3.4. Connections to Stellar Properties

The physical properties of a young star and its circumstellar disk could be related due to their mutual formation and subsequent gravitational and thermal links. Generally, observational indications of any such relationship are absent, presumably due to a wide range of initial circumstellar conditions for individual sources and the relatively small ranges of stellar masses and ages. As with Beckwith et al. (1990), we do not find any correlations between measured submillimeter properties and any characteristic of the stellar photosphere (e.g., effective temperature, luminosity, optical fluxes or colors, etc.). One perhaps notable exception is the large value of {tex}T_1{/tex} derived for the two A stars in this sample (AB Aur and V892 Tau). Natta, Grinin, & Mannings (2001) also suggest that hotter stars have generally higher dust temperatures in their disks, but there is no noticeable trend for the cooler (K and M) majority of this sample. This disconnect between the stellar photosphere and the outer disk, where the submillimeter emission is generated, is not surprising. Despite the increase in vertical scale height of the disk with radius expected from hydrostatic equilibrium (e.g., Kenyon & Hartmann 1987), radiative transfer models for structurally realistic disks indicate that the bulk of the submillimeter emission comes from the dust near the disk midplane, and not in the flared atmosphere which can be more directly affected by the stellar photosphere (Chiang & Goldreich 1997, 1999).

The gravitational link between a young star and its disk suggests that the stellar and disk masses may be related. Circumstellar disks are self-gravitationally stable if their mass is less than a fraction (a few tenths) of the stellar mass (Shu et al. 1990; Laughlin & Bodenheimer 1994).  In principle, this could allow more massive stars to harbor more massive disks. Natta, Grinin, & Mannings (2001) combine interferometric measurements of disks around early-type stars with the 1.3mm survey of Beckwith et al. (1990) and claim a marginal correlation between the disk mass and stellar mass ({tex}M_*{/tex}) over 2 orders of magnitude in {tex}M_*{/tex} for roughly 100 objects (however, see Mannings & Sargent 2000), although the dispersion is substantial. To revisit this issue, we have collected optical/near-infrared magnitudes and spectral classifications from various sources in the literature (Cohen & Kuhi 1979; Jones & Herbig 1979; Slutskiï, Stal’bovskiï, & Shevchenko 1980; Herbig, Vrba, & Rydgren 1986; Herbig & Bell 1988; Strom et al. 1989; Hartmann et al. 1991; Gomez et al. 1992; Bouvier et al. 1993; Briceño et al. 1993; Hartigan, Strom, & Strom 1994; Martín et al. 1994; Kenyon & Hartmann 1995; Hernández et al. 2004; White & Hillenbrand 2004, spectral types are listed in Table 1). A consistent set of visual extinctions was determined from the (V I) color excesses, using the intrinsic colors tabulated by Kenyon & Hartmann (1995) and the interstellar extinction law derived by Cohen et al. (1981). De-reddened visual magnitudes and spectral types were converted to bolometric luminosities and effective temperatures again using the intrinsic values of Kenyon & Hartmann (1995). Stellar masses and ages were determined by reference to theoretical pre-mainsequence evolution tracks and isochrones (D’Antona & Mazzitelli 1997) in a Hertzsprung-Russell diagram.

As Figure 9 demonstrates, there are no correlations between the submillimeter properties listed in Table 1 and stellar mass or age, but the ranges of those stellar properties (see Figure 1) may be too limited to infer a direct evolutionary sequence. However, the upper right panel of this figure shows that the region corresponding to higher mass disks at late times ({tex}\geq 6Myr{/tex}) is significantly depopulated. While there are not many objects in Taurus-Auriga with such ages, this unoccupied region in the diagram is consistent with other studies that indicate disk fractions approaching zero in the 6 to 10 Myr age range (e.g., Haisch, Lada, & Lada 2001). Figure 10 shows the cumulative distributions of the mass ratio of disk to star, constructed with the Kaplan-Meier estimator. Log-normal distributions provide poor fits in this case, but these distributions are fit fairly well with power laws of index between 1.5 and 2 for mass ratios larger than ~10^-3. The median disk to star mass ratio is 0.5%. The fraction of disks which may be self-gravitationally unstable (mass ratios larger than ~0.1) is negligible in Taurus-Auriga: roughly 6%, which itself may be an overestimate due to envelope emission for some of the Class I objects at the high end of the distribution. However, if {tex}\beta =2{/tex} is more appropriate, then the fraction of unstable disks can be as high as one third. A small fraction of objects (a few percent) has a mass ratio less than 10^-3.