Infrared Excesses around Bright White Dwarfs from Gaia and unWISE I

We start with white dwarf candidates identified from the Gaia Data Release 2 reported in Gentile Fusillo et al. (2019). We focus on bright white dwarfs with (i) Gaia G $<$ 17.0 mag, which are more likely to have detections at the WISE bands and well suited for further characterization. We also require (ii) the white dwarf probability P_WD $>$ 0.75, which has an estimated false positive rate of 4%. Gentile Fusillo et al. (2019) reported white dwarf parameters (e.g., effective temperature T_eff and surface gravity log g) using the Gaia photometry and parallaxes and we use results from the H-atmosphere fits for the rest of the paper. We also limit the sample to (iii) T_eff $<$ 50,000 K and log g $>$ 7.0 cm s^-2. The temperature limit is to exclude hot white dwarfs and pre-white dwarfs in planetary nebulae. The surface gravity limit is to exclude unresolved white dwarf and main sequence binaries, which can appear to have a small surface gravity for photometrically determined parameters. There are 6002 high probability white dwarf candidates in our starting sample, which also includes 36 known dusty white dwarfs and 4 white dwarfs with low-mass companions in Table 1.

WISE photometry is crucial in identifying white dwarfs with infrared excesses because the excess flux is most apparent in the first two WISE bands (see Figure 1). Previously, the WISE Preliminary Release Catalog, the WISE All Sky Survey, and the ALLWISE data release have been used to search for infrared excesses (Debes et al., 2011; Hoard et al., 2013; Dennihy et al., 2016, 2017; Rebassa-Mansergas et al., 2019). Recently, there is a new data release called the unWISE catalog, which combines five years (i.e., 2010, 2014–2017) of WISE images at 3.4 $\mu$m and 4.6 $\mu$m (Lang, 2014; Meisner et al., 2017; Schlafly et al., 2019). The exposure time of the unWISE co-adds is about a factor of five of the ALLWISE co-adds (Cutri & et al., 2013), leading to 0.7 mag fainter detection limits at 5$\sigma$. In addition, thanks to the improved modeling using the forced photometry algorithm and the crowdsource photometry pipeline (Schlafly et al., 2018), the unWISE photometry is more reliable, particularly in crowded regions.

To have an independent assessment of the unWISE catalog, we cross-correlated the 6002 Gaia white dwarfs with unWISE and ALLWISE separately. unWISE returned 2886 reliable detections in both W1 and W2 while ALLWISE only returned 1858 detections²²2Reliable photometry means that the measured position in the WISE catalog agrees to within 3$\sigma$ of the calculated position from Gaia and the white dwarf is the only source detected within a 3$\farcs$0 radius in different catalogs. See description for Steps I and III in Section 3.3.. For the unWISE photometry, we added an additional 3% systematic uncertainty in quadrature to the reported statistical uncertainty to account for the fluctuation of the zero points throughout the unWISE coadds (Lang, 2014; Meisner et al., 2017). A comparison between the unWISE photometry and ALLWISE photometry with the expected single H-atmosphere white dwarf photometry from models (P. Bergeron, private communications) is shown in Figure 2. At the bright end, the ALLWISE and unWISE performances are similar. At the faint end, the unWISE magnitudes have a much smaller scatter compared to those of ALLWISE, thanks to the better photometry algorithm of unWISE (Schlafly et al., 2018). However, the faintest objects are at the sensitivity limit of unWISE and our assessment of their infrared excess might not be reliable.

We also calculated the median uncertainty in each magnitude bin for ALLWISE and unWISE respectively in Table 2. On the bright end ($<$ 16.0 mag), the uncertainties are comparable between ALLWISE and unWISE. On the faint end ($>$ 16.0 mag), the unWISE uncertainties are significantly smaller, particularly at W2.

unWISE is a static-sky catalog and it did not account for proper motion – one major drawback compared to ALLWISE (Schlafly et al., 2019). Fortunately, for the 6002 white dwarfs of interest, 5910 systems (98.5%) move less than four arcseconds over the seven year time period of the unWISE co-adds. Four arcseconds is about half of the WISE beam size, which is also our crossmatch search radius. Therefore, proper motion is not a concern for most white dwarfs in this sample. Given unWISE’s smaller uncertainty, larger number of detections, and more reliable photometry for faint objects, we decided to use it for our analysis.

There are four main steps to identify infrared excess candidates, as shown in the flowchart in Figure 3. We start with the sample of 6002 white dwarfs presented in section 3.1 (sample A) and describe each step in the following.

