Roughly 2% of white dwarfs harbor planetary debris disks detectable via infrared excesses, but only a few percent of these disks show a gaseous component, distinguished by their double-peaked emission at the near-infrared calcium triplet. Previous studies found that most debris disks around white dwarfs are variable at 3.4 and 4.5 μm, but they analyzed only a few of the now 21 published disks showing calcium emission. To test if most published calcium emission disks exhibit large-amplitude stochastic variability in the near-infrared, we use light curves generated from the unWISE images at 3.4 μm that are corrected for proper motion to characterize the near-infrared variability of these disks against samples of disks without calcium emission, highly variable cataclysmic variables, and 3215 isolated white dwarfs. We find that most calcium emission disks are extremely variable: 6/11 with sufficient signal-to-noise show high-amplitude variability in their 3.4 μm light curves. These results lend further credence to the notion that disks showing gaseous debris in emission are the most collisionally active. Under the assumption that 3.4 μm variability is characteristic of white dwarfs with dusty debris disks, we generate a catalog of 104 high-confidence near-infrared variable white dwarfs, 84 of which are published as variable for the first time. We do near-infrared spectroscopic follow-up of seven new candidate 3.4 μm variables, confirming at least one new remnant planetary system, and posit that empirical near-infrared variability can be a discovery engine for debris disks showing gaseous emission.
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