We present a substantial extension of the millimeter-wave continuum photometry catalog for circumstellar dust disks in the Taurus star-forming region , based on a new “ snapshot ” \lambda = 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 ( L _ { mm } ) , 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 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 L _ { mm } 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 L _ { mm } and the disk mass , M _ { d } , 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 \sim 25 mJy for 1 M _ { \odot } hosts and a power-law scaling L _ { mm } \propto M _ { \ast } ^ { 1.5 - 2.0 } .
We suggest that a reasonable treatment of dust temperature in the conversion from L _ { mm } to M _ { d } favors an inherently linear M _ { d } \propto M _ { \ast } scaling , with a typical disk-to-star mass ratio of \sim 0.2–0.6 % .
The measured RMS dispersion around this regression curve is \pm 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 \sim 40 on the inferred M _ { d } ( or L _ { mm } ) at any given host mass .
We argue that this relationship between M _ { d } and M _ { \ast } 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 ( L _ { mm } ) between the Taurus catalog presented here and incomplete subsamples in the Ophiuchus , IC 348 , and Upper Sco young clusters .