the multi reference-star differential imaging (MRDI) PSF subtraction method developed for the ALICE program (Soummer et al. 2011; Choquet et al. 2014). We assembled and registered large and homogeneous libraries of coronagraphic images from the NICMOS archive, gathering images from multiple reference stars observed as part of several HST programs. These libraries were used to subtract the star PSF from each exposure of the science target with the Principal Component Analysis (PCA) KLIP algorithm (Soummer et al. 2012).

All of the images used to process the HD 104860 data set (PSF library and science images) were calibrated with contemporary flat-field images and observed dark frames as part of the Legacy Archive PSF Library and Circumstellar Environments (LAPLACE) program.¹² Conversely, HD 192758's data were obtained in HST cycle 16, the last operational cycle of NICMOS, and were not included in the LAPLACE calibration program. To have libraries large enough to sample the PSF variations as well as representative of HD 192758's images, we assembled PSF libraries both from LAPLACE programs and from the non-LAPLACE HST-GO-11157 program. The latter was processed with the NICMOS calnica calibration pipeline and bad pixel corrected. For HD 104860's and HD 192758's data sets, we respectively down-selected 60% and 30% of the images in the libraries most correlated with their respective science frames. This selective criterion ensures that the images in the libraries are well representative of the star PSF in each science frame (Choquet et al. 2014), and minimizes the oversubtraction of the astrophysical signal, especially in the case of extended objects, which project more strongly on poorly matched PSF components with PCA-type algorithms.

We applied the KLIP algorithm to the cropped sub-images of the science target excluding a central circular area. The number of principal components (PCs) used for the PSF subtraction was selected to maximize the S/N on the disks after visual inspection of the final images. The PSF-subtracted exposures were then rotated to have north pointing up, co-added, and scaled to surface brightness units based on the exposure time, HST's calibrated photometric factors (F_ν), and plate scale. The post-processing parameters (crop size, mask radius, PSF library size, number of PCs) are listed in Table 1.

To estimate the noise in the final images, we processed the reference star images from the PSF libraries with the same method and reduction parameters as the science images. The PSF-subtracted libraries were then partitioned into sets with the same number of frames as the science targets, rotated with the target image orientations, and combined. The noise maps were computed from the pixel-wise standard deviation across these sets of processed reference star images.

HD 104860 is an F8 field star at 45.0 ± 0.5 pc (Gaia Collaboration et al. 2016). Its age was estimated, based on its chromospheric activity, to be 32 Myr by Hillenbrand et al. (2008), and to be 19–635 Myr by Brandt et al. (2014). The system has a significant infrared excess at 70 μm identified with Spitzer with a fractional infrared luminosity of L_dust/L_⋆ ∼ 6.3 × 10⁻⁴ (Hillenbrand et al. 2008). Its SED is well-described by a two-temperature blackbody model, with a warm dust population at 210 ± 27 K with a fractional luminosity of 2.4 × 10⁻⁵ and a cold dust population at 42 ± 5 K with a large infrared fractional luminosity of 2.8 × 10⁻⁴ (Chen et al. 2014). Without a prior on the dust separation to the star and assuming that the disks are in radiative and collisional equilibrium, these blackbody emissions correspond, respectively, to a ∼10⁻⁵ M_Moon disk at a radius of 3 au from the star, and to a massive ∼1.5 M_Moon cold disk at a radius of 366 au, based on silicate spherical grain compositions. By measuring the cold disk spectral index in the millimeter from VLA and ATCA observations, MacGregor et al. (2016b) estimated a dust size distribution in the system with a power-law q = 3.64 ± 0.15, consistent with steady-state collisional cascade models (Dohnanyi 1969; Gáspár et al. 2012; Pan & Schlichting 2012). Assuming a disk composed of astro-silicates (Draine 2003), a stellar luminosity of L_⋆ = 1.16 L_⊙, and mass of M_⋆ = 1.04 M_⊙, the radiative pressure blowout grain size limit is estimated as a_blow ∼ 0.4 μm, but the minimum grain size is inferred to be ∼7 μm from joint modeling of the system's SED and Herschel images (Pawellek et al. 2014).

