STRENGTHENING THE CASE FOR ASTEROIDAL ACCRETION: EVIDENCE FOR SUBTLE AND DIVERSE DISKS AT WHITE DWARFS

Mid-infrared imaging observations of the white dwarf targets were obtained with the Spitzer Space Telescope (Werner et al. 2004) during Cycle 5 using the Infrared Array Camera (IRAC; Fazio et al. 2004) at all four wavelengths, namely 3.6, 4.5, 5.7, and 7.9 μm. The total integration time in each channel was 600 s, where the observations consisted of 20 frames taken in the cycling (medium) dither pattern with 30 s individual exposures. All images were analyzed, including photometry and upper limits, as in Farihi et al. (2009) using both 12 and 06 pixel⁻¹ mosaics created using MOPEX.

In cases where the flux of a neighboring source was a potential contaminant of the white dwarf photometry, steps were taken to minimize or remove any such external contributions, including small aperture radii and point-spread function (PSF) fitting with daophot. To this end, the newly available (beginning with pipeline version S18.5) 06 pixel⁻¹ mosaics were useful to better constrain and eliminate sources of photometric confusion. While the IRAC Data Handbook (Spitzer Science Center 2006) provides information necessary to perform photometry on point sources in the native 12 pixel⁻¹ scale images, the provided aperture corrections do not take advantage of the available smaller pixel scale. A comparison of identical observation sets, processed into both 12 and 06 pixel⁻¹ mosaics, reveals a modest but clear increase (around 20% by full width at half-maximum) in spatial resolution. This information gain at the smaller pixel scale is most evident at the two shortest wavelength channels, where the diffraction limited PSF of the telescope is significantly undersampled (Spitzer Science Center 2006).

Observations with AKARI (Murakami et al. 2007) were executed using the Infrared Camera (IRC; Onaka et al. 2007) in the N2, N3, and N4 filters (2.34, 3.19, and 4.33 μm) for three white dwarfs listed in Table 1. These stars were imaged in 2008 November and 2009 March–April using the Astronomical Observational Template IRCZ3, which was designed for imaging with the N2, N3, and N4 filters in a pointed observation. The basic data reduction, including dark subtraction, linearity correction, distortion correction, flat fielding, image stacking, and absolute position determination were performed by the standard IRC Imaging Data Reduction Pipeline for Phase 3 data (version 080924P3). The IRAF package daophot was used for photometry, with an aperture radius of 5 pixels (73) and corrected to the standard 10 pixel radius using aperture corrections derived from bright sources within individual images. Flux calibration was achieved using conversion factors provided by the IRC team.⁴

HE 0106−3253. The IRAC images of this star reveal another source separated by 44 at position angle 299°, as measured by daophot using the 06  pixel⁻¹ images (Figure 4). The neighboring source appears to be a background galaxy based on its half-maximum intensity at 3.6 and 4.5 μm, measured in a direction orthogonal to its position angle relative to the white dwarf. Two independent methods were used to measure the flux of the white dwarf without contamination from the nearby galaxy. First, daophot was employed to fit both the white dwarf and the nearby galaxy (thus treating it as a point source) simultaneously. This was done with two independent sets of PSF stars, one derived from archival IRAC images taken for the Galactic component of the First Look Survey and the other created using a few to several of bright point sources within the science target images. Additionally, daophot was run to fit the white dwarf only, with no information provided on the neighboring source. It is noteworthy that the task returned similar results for these two approaches, within 3% at all four IRAC wavelengths.

