  Young stars surrounded by disks with very low mass accretion rates are likely
in the final stages of inner disk evolution and therefore particularly
interesting to study. We present ultraviolet (UV) observations of the ~5-9 Myr
old stars RECX-1 and RECX-11, obtained with the Cosmic Origins Spectrograph
(COS) and Space Telescope Imaging Spectrograph (STIS) on the Hubble Space
Telescope (HST), as well as optical and near infrared spectroscopic
observations. The two stars have similar levels of near UV emission, although
spectroscopic evidence indicates that RECX-11 is accreting and RECX-1 is not.
The line profiles of Halpha and He I 10830 in RECX-11 show both broad and
narrow redshifted absorption components that vary with time, revealing the
complexity of the accretion flows. We show that accretion indicators commonly
used to measure mass accretion rates, e.g. U band excess luminosity or the Ca
II triplet line luminosity are unreliable for low accretors, at least in the
middle K spectral range. Using RECX-1 as a template for the intrinsic level of
photospheric and chromospheric emission, we determine an upper limit of 3 x
10^-10 solar masses/ year for RECX-11. At this low accretion rate, recent
photoevaporation models predict that an inner hole should have developed in the
disk. However, the spectral energy distribution of RECX-11 shows fluxes
comparable to the median of Taurus in the near infrared, indicating that
substantial dust remains. Fluorescent H_2 emission lines formed in the
innermost disk are observed in RECX-11, showing that gas is present in the
inner disk, along with the dust.