The disk was first resolved in thermal emission at 100 and 160 μm with Herschel-PACS (Morales et al. 2013) then marginally resolved at 1.3 mm with CARMA (Steele et al. 2016). The Herschel image at 100 μm shows a disk of radius 116 ± 6 au, three times smaller than the radius inferred from SED modeling, and inclined by 54° ± 7° from face-on with a position angle (PA) of 1° ± 7°. Such a significant difference in radius between observations and SED modeling is found for many resolved systems and stresses the need for resolved images to put constraints on debris disk properties. Using the radius inferred from the Herschel image to constrain SED modeling, Morales et al. (2016) found that both pure astro-silicate grains and a mixture of water ice and astro-silicates could compose the dust in the system.

In our F110W NICMOS image, we detect a large ring-shape debris disk around HD 104860 with a radius of ∼112 au (∼25), inclined by ∼60° from face-on. The disk is detected at S/N ∼ 2–4 per pixel and S/N ∼15 integrated over the disk area detected above 1.5σ. This detection enables us to put strong constraints on the disk's general morphology (see Section 4), but the S/N is too low to reliably comment on the substructures within the disk. The observed morphology largely agrees with the Herschel thermal emission image, with a 60 times better angular resolution (95 mas versus 59 resolution), and provides the first image of the dust in the scattered-light regime. The east side is significantly brighter than the west side, indicative of anisotropic scattering from the dust and showing the near side of the disk, assuming grains preferentially forward-scatter. Our image unambiguously reveals a cleared cavity from the disk's inner edge and down to ∼45 au from the star, which we further characterize in Section 4.

We detect a bright point source ∼35 northwest from the star. We report its astrometry in Table 3. We identify it as candidate #1 detected in Metchev & Hillenbrand (2009), and we confirm that its astrometry is consistent with a background star, as noted by the authors. We note that this object is wrongly reported as a binary companion in the Washington Double Star catalog (WDS 12046+6620AB). To further confirm the background nature of this point source, we reprocessed a Keck-NIRC2 archival data set acquired on UT 2013 January 27 using the K' filter (program N117N2, PI: F. Morales). After standard processing and registration steps, we detect the point source using the classical Angular Differential Imaging (Marois et al. 2006) PSF subtraction method. We report the measured astrometry of the point source relative to HD 104860 in Table 3. The point source indeed follows the background track between the three epochs, although we note a significant shift between the measured position and the background-track-predicted astrometry over the 11 year baseline that is likely due to the background star's own proper motion (see Figure 3).

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HD 192758 is an F0V star at 67 ± 2 pc (Gaia Collaboration et al. 2016). Moór et al. (2006) reported a 50% probability for the star, of age 50 ± 5 Myr, to be a member of the IC 2391 supercluster (Navascués et al. 2004). On the other hand, Chen et al. (2014) found the system to be a field star of isochronal age ∼830 Myr. The system has a fractional infrared excess around 100 μm with L_dust/L_⋆ ∼ 5.6 × 10⁻⁴ (Moór et al. 2006). It is well modeled by a two-temperature blackbody emission, with a warm disk at 164 ± 7 K with a fractional luminosity of ∼0.38 × 10⁻⁴ and a cold dust belt at 54 ± 6 K with a fractional luminosity of ∼4.1 × 10⁻⁴ (Chen et al. 2014). Assuming the disks to be in radiative and collisional equilibrium and composed of silicate spherical spheres, these blackbody emission corresponds to dust belts of mass ∼1.3 × 10⁻⁴ M_Moon and ∼8.7 × 10⁻¹ M_Moon, respectively, and at radii ∼6 au and ∼152 au, respectively.

