The Mass Dependence Between Protoplanetary Disks and Their Stellar Hosts

We present a substantial extension of the mm-wave continuum photometry catalog for Taurus circumstellar dust disks. Combining new Submillimeter Array data with measurements in the literature, we construct a mm-wave luminosity distribution for Class II disks that is statistically complete for stellar hosts with spectral types earlier than M8. 5 and has a (3-sigma) depth of ~3 mJy. The resulting census eliminates a longstanding bias against disks with late-type hosts, and thereby reveals a strong correlation between Lₘm and the host spectral type. We confirm that this 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: the results indicate a typical 1. 3 mm flux density of 25 mJy for solar mass hosts and a power-law scaling Lₘm Mₛtar¹. 5-2. 0. We suggest that a reasonable treatment of dust temperature in the conversion from Lₘm to Mdisk favors an inherently linear Mdisk Mₛtar scaling, with a typical disk-to-star mass ratio of 0. 2--0. 6%. The RMS dispersion around this regression is 0. 7 dex, suggesting that the combined effects of diverse evolutionary states, dust opacities, and temperatures in these disks imprint a FWHM range of a factor of 40 on the inferred Mdisk (or Lₘm) at any given host mass. We argue that this relationship between Mdisk and Mₛtar 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 selection bias must be considered in comparative studies of disk evolution, and illustrate that fact with statistical comparisons of Lₘm between Taurus and other clusters (abridged).