HUBBLE SPACE TELESCOPE OBSERVATIONS OF THE HD 202628 DEBRIS DISK

As shown in Figure 1, positive and negative images of a disk, along with background sources, are apparent when the image from the second roll is directly subtracted from the one from the first. Application of the iterative subtraction algorithm reveals that the disk is a ring inclined from face-on by ∼64° (based on the apparent major/minor axes ratio) with the apparent major axis aligned along P.A. = 130°. Most of the disk along the minor axis is obscured by large subtraction residuals, the STIS occulter, and the HST diffraction spikes. Within r < 35 (85 AU) there is a halo of unsubtracted starlight; such residuals are expected due to PSF mismatches caused by time-dependent telescope aberrations and pointing errors (Krist 2004).

The ring is asymmetric. The inner and outer apparent edges of the northwest ansa are at 58 (142 AU) and 87 (212 AU), respectively. In the SE ansa they are at 66 (162 AU) and 104 (254 AU). The outer radius is noise limited, so based on the apparent image the fractional width is Δr/r ≈ 0.4.

There are azimuthal brightness asymmetries, as shown in Figure 3. The ring appears clumpy due to the noise, but it is probably azimuthally smooth. The per pixel signal-to-noise ratio is about 1.0 in the ansae; the mean surface brightness in the SE ansa is ∼80 × less than the PSF at the same location before subtraction. We would not expect any significant amount of material within the ring interior due to the lack of 24 μm emission (Koerner et al. 2010). Without any color information, we assumed neutral scattering by the dust and measured peak and mean surface brightnesses, respectively, of V = 23.6 and 24.0 mag arcsec⁻² (±0.2 mag) in the NW ansa.⁴ The SE ansa is about half as bright. Visible portions of the NE section of the ring are about 20%–50% brighter than the opposite side. For comparison, the Fomalhaut ring has a surface brightness of ∼21.5 mag arcsec⁻² (Kalas et al. 2005) and HD 207129's is 23.7 (Krist et al. 2010).

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The ring is eccentric, and the offset of the ring center from the star is apparent in Figure 4. Due to the low signal that prevented a reliable least-squares fit, we visually fitted an inclined ellipse to the ring inner edge while fixing one focus to the position of the star. The size of the ring, its aspect ratio, position angle (P.A.), and two-dimensional offset of the star from the center of the ellipse provide five independent observables. These are sufficient to constrain the five parameters needed for the model ellipse: semimajor axis, eccentricity, inclination, major axis P.A., and argument of periapse relative to the sky plane. Trial model runs showed that the semimajor axis, P.A., and inclination are strongly constrained, while the eccentricity and argument of periapse are slightly degenerate with each other. The latter interaction arises in this case because the stellar offset from the ring center is aligned along its projected minor axis, rather than along the major axis as in the case of Fomalhaut (Kalas et al. 2005).

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The best-fit parameters are an inner edge semimajor axis of 158 AU at P.A. = 134°, inclination of 61°, e = 0.18, and ellipse major axis aligned 60° behind the plane of the sky. While a smaller eccentricity combined with a major axis close to the sky plane would adequately fit the observed image, the parameters reported provided a much better fit to the deprojected image of the system. We estimate a ±0.02 uncertainty in e. The geometric center of the ellipse is offset from the star in the non-deprojected image by 19.5 AU (16.0 AU along P.A. = 130° and 11.3 AU along P.A. = 40°). Deprojected, the offset is 28.4 AU (16.0 AU along P.A. = 130°and 23.4 AU along P.A. = 40°).

Koerner et al. (2010) observed HD 202628 with Spitzer/MIPS, finding a strong 70 μm excess but only a photospheric flux density at 24 μm. An upper limit to the 24 μm excess can be assumed to be 3× the uncertainty in the absolute calibration, which is approximately 10% of the 24 μm flux density or 3.9 mJy. This, in combination with the 70 μm excess of 100 mJy, implies a dust temperature upper limit of ∼65 K. If a minimum grain size of a few microns and silicate emissivities are assumed (following Krist et al. 2010), the dust would need to be located at least 80 AU from the star to reproduce the Spitzer photometry. The observed ring inner radius of 160 AU implies a substantially colder dust temperature than the current Spitzer limit. Upcoming Herschel observations should clarify the spectral energy distribution and characteristic dust temperature for the disk.