I. Cross-correlate with unWISE. We first cross-correlated the Gaia white dwarf sample with the unWISE catalog. Using the 2015.5 epoch Gaia coordinates and their proper motions, we calculated the coordinate of each white dwarf back to the 2014.4 epoch, which is the middle point of the unWISE catalog (Schlafly et al., 2019). The unWISE position uncertainty varies between 0$\farcs$01 for the brightest white dwarfs to 1$\farcs$5 for the faintest ones. We consider a source to have a positive detection in the unWISE catalog if the measured unWISE coordinate and the calculated coordinate using the Gaia position and proper motion agree to within 3$\sigma$. There are 3065 white dwarfs with both unWISE W1 and W2 detections (sample B).

II. Cross-correlate with SIMBAD. We cross-correlated Sample B with SIMBAD and found 1688 systems with an entry in the spectral type. The majority (1649) are indeed white dwarfs but 39 systems are rejected because they are either not white dwarfs (e.g., subdwarfs) or are accreting white dwarfs (e.g., cataclysmic variables). We caution that there will be other outliers and spectroscopy is needed to confirm the white dwarf nature of these objects in our sample.

III. Search for nearby contamination. WISE has a large 6$\farcs$0 beam and therefore is subject to background confusion, particularly for faint sources like white dwarfs. Therefore, we cross-correlated our sample with as many surveys as possible to search for background contamination. We started with the coordinates and proper motions from Gaia DR2 (J2015.5) and calculated the expected positions in each catalog, which includes the Sloan Digital Sky Survey (SDSS) DR 12 (J2007.5), UKIRT Infrared Deep Sky Survey (UKIDSS) DR9 LAS/GCS/DXS (J2008.5), the Vista Hemisphere Survey (VHS) DR6 (J2012), the Vista Variables in the Via Lactea (VVV) DR4 (J2012), the VISTA Kilo-degree Infrared Galaxy Survey (VIKING) DR5 (J2013), the UHS (UKIRT Hemisphere Survey) DR1 (J2015), and the Gaia DR2 (J2015.5). If more than one source is detected within 3$\farcs$0 of the position of the white dwarf, the unWISE photometry is considered to be contaminated and the system is excluded from the following analysis. In some cases, multiple detections of the white dwarf at different epochs could lead to multiple entries in a given catalog, mimicking background contamination. Fortunately, Gaia, SDSS and UKIDSS have generated a duplication flag when the same source is detected twice. For UHS, VIKING, VHS, and VVV, we have manually checked all the images where more than one source was detected within 1$\farcs$6 of the expected position of the white dwarf and independently confirmed the number of sources. Out of the 3065 white dwarfs in sample B, 2691 objects are detected in at least one other catalog in addition to Gaia DR2 and unWISE. There are 2847 white dwarfs with no background objects within 3$\farcs$0 (Sample D, including 28 known dusty white dwarfs and four white dwarf-brown dwarf pairs), as listed in Table 3.

IV. Identify white dwarfs with unWISE excesses. Following the methods described in Wilson et al. (2019), we adopted two methods to identify white dwarfs with infrared excesses, i.e., the W1 & W2 magnitude excess and the (W1-W2) color excess. At a given wavelength $i$, the magnitude excess is characterized by $\chi$($i$) ,

where $i$ = W1 or W2. $m_{\mathrm{obs,i}}$ and $\sigma_{\mathrm{obs,i}}$ is the observed unWISE magnitude and uncertainty, respectively. $m_{\mathrm{mod,i}}$ is the calculated WISE magnitude (P. Bergeron, private communications) given the white dwarf parameters and Gaia distances. The median extinction in Gaia G band for the unWISE sample is 0.13 mag (Gentile Fusillo et al., 2019) so no correction for reddening is applied. $\sigma_{\mathrm{mod,i}}$ is the model uncertainty, which is taken as 5% of the model flux. We calculated $\chi$ for both W1 and W2, as shown in Figure 4. Rejecting the top and bottom 10% $\chi$ values, we find that the mean and the standard deviation is $\bar{\chi}$ (W1) = 0.17 $\pm$ 1.09, $\bar{\chi}$ (W2) = -0.05 $\pm$ 1.27. Higher $\chi$ values mean more significant infrared excesses. In this work, we consider a white dwarf to be an infrared excess candidate from the magnitude excess method if they have both $\chi$(W1) $>$ 5 and $\chi$(W2) $>$ 5.