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Second, relative aperture photometry was performed on HE 0106−3253 and a moderately bright, nearby star 2MASS J01083497−3237486; this star can be seen in Figures 4 and 5, 336 distant from the white dwarf. Robust centroids were determined for each star using both Gaussian profile analysis and daophot PSF fitting; the centroids in all four channels were averaged for each star and found to agree to within 1 standard deviation of 0.10 pixels. The centroid for the comparison star was taken to be fixed while photometry for the white dwarf was performed at a total of nine positions; at the nominal centroid plus at eight positions along a circle of radius 0.10 pixels about this center, spaced evenly from 45° to 360° in the xy image plane. Photometry was executed in half-pixel steps from 1 to 4 pixels. The same relative photometric analysis was also performed for two randomly selected point sources within the HE 0106−3253 IRAC field of view. Lastly, the 2MASS comparison star was input to daophot as a reference PSF, and the white dwarf flux was re-measured as above.

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Figure 6 plots the results of the relative flux measurements between the white dwarf and 2MASS comparison star. Each datum is the average and 3σ error among the nine positions where the white dwarf flux was measured. Also shown in the plot are the fluxes as determined by daophot, averaged over the three sets of PSF stars, and the expected white dwarf photospheric fluxes as determined by the model shown in Figure 1. Two things are apparent from the figure and analysis: (1) HE 0106−3253 is photometrically extended beyond r = 2 pixels, and possibly beyond 1.5 pixels; (2) the daophot flux measurements are in good agreement with the fluxes determined by relative photometry with the 2MASS comparison star at r = 2 pixels.

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The fluxes determined by these methods are listed in Table 4, and a series of representative images are shown in Figures 4 and 5. Both methods yield IRAC fluxes in excess of the predicted photospheric emission of the white dwarf based on the model plotted in Figure 1; the weighted average of these is plotted in the figure and listed in Table 2. The excess at each IRAC wavelength lies in the range 3–5σ using the errors derived via the individual measurements, or within 5–6σ using the weighted average errors. The nearby galaxy cannot account for the results of the PSF fitting photometry where extracted sources must conform to a relatively static, model point source. The last panel of Figures 4 and 5 displays the PSF fit and removal of the white dwarf at the expected photospheric level; a point-like residual (excess) is seen at the location of the white dwarf.

To assess the potential flux contamination by the galaxy, a radial profile and vector analysis of the white dwarf flux was performed. Both one-dimensional Gaussian profile fitting and a raw vector cut (each of 3 pixel width) were executed across the white dwarf in the direction toward and away from the galaxy, and the fluxes on either side were compared. From these analyses, it is found that at r = 2 pixels from the white dwarf centroid, the side nearest the galaxy contains at most 15% more flux than the side opposite at 3.6 μm, and no more than 10% at the three longer wavelengths. Assuming a worst case scenario where one-half of the photometric aperture is biased in this manner—certain not to be the case—then the galaxy contributes a maximum of 5% of the measured flux at all wavelengths except 3.6 μm, where it is limited to 7.5%. The excess flux (measured − photosphere) relative to the measured flux is 27%, 32%, 39%, and 55% at 3.6, 4.5, 5.7, and 7.9 μm, and hence the potential influence of the galaxy cannot account for this excess. From this analysis, it appears that HE 0106−3253 has an infrared excess.

HS 0307+0746. Figure 1 reveals an infrared excess around this star based on the plotted 10,500 K DA model and the short wavelength photometry. The H–K data are anchored to the 2MASS J-band measurement of 16.39 ± 0.14 mag, where the J−H and H−K colors were derived spectroscopically by Kilic et al. (2006). The only optical, photoelectric photometry comes from the CMC where two measurements are given as r' = 16.48 ± 0.08 mag. Koester & Wilken (2006) give T_eff = 10,200 K and log  g = 7.9 for the white dwarf, similar to the plotted model that agrees well with the GALEX far- and near-ultraviolet fluxes. If the model used here is sufficiently accurate, the putative excess at HS 0307+0746 appears at the 4–6σ level at all IRAC wavelengths.

Ton 345. The Spitzer data for this star are analyzed elsewhere, but the AKARI IRC fluxes reported here are original and appear broadly consistent with the near-infrared and Spitzer IRAC fluxes (Melis et al. 2010; C. S. Brinkworth et al. 2010, in preparation).

