  We investigate the effect of planetary rotation on the transit spectrum of an
extrasolar giant planet. During ingress and egress, absorption features arising
from the planet's atmosphere are Doppler shifted by of order the planet's
rotational velocity (~1-2 km/s) relative to where they would be if the planet
were not rotating. We focus in particular on the case of HD209458b, which ought
to be at least as good a target as any other known transiting planet. For
HD209458b, this shift should give rise to a small net centroid shift of ~60
cm/s on the stellar absorption lines. Using a detailed model of the
transmission spectrum due to a rotating star transited by a rotating planet
with an isothermal atmosphere, we simulate the effect of the planet's rotation
on the shape of the spectral lines, and in particular on the magnitude of their
width and centroid shift. We then use this simulation to determine the expected
signal-to-noise ratio for distinguishing a rotating from a non-rotating planet,
and assess how this S/N scales with various parameters of HD209458b. We find
that with a 6 m telescope, an equatorial rotational velocity of ~2 km/s could
be detected with a S/N~5 by accumulating the signal over many transits over the
course of several years. With a 30 m telescope, the time required to make such
a detection reduces to less than 2 months.
