A SPITZER SPACE TELESCOPE STUDY OF THE DEBRIS DISKS AROUND FOUR SDSS WHITE DWARFS

We were awarded 2.7 hr in Cycle 4 (P40048), 0.7 hr in Cycle 5 (P50118), and 2.5 hr in Cycle 7 (P70012) to search for a dusty component to the disks around our four targets (see Table 1 for a full list of observations). For SDSS1043, we obtained Infrared Array Camera (IRAC; see Fazio et al. 2005) data in all four channels (3.6–8.0 μm). For SDSS0845, we obtained IRAC data at 4.5 μm and 8.0 μm, Infrared Spectrograph (IRS; Houck et al. 2004) Blue Peak-Up Imaging at 16 μm, and Multiband Imaging Photometer (MIPS; Rieke et al. 2004) imaging at 24 μm. For SDSS1617 and SDSS0738, we obtained warm IRAC data at 3.6 μm and 4.5 μm.

The IRAC data reduction for all sources was carried out on the individual corrected basic calibrated data (CBCD; cbcd.fits) frames downloaded from the Spitzer archive. The CBCDs were initially combined with the standard SSC software, MOsaic and Point Source Extraction (MOPEX; Makovoz et al. 2006) with dual outlier rejection to create a single mosaicked image for each channel. This was used to determine the position of the target. All of the original downloaded CBCD frames were then corrected for array location dependence, using the correction frames supplied by the Spitzer Science Center (SSC). Aperture photometry was carried out on the corrected CBCD frames with IRAF, using an aperture radius of 3.0 pixels. The sky subtraction was applied using an annulus from 12 to 20 pixels in radius.

SDSS1043 was found to have a blended neighbor in the extraction aperture. We calculated the individual flux densities for each of the blended sources by measuring the combined flux, then splitting this by the ratio of peak brightness of a Gaussian fit to each source in each channel.

The IRAC photometry for all sources was then converted from MJy sr⁻¹ to μJy, and aperture corrected using the standard aperture corrections provided by the SSC. We did not apply a pixel phase correction to the channel 1 data, but included an extra 1% in our error budget to account for this (Reach et al. 2005). No color correction was applied, since we quote the isophotal wavelengths, thus eliminating most of the color dependency of the flux calibration and rendering the magnitude of the correction negligible compared to our uncertainties. Uncertainties were estimated using the rms scatter in the photometry in the individual frames, divided by the square root of the number of frames. The quoted uncertainties are either our calculated uncertainty or the IRAC calibration uncertainty derived by Reach et al. (2005), whichever was larger.

The IRS Peak-Up Imaging and MIPS data for SDSS0845 were combined in much the same way, using MOPEX to create a mosaic to measure the source positions, and carrying out the photometry on the individual basic calibrated data frames. The sky background was found to be variable across the IRS Peak-Up array, and so we created a sky flat by combining all of the dithers and rejecting the sources. This sky flat was subtracted from the individual frames before carrying out the photometry, bringing the sky background to zero. The photometry for both the IRS and MIPS data was obtained via IRAF, using an aperture radius of 3.0 pixels with no sky subtraction for IRS, and an aperture radius of 3'' (1.224 pixels) with a background aperture of 20''–32'' for MIPS. After converting from MJy sr⁻¹ to μJy, the flux densities were aperture corrected to the calibration apertures using the standard corrections provided by the SSC.

Finally, for all of the data for the four targets, we rejected the photometry from the original frames that had been flagged by the MOPEX dual outlier rejection algorithm. We take the unweighted mean of the remaining photometry in each channel as the quoted flux densities. An estimate of the uncertainties was measured using (rms scatter)/sqrt(number of frames), consistently giving uncertainties lower than the instrument calibration uncertainties. We therefore adopt the instrument calibration uncertainties from the SSC as the uncertainties on our data. For MIPS this is 4%, and for IRSPUI this is 5%.

