4. Discussion

A summary of representative numbers derived from this submillimeter survey of Taurus-Auriga is provided in Table 5. Listed are submillimeter detection fractions as well as median values and standard deviations of disk masses and submillimeter continuum slopes for the total sample and various subsamples of interest. Of the complete sample of 153 YSOs, 61 ± 6% were detected for at least one submillimeter frequency, with a median {tex}M_d\approx 5\times 10^{-3}M_\odot{/tex} and {tex}\alpha \approx 2.0{/tex}.  Single and multiple star systems have essentially identical detection rates and similar continuum slopes. However, as discussed in detail in the previous section, closer binaries have statistically lower disk masses than wider systems or single stars. Although Figure 12 demonstrates that there is no direct correlation between {tex}M_d{/tex} or {tex}\alpha{/tex} and the equivalent width or luminosity of the {tex}H\alpha{/tex} emission line, there is an obvious difference in the submillimeter detection fraction between WTTS and CTTS disks. The very high submillimeter detection rate for CTTS disks (91 ± 11%) is consistent with all CTTSs having disk masses greater than {tex}\sim 10^{-4}M_\odot{/tex}.  The bulk of the detected WTTS disks are clustered near {tex}W (H\alpha) = 10{/tex}Å:  when the WTTS/CTTS division criterion is slightly relaxed, this result suggests that nearly all WTTSs are either diskless or have very low disk masses. Therefore, the equivalent width of the {tex}H\alpha{/tex} emission line appears to be a fairly robust predictor of the presence of a "massive" disk.

Spectral energy distribution classifications of objects in the sample were determined based on power-law fits from 2 to 60 µm (when possible) with data from the literature (Strom et al. 1989; Weaver & Jones 1992; Kenyon & Hartmann 1995; Hartmann et al. 2005, and references therein).  We adopt the classification breakdown of Greene et al. (1994), using the values of the powerlaw index n (defined by {tex}vF_v\propto v^n{/tex})  to distinguish between Class I, Flat Spectrum, Class II, and Class III sources. The derived classifications are listed in Table 1. Although it is not absolutely calibrated in time, the YSO evolution sequence defined by the shape of the infrared SED is certainly indicative of changes in the physical structure of the inner regions of the circumstellar disk and/or envelope. With the large sample of submillimeter data presented above, we can address the issue of corresponding changes in the physical properties of the outer disk.

Motivated by the differences in the detection rates and median properties of the various SED classes listed in Table 5, the same survival analysis two-sample statistical tests used in §3.4 were employed to determine the probabilities that the 850 µm flux densities, inferred disk masses, and submillimeter continuum slopes for various SED and {tex}H\alpha{/tex} line strength classes are drawn from different parent populations. The test results are given in Table 6, and the cumulative distributions of {tex}F_v{/tex}, {tex}M_d{/tex}, and {tex}\alpha{/tex} for different classes are shown in Figure 13. There are statistically significant progressions of decreasing submillimeter flux densities, disk masses, and continuum slopes along the infrared SED evolution sequence. Flat Spectrum objects fit between Class I and II objects in these respects, with somewhat more similarity to the latter. Incorporating the Flat Spectrum objects with either the Class I or II objects does not make any significant difference in these results. Apparently the properties of the outer disk/envelope evolve along a similar evolutionary sequence as the inner disk.

Figure 13 clearly shows that Class I objects have significantly larger submillimeter flux densities, disk masses, and continuum slopes than Class II objects. It should again be stressed that the extent to which these values are representative of Class I disks, rather than disks + inner envelopes, is questionable. It has been suggested that many Class I disk properties could be mimicked by a Class II disk viewed at high inclination (e.g., Chiang & Goldreich 1999; White & Hillenbrand 2004).  It is shown in Figure 14 that for a given mass, a high inclination angle produces both a lower flux density and a lower continuum slope; the opposite is seen in Figure 13 and Table 6. If the Class I emission is primarily from a disk (with only a comparatively small contribution from the inner envelope), a simple re-orientation of a Class II disk will not reproduce the Class I submillimeter properties without additional changes in mass, temperature, or opacity. The distributions found here of the empirical (model-independent) flux densities and continuum slopes corroborate the original picture of Class I sources as disk + envelope systems: the higher flux densities and "disk" masses may be due to additional envelope mass, and the higher continuum slopes may be due to the less-processed (i.e., lower amount of grain growth) dust in the envelope. A large interferometric sample will be required to definitively settle the issues involved in a comparison of Class I and II disks.

