  The direct study of molecular gas in inner protoplanetary disks is
complicated by uncertainties in the spatial distribution of the gas, the
time-variability of the source, and the comparison of observations across a
wide range of wavelengths. Some of these challenges can be mitigated with
far-ultraviolet spectroscopy. Using new observations obtained with the
HST-Cosmic Origins Spectrograph, we measure column densities and rovibrational
temperatures for CO and H2 observed on the line-of-sight through the AA Tauri
circumstellar disk. CO A-X absorption bands are observed against the far-UV
continuum. The CO absorption is characterized by log(N(^{12}CO)) = 17.5 +/- 0.5
cm^{-2} and T_rot(CO) = 500$^{+500}_{-200} K, although this rotational
temperature may underestimate the local kinetic temperature of the CO-bearing
gas. We also detect ^{13}CO in absorption with an isotopic ratio of ~20. We do
not observe H2 absorption against the continuum; however, hot H2 (v > 0) is
detected in absorption against the LyA emission line. We measure the column
densities in eight individual rovibrational states, determining a total
log(N(H2)) = 17.9^{+0.6}_{-0.3} cm^{-2} with a thermal temperature of T(H2) =
2500^{+800}_{-700} K. The high-temperature of the molecules, the relatively
small H2 column density, and the high-inclination of the AA Tauri disk suggest
that the absorbing gas resides in an inner disk atmosphere. If the H2 and CO
are co-spatial within a molecular layer ~ 0.6 AU thick, this region is
characterized by <n_H2> ~ 10^{5} cm^{-3} with an observed <CO/H2> ratio of ~
0.4. We also find evidence for a departure from a purely thermal H2
distribution, suggesting that excitation by continuum photons and H2 formation
may be altering the level populations in the molecular gas.