Near-infrared imaging of SDSS0845 was obtained at the Australian Astronomical Observatory's Anglo-Australian Telescope (AAT) using the InfraRed Imaging Spectrograph 2 on 2008 February 22, and retrieved from the public AAT archive. A nine-point dither pattern was used, with individual exposure times of 30 s, 42 s, and 67 s, and total exposure times of 270 s, 378 s, and 603 s in J, H, and K_s, respectively. SDSS1617 was observed in the K_s band on 2010 May 1 using SOFI on the ESO New Technology Telescope (NTT). A total of twenty 5 s images were obtained, offset randomly within a 15'' box. The data were sky-median subtracted, astrometrically calibrated using the WCSTools⁵, and co-added using SWarp.⁶ Object detection and the aperture photometry were done using the SExtractor (Bertin & Arnouts 1996). Instrumental magnitudes were converted to the Two Micron All Sky Survey (2MASS) system using a set of five bright stars near SDSS0845 and ten stars near SDSS1617. The uncertainty in the calibration is 0.02 mag in all bands, and was added in quadrature to the statistical uncertainties in the photometry. The J, H, and K_s magnitudes, fluxes, and uncertainties are reported in Table 2.

Observations of SDSS1043 in Y, J, H, and, K bands have been obtained with UKIRT/WFCAM as part of UKIDSS (Lawrence et al. 2007) on 2009 May 22 and December 15 (Table 2). The Galaxy Evolution Explorer (GALEX; Martin et al. 2005), SDSS (Abazajian et al. 2009), and 2MASS (Skrutskie et al. 2006) archives and the Wide-field Infrared Survey Explorer (WISE) Preliminary Data Release were searched for additional photometry of our targets. The archival and WISE photometry are also listed in Table 2.

The NIRI imaging of SDSS0845 obtained by Melis et al. (2010) revealed the presence of a faint galaxy at a 18 separation northeast of the white dwarf. We have downloaded the NIRI J-, H-, and K_s-band images of SDSS0845 from the Gemini Science Archive and, after correction for nonlinearity using the python scripts provided by Gemini, processed them in the same manner as the AAT and NTT data described above. In order to measure the relative contributions of the star and the galaxy, first an annulus was defined, centered on the star, with inner and outer radii of 4'' and 7'' on the sky (large enough to avoid the galaxy) to measure the sky background. The star's contribution was then measured from the flux summed over a 16 diameter aperture, while the galaxy's flux was measured from the union of pixels covered by three overlapping circular apertures covering its major axis. To estimate the degree to which the galaxy flux was contaminated by light from the star, three identical control apertures were placed diametrically opposite to the galaxy apertures relative to the star. The instrumental magnitudes were photometrically calibrated using a bright 2MASS star in the field. We find J = 16.44 ± 0.05, H = 16.30 ± 0.06, and K = 16.04 ± 0.07 for SDSS0845, and J = 20.33 ± 0.79, H = 19.29 ± 0.32, and K = 18.65 ± 0.24 for the nearby galaxy. These results agree well with the NIRI magnitudes of Melis et al. (2010), apart from the fact that we have somewhat larger uncertainties.

To estimate the contamination of the galaxy in the Spitzer beam, we obtained the galaxy SEDs of Maraston (1998, 2005) based on the initial mass function of Kroupa (2001). We then redshifted all galaxy SEDs by redshifts 0 ⩽ z ⩽ 3, in steps of 0.2, and discarded all combinations of redshift and age that would disagree with the observed J − H and H − K_s colors and the apparent K_s magnitude. The NIRI data constrain the redshift of the galaxy to 1.4 ≲ z ≲ 3.0, with the range 2.4–3.0 only feasible for young (<1 Gyr) galaxies. The spatial extension of the galaxy is suggestive of a redshift at the lower end of the range allowed by the NIRI photometry (Ferguson et al. 2004).