The ring's diameter of ∼14'' (300 AU) observed with STIS is large enough to produce a resolved 70 μm source to Spitzer/MIPS. Koerner et al. (2010) do not report any size information for their 70 μm detections, so we investigated the source size in post-BCD mosaics retrieved from the Spitzer Heritage Archive. A two-dimensional elliptical Gaussian fit to the 70 μm source has a full width at half-maximum of 221 × 191 extended along P.A. 138°. Quadrature subtraction of the nominal MIPS 70 μm 16'' beam suggests an intrinsic source size of 15'' × 10'', consistent with the inclined ring seen in scattered light and elongated at essentially the same P.A. A small 06 offset between the centers of the 24 and 70 μm sources is not significant given the 70 μm signal-to-noise ratio of 11 (Koerner et al. 2010), so an assessment of a possible pericenter glow (Wyatt et al. 1999) awaits more sensitive Herschel data.

Figure 5 shows the ring's radial (relative to the disk center) surface brightness profile. It was derived from the filtered, deprojected image by computing the median value at each radius within the two 90° sectors on opposite sides of the star aligned along the apparent major axis of P.A. = 130° (horizontal axis in the deprojection). Note that no correction for azimuthal brightness variations was applied. The azimuthal root-mean-square (rms) values were concurrently determined. The radius was measured from the fitted ellipse's geometric center. The low signal-to-noise ratio of the image results in large error bars, but a rapid dropoff along the inner edge is evident and indicates a rather sharp truncation. However, we cannot discern whether the slope is due to the difference between a mid-plane radial density variation, the vertical disk structure seen integrated along the lines of sight, or a combination of both, though for a geometrically and optically thin disk the projection effect would be insignificant. The profile extends above the field noise (which has an rms equivalent surface brightness of ∼24.7 mag arcsec⁻²) over 120–300 AU (Δr/r ≈ 0.7). Between 150 and 220 AU (Δr/r = 0.4) the intensity is >50% maximum brightness, which is commonly used to define widths of ring-shaped disks. Rough estimates of radial power laws that describe the different zones of the surface brightness profile were determined: r¹² (100 AU <r < 156 AU), r² (156 AU <r < 182 AU), r^−4.7 (r > 182 AU). The true outer radius is indeterminate due to the noise.

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The western inner edge of the ring is closest to the star. A line drawn through the star and along P.A. = 130°, the apparent major axis of the ring (i.e., a horizontal line in Figure 4), intercepts the ring (as located by the fitted ellipse) at distances 137 (NW) and 172 (SE) AU from the star. In an azimuthally uniform disk, the brightness at the SE intercept of the line and ring should be 63% of that in the NW due to the difference in distances from the star. The SE is actually more than 50% fainter, so the ring probably does not have an azimuthally uniform dust distribution. Since both locations are at the same scattering angle, the degree of forward scattering does not affect the ratio. However, if we assume isotropic scattering, then the SW side, being closer to the star, should be brighter than the NE, but it is not. If we assume that the NE side of the ring is closest to us, forward scattering could cause the NE/SW brightness asymmetry.