We spatially resolve the outer disk in HD 192758 in both the F110W and the F160W data sets. In the F110W image, the disk is detected up to S/N ∼ 6 per pixel, and S/N ∼ 45 integrated over the pixels above 1.5σ. In F160W, the detection is found with S/N up to ∼4 per pixel, and with S/N ∼ 21 integrated over the disk area above 1.5σ. The disk presents a similar morphology in the two images. They both reveal a disk of radius ∼100 au (∼15) and inclined by ∼60° from face-on. As for HD 104860, the disk radius is significantly smaller than the disk radius estimated from SED modeling, which stresses again the need for imaging to put reliable constraints on disk properties. The south side of the disk is not detected, which also indicates anisotropic scattering by the dust grains, presumably showing the near side of the disk north of the star.

Assuming that the morphology of the astrophysical source is known, the post-processing throughput can be inferred though forward modeling. To constrain the morphology and photometry of the disks detected around HD 104860 and HD 192758, we used the same methodology as in Choquet et al. (2016), using parametric modeling and the analytical forward modeling method (valid with PCA-type algorithms; Soummer et al. 2012; Pueyo 2016). This method consists of subtracting from the source's model its projection on the eigenvectors used to process the data.

We generated a grid of disk models with a set of free parameters that we wish to constrain, and convolved each model with a synthetic unocculted NICMOS PSF generated in the corresponding filter with the Tiny TIM package (Krist et al. 2011). From each model, we then subtracted its projection on the same eigenvectors as used for the science data, intrinsically using the same reduction zone and number of PCs. This process removes from the raw input model the part oversubtracted during post-processing and reveals the (hereafter) forward model. We then rotated and combined these forward models with the same parameters and angles as the science images, and we scaled the resulting model to the total flux of the disk in the science image. Each forward model is then directly compared to the disk image.

We used the GRaTer radiative transfer code to create the disk models (Augereau et al. 1999b; Lebreton et al. 2012). This code computes optically thin centro-symmetric disk models assuming a Henyey & Greenstein (1941) SPF of asymmetric parameter g. The dust density distribution n(r, z) is parametrized with a radial profile R(r) falling off with power laws α_in and α_out inward and outward from a parent belt at radius R₀, and with a Gaussian vertical density Z(r, z) profile with a scale height ζ(r) rising linearly with an aspect ratio h:

$$\begin{eqnarray}&&n(r,z)\propto R(r)Z(r,z),\end{eqnarray} \tag{ 1 }$$

with

$$\begin{eqnarray}&&R(r)={\left({\left(\displaystyle \frac{r}{{R}_{0}}\right)}^{-2{\alpha }_{\mathrm{in}}}+{\left(\displaystyle \frac{r}{{R}_{0}}\right)}^{-2{\alpha }_{\mathrm{out}}}\right)}^{-1/2},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&Z(r,z)=\exp \left(-{\left(\displaystyle \frac{| z| }{\zeta (r)}\right)}^{2}\right),\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&\zeta (r)={hr}.\end{eqnarray} \tag{ 4 }$$

The disk center relative to the star's position is parametrized by the offsets du and dv in the disk plane, with du along the major axis (unaffected by projection effects) and dv along the perpendicular axis (appearing projected along the disk's minor axis). The model image is simulated with a PA parametrized by θ and inclination i. Given the geometry of the two systems, the vertical scale heights of the disks are not properly constrained by our data. We fix the aspect ratio to h = 0.05, a reasonable thickening assumption for unperturbed debris disks due to the combined action of radiation pressure and the grains' mutual collisions (Thébault 2009). Furthermore, given the inclinations of the disks, a Henyey–Greenstein SPF model will describe the surface brightness variations in the disks over a range of scattering angles limited by the disk inclinations, but it might not properly describe the actual SPF over all angles (see Hedman & Stark 2015).

