NEAR-INFRARED IMAGING OF WHITE DWARFS WITH CANDIDATE DEBRIS DISKS

We carried out observations with the 5.1 m Hale telescope at Palomar Observatory in the United States. Through the Chinese Telescope Access Program, we were awarded two nights in 2012 November and two half nights in 2013 February. Unfortunately, only the night of 2012 November 27–28 was clear and useful data were taken. The instrument used was the Wide field IR Camera (WIRC; Wilson et al. 2003), which has a 2048 × 2048 pixel² Hawaii-II HgCdTe detector. The pixel scale was 0249 pixel⁻¹ and the field of view was 87.

For the 86 WDs we chose to observe, we used published results of their effective temperature and optical magnitudes to estimate their lower flux limits at JHK_s bands (Debes et al. 2011; Kleinman et al. 2013; see also Table 1), assuming pure blackbody emission. Based on the estimated flux limits, exposure times at the bands for each target were estimated accordingly. Due to weather limitations, we observed only 12 WDs; the exposure times are given in Table 2. During each exposure, the telescope was dithered in a five-point grid with offsets of ∼40'' to obtain a measurement of the sky background. The observing conditions were mediocre, with the seeing having a median value of 09 but occasionally dropping to 15.

Table 1. Properties of 12 WD Targets

Name	u'	g'	r'	i'	z'	T	log a	$A_{g^{\prime }}$	d
						(K)	(g)		(pc)
i000410.42−034008.6	17.46	16.93	16.76	16.72	16.74	6887	7.71	0.15	51
i011616.95−094347.9	20.09	19.39	19.08	18.97	18.95	6309	8.06	0.16	104
i073018.36+411320.4	17.03	16.61	16.92	17.10	17.38	15126	7.83	0.26	133
i074631.42+173448.2	17.93	17.57	17.59	17.66	17.82	9282	8.59	0.14	66
d081308.52+480642.3	16.30	16.54	16.97	17.30	17.60	32727	7.86	0.20	279
i083633.00+374259.4	19.21	18.71	18.67	18.66	18.73	7798	8.11	0.12	116
i085650.58+275118.0	18.76	18.63	18.92	19.21	19.35	19333	7.86	0.12	428
d090611.00+414114.3	16.73	17.14	17.64	17.97	18.19	47637	7.91	0.05	469
i091312.74+403628.8	18.14	17.64	17.86	18.02	18.25	11726	8.02	0.07	153
i101007.89+615515.7	19.38	18.89	18.73	18.71	18.68	7252	8.31	0.04	94
i102915.97+300251.6	19.42	18.98	18.88	18.97	18.93	7755	7.86	0.08	153
i231725.29−084032.9	18.94	18.38	18.19	18.13	18.14	6862	7.34	0.13	124

Note. ^alog (g) is in units of cm s⁻².

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We used IRAF for our data reduction. The images were dark-subtracted and flat-field corrected. In addition, a sky image was made by filtering out stars from each set of the dithered images in one exposure. The sky image was subtracted from the set of images, and then the sky-subtracted images were shifted and combined into one final image of a target field.

To calibrate our target images astrometrically, we used the in-field, relatively bright 2MASS stars (Skrutskie et al. 2006), the numbers of which were between 8 and 50, depending on the fields. The resulting nominal uncertainties of the calibrated images are in a range of 003–011. For most of our images, the uncertainties are dominated by the 2MASS systematic uncertainty of ≃015 (with respect to the International Celestial Reference System).

We used the IRAF aperture photometry package apphot to measure the brightnesses of our sources for most of the images. For a few cases in which a target was resolved to have a nearby source, the point-spread function fitting package daophot was used. Flux calibration was conducted by comparing to bright 2MASS stars detected in our images.

Launched in 2009 December 14, WISE mapped the entire sky at 3.4, 4.6, 12, and 22 μm (called W1, W2, W3, and W4 bands, respectively) in 2010 with FWHMs of 61, 64, 65, and 120 in the four bands, respectively (see Wright et al. 2010 for details). The WISE all-sky images and source catalog were released in 2012 March. We downloaded the flux measurements of each target in the source catalog and the WISE image data of each target field from the Infrared Processing and Analysis Center. Debes et al. (2011) provided all magnitudes or magnitude upper limits of the WISE candidate counterparts to the WD targets, but because they used the WISE preliminary catalogs, the values were slightly different from those in the all-sky source catalog. We therefore re-provided the magnitudes or magnitude upper limits of our 12 WD targets from the all-sky source catalog in Table 2.