To demonstrate this qualitatively and to constrain the degree of forward scattering, we generated three-dimensional-scattered light models. For simplicity, a circularly symmetric, azimuthally uniform disk with the measured offset from the star was implemented (the deviation of an elliptical ring from a circular one would not qualitatively change the results; the bulk of the illumination effect is due to the ring offset from the star). The model's dust distribution was specified by the three power laws described previously (though with +2 added to the exponents to account for the additional r⁻² stellar illumination falloff in the surface brightness). Without any strong constraint from the noisy data, an outer disk radius of 450 AU was assumed. We used a flat (non-flaring) disk with a 2 AU scale height (this is largely unimportant for these purposes). The Henyey-Greenstein scattering phase function was used with the amount of forward scattering defined by the parameter g (0 = isotropic, 1 = full forward scattering). To aid visual comparisons with the data, the models were PSF convolved, and then Poisson and read noise was added. Given the poor signal-to-noise level, we did not attempt to fit these models to the data but used them only to provide qualitative comparisons.

The models are shown in Figure 6. The top side of the model ring is closest to us. With isotropic scattering (g = 0), regions of the ring closest to the star are brighter. Once forward scattering is introduced, the near side becomes brighter, though the left/right asymmetry remains. It appears from a qualitative comparison with the data that the grains are only mildly forward scattering (0.15 < g < 0.25).

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Valenti & Fischer (2005) placed HD 202628 on a theoretical isochrone using its distance and absolute luminosity (assumed to be solar) to derive a best-fit age of 5.0 Gyr and an allowable range of 1.8–6.8 Gyr. Holmberg et al. (2009) estimated 5.9 Gyr with an even wider range of 1.6–10.2 Gyr, also based on isochrone fitting. However, the Ca ii H and K lines suggest activity consistent with a younger star (log R'_HK = −4.73; Henry et al. 1996), as does the X-ray emission (log L_X = 28.41; Hünsch et al. 1999). Using the methods described by Plavchan et al. (2009, hereafter P09), we derive ages of 2.3 Gyr using R'_HK and 1.2 Gyr using L_X. The star is clearly younger than the Sun but older than 1 Gyr, so we assume an age of 2.3 ± 1 Gyr. This makes HD 202628 one of the oldest stars with an imaged debris disk.

The eccentricity and sharp inner edge of Fomalhaut's ring suggested perturbations from a planetary-mass object (Kalas et al. 2005). Quillen (2006) predicted that a planet should be orbiting just inside the ring edge and with the same eccentricity. The discovery of Fomalhaut b near this predicted location appeared to validate this model (Kalas et al. 2008). The similar ring structures between HD 202628 and Fomalhaut likewise suggest the action of planetary perturbations in this new system. Two noteworthy differences are the higher eccentricity and broader width (in Δr/r terms) of HD 202628's ring. The former likely reflects a higher eccentricity for the perturbing planet. A possible explanation for the latter is suggested by the Chiang et al. (2009) models for the spatial distribution of small dust particles derived from parent bodies in an eccentric ring. Their Figure 3 shows how the steepness of the ring inner edge can be produced by either a lower-mass planet close to the ring or a higher-mass planet at a greater interior distance. Predictions for the outer profile differ substantially between these two scenarios, however, depending on mass and orbital radius. Specific simulations for HD 202628 are needed, but a semimajor axis of ∼120 AU and mass <10 M_Jupiter seem plausible.

There are significant limits to detecting planets at large orbital radii (>100 AU) and older than a couple hundred million years in the infrared (due to low thermal emission from mature planets) and in the visible with future space coronagraphs (due to low reflected light contrast, even from giant planets). Debris disk structures are thus critical, indirect indicators of planetary system properties at large radii. The structure of debris rings such as HD 202628 and Fomalhaut indicates that planets must exist at larger scales than previously thought, a significant challenge for planet formation theory. It is believed that in situ core accretion cannot take place rapidly enough at these distances to form a planet before the dissipation of the primordial disk (Dodson-Robinson et al. 2009). In Fomalhaut, HR 8799 (Marois et al. 2008; Su et al. 2009), and now HD 202628, the distant planets are seen or inferred within their circumstellar debris belts—thus indicating that they must have formed from within a circumstellar disk and not (as binary stars do) from adjacent collapsing cloud cores. Both Fomalhaut and HR 8799 are A stars, and their protoplanetary disks would likely have been fairly massive. HD 202628, a G star, would have had a less massive accretion disk, so the presence of a planet even further from the star than those around the A stars would be a mystery. The eccentricity of the purported planet, as suggested by that of the ring, would indicate that it formed closer to the star and then scattered outward by a more massive planet. Such a planet could not have been captured from outside the system, otherwise the bodies creating the debris disk would have been scattered.