We estimated the goodness of fit of our models to the disk image by computing the reduced χ²_red value over a large area encompassing the disk in the image. After identifying the best model within the grid, we refine the best-fit parameters by interpolating the reduced chi-squared values around the best model in the grid, independently for each parameter. The best chi-squared values are larger than 1 because the noise maps are overall slightly underestimated, although very representative of the noise spatial distribution (e.g., the noise signature from spider residuals). To estimate the uncertainties on the model parameters, we thus normalize the chi-squared value by its best value, assuming that the noise underestimation is common to all pixels. We then estimated the uncertainty on each parameter assuming that our estimator follows a chi-squared distribution, from the values at which the interpolated ${\chi }_{\mathrm{red}}^{2}$ increased by $1\sigma =\sqrt{2/{N}_{\mathrm{dof}}}$ from 1, with N_dof the number of degrees of freedom in the fit.

For HD 104860, we generated a grid of 546,875 models with eight free parameters to constrain its morphology. Table 4 describes the simulated parameter ranges and best-fit values. The goodness of fit of each parameter is also presented in Figure 4. The data were fit within an elliptical area of semimajor axis 42 oriented north–south and semiminor axis 26, excluding the central area masked during post-processing, which resulted in N_dof = 5536 degrees of freedom in the fit. This area excludes the background star ∼35 from the star. The image of the best model and the comparison to the NICMOS image and noise map are presented in Figure 5 within the fit area.

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Table 4.  Parameter Grid and Best Model for HD 104860

Parameter	Minimum	Maximum	Nval	Best Model	Best Model
				(in grid)	(interpolated)a
R0 (au)	106	122	5	114	114 ± 6
$| g|$	0.0	0.4	5	0.2	0.17 ± 0.13
θ (°)	−5	7	5	1	1 ± 5
i (°)	52	64	5	58	58 ± 5
αin	2	10	5	10	≥4.5
αout	−6	−2	5	−4	−3.9 ± 1.6
du (au)	−10	10	5	0	2 ± 7
dv (au)	−20	10	7	−5	−7 ± 13
${\chi }_{\mathrm{red}}^{2}$	⋯	⋯	⋯	1.833	1.826

Note.

^aShows 1σ uncertainties.

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We find that the best fit to HD 104860's data is a disk of radius R₀ = 114 ± 6 au, inclined by i = 58° ± 5° from face-on, with a PA of θ = 1° ± 5° east of north. These values are consistent with the morphology of the disk observed at 100 μm and 160 μm by Morales et al. (2013). We find a relatively low value for the Henyey–Greenstein parameter of anisotropic scattering, with $| g| =0.17\pm 0.13$, indicative of grains favoring forward scattering. This value is expected for a disk of moderate inclination such as HD 104860, which does not probe very small scattering angles (>32°): slightly forward scattering SPFs with a Henyey–Greenstein parameter around $| g| =0.1\mbox{--}0.3$ have been observed for many debris disks with similar or lower inclinations (HD 92945, HD 107146, HD 141569, HD 207129, Fomalhaut; Ardila et al. 2004; Kalas et al. 2005; Krist et al. 2010; Golimowski et al. 2011; Mawet et al. 2017). As mentioned before, this may not be representative of the SPF at smaller scattering angles, as it was shown that, for some dust grains, it may significantly differ from a Henyey–Greenstein model and sharply peak at angles below 40° despite a relatively flat phase function at large angles (Hedman & Stark 2015; Milli et al. 2017b).

Our analysis shows that the disk has a ring shape with an asymmetric radial density profile. We find that the disk outer edge follows a power law in α_out = −3.9 ± 1.6, corresponding to a surface density in ${r}^{{{\rm{\Gamma }}}_{\mathrm{out}}}$ with Γ_out = α_out + 1 =−2.9 ± 1.6, assuming a scale height rising linearly with radius (Augereau et al. 1999b). This is consistent within our uncertainties with disk evolution models, which predict an outer surface density profile in Γ_out = −1.5 for small grains created under steady-state collisions and set on eccentric orbits by radiative pressure, accumulating in the outskirts of their birth ring (Strubbe & Chiang 2006; Thébault & Wu 2008). We find that the disk inner edge is very sharp, with a lower limit of ${\alpha }_{\mathrm{in}}\geqslant 4.5$ on the inward power law of its radial density profile. The sharp inner edges in debris disks can be sculpted by planets orbiting within the disk, confining the dust out of a chaotic zone through mean motion resonances (Wisdom 1980; Mustill & Wyatt 2012), while unperturbed systems have smoother inner edges filled by small grains due to Poynting–Robertson drag. We do not find significant offsets of the ring with respect to the star within ±7 au along the disk major axis, and within ±13 au projected on the minor axis, indicating that a planet responsible for carving the disk inner edge would have a low eccentricity.

