  We analyze high angular resolution ALMA observations of the TW Hya disk to
place constraints on the CO and dust properties. We present new, sensitive
observations of the $^{12}$CO $J = 3-2$ line at a spatial resolution of 8 AU
(0\farcs14). The CO emission exhibits a bright inner core, a shoulder at
$r\approx70$ AU, and a prominent break in slope at $r\approx90$ AU. Radiative
transfer modeling is used to demonstrate that the emission morphology can be
reasonably reproduced with a $^{12}$CO column density profile featuring a steep
decrease at $r\approx15$ AU and a secondary bump peaking at $r\approx70$ AU.
Similar features have been identified in observations of rarer CO
isotopologues, which trace heights closer to the midplane. Substructure in the
underlying gas distribution or radially varying CO depletion that affects much
of the disk's vertical extent may explain the shared emission features of the
main CO isotopologues. We also combine archival 1.3 mm and 870 $\mu$m continuum
observations to produce a spectral index map at a spatial resolution of 2 AU.
The spectral index rises sharply at the continuum emission gaps at radii of 25,
41, and 47 AU. This behavior suggests that the grains within the gaps are no
larger than a few millimeters. Outside the continuum gaps, the low spectral
index values of $\alpha\approx 2$ indicate either that grains up to centimeter
size are present, or that the bright continuum rings are marginally optically
thick at millimeter wavelengths.