The (W1-W2) color excess is characterized by $\Sigma_{\mathrm{W12}}$,

Rejecting the top and bottom 10% of $\Sigma_{\mathrm{W12}}$ values, the mean and the standard deviation is $\bar{\Sigma}_{\mathrm{W12}}$ = -0.13 $\pm$ 0.76. A larger $\Sigma_{\mathrm{W12}}$ value indicates a stronger infrared excess. Here, a system is considered to display an infrared excess from the color excess if $\Sigma_{\mathrm{W12}}$ $>$ 3 (see Figure 4). There are 106 such systems, including 52 also having W1 & W2 magnitude excess.

To be as complete as possible, we also included 179 white dwarfs that have unWISE photometry but are likely to suffer from background contamination in Table 4. Essentially, these are the white dwarfs that are in sample C but not in sample D of Figure 3. We performed the exact same kind of analysis and listed $\chi$(W1), $\chi$(W2), and $\Sigma_{\mathrm{W12}}$ in the table. Some of them might have a real infrared excess but the nearby source complicates the interpretation. Further investigation is needed and we exclude this sample for our following analysis.

We have identified a total of 188 white dwarfs that show an infrared excess via either the magnitude excess or the color excess (sample E). Before interpreting the results, we will discuss three caveats for this analysis.

The starting sample are white dwarf candidates. Our starting sample are white dwarf candidates identified using Gaia photometry and parallax (Gentile Fusillo et al., 2019). Out of the 188 white dwarfs with an infrared excess, 83 are spectroscopically confirmed white dwarfs, including two white dwarf-M dwarf pairs. The rest 105 systems have no spectroscopic classification. Most of them are likely real white dwarfs but there will be contaminants and optical spectroscopy is needed to confirm the nature of these objects. Their positions in the Gaia Hertzsprung-Russell (HR) diagram is shown in Figure 5.

Pure hydrogen atmosphere models are assumed for all white dwarfs. In this analysis, the white dwarf parameters are all taken from pure hydrogen atmospheres fits reported in Gentile Fusillo et al. (2019) and the infrared excess is identified from assuming pure hydrogen atmosphere models (P. Bergeron, private communication). Atmospheric composition can affect the white dwarf parameters (Bergeron et al., 2019) and in return affect the assessment of the infrared excess.

Background contamination is unavoidable for the infrared excess candidates. Previous studies show that the cause of false positive for WISE-selected infrared excess objects is background contamination (Barber et al., 2014; Dennihy et al., 2020). This sample should be treated as infrared excess candidates until further confirmation.

Magnitude excess and color excess have been widely used to identify white dwarfs with an infrared excess. Essentially, magnitude excess requires the measured flux to be above the white dwarf’s photosphere. This method is used in most Spitzer searches and some WISE searches of white dwarf disks (e.g., Jura et al., 2007; Farihi et al., 2009; Debes et al., 2011). Magnitude excess has no requirement for the shape of the infrared excess. Its accuracy is strongly dependent on white dwarf models and the flux calibrations of the observations. On the other hand, color excess requires the excess to be brighter in W2 than W1 and it has been used in some disk searches (Hoard et al., 2013; Wilson et al., 2019). Color excess is less sensitive to the accuracy of the white dwarf models but it tends to miss objects with an unusual shape of the infrared excess.

Unresolved white dwarf-M dwarf pairs can also have WISE excesses and thousands such systems have been discovered in the SDSS (Rebassa-Mansergas et al., 2016). The frequency of M dwarf companions to white dwarfs is estimated to be 30% (Debes et al., 2011), much more common than white dwarf debris disks and white dwarf-brown dwarf pairs. In this study, most white dwarfs with main sequence companions are excluded because of the color cut used by Gentile Fusillo et al. (2019) to select Gaia white dwarf candidates and the log g $>$ 7.0 cm s^-2 requirement in our initial sample. In addition, out of the 83 spectroscopically confirmed infrared excess candidates, only two are white dwarf-M dwarf pairs. Likely, the frequency of M dwarf companions is low for this sample.

Our assessments for known white dwarfs with an infrared excess are listed in Table 1. For the systems with unWISE detections, most dusty white dwarfs (18 out of 28) show both magnitude excess and color excess. There are three systems that only show the magnitude excess and one system that only shows the color excess. Interestingly, the three known white dwarf-brown dwarf pairs only show magnitude excess and not color excess, likely due to the methane and water absorptions in the WISE bands (see Figure 1).

For the infrared excess candidates in Table 3, 29 new white dwarfs (excluding the known systems) show both color excess and magnitude excess – this is the most promising sample of disk candidates. For the following analysis, to be as complete as possible, we decided to include objects selected from either the magnitude excess or the color excess as infrared excess candidates.