Using the best-fit morphological parameter values, we de-project the NICMOS image based on the disk inclination, PA, and offsets, and compute its radial and azimuthal average profiles (see Figure 6). In the following, we quantify the disk photometry using both the NICMOS image, which is affected by oversubtraction as shown in Figure 5, and the best model before forward modeling, which is free of post-processing artifacts but is entirely model dependent.

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In the NICMOS image, we measure a surface brightness on the disk spine of 11.7 ± 0.8 μJy arcsec⁻² averaged over all scattering angles excluding 91° ± 23° and 271° ± 26°, where stellar residuals from the telescope spider dominate the disk brightness. We find a corresponding average surface brightness of S = 17.8 μJy arcsec⁻² in the best model unbiased by oversubtraction. The south ansae is ∼30% brighter than the north one in the NICMOS image (S_S = 16 ± 6 μJy arcsec⁻² and S_N = 12 ± 5 μJy arcsec⁻² respectively), but the asymmetry is not significant given our uncertainties. From the stellar flux (F_⋆ = 3.1 Jy in the NICMOS F110W filter), we estimate that the disk has a typical reflectance of R = S/F_⋆ =(5.7 ± 0.3) × 10⁻⁶ arcsec⁻², based on the mean surface brightness of the model. We estimate the disk flux density to F_scat = 200 ± 5 μJy, integrated in the best model over an elliptical surface of 20 arcsec² with outer semimajor axis 39, inner semimajor axis 16, and the inner and outer semiminor axes projected from the semimajor axis values by the best-fit inclination $\cos (i)$, and with a PA equal to the best-fit value θ. The flux density integrated in the NICMOS image over the same surface is 92 ± 5 μJy, significantly affected by the post-processing throughput. Compared with the flux of the star, this correspond to a scattering efficiency of f_scat = F_scat/F_⋆ =(67 ± 2) × 10⁻⁶, based on the model's flux density.

The scattering efficiency provides a measure of the dust-scattering albedo ω knowing the total luminosity received by the grains (Krist et al. 2010; Golimowski et al. 2011):

$$\begin{eqnarray}&&\omega =\displaystyle \frac{{f}_{\mathrm{scat}}}{{f}_{\mathrm{emit}}+{f}_{\mathrm{scat}}},\end{eqnarray} \tag{ 5 }$$

with ${f}_{\mathrm{emit}}={L}_{\mathrm{dust}}/{L}_{\star }$ the disk infrared fractional luminosity. The scattering albedo is an empirical quantity that provides a degenerate, wavelength-averaged combination of the grains' albedo and of the disk SPF integrated over the scattering angles probed by the disk geometry. The true albedo of the dust can only be recovered with assumptions on the disk's SPF. Assuming that our scattering efficiency measurement integrates the light scattered by the grains responsible for the thermal emission and using the infrared fractional luminosity of f_emit = 6.4 × 10⁻⁴ reported for the outer disk by Morales et al. (2016; well-constrained from 24 μm to 1.3 mm photometry), we find a scattering albedo of ω = 9.5% ± 0.3%.

