How long does the dissipation process take once initiated

Once the process of disk dissipation starts, how long does it take for an individual object to transition from optically thick to optically thin dust? The expectation is for a short transition, based on calculations of initial grain growth via pairwise sticking collisions followed by runaway growth that forms large planetesimals (Moon-sized) on timescales of only ~105 yr (e.g., Wetherill & Stewart 1993; Weidenshilling & Cuzzi 1993). Is there a radial dependence to the disk clearing or do inner-, mid-, and outer-disk regimes dissipate simultaneously? While there are clear decreasing trends with advancing stellar age, both in the fraction of objects exhibiting infrared excess and in the mean magnitude of the infrared excess (not addressed in the discussion above), this does not inform us about the disk dissipation time for an individual object. The observed trends and their dispersion can be used, however, to construct statistical arguments that address the duration of the disk dissipation process, as a function of radius.

Historically, a relatively short, less than a few hundred-thousand-year timescale, has been inferred for the transition from an optically thick circumstellar disk to an optically thin circumstellar disk. The logic is based on two arguments—first, the disk statistics in binary pairs, and second, the small number (and therefore fraction) of objects found in transition between the optically thick and optically thin stages. Binary pairs, particularly in Taurus, have been well characterized in terms of the well-known CTTS (disked) and WTTS (diskless) categories. Numerous studies (e.g., Hartigan, Strom, & Strom 1994; Prato & Simon 1997; Duchene et al. 1999, Hartigan & Kenyon 2003) have found that the vast majority, >80%, of binary pairs are either both CTTS, or both WTTS, with mixed pairs relatively rare. This argues that the disk dissipation time is shorter than the absolute age difference between the members of stellar binaries.

Concerning transition objects, in the well-studied Taurus star-forming region, for example, V819 Tau and V773 Tau were argued by Skrutskie et al. (1990) to be the only two members out of approximately 150 known found with little or no near-infrared excess but small mid-infrared excess, j a result confirmed by Simon & Prato (1995) and Wolk & Walter (1996). This argument relies on the assumption of cluster coevality. As discussed above, this may not be a valid assumption at the few (2-3) Myr level. Spitzer data presented by Hartmann et al. (2005) appear to add several other objects to the "transition" category, such as CIDA 8, CIDA 11, CIDA 12, CIDA 14, DH Tau, DK TauB, and FP Tau.

Yet other Taurus objects have no evidence for excess out to 10 ¡m, but substantial excess at longer wavelengths. These are different from the sources detected with excess at or short-wards of 10 ¡m, but in transition from having optically thick to optically thin inner disks. They may be even slightly more evolved (in a circumstellar sense). One interpretation is that on the timescale that inner disk clearing has completed, these disks may be transitioning from optically thick to optically thin in the mid- or outer-disk regions. GM Aur has long been appreciated in this category (e.g., Koerner et al. 1993; Rice et al. 2003). Others with excesses only at long wavelengths were not detectable with the sensitivity of IRAS but are being revealed by Spitzer, for example CoKu Tau4 (D'Alessio et al. 2005) and DM Tau (Calvet et al. 2005b).

Collectively, both the optically thin and the inner cleared disks can be referred to as "transitional." In regions other than Taurus, the case for transitional disks has also been made. For example, Gauvin & Strom (1992) highlighted CS Cha in Chamaeleon as having a large inner cleared region (tens of AU), but a substantial far-infrared excess indicative of a robust outer disk. Nordh et al. (1996) show 7-15 ¡m flux ratios in Chamaeleon that are scattered around either the colors expected from flat/flared disks, or around photospheric colors, with essentially no objects located in between these groupings. These observations support the rapid transition timescales argued for Taurus members. Low et al. (2005) observed the same effect at longer wavelengths, 24 ¡m, in the much older TW Hya association.

In summary, in young (<3 Myr) star forming regions transition disks rare, with most stars having circumstellar material that is either consistent with an optically thick disk or not apparent at all. Further, there are specific examples of stars with dust in the terrestrial planet zone (0.1-3 AU) but not in the very inner disk (<0.05 AU). This suggests that material closest to the star may disappear first, as accretion subsides, and that the disk is cleared from the inside out. In slightly older (10 Myr) regions, the only disks left appear to be those in transition, already evolved or fully cleared in the inner disk regions, but retaining mid-infrared excesses indicative of mid-range disks.

How does disk clearing occur? While photometric studies at infrared and millimeter wavelengths such as those discussed above can provide statistics for assessing the dust disk dissipation timescale—and hence the dust disk lifetime—they tell us very little about the physics of the process. Studies of evolutionary changes in the disk structure or dust grain processes, by contrast, do provide physical insight, but are restricted to much smaller samples which can be studied in detail. Spectral energy distributions and mineralogy are two tools that can provide insight.

f See Duchene et al. 2003 for evidence concerning the multiplicity of V773 Tau and argument that the apparent excess can be attributed to one of the companions rather than betraying a "fossil" disk.

Typically, grain growth and disk evolution arguments have been made from measurement of the frequency dependence of continuum opacity in the expression tv (r) = kv x £(r), where kv <x v3. The ¡3 = 2 appropriate for interstellar dust often yields in measurements of optically thin sub-/millimeter spectral energy distributions to 3 = 0-1 (see Miyake & Nakagawa 1993). The effects on the overall spectral energy distribution of grain growth are presented in a parameter study of disk geometry and grain properties by D'Alessio et al. (2001).

Detailed spectral energy distributions are most useful when combined with spatially resolved imaging at one or more wavelengths, enabling degeneracies in model parameters to be removed. Modeling studies of objects in different circumstellar evolutionary stages e.g., Class 0, Class I, Class II—and perhaps even Class III someday—spectral energy distributions can provide constraints on disk geometry. Some examples of such work are the analyses by Wood et al. (1998), Wolf et al. (2003), Eisner et al. (2005a), Kitamura et al. (2002), and Calvet et al. (2002). It should be borne in mind, however, that the connections between circumstellar and stellar evolutionary states are not yet clear.

As the dust transitions from optically thick to optically thin, perhaps as a function of radius, spectroscopy becomes an especially important tool for assessing grain size distribution and composition. Mineralogical studies reveal information about dust processing for example changes in chemical composition or mean grain size. There is evidence already for the growth of grains in young disks to sizes larger than are expected, based on the assumption that disk grain properties are consistent with those of interstellar dust. Direct probes of grain growth are spectroscopic studies that are sensitive to the opacity from particular species having particular size ranges. Work in the 8-13 ¡m atmospheric window (e.g., Kessler-Silacci et al. 2005, van Boekel et al. 2005) is being complemented, improved, and extended by Spitzer studies from 5-40 ¡m. Especially compelling observations would be those that can obtain spatially resolved mineralogical information. Intriguing results in this area have emerged recently from the VLTI (e.g., van Boekel et al. 2004).

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