PG 1225−079 and GD 303. The 7.9 μm IRAC flux at PG 1225−079 indicates a 4σ excess (Figure 2) while all other photometric data are consistent with photospheric emission. If real, this star joins G166-58 as a metal-rich white dwarf with a long wavelength IRAC excess but no short wavelength excess; these two objects may form a class of object whose orbiting disks have large inner holes. GD 303 may have a marginal photometric excess at the 2σ level (Figure 2).

HE 2221−1630. This metal-polluted white dwarf shows the clearest mid-infrared excess (Figure 3) of all the science targets. Koester & Wilken (2006) give T_eff = 10,100 K for this star.

GD 190. The 2MASS K_s = 14.96 ± 0.13 mag measurement (Figure 2) for this helium- and carbon-rich white dwarf appears erroneous at the 2.5σ level.

GD 205. The fit to the spectral energy distribution (SED) shown in Figure 2 employs a higher T_eff than that found by previous studies; 18,500 K (Voss et al. 2007), 19,700 K (Koester et al. 2005). However, the 20,500 K model better matches all the photometric data, including the GALEX fluxes.

HS 2229+235. While the native pixel scale IRAC images of this star reveal a single source (single Airy disk) with an elongated core, the 06 pixel⁻¹ mosaics spatially resolve a neighboring source at 20 and position angle 336°, as measured by daophot. The 2MASS J- and H-band images of the white dwarf may show a slight elongation in the expected direction, but the signal-to-noise ratio in these images is too low to be certain (especially at H band). Photometric deconvolution was performed with daophot, yielding good results at 3.6 and 4.5 μm; errors of 6% and 8%, respectively for the white dwarf. While the neighboring source is likely extragalactic in nature, there is no evidence of elongation in the IRAC images, and there are no significant residuals in the PSF subtracted images of both sources at either of the shorter wavelengths.

Unfortunately, reliable optical or near-infrared photometry of HS 2229+2335 is lacking; the best data are r' = 16.18 ± 0.25 mag (Copenhagen University Observatory 2006) and J = 16.16 ±  0.09 mag (Skrutskie et al. 2006). The flux plotted at V band is the average and standard deviation of five photographic plate magnitudes from NOMAD, GSC2.3, and USNO-B1.0 (Space Telescope Science Institute 2006; Zacharias et al. 2005; Monet et al. 2003). If interstellar extinction toward the white dwarf is negligible, the GALEX and IRAC data agree with an 18,500 K, log  g = 8.0 DA model (Koester & Wilken 2006). Near-infrared photometry would better constrain the SED of this white dwarf, but it does not appear to have a mid-infrared excess.

The infrared excesses at HE 0106−3253, HS 0307+0746, and HE 2221−1630 were fitted with the circumstellar disk models of Jura (2003). These disks are geometrically thin, flat rings of dust vertically optically thick at wavelengths up to 20 μm. Figure 7 shows the model fits, while Table 6 gives the model parameters. The models do a reasonable job of reproducing the disk fluxes. Both HE 0106−3253 and HS 0307+0746 have a high 3.6 μm flux relative to the model; this behavior is also seen for the inner disk region at PG 1457−086 (Farihi et al. 2009). It is conceivable that some disk warping in the inner regions is responsible for the relatively high observed flux at short infrared wavelengths, similar to that seen and modeled for GD 56 (Jura et al. 2009a, 2007a).

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Two white dwarfs in this study—HE 0106−3253 and HS 0307+0746—appear to have narrow (Δr < 0.1 R_☉) rings of dust similar to PG 1457−086, when compared to the ensemble of white dwarfs with warm circumstellar disks (Farihi et al. 2009). In fact, their disk widths could be even smaller as the models presented here are degenerate between disk width and inclination. For example, if the inclination of the disks at HE 0106−3253 or PG 1457−086 is actually close to face-on (i = 0°), the radial extent of their dust is only 0.01 R_☉, roughly 1 R_⊕ and 10 times smaller than the rings of Saturn, yet still over 10 times the diameter of all solar system asteroids save Ceres. This finding has an important implication.

