## An indirect probe of gaseous disks Stellar accretion rates

As the above discussion suggests, the study of the evolution of gaseous disks using in situ diagnostics is still in its infancy, despite the significant progress that has been made. Given this situation, it may be interesting to explore the possibility of using surrogate diagnostics, such as stellar accretion rates, to probe the evolution of gaseous disks. As mentioned in Section 3, an obvious issue in doing this is how to convert stellar accretion rates into estimates of disk masses or column densities. For a steady a accretion disk, the disk accretion rate M is related to the disk column density E at a radius r through a relation of the form E x M/aT, where T is the disk temperature at r and the parameterized viscosity is v = acsH. Using a relation of this form and given a measured mass accretion rate and a value for a, we can infer a disk column density.

Before going forward, we might want to confirm that such a relation is really valid. For example, we might try to directly measure disk column densities using any of the diagnostics discussed in the previous section, and compare these with measured accretion rates in order to determine the value of a. We might carry out suites of observations covering a range of disk radii and for several sources in order to determine if a is constant with radius and from source to source. Observations of this kind, which can be carried out in the future, would help to calibrate the relation between E and M.

It might be fun to look ahead and imagine what such a relation might imply for the evolution of gaseous disks given what we already know about stellar accretion rates as

Figure 5. Stellar mass accretion rates as a function of age, based on data from Gullbring et al. (1998); Hartmann et al. (1998); Muzerolle et al. (1998, 2000); Lawson et al. (2004); and Sicilia-Aguilar et al. (2005). (Figure courtesy of James Muzerolle.)

log Age(yrs)

Figure 5. Stellar mass accretion rates as a function of age, based on data from Gullbring et al. (1998); Hartmann et al. (1998); Muzerolle et al. (1998, 2000); Lawson et al. (2004); and Sicilia-Aguilar et al. (2005). (Figure courtesy of James Muzerolle.)

a function of age (Fig. 5). If a is a constant as a function of radius and from source to source, the wide range in mass accretion rates at any given age (which can vary over more than an order of magnitude) imply a similarly large range in disk masses and column densities. For example, for a = 0.01, a value that is commonly assumed in the literature, E ~ 100 g cm-2 at 1 AU for a typical T Tauri accretion rate of M = 10 8 Mq yr 1 (D'Alessio et al. 1998); the range of stellar accretion rates at 0.5 Myr suggests that the mass column density at 1 AU can range between ^30-1000 gcm-2 from source to source. At 5-10 Myr, the detection of stellar accretion rates as large as 10-8 Mq yr-1 (e.g., Sicilia-Aguilar et al. 2005) suggest the possibility of long-lived gaseous disks in some systems.

Even at much lower accretion rates and/or older ages, the implied gas column densities would be dynamically significant. For example, for the weakly accreting T Tauri star V836 Tau at an age of 3 Myr, the measured mass accretion rate of 4 x 10-10 Mq yr-1, which is totally irrelevant for the buildup of the central stellar mass, nevertheless implies a gas column density of 4 g cm-2 at 1 AU. This column density is in the right range for a residual gas disk to have a favorable impact on the outcome of terrestrial planet formation. Perhaps more interesting is the case of the T Tauri star St34, which has a Li depletion age of 25 Myr (White & Hillenbrand 2005). The tiny mass accretion rate for the source of 2 x 10-10 Mq yr-1 implies a gas column density of 2 gcm-2 at 1 AU, again in the right range to play a role in producing planets with Earth-like masses and eccentricities. These examples illustrate the possibility that dynamically significant gaseous reservoirs persist over the age range (1-30 Myr) during which terrestrial planet formation is believed to occur. These arguments suggest that stellar accretion rates may prove to be a valuable probe of the gas content of disks. Making use of accretion rates as a diagnostic relies on being able to calibrate them against gas content. Thus it is of great interest to understand what the value of a is and whether it is a constant.