The contribution of the galaxy to the IRAC-1 and -2 channels is 0.04 ± 0.01 mJy and 0.05 ± 0.01 mJy, relatively independent of the galaxy type. The maximum contribution in the IRAC-3 and -4 channels is ∼8 mJy for a young (<1 Gyr) high-redshift (z ∼ 3) galaxy. However, given the combined constraint from morphology and near-infrared photometry, the contribution of the galaxy to the IRAC-3 and -4 channels is likely to be <5 mJy. Galaxy models are poorly constrained in the mid-IR, and so we are unable to learn anything more about the galaxy from the IRS-PU and MIPS channels, other than the fact that the galaxy flux continues to drop out to longer wavelengths. At these longer wavelengths, the SED is dominated by the flux density from the dust disk. In Figure 2, we show an 8 Gyr old, redshift z = 1.6 galaxy as an example of the flux contribution to the Spitzer bands.

The flux densities from GALEX and Spitzer are given in Table 2, and are plotted in light gray in Figure 1, along with the SDSS DR7 spectrum (gray line). We also included near-IR photometry from Dufour et al. (2010), also plotted in dark gray. The DB white dwarf model is shown as a dashed black line, with T_eff = 13,600 K, log (g) = 8.5, R_WD = 0.00886 R_☉ (Table 3; see Dufour et al. 2010). We use a distance of d = 120 pc, rather than the 136 ± 22 pc quoted in Dufour et al. (2010), as this gives a better fit to the white dwarf SED. This is still consistent with the Dufour et al. value.

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The photometry of SDSS0738 shows a clear flux density excess in the infrared wavelengths, compared to the white dwarf model. The best-fitting disk model (Figure 1(a)) has T_in = 1800 K, T_out = 830 K, and an inclination of 60°, which is consistent with the modeling results from Dufour et al. (2010). The best physically motivated model with T_in = 1400 K has T_out = 930 K and a face-on inclination of 0° (Figure 1(b)). This corresponds to inner and outer disk radii of R_in = 12.4 R_WD (0.11 R_☉) and R_out = 21.3 R_WD (0.19 R_☉). The coolest possible inner disk temperature is constrained by the need for a high enough flux density to match the JHK data points, and has T_in = 1350 K, T_out = 880 K, and an inclination of 0°. These models are both consistent with the modeling carried out by Dufour et al. (2012), who used T_in = 1600 ±100 K, T_out = 900 +100/−200 K, and an inclination of 40° ± 20°.

Analysis of the Ca ii emission lines gives an outer radius of the gaseous disk component of R_out ≃ 1 R_☉sin ²i, i.e., a maximum value of R_out ∼ 110R_WD (B. T. Gänsicke et al. 2012, in preparation). While the Ca ii emission lines provide no formal lower limit on R_out, a low-inclination, practically face-on geometry seems unlikely, as it would imply a very narrow ring for the gaseous component, narrower than the dusty component.

The GALEX, AAT, and Spitzer photometry for SDSS0845 are given in Table 2, and are plotted in light gray in Figure 2, along with the SDSS DR7 spectrum, SDSS photometry, NIR photometry from Melis et al. (2010) and Farihi et al. (2010), and the WISE Preliminary Data Release (dark gray). The data show a clear excess at wavelengths longer than 2 μm, above the flux density expected from the white dwarf and the contaminating background galaxy. For the white dwarf contribution, we adopted a DB model with T_eff = 18, 621 K, log (g) = 8.2, d = 85 pc, and R_WD = 0.009 R_☉. The resultant model is plotted as a dashed gray line, while the white dwarf model with the background galaxy added is shown as a dash-dot-dot-dot line.

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The models for SDSS0845 are shown in Figure 2. The first shows the best-fitting disk model, with an inner temperature of 1800 K, an outer temperature of 250 K, and an inclination of 85°. Figure 2(b) shows the closest physical model with an inner disk temperature constrained to 1400 K, T_out = 400 K, and inclination = 80°. This corresponds with inner and outer disk radii of R_in = 18.8 R_WD (0.17 R_☉) and R_out = 99.7 R_WD (0.89 R_☉). The coolest disk model still within 3σ of the plotted data points has T_in = 1100 K, T_out = 600 K, and an inclination of 70°.