The detection of narrow dust rings suggests the asteroid accretion model may apply to additional, and potentially many, stars without a clear infrared excess. Take the most modest excess yet detected, that of PG 1457−086: a face-on disk of width 0.01 R_☉ and producing a 15% (3σ) excess would become difficult to confirm above i = 50°, corresponding to an excess of only 10%. While such disks may appear slight when compared to the majority of infrared excesses discovered so far, they could easily contain sufficient mass to fuel the observed photospheric pollutions in DAZ and DBZ stars. At the high densities necessary to prevent collisional dust erosion within the disk (Farihi et al. 2008), the thin ring above could harbor over 10²² g of matter within a disk height of 10 m, and readily supply heavy elements at 10⁹ g s⁻¹ for nearly 10⁶ yr. The discovery of three relatively narrow rings indicates there may be more subtle excesses awaiting detection.

Table 7 lists a comparison of the infrared excesses at all known white dwarfs with dust. To calculate the fractional dust continuum luminosity, τ = L_IR/L_WD, the excess flux in the 2–6 μm region was fitted by a single temperature blackbody and its bolometric flux divided by the stellar flux (similar to those plotted in the SED figures). There are currently three white dwarfs with T ∼ 1000 K dust whose infrared excesses are less than 10⁻⁴ of the incident starlight: HE 0106−3253, WD 1041+091 (SDSS J104341.53+085558.2), and PG 1457−086. The stars G166-58 and PG 1225−079 owe their modest excesses to a lack of T>500 K dust, hence their low τ are qualitatively different. It is noteworthy that all stars with τ>0.02 had their disks discovered via ground-based observations.

A disk of radial width 0.01 R_☉ may result from the tidal disruption of an asteroid perturbed into an orbit with periastron near 0.2 R_☉, and dust spreading timescales suggest the material need not expand to a much greater radius. In the context of Spitzer searches for dust at polluted white dwarfs, highly attenuated rings of dust may persist at some white dwarfs that lack apparent infrared excess. Without supplementary ground-based, near-infrared photometry, the mild infrared excess at PG 1457−086 would not be obvious (Farihi et al. 2009; Farihi 2009). A combination of accurate optical and near-infrared photometry with appropriate atmospheric models may reveal excesses previously missed. Ideally, high signal-to-noise mid-infrared spectroscopy spanning the 10 μm silicate feature should be capable of detecting very modest dust emission, such as that seen at HD 69830 (Lisse et al. 2007). Spectroscopy with the Mid-Infrared Instrument for James Webb Space Telescope (JWST) would be an ideal choice to reveal the most subtle infrared excesses.

Among white dwarfs with circumstellar dust, G166-58 was the first star observed to have an excess beginning longward of 4 μm (Farihi et al. 2008). Figure 8 revisits the available photometry for this DAZ star and plots the IRAC data, together with IRTF JHK, Sloan Digital Sky Survey (SDSS) ugriz, and GALEX near-ultraviolet photometry. These data are fitted with a 7500 K, log  g = 8.0 DA model that reproduces the photometry well to 4.5 μm. The IRAC fluxes have changed marginally following analysis of the newly available 06 pixel⁻¹ mosaics for this star. The excess can be reproduced by a 500 K blackbody, implying the inner dust disk edge cannot be significantly warmer. The flat ring model then predicts that the innermost dust is located at 0.28 R_☉ and far from where silicate grains should rapidly sublimate. Therefore, the dust disk appears to have an enlarged, dust-free inner region.

