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We present an Advanced Camera for Surveys/ Solar Blind Channelfar-ultraviolet (FUV) study of \h2 gas in 12 weak T Tauri stars in nearbystar-forming regions. The sample consists of sources which have no evidence ofinner disk dust. Our new FUV spectra show that in addition to the dust, the gasis depleted from the inner disk. This sample is combined with a larger FUVsample of accretors and non-accretors with ages between 1 and 100 Myr, showingthat as early as 1--3 Myr, systems both with and without gas are found.Possible mechanisms for depleting gas quickly include viscous evolution, planetformation and photoevaporation by stellar radiation fields. Since thesemechanisms alone cannot account for the lack of gas at 1--3 Myr, it is likelythat the initial conditions (e.g. initial disk mass or core angular momentum)contribute to the variety of disks observed at any age. We estimate the angularmomentum of a cloud needed for most of the mass to fall very close to thecentral object and compare this to models of the expected distribution ofangular momenta. Up to 20% of cloud cores have low enough angular momenta toform disks with the mass close to the star, which would then accrete quickly;this percentage is similar to the fraction of diskless stars in the youngeststar forming regions. With our sample, we characterize the chromosphericcontribution to the FUV luminosity and find that $L_{FUV}/L_{bol}$ saturates at$\sim10^{-4.1}$.

Short Gas Dissipation Timescales: Diskless Stars in Taurus and Chamaeleon I