We compared this value to the scattering albedo of grains with various compositions and porosities, computed under the Mie theory for a disk with the best-fit morphology found for HD 104860 in the F110W filter (Figure 7). We find that our scattering albedo estimation rules out pure water ice composition and is consistent with dirty ice grains (Preibisch et al. 1993) larger than ∼3 μm in the case of compact grains and larger than ∼1 μm in the case of 90% porous grains. Assuming compact grains, this is consistent with particles larger than the blowout size, as was suggested by Pawellek et al. (2014) for this disk (typical grain size of 7 μm, blowout size of 0.4 μm), although they used pure silicate grains in their study. Assuming 90% porous grains, the blowout size is 10 times larger than that for compact grains, which is consistent with our scattering albedo value. A few other debris disks, e.g., HD 181327 and HD 32297, are suspected to have porous grains (Lebreton et al. 2012; Donaldson et al. 2013). However, they are also much brighter than HD 104860, which may also indicate a different composition.

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For HD 192758, we generated a single grid of models that we fit separately to the F110W and F160W images. It is indeed reasonable to assume a similar dust density distribution in both images but possibly different scattering properties at the two different wavelengths (albedo, SPF). We simulated 604,800 models with seven free parameters, fixing the offset along the disk minor axis to dv = 0, as this parameter is unconstrained by our data given the disk geometry. We present the simulated parameter ranges and best-fit values in Table 5 for both filters. The goodnesses of fit are presented jointly in Figure 8. The shaded areas show better constraints on some parameters when combining the fits to both data sets. We computed the chi-squared values in an elliptical area of semimajor axis 26 oriented east–west and semiminor axis 19, and excluding the central area masked during post-processing. The same area was used for both data sets and corresponds to N_dof = 2525 degrees of freedom. We show in Figure 9 the best fit to the F110W data set and in Figure 10 the best fit to the F160W data, along with their respective comparison to the NICMOS images and noise maps.

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Table 5.  Parameter Grid and Best Models for HD 192758

				F110W	F110W	F160W	F160W
Parameter	Minimum	Maximum	Nval	Best Model	Best Model	Best Model	Best Model
				(in grid)	(interpolated)a	(in grid)	(interpolated)a
R0 (au)	81	109	5	95	95 ± 12	95	95 ± 9
$| g|$	0.15	0.6	10	0.3	0.29 ± 0.12	0.4	0.41 ± 0.16
θ (°)	−101	−77	7	−93	−93 ± 7	−85	−85 ± 8
i (°)	50	70	6	62	60 ± 8	58	58 ± 7
αin	1	11	6	7	$\geqslant 1.4$	11	$\geqslant 2.9$
αout	−3.5	−1	6	−2	−2.0 ± 0.8	−2	−2.0 ± 0.9
du (au)	−10	25	8	10	11 ± 15	5	4 ± 12
${\chi }_{\mathrm{red}}^{2}$	⋯	⋯	⋯	4.864	4.857	2.247	2.246

Note.

^aShows 1σ uncertainties.

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We find that the best-fit parameters are consistent for both data sets. In the following, we describe the best model by averaging the F110W and F160W best parameter values and the uncertainties combined from the two fits, which provides better constraints, except for two parameters ($| g|$ and θ) as discussed below. The disk has a radius of R₀ = 95 ± 9 au and is seen inclined by i = 59° ± 7° from face-on. The best-fit PA differs by 8° between the two data sets. This may be due to starlight residuals from the telescope spider, at a comparable orientation to the disk major axis, which may bias the disk PA. The mean PA between both fits is θ = −89° ± 12° east of north, using conservative error bars encompassing uncertainties from the two fits. The disk has a relatively low Henyey–Greenstein parameter of anisotropic scattering, with values of $| g| =0.29\pm 0.12$ in the F110W image and $| g| =0.41\pm 0.16$ in the F160W image. Differing values can be explained by different scattering properties at different wavelengths, although we do not expect a significant difference, as the two bandpasses are relatively close. As for HD 104860, these relatively low values are consistent with the finding of Hedman & Stark (2015) about the apparently low g values of inclined disks observed only near scattering angles of 90°.