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Interestingly, PG 1225−079 appears to have an excess only at 7.9 μm and may also represent a dust disk with a large inner "hole." An excess flux is difficult to confirm with the current data alone, yet the IRAC images are of good quality and free of neighboring sources. If the excess is confirmed, the dust-free, inner region at PG 1225−079 should be around three times larger than that inferred for G166-58, but still located well within the Roche limit for kilometer size or larger solid (rocky or icy) bodies (Davidsson 1999). There are two distinct possibilities for such large dust-free zones: (1) the region is dominated by gaseous matter emitting inefficiently in the infrared or (2) the region is depleted relative to the dust inferred from the observed infrared excess.

The first possibility can arise if the inner dust disk region is impacted by a moderate size asteroid whose solid mass and angular momentum are dissipated via collisions prior to vaporizing the entire disk (Jura 2008). In Saturn's rings, the observed radial dark lanes or spokes are the result of meteorite impacts, whose kinetic energies are sufficient to produce fine dust, gas, and (importantly) plasma, which interact dynamically within this environment to obscure the rings (Goertz & Morfill 1983; Morfill & Goertz 1983). Similar impacts upon dust disks at white dwarfs should release kinetic energies 1000 times higher due to the difference in gravitational potential; the model radii and sizes of dust rings at white dwarfs are very similar to those of Saturn.

This model is attractive because it can account for disks with enlarged, dust-free inner regions or small outer radii (including narrow rings) as well as high accretion rate DAZ white dwarfs that lack infrared excess out to 7.9 μm yet require a nearby, ongoing source of photospheric heavy element pollution. G166-58 has a relatively long diffusion timescale for a DAZ star, around 2000 yr for the observed calcium (Koester 2009a). This calculated lifetime does not guarantee accretion is ongoing, but the presence of orbiting dust makes it likely.

Perhaps more important, the absence of detectable dust need not imply an absence of accretion and photospheric pollution. While the disks at G166-58 and PG 1225−079 may be partly composed of dust particles which are detected in the infrared, and partly of gaseous heavy elements which remain unseen, most metal-contaminated white dwarfs lack infrared dust signatures altogether (Farihi et al. 2009). In many of these cases accretion must be ongoing and can be accounted for by the presence of either tenuous dust rings or completely gaseous disks (Jura 2008); unseen brown dwarf companions have been ruled out (Farihi et al. 2009, 2008).

The second possibility for dust disks with large inner holes is a relative dearth of dust (and gas) due to prior accretion; i.e., a partly consumed disk. PG 1225−079 has a heavy element diffusion timescale typical of cooler DBZ stars, over 1 Myr for calcium (Koester 2009a). In this case the lifetime of metals implies that accretion need not currently proceed at a high rate, and the observed metals may be residuals from an older event. Although the presence of an infrared excess, and hence the possibility of orbiting dust, makes an ongoing accretion scenario likely, it raises an important question about the disk depletion timescale at white dwarfs. A prediction of ceased accretion would be higher relative atmospheric abundances of lighter elements (Koester 2009a) and is testable with good abundance data for PG 1225−079.

In the Appendix, a simple calculation demonstrates that radiation drag (the Poynting–Robertson effect) on particles is insufficient to drive the infall of disk material and account for the distribution of inferred heavy element accretion rates at disk-polluted DAZ stars (Farihi et al. 2009; Jura et al. 2007b; Koester & Wilken 2006). At the inner disk edge, viscous spreading due to collisions between differentially rotating ring annuli and random motions among solids (Esposito 1993) must be boosted by the presence of gas (via sublimated or collisionally vaporized dust); such enhancement must be significant. Farihi et al. (2008) have shown that grains within white dwarf disks will collide on a timescale at least an order of magnitude shorter than their Poynting–Robertson lifetime. Therefore, high viscosity resulting from dust–gas interactions must be ultimately responsible for the implied accretion rates from observed disks. For a disk that is otherwise optically thick at all relevant wavelengths, only a tiny fraction of its total volume—only the inner edge–will be illuminated by the central star. There is no compelling reason why the remainder of the disk should not evolve as a particulate ring, having a very low dust viscosity (Esposito 1993), and be gradually whittled away via gas drag at the inner edge.