The deprojected image was used to estimate a disk/star scattered light fraction. The total flux was measured within the two 90° sectors centered on P.A. = 130° and 310° (along the ring apparent major axis) and the sum doubled to account for the obscured sections of the ring along the line of sight. By this technique, F_scat = F_disk/F_star = 6.8 × 10⁻⁶ with an estimated error of ±8%. We can make a rough estimate of the albedo by computing the ratio of the scattered light fraction to the sum of scattered and emitted flux fractions (F_emit = L_dust/L_star = 1.4 × 10⁻⁴ from Koerner et al. 2010): a ≈ F_scat/(F_scat + F_emit)  ≈ 4.6%. This is quite similar to HD 207129 (F_emit = L_dust/L_star = 7.6 × 10⁻⁶, a  ≈ 5%; Krist et al. 2010). Note that Fomalhaut has an intrinsically fainter disk (F_scat = 9.6 × 10⁻⁷), but the star is much brighter (V = 1.2) so its disk has a higher apparent surface brightness (V ≈ 21.5 mag arcsec⁻²).

Grain–grain collisions dominate the evolution of the dust in the HD 202628 disk until the grains are ground down to a radiative blowout radius of ∼1 μm and are expelled from the system. HD 202628 is younger than the Sun with an enhanced X-ray luminosity of $L_X/L_{X_\odot } = 10^{28.41}/10^{27.35} = 11.5$. Using Equation (3) from P09, we estimate a stellar wind with ∼26 × the solar wind mass-loss rate, assuming that the radius of HD 202628 is approximately equal to that of the Sun. Using Equations (A10) and (A16) in P09, we estimate the factor P_CPR ≈ 9.7 that the enhanced stellar wind contributes to shortening the Poynting–Robertson drag timescale. Finally, using Equation (A23) in P09, with L_dust/L_star = 1.4 × 10⁻⁴, D_ring = 158 AU, Q_coll = 1, and assuming the mass and luminosity of HD 202628 match the Sun, we estimate that the grain–grain collision timescale is ∼100 times shorter than that for the grains to spiral inward toward the star under the combined effects of stellar wind and Poynting–Robertson drag. Equation (A23) in P09 is independent of factors such as the grain size and density; it assumes a relative disk annulus of 0.1 times the disk diameter, whereas the disk for HD 202628 is four times as thick in annular diameter. Therefore, this timescale ratio is only a lower bound, but we can definitively conclude that grain–grain collisions dominate the dust grain evolution of this disk and that the dust grains originate from the collisions of larger parent bodies within the same annulus (e.g., Kuiper Belt object analogs).

There are a variety of ring-shaped debris disks that have been imaged in scattered light. The widths of the rings, the sharpness of their inner and outer edges, their ellipticities (or lack thereof) vary widely. Here, we summarize them to provide some context for the HD 202628 ring. Note that we omit extended disks with central clearings (e.g., β Pic).

Of all the other disks, HD 202628's seems most like Fomalhaut's. Fomalhaut's ring has a sharp inner edge with similar surface brightness profiles of r^10.9 along the inner edge and an outer falloff of r^−4.6 (Kalas et al. 2005). The Fomalhaut ring is smaller than HD 202628's (113–158 AU; Δr = 25 AU; Δr/r = 0.2; unless otherwise noted, ring sizes given here represent the >50% of maximum surface brightness zones), and it has a lower eccentricity (e = 0.11 versus 0.18) with a smaller star/ring offset (15.3 AU versus 28.4 AU). The Fomalhaut L_dust/L_star = 8 × 10⁻⁵ is about half that of HD 202628, and the star is younger (∼200 Myr).