In the sample of 2847 white dwarf candidates with unWISE photometry, we have identified a total of 188 white dwarfs that show WISE excesses. Apart from the 25 known objects, 14 candidates reported previously in Rebassa-Mansergas et al. (2019), and 2 white dwarf-M dwarf pairs, the rest are all new systems that are reported here for the first time. Out of the 32 known infrared excess objects that also have unWISE photometry, our selection criteria have recovered 22 out of the 28 white dwarf debris disks and 3 out of 4 white dwarf-brown dwarf pairs. Nominally, the completeness rate of our study is 25/32 = 78%. The seven systems that are missed by our selection criteria tend to have a weak infrared excess. For example, WD 2132+096 shows no excess at shorter wavelengths and only a 4$\sigma$ excess at 4.5 $\mu$m in Spitzer observations (Bergfors et al., 2014), while WD 2328+107 requires a very high disk inclination to fit the subtle excess (Rocchetto et al., 2015). The poorer sensitivity of WISE limits us from detecting subtle infrared excess objects. However,WISE is well suited for finding the brightest and most prominent infrared excesses around white dwarfs – the focus of this work.

The frequency of infrared excesses around white dwarfs in this sample is 188/2847 = 6.6 $\pm$ 0.5% assuming a Poissonian probability distribution for calculating the uncertainty. Using the 78% completeness rate calculated above, the corrected frequency is 8.4 $\pm$ 0.6%. We caution that this number should be treated as an upper limit because our sample is limited by source confusion (Dennihy et al., 2020). Studies using Spitzer show that the white dwarf disk fraction is about 2-4% (Barber et al., 2014; Rocchetto et al., 2015; Wilson et al., 2019). The frequency of white dwarf-brown dwarf systems is estimated to be 0.5-2.0% (Girven et al., 2011; Steele et al., 2011). Assuming a true infrared excess (disk and brown dwarf combined) frequency of 3%, it implies a false positive rate of (100% - 3%/8.4%) = 64% for this sample. Even so, there would be 188 $\times$ (1 - 64%) - 25 = 42 new white dwarfs with a real infrared excess, which will more than double the known sample.

The sky positions of the infrared excess objects are shown in Figure 6. This study has significantly increased the number of infrared excess candidates. These new candidates are evenly scattered all over the sky except for areas around the Milky Way disk, where the stellar density increases significantly and the unWISE sensitivity becomes a lot worse.

Now we assess the overall properties of the Gaia white dwarf sample (sample A), the unWISE sample (sample D), and the infrared excess candidate sample (sample E). A comparison of these three distributions as a function of the unWISE magnitude, the white dwarf temperature, and the white dwarf mass is shown in Figure 7. We performed Kolmogorov-Smirnov tests between these distributions and did not find any significant differences, particularly between the unWISE sample and the infrared excess candidate sample.

The unWISE magnitude distribution: The P-values for both unWISE W1 and W2 are very small between the unWISE sample and the infrared excess candidate sample. It shows that generally our selection method is not biased against the brightness of a white dwarf in unWISE. However, we can see in Figure 4 that the scatters in $\chi$ and $\Sigma$ become larger for fainter white dwarfs. Extra caution is needed to interpret the origin of the infrared excess at the faint end.

The temperature distribution: At the cool end (T_eff $<$ 10,000 K), we have identified 21 infrared excess candidates. This is contrary to previous findings that there is a lack of dust disks around cool white dwarfs (Xu & Jura, 2012). At the hot end, there are 23 white dwarfs with a temperature higher than 25,000 K, which is the hottest known white dwarf with an infrared excess (PG 0010+280, Table 1). At these high temperatures, dust particles are expected to fully sublimate within the tidal radius of the white dwarf (von Hippel et al., 2007). The origins of the infrared excesses around those cool (T_eff $<$ 10,000 K) and hot white dwarfs (T_eff $>$ 25,000 K) deserve further investigation.

The mass distribution: There is little difference in the mass distributions between the unWISE sample and the infrared excess candidate sample. We have identified 11 white dwarfs with with a mass $\lesssim$ 0.3 M_⊙, which are called extremely low mass (ELM) white dwarfs and are often in binaries (Brown et al., 2020). It is very unusual to see a strong infrared excess around an ELM white dwarf and follow-up study is needed to understand its origin. In addition, there are 14 disk candidates around white dwarfs with a mass larger than 0.75 M_⊙. However, most of these white dwarfs are not spectroscopically confirmed and the white dwarf parameters could be different depending on the atmospheric composition (Bergeron et al., 2019). If the infrared excess is confirmed, it can help us understand the frequency of planetary systems around massive stars which is otherwise hard to constrain (Barber et al., 2016).