Dusty WDs in the $WISE$ All Sky Survey $\cap$ SDSS

A recent cross-correlation between the SDSS DR7 White Dwarf Catalog with the Wide-Field Infrared Survey Explorer ($WISE$) all-sky photometry at 3.4, 4.6, 12, and 22 microns performed by Debes et al. (2011) resulted in the discovery of 52 candidate dusty white dwarfs (WDs). The 6'' $WISE$ beam allows for the possibility that many of the excesses exhibited by these WDs may be due to contamination from a nearby source, however. We present MMT$+$SWIRC $J$- and $H$-band imaging observations (0.5-1.5'' PSF) of 16 of these candidate dusty WDs and confirm that four have spectral energy distributions (SEDs) consistent with a dusty disk and are not accompanied by a nearby source contaminant. The remaining 12 WDs have contaminated $WISE$ photometry and SEDs inconsistent with a dusty disk when the contaminating sources are not included in the photometry measurements. We find the frequency of disks around single WDs in the $WISE$ $\cap$ SDSS sample to be 2.6-4.1%. One of the four new dusty WDs has a mass of $1.04 M_{\odot}$ (progenitor mass $5.4 M_{\odot}$) and its discovery offers the first confirmation that massive WDs (and their massive progenitor stars) host planetary systems.