Unfortunately, there are no measurements of a submillimeter continuum slope for any of the Class III objects in the sample, and the {tex}3-\sigma{/tex} upper limits are too large to make any definitive statements on an evolutionary trend in {tex}\alpha{/tex}. The direct relationships between {tex}M_d{/tex} or {tex}\alpha{/tex} and the infrared SED slope are shown in Figure 15. There is no direct correlation with {tex}M_d{/tex},⁴ but differences between the SED classes in general are apparent. A more steady decrease in {tex}\alpha{/tex} is seen across the evolution sequence, which if it continues would imply very shallow continuum slopes for Class III disks ({tex}\alpha{/tex} ~ 11.5). The Spearman rank correlation coefficient in this case is 0.50, with a 99.98% confidence level ({tex}3.7-\sigma{/tex}).  The best-fit linear relation between the submillimeter and infrared continuum slopes is {tex}\alpha = 0.40(\pm 0.04)n + 2.09(\pm 0.03){/tex}.  This trend can not be explained solely by decreasing optica depths in the disks along an evolutionary sequence: lower optical depths produce steeper continuum slopes. Another effect, such as a shallow opacity function or temperature/surface density evolution, must be acting to decrease in this manner. However, interferometric observations of the Class I sources at several wavelengths would be required to confirm the validity of this trend.

The submillimeter detection fraction and the fraction of objects with a near-infrared ({tex}K_s-L{/tex})  excess are identical: 60 ± 7%.⁵ Figure 16 is a near-infrared color-color diagram that indicates the sources with submillimeter detections. Of the 6 sources with infrared excesses that were not detected in the submillimeter, 5 could have anomalous colors due to mismatched photometry and/or infrared companions (see the Appendix). Three of the 55 sources with essentially no near-infrared excess, or 5 ± 3%, were detected in the submillimeter: GM Aur, V836 Tau, and CoKu Tau/4.⁶ All three of these YSOs also have mid- and far-infrared emission, indicating that the lack of near-infrared excess may be due to a clearing of dust in the inner ~1AU of their disks. In addition to these "transition" objects, three Class III sources, V807 Tau, FW Tau, and LkH{tex}\alpha{/tex} 332/G1, were also detected in the submillimeter (a 5.6 ± 3.2% detection rate), along with another possible Class III candidate whose SED classification remains to be confirmed due to lack of infrared data (HQ Tau). However, in general a YSO with a near-infrared excess also has submillimeter emission consistent with a disk mass greater than {tex}\sim 10^{-4}M_\odot{/tex} and vice versa. The small fraction of objects, less than 10%, with evidence for an outer disk (from submillimeter data) and no inner disk suggests that the timescale for the disappearance of both infrared and submillimeter disk emission is relatively short; no more than a few hundred thousand years (i.e., {tex}\frac{\lt}{\sim}{/tex} 10% of the typical YSO age in Taurus-Auriga).  In agreement with the comparatively low detection fraction for WTTS disks (16 ± 5%) and other similar analyses (e.g., Skrutskie et al. 1990; Wolk & Walter 1996; Duvert et al. 2000), these results imply that the inner and outer disk dissipate, or become unobservable, almost simultaneously.