Figures 9 and 10 plot the metal abundances versus effective temperature and time-averaged metal accretion rate versus cooling age for 60 Spitzer observed metal-rich white dwarfs. All accretion rates were re-calculated following Farihi et al. (2009) using recent results on metal diffusion timescales and convective envelope masses for both DAZ and DBZ white dwarfs, including mixed cases (Koester 2009a; D. Koester 2009, private communication); parameters for the newly observed Cycle 5 stars are listed in Table 8. Plotted as newly discovered disks are HE 0106−3253, HE 0307+0746, HE 2221−1630, and tentatively PG 1225−079. To these are added three white dwarfs orbited by both dust and gaseous metals (Brinkworth et al. 2009; C. Brinkworth 2008, private communication), while PG 1632+177 (observed by Farihi et al. 2008 and listed as DAZ in Farihi et al. 2009) has been removed from this growing sample, as it is not metal-lined (Zuckerman et al. 2003).

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The new additions to the plots continue the trend that metal accretion rates dM/dt ≳ 3 × 10⁸ g s⁻¹ are those that are most likely to exhibit infrared excess (Farihi et al. 2009); the sole exception is G166-58. Two of the disks discovered in this work orbit relatively cool white dwarfs with cooling ages of 0.73 and 0.94 Gyr. These are somewhat older than the previous average cooling age of white dwarfs with disks as found in Farihi et al. (2009), and may indicate relative longevity for orbiting dust.

Viscous spreading among solids may allow optically thick dust rings at white dwarfs to persist for at least 10 Myr timescales, possibly orders of magnitude longer, analogous to planetary rings. The inner radius of Saturn's rings represents the furthest inner extent of its spreading over a period up to a few billion years (Esposito et al. 2008). For dust rings at white dwarfs, gas drag should decrease the viscous timescale by orders of magnitude, but the gas content in most white dwarf disks is presently unconstrained. At the inner edge of a typical dust disk, rapid sublimation of dust will produce significant gas, as may grain–grain collisions. Such viscosity enhancements are necessary to reproduce the dust accretion rates inferred for stars with short photospheric metal lifetimes.

Dust rings at white dwarfs are unlikely to be as simple as modeled here; calcium triplet emission lines at three metal-polluted stars can be approximately reproduced by orbiting disks, but there are asymmetries which indicate deviations from the model (Gänsicke et al. 2008). Yet it is noteworthy that the simple model works rather well given only three free parameters, two of which—the inner and outer radii—are physically well motivated.

Significant orbital energy must be shed to transform an asteroid on a perturbed, eccentric orbit into a disk contained entirely within the Roche limit of a white dwarf. The primordial energy may dissipate partially via collisions which initially widen the disk (or perhaps not in the case of narrow rings), yet an efficient way to discard orbital energy is within a large fragment of the tidally disrupted parent body. Surviving fragments may be responsible for warps invoked in some disk models, such as GD 362 and GD 56 (Jura et al. 2009a, 2007b). Saturn's ring-moon Daphnis—8 km in diameter and comparable to a small asteroid—causes 1 km vertical disturbances in the A ring; 100 times larger than the height of the unperturbed rings (Weiss et al. 2009). The more substantial Mimas, lying just outside Saturn's main rings (and its Roche limit) with a mass nearly identical to the total mass of the rings, is responsible for the Cassini Division between the A and B rings. A Mimas-analog of 10²² g could orbit a white dwarf beyond 2.0 R_☉ and not be tidally destroyed. Such a body with an inclined (relative to the disk) or eccentric orbit could easily excite warping or eccentricity within a white dwarf dust ring (Borderies et al. 1984). Dynamical modeling of tidal disruption events may shed light on the frequency, size, and orbital distribution of residual fragments.