While the rate of accretion onto T Tauri stars is predicted to decline with age, objects with strong accretion have been detected up to ages of 10 Myr. We analyze a sample of these old accretors identified by having a significant $U$ band excess and infrared emission from a circumstellar disk. Objects were selected from the ~3 Myr sigma Ori, 4-6 Myr Orion OB1b and 7-10 Myr Orion OB1a star forming associations. We use high resolution spectra from the Magellan Inamori Kyocera Echelle to estimate the veiling of absorption lines and calculate extinction for our T Tauri sample. We also use observations, obtained with the Magellan Echellette and in a few cases the SWIFT Ultraviolet and Optical Telescope, to estimate the excess produced in the accretion shock, which is then fit with accretion shock models to estimate the accretion rate. We find that even objects as old as 10 Myr may have high accretion rates, up to ~10^-8 msun/ yr. These objects cannot be explained by viscous evolution models, which would deplete the disk in shorter timescales, unless the initial disk mass is very high, a situation which is unstable. We show that the infrared spectral energy distribution of one object, CVSO 206, does not reveal evidence of significant dust evolution, which would be expected during the 10 Myr lifetime. We compare this object to predictions from photoevaporation and planet formation models and suggest that neither of these processes have had a strong impact on the disk of CVSO 206.
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