The physical mechanism responsible for the rapid and essentially radially constant "disappearance" timescale remains to be explained. Viscous accretion onto the central star alone does not readily produce the apparently rapid inner-outer disk dissipation (Hollenbach, Yorke, & Johnstone 2000). In fact, evolution under accretion processes predicts only small changes in submillimeter emission with time (e.g., Hartmann et al. 1998). Models which incorporate the ultraviolet photoevaporation of the outer disk along with viscous accretion have more success in reproducing the inferred dissipation timescale, particularly for disk emission out to ~100 µm (Clarke, Gendrin, & Sotomayor 2001; Armitage, Clarke, & Palla 2003). However, these "ultraviolet switch" models also suggest that submillimeter emission is relatively unaffected, and could therefore predict a fairly large fraction of WTTSs or Class III sources with submillimeter emission. Clarke, Gendrin, & Sotomayor (2001) suggest that the low observed fraction of such transition objects noted by Duvert et al. (2000) and confirmed by the larger sample presented here may be accomodated in their models if different surface density profiles or viscosity values are adopted.

An alternative explanation to actually losing disk material, onto the star or elsewhere, is a process which renders the dust invisible to conventional observations. A compelling possibility is the collisional agglomeration of dust grains in the disk. Accelerated by gravitational settling to the disk midplane, the characteristic grain growth timescales even at fairly large disk radii are thought to be shorter than the transition timescale inferred above (e.g., Weidenschilling & Cuzzi 1993).  Perhaps the grain growth process has rendered the disks around many of the evolved (e.g., Class III) sources invisible by creating a significant population of large (~cm-sized) grains which are inefficient emitters at both infrared and submillimeter wavelengths. If this is to be the case, any collisional fragmentation process of the aggregate grains should not produce more than {tex}\sim 10^{-4}M_\odot{/tex} of particles which are efficient submillimeter emitters. The shallow submillimeter slopes measured in §3.3 and the implied low values of the opacity index {tex}\beta{/tex} lend some credibility to the grain growth argument. Theoretical studies indicate that {tex}\beta{/tex} values such as those inferred in this sample ({tex}\beta \sim 1{/tex} or less) can be the result of a significant population of large grains (Miyake & Nakagawa 1993; Pollack et al. 1994; Dullemond & Dominik 2005). The collisional growth of dust grains has also been inferred from submillimeter observations of both young (e.g., Beckwith & Sargent 1991; Mannings 1994; Koerner, Chandler, & Sargent 1995) and old (e.g., Calvet et al. 2002; Hogerheijde et al. 2003) low mass disks, and particularly for those around the more massive Herbig Ae stars (Testi et al. 2001, 2003; Natta et al. 2004). Complementary studies of scattered light (e.g., McCabe, Duchêne, & Ghez 2003; Duchêne et al. 2004b) and mid-infrared spectra (Meeus et al. 2003; Przygodda et al. 2003; van Boekel et al. 2004; Kessler-Silacci et al. 2005) also suggest that typical grain sizes are larger in these disks than for the ISM. The feasibility of this hypothesis depends critically on coupling with another mechanism which can diminish the accretion of gas, and therefore also explain the low submillimeter detection fraction for WTTSs.

The distribution of {tex}M_d{/tex} shown in Figure 5 indicates that typical disks have masses significantly lower than those required by two of the leading theoretical models for giant planet formation. Both the core accretion (Pollack et al. 1996) and disk instability (Boss 1998) scenarios require disk masses at least a few times that of the MMSN to form a Jupiter-like planet; roughly an order of magnitude higher than the median mass inferred for Taurus-Auriga disks. Radial velocity surveys suggest that roughly 10% of stars harbor a gas giant planet within a few AU (e.g., Marcy et al. 2005), with the prospect that better sensitivity to long-period planets could significantly increase that fraction (e.g., Fischer et al. 2001). This shows that planet formation is a fairly common process. In order for that to be the case, the disk mass distribution constructed in §3.2 needs to be reconciled with the theoretical requirements of the planet formation models. Possible remedies could be extracted from changes to the simple disk model used in §3: for example, adjustments to the disk surface density profile, or a significant decrease in the normalization of the opacity function. Unfortunately, solutions like these will remain untested until more advanced observations become available (e.g., interferometers with ~0.′′1 spatial resolution). A likely alternative explanation, as discussed above, is that a significant fraction of the disk mass is locked up in large grains or planetesimals which are inefficient emitters at submillimeter wavelengths.