The outer radius of the gaseous component was estimated by Gänsicke et al. (2008) to be ∼0.8–0.9 R_☉, which is comparable to that of the dust disk derived above.

The GALEX, UKIDSS, and Spitzer flux densities for SDSS1043 are given in Table 2, and are plotted in Figure 3 together with the SDSS DR7 spectrum. The uncertainties on the Spitzer photometry for SDSS1043 are notably large, due to the faint nature of the source (only 30 μJy in IRAC channel 1). In addition to these data points, we include Canada–France–Hawaii Telescope and Lick near-IR photometry from Melis et al. (2010) to constrain our model. All previously published data are shown in dark gray in Figure 3, while the GALEX, UKIDSS, and Spitzer data are shown in light gray. We have fitted the DR7 spectrum of SDSS1043 using DA model spectra computed with the code of Koester (2010), which incorporates the updated Stark broadening calculations of Tremblay & Bergeron (2009), and find T_eff = 17912 ± 362 K and log (g) = 8.07 ± 0.08, corresponding to M_WD = 0.66 ± 0.05 M_☉ and R_WD = (8.67 ± 0.47) × 10⁸ cm (Table 3). These values are, within the uncertainties, consistent with those derived from the DR4 spectrum by Gänsicke et al. (2007), but given the improvement in the SDSS data reduction and line broadening, the new values reported here should be preferred.

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The IRAC data points show a 3σ excess above the expected flux density of the white dwarf, increasing dramatically at 8 μm.

As with the other targets, we show the best-fit optically thick dust disk model in Figure 3(a), with an inner disk dust temperature of T_in = 1800 K, T_out = 1700 K, and an inclination of 40°. When constraining the inner disk temperature below the sublimation threshold of 1400 K, we find a best-fit model with T_in = 1400, T_out = 800 K, and i = 85°. This corresponds with inner and outer disk radii of R_in = 17.9 R_WD (0.23 R_☉) and R_out = 37.6 R_WD (0.49 R_☉). The coolest model allowed by the fit has T_in = 900 K, T_out = 800 K, and i = 56°.

Modeling the double-peaked Ca ii line profiles, B. T. Gänsicke et al. (2012, in preparation) find, similar as for SDSS0738 and SDSS0845, R_max ∼ 1 R_☉ (see also Melis et al. 2010).

The flux densities from GALEX, SOFI, and Spitzer are given in Table 2, and are plotted in light gray in Figure 4, together with the SDSS DR7 spectrum (dark gray). The data show a clear excess above the flux density from the white dwarf at the Spitzer wavelengths. The white dwarf model, also based on Gänsicke et al. (2011), is shown as a dashed black line and is a DA white dwarf model, with T_eff = 13,432 K, log (g) = 8.04, d = 122 pc, R_WD = 0.01261 R_☉, reddened by E(B − V) = 0.04 to better match the optical SDSS spectrum. The reddening has a negligible effect at infrared wavelengths.

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The best-fit dust disk model has an inner disk effective temperature T_in = 1800 K, outer disk T_out = 950 K, and an inclination of 70°, plotted as a gray dash-dotted line in Figure 4(a). The closest fit with T_in fixed at 1400 K has T_out = 950 K and i = 50° (Figure 4(b)). This corresponds with inner and outer disk radii of R_in = 12.2 R_WD (0.15 R_☉) and R_out = 20.4 R_WD (0.26 R_☉). The model with the coolest possible inner disk temperature has T_in = 1100 K, T_out = 620 K, and i = 53°.

The peak separation of the Ca ii emission lines implies a maximum outer radius of the gaseous component of 90 R_WD (B. T. Gänsicke et al. 2012, in preparation).