HD 181327 (F5V, Schneider et al. 2006; Lebreton et al. 2012) has a ring-shaped disk extending from 80 to 100 AU (Δr = 20 AU; Δr/r = 0.2), though a faint halo of dust can be seen out to ∼455 AU. This is a much brighter and more massive disk (L_dust/L_star = 2 × 10⁻³) than HD 202628's or Fomalhaut's. Curiously, its surface brightness profile is very similar to Fomalhaut's and HD 202628's, with the inner edge rising as r¹⁰ and the outer disk falling as r^−4.7 (Lebreton et al. 2012). There is no reported eccentricity.

HR 4796 (A0V) is quite young (8 Myr), and it has one of the brightest debris disks (L_dust/L_star = 5 × 10⁻³). Its ring-shaped disk is small and narrow (r_in ≈ 65 AU, r_out ≈ 91 AU; Δr = 25 AU; Δr/r = 0.3). Both its inner and outer edges are sharp; the cause of the outer edge truncation has yet to be satisfactorily explained, but it has been demonstrated that it cannot be due to a known, nearby stellar companion (Thébault et al. 2010). Recent adaptive optics imaging (Thalmann et al. 2011) verified a 1.2 AU offset along the apparent major axis seen by Schneider et al. (2009), but a ∼5 AU offset along the line of sight was also seen. This suggests an eccentricity of e ≈ 0.07.

HD 207129 (G0V; Krist et al. 2010) has a faint (V = 23.7 mag arcsec⁻²), ring-shaped disk extending over 148–178 AU (Δr = 30 AU; Δr/r ≈ 0.2; note that these are the visible, not 50% brightness, extents). There is no indication of an offset of the ring or any significant azimuthal density variations. Due to low signal, reliable surface brightness profiles could not be obtained. It has little or no forward scattering.

HD 107146 (G2V; Ardila et al. 2004) has a low-inclination disk with an inner clearing at r ≈ 60 AU. The surface brightness increases gradually out to 130 AU and then falls just as gradually further out. The 50% surface brightness radii are 87 AU and 168 AU (Δr = 81 AU; Δr/r = 0.6). There is no observed eccentricity.

HD 92945 (K1V; Golimowski et al. 2011) has a disk that extends from r = 43–140 AU. The inner clearing is not fully defined in the HST images, but there is a density enhancement along the inner edge at 40–70 AU. The outer edge also has enhanced density up to 100 AU, beyond which the surface brightness falls off dramatically (∼r⁻¹⁰). This may indicate that there are blended inner and outer rings. The disk has no notable eccentricity.

Table 1 summarizes some of the important properties of these disks. There seems little in common among them, except that they are, by selection, rings. The inner radii (based on >50% intensity) vary considerably, from 40 to 150 AU. The sharp inner edges of some (HD 202628, Fomalhaut, HR 4796, and perhaps HD 181327) are likely defined by the orbital radii and masses of planets that are truncating them. The existence of planets is further bolstered by the eccentricities seen in at least three of the rings (HD 202628, Fomalhaut, and HR 4796). In contrast, HD 107146 has a gentle radial brightness profile without a sharp inner edge. Ertel et al. (2011) and Hughes et al. (2011) suggest that this favors a morphology induced by a collisional cascade of planetesimals unaltered by planetary perturbation. The sharpness of the inner edge of HD 92945 is uncertain due to subtraction residuals near the star (Golimowski et al. 2011) and of HD 207129 due to poor signal (Krist et al. 2010). In two cases, HR 4796 and HD 92945, the outer disk extents are sharply truncated, perhaps due to unseen companions (note that the outer radii of both are smaller than the inner radius of HD 202628). All of the other disks have gradual brightness falloffs with increasing radius, characteristic of grains being blown out by radiation pressure and winds, and, likely in some cases, bumped into higher eccentricities by planets (HD 202628 is uncertain due to poor definition).