  We find that the initial dust masses in planetary debris disks are correlated
with the metallicities of their central stars. We compiled a large sample of
systems, including Spitzer, the Herschel DUNES and DEBRIS surveys, and WISE
debris disk candidates. We also merged 33 metallicity catalogs to provide
homogeneous [Fe/H] and $\sigma_{[Fe/H]}$ values. We analyzed this merged
sample, including 222 detected disks (74 warm and 148 cold) around a total of
187 systems (some with multiple components) and 440 disks with only upper
limits (125 warm and 315 cold), around a total of 360 systems. The disk dust
masses at a common early evolutionary point in time were determined using our
numerical disk evolutionary code, evolving a unique model for each of the 662
disks backward to an age of 1 Myr. We find that disk-bearing stars seldom have
metallicities less than [Fe/H] = -0.2 and that the distribution of warm
component masses lacks examples with large mass around stars of low metallicity
([Fe/H] < -0.085). Previous efforts to find a correlation have been largely
unsuccessful; the primary improvements supporting our result are: 1.) basing
the study on dust masses, not just infrared excess detections; 2.) including
upper limits on dust mass in a quantitative way; 3.) accounting for the
evolution of debris disk excesses as systems age; 4.) accounting fully for the
range of uncertainties in metallicity measurements; and 5.) having a
statistically large enough sample.