We find that the dust density follows a radial power law in α_out = −2 ± 0.8 outward from the parent radius, which is very consistent with the sharpness expected from evolution models with small grains on eccentric orbits accumulating outside of the main belt colliding zone (Thébault & Wu 2008). Given the disk inclination and the quality of our images, we can only put a weak constraint on the radial profile inward from the parent radius R₀, with a power-law coefficient steeper than α_in > 2.9. We find that the disk center may be offset by du = 7 ± 12 au along the major axis but we cannot rule out a system centered with the star.

As shown in Figures 9 and 10, oversubtraction from post-processing strongly affects the disk photometry, due to its compact appearance in the image (14 semimajor axis, and 07 semiminor axis at the edge of the reduction mask). The averaged radial and azimuthal profiles measured in the NICMOS images are thus noisy and biased by oversubtraction so we relate hereafter photometric values from the best models before forward modeling only. In the F110W filter, we measure a mean surface brightness of S^F110W = 108 ± 3 μJy arcsec⁻² in the north ansae and S^F160W = 81 ± 5 μJy arcsec⁻² in the F160W data. Given the stellar flux in these bands (F_⋆^F110W = 4.85 Jy and ${F}_{\star }^{{\rm{F}}160{\rm{W}}}\,=3.26$ Jy, respectively), the disk reflectances in the north ansae are R^F110W = (22.3 ± 0.6) × 10⁻⁶ arcsec⁻² and R^F160W =(25 ± 2) × 10⁻⁶ arcsec⁻² in the F110W and F160W NICMOS filters. By integrating the disk flux over a 7.1 arcsec² elliptical area (outer and inner semimajor axes 23 and 10, oriented with the best PA θ east of north, minor axes projected by $\cos (i)$ from the major axis values), we find flux densities of ${F}_{\mathrm{scat}}^{{\rm{F}}110{\rm{W}}}\,=411\pm 9\,\mu \mathrm{Jy}$ in the F110W filter and ${F}_{\mathrm{scat}}^{{\rm{F}}160{\rm{W}}}=319\pm 12\,\mu \mathrm{Jy}$ in the F160W filter. After normalizing by the stellar contribution, we find that the disk around HD 192758 has scattering efficiencies of ${f}_{\mathrm{scat}}^{{\rm{F}}110{\rm{W}}}=(85\pm 2)\times {10}^{-6}$ and ${f}_{\mathrm{scat}}^{{\rm{F}}160{\rm{W}}}\,=(98\pm 4)\times {10}^{-6}$, respectively, in the two NICMOS filters.

From these scattering efficiency measurements in two different NICMOS filters, we can measure the disk color. We find that it has a scattering efficiency ratio of ${f}_{\mathrm{scat}}^{{\rm{F}}110{\rm{W}}}/{f}_{\mathrm{scat}}^{{\rm{F}}160{\rm{W}}}=0.87\,\pm 0.05$ (F110W – F160W color index of 0.15), indicating a red color for the disk. Assuming spherical silicate grains following the Mie theory, this color is consistent with the lack of particles smaller than ∼0.5 μm in the parent belt, which is also consistent with the minimum size a_blow = 1.4 μm under which silicate grains are blown out from the system by radiative pressure, assuming a stellar luminosity L = 4.9 L_⊙, stellar mass of M = 1.2 M_⊙, and a dust mass density of ρ = 3.3 g.cm⁻³.

Based on the disk infrared fractional luminosity f_emit = (5.7 ± 0.3) × 10⁻⁴ from Moór et al. (2011), we find scattering albedo values of ω^F110W = 13.0% ± 0.6% and ω^F160W = 14.7% ± 0.7% in the F110W and F160W filters, respectively. As found for HD 104860, these values rule out pure water ice composition (see Figure 11). They are consistent with compact silicate grains larger than ∼6 μm, which is significantly larger than the blowout size of a_blow = 1.4 μm for this system, as well as with dirty ice grains larger than ∼3 μm.

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