In our ground-based images, we detected all 12 targets, but we found that 4 of them were resolved as 2 sources at/near the WISE source position. The fields of the four WDs are shown in Figure 1. From our astrometry, we determined the counterparts based on the measured positions and they are marked as object A in Figure 1. The nearby non-counterpart sources, which are 1''–2'' away from the counterparts, are marked as object B. We also determined the positions and JHK_s magnitudes of these nearby sources, and the values are given next to the counterparts in Table 2. For the other eight targets, one single source was clearly detected at or near the SDSS position. Among them, i0004 was detected by the 2MASS survey, but because it had significant proper motion, Δα = 286 ± 006 and Δδ = −022 ± 004 (our Palomar measurement with respect to that of 2MASS, which was made on 1998 September 17), it was not reported to have the 2MASS detections (the positional criterion for candidate counterpart identification was 20 in Debes et al. 2011).

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Combining SDSS u'g'r'i'z' flux measurements (Kleinman et al. 2013) and that from the WISE all-sky source catalog with our JHK_s measurements, we constructed the flux density spectra for the 12 WD targets. The spectra are shown in Figures 2 and 3. For the four WDs with a nearby source, the nearby sources are included correspondingly in the figure (displayed as circular data points). We compared our observational spectra with WD model spectra in the infrared bands (kindly provided by P. Bergeron), whose properties were determined by Kleinman et al. (2013; see also Debes et al. 2011), and found that no significant excess emission at JHK_s bands was detected for most of the WDs except i0856. For i0730, d0813, d0906, and i0913, the emission detected by WISE more likely came from their nearby source (see Section 4.2 below), and our observations excluded them as the WDs with excess infrared emission.

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For the seven WDs without significant JHK_s excess emission, they are not likely to have a very low mass (VLM) star or a brown dwarf companion. For example, the K_s magnitudes and their uncertainties are 15–18 and ∼0.1, respectively. The uncertainties only allow the possible existence of 10% excess emission or 2.5 mag fainter sources. Adding 2.5 mag to K_s and comparing it to W1 magnitudes, which are slightly lower than K_s values (see Table 2), such infrared sources would have a K_s − W1 color of >2.5 mag. The color is too red for VLM dwarfs (see Kirkpatrick et al. 2011 for the colors of the known VLM dwarfs).

With constraints from our JHK_s measurements, we fit these sources with the debris disk model given by Jura (2003) to study if the excess emission could arise from a debris disk. In the model, the disk temperature follows T(r)∝T_WDr^−3/4, where T_WD is the effective temperature of a WD and r the disk radius (Jura 2003). We adopted the model parameters used in Debes et al. (2011), assuming a temperature of T = 1200 K at the inner edge of the debris disk and an outer disk radius of 80r_WD, where r_WD is the radius of a WD. The distance, effective temperature, and extinction of each WD target were fixed at the values given in Table 1 (Debes et al. 2011; Kleinman et al. 2013). The free parameter was the inclination angle i of the disk. We fit K_s, W1, and W2 (or only K_s and W1 when there was no W2 detection) fluxes, where K_s was included to serve as the additional constraint (for i2317, which had K_s excess emission, H-band flux was included as well). We also required that the model flux at W2 band must be lower than the WISE flux upper limit for the sources not detected at W2. We found that the excess emission from most of the sources is generally consistent with arising from a debris disk, and the resulting best-fit cos i and χ² values are summarized in Table 3. The best-fit model fluxes for each source are shown in Figure 2.

For i0836 and i2317, the requirement of the model for the W2 flux lower than the WISE upper limit provided a constraint in the fitting. If this requirement is not considered, χ² values would be much smaller. For i1010 and i1029, the χ² values are quite large for cos i = 1. This is because their W1 fluxes are significantly higher than their K_s fluxes, and in order for the model to match the W1 fluxes, the model fluxes were increased, thus inducing large χ² values at K_s band. We note that since the WISE magnitudes of the WDs are in a range of 15–17 and WISE photometry of such faint sources is known to have as large as ∼0.4 mag systematic uncertainty,³ the poor fitting can be caused by the large uncertainties on WISE photometry that are not included in the catalog data. For the same reason, we did not further search for better fitting by varying the model parameters.

However, for the WDs that show clear excess emission and are believed to have a debris disk, we know that (1) they nearly all have effective temperatures in a range of 9500–24,000 K (except G 166−58 for its T_WD = 7400 K; Farihi et al. 2008); (2) they nearly all are known to be metal-rich from optical spectroscopy (Xu & Jura 2012); and (3) nearly half of them show significant emission excesses at infrared K band relative to their WD model spectra. These properties make the identification of the seven WDs as candidates with debris disks highly questionable. The seven WDs generally do not fit in any of them (Tables 1 and 3; Debes et al. 2011).

