THE MASS DEPENDENCE BETWEEN PROTOPLANETARY DISKS AND THEIR STELLAR HOSTS

We present a substantial extension of the millimeter (mm) wave continuum photometry catalog for circumstellar dust disks in the Taurus star-forming region, based on a new ''snapshot'' λ = 1.3 mm survey with the Submillimeter Array. Combining these new data with measurements in the literature, we construct a mm-wave luminosity distribution, f(Lmm), for Class II disks that is statistically complete for stellar hosts with spectral types earlier than M8.5 and has a 3σ depth of roughly 3 mJy. The resulting census eliminates a longstanding selection bias against disks with late-type hosts, and thereby demonstrates that there is a strong correlation between Lmm and the host spectral type. By translating the locations of individual stars in the Hertzsprung-Russell diagram into masses and ages, and adopting a simple conversion between Lmm and the disk mass, Md , we confirm that this correlation corresponds to a statistically robust relationship between the masses of dust disks and the stars that host them. A Bayesian regression technique is used to characterize these relationships in the presence of measurement errors, data censoring, and significant intrinsic scatter: the best-fit results indicate a typical 1.3 mm flux density of ∼25 mJy for 1 M☉ hosts and a power-law scaling Lmm∝M*1.5-2.0. We suggest that a reasonable treatment of dust temperature in the conversion from Lmm to Md favors an inherently linear Md ∝M* scaling, with a typical disk-to-star mass ratio of ∼0.2%-0.6%. The measured rms dispersion around this regression curve is ±0.7 dex, suggesting that the combined effects of diverse evolutionary states, dust opacities, and temperatures in these disks imprint a full width at half-maximum range of a factor of ∼40 on the inferred Md (or Lmm) at any given host mass. We argue that this relationship between Md and M* likely represents the origin of the inferred correlation between giant planet frequency and host star mass in the exoplanet population, and provides some basic support for the core accretion model for planet formation. Moreover, we caution that the effects of incompleteness and selection bias must be considered in comparative studies of disk evolution, and illustrate that fact with statistical comparisons of f(Lmm) between the Taurus catalog presented here and incomplete subsamples in the Ophiuchus, IC 348, and Upper Sco young clusters.