  We monitored the planet-bearing solar-type star HD209458 for sodium
absorption in the region of the stellar NaI D1 line that would be indicative of
cometary activity in the system. We observed the star using the HET HRS with
high S/N and high spectral resolution for 6 nights over the course of two
years, from July 2001 to July 2003. From modelling we determine a 20%
likelihood of a detection, based on a predicted number of comets similar to
that of the solar system. We find that our analytical method is able to recover
a signal and our S/N is sufficient to detect this feature in the spectral
regions on either side of the core of the D1 line, where it is most likely to
appear. No significant absorption was detected for any of the nights based on a
3 sigma detection limit. We derive upper limits on the column density of sodium
of < ~6 x 10^{9} cm^{-2} for a signal in the region around the line core and <
\~2 x 10^{10} cm^{-2} for a signal in the core of the photospheric D1 line.
These numbers are consistent with the sodium released in a single periodic
comet in our own system, though higher S/N may be necessary to uncover a signal
in the core of the D1 line. Implications for cometary activity in the HD209458
system are discussed.