Since WISE imaging had relatively low spatial resolution, it cannot be determined solely based on the positions whether or not the WISE sources are the counterparts to the nearby sources of i0730, d0813, d0906, and i0913 (object B in Figure 1). Combining our JHK_s measurements with the WISE fluxes, as shown in Figure 3, the overall broadband spectra suggest that the WISE sources are the counterparts to the four nearby sources, or at least emission from the nearby sources dominated over that from the four WDs (otherwise these nearby sources would have to have an unlikely, large flux decrease from K_s to W1). Since the sources are red and three of them (nearby to ixxxx sources) were classified by Debes et al. (2011) to be possible candidate brown dwarfs, we fit their broadband spectra with that of VLM stars and brown dwarfs. Following Debes et al. (2011), we used the empirical spectra for M, L, and T dwarfs (Hawley et al. 2002; Kirkpatrick et al. 2011). We first fixed the distances at the values of the WDs and found that the resulting χ² were large (the values and the best-fit spectral types are given in Columns 4 and 3, respectively, of Table 4). Setting the distance as a free parameter, the best-fit χ² can be significantly reduced (see the values at column seven of Table 4). Therefore, if the sources are M or L dwarfs, as identified from our fitting, they are most likely not associated with the WDs. The best-fit spectra of the four sources are shown in Figure 3.

In addition for i0856, since it had significant excess emission starting from the optical z' to JHK_s bands comparing to the WD model spectrum, the debris-disk model we used, which assumed a low-temperature disk, could not provide a reasonably well fit. We thus tested with the VLM dwarf models and found that an L0 dwarf at the WD's distance of 428 pc can generally describe the excess emission except at the W1 band (Figure 3). Here again given the large uncertainties on the WISE measurements of faint sources, we considered the fitting was acceptable although the reduced χ² is ≃ 16 (Table 4).

The WD targets are located away from the Galactic plane having clean source fields according to the SDSS optical and our JHK_s images. However, it has been shown from Spitzer imaging that at m > 14 mag in the wavelength range of 3–10 μm, galaxies dominate in such regions (Fazio et al. 2004). For example, as our WD targets have W1 magnitudes in a range of 15–17 mag, at its middle value of 16 mag, the Spitzer galaxy count at 3.6 μm was ≃2300 mag⁻¹ deg⁻² (Fazio et al. 2004) or 1.8× 10⁻⁴ mag⁻¹ arcsec⁻². Considering the 2'' radius circular region, which was used by Debes et al. (2011) for searching for WD counterparts, there will be a chance of 0.23% to randomly find at least one 16 mag galaxy in such a region. The percentage is low, but there were nearly 18,000 times searches (for 17,955 unique and valid targets; Debes et al. 2011), which would result in 40 randomly detected galaxies. Approximately 300 WDs per mag were detected at W1 = 16 mag, but excluding 23% naked WDs (detection of WD photosphere only) and 67% candidate WD plus M dwarf binaries (Debes et al. 2011), the latter we consider rather certain due to their brightnesses and colors, only 30 per mag would be either debris-disk or brown-dwarf companion systems among the candidates. The numbers thus suggest that the detected excess emission is likely caused by unresolved background galaxies due to WISE's relatively low spatial resolution, and those nearby sources are also likely galaxies.

Among the 12 WD targets identified with excess emission from the WISE data, our observations and analysis show that 7 are consistent with having a debris disk, but their properties are not in the likely range for the detectable disks on the basis of the currently known debris-disk WDs. Among the other five WD targets, four are found that their excess emission is caused by the existence of a nearby red source and the remaining one, i0856, shows significant excess emission at JHK_s bands. Our analysis suggests that the nearby sources are possibly unassociated VLM stars or brown dwarfs while excess emission from i0856 is suggestive of an L0 dwarf. However, we also realize that the excess emission (and the nearby sources) might well be caused by background galaxies, which are known to be the dominant, relatively faint sources at wavelengths between 3–10 μm. Therefore, in order to investigate the true nature of the observed excess emission or nearby sources, imaging with Spitzer is needed. The Spitzer observations will possibly resolve background galaxies from the WD targets and provide accurate flux measurements at the infrared wavelengths of W1 and W2 bands, both helping identify the debris disks and VLM dwarfs.