We present an analysis of high-resolution synoptic spectra of ten F- and G-
type stars, seven of which exhibit periodic radial velocity variations due
to the presence of one or more substellar companions. We searched for subtl
e periodic variations in photospheric line asymmetry, as characterized by l
ine bisectors. In principle, periodic variations in line asymmetry observed
at lower spectral resolution could mimic the radial velocity signature of
a companion, but we find no significant evidence of such behavior in our da
ta. Observations were obtained from 1998 March to 1999 February using the N
ational Solar Observatory (NSO) 1.52 m McMath-Pierce Solar Telescope Facili
ty on Kitt Peak in conjunction with the solar-stellar spectrograph, achievi
ng a resolving power of 1.2 x 10(5). To characterize line asymmetry, we fir
st measured line bisectors for the unblended Fe I photospheric line at 625.
26 nm. To improve sensitivity to small fluctuations, we then combined point
s in each bisector to form a velocity displacement with respect to the line
core. We searched for periodic variations in this displacement, finding no
substantial difference between stars with substellar companions and those
without reported companions. We find no correlation between bisector veloci
ty displacement and the known orbital phase of substellar companions around
our target stars. Simulations of a periodic signal with noise levels that
mimic our measurement errors suggest that we can exclude bisector variation
s with amplitudes greater than about 20 m s(-1). These results support the
conclusion that extrasolar planets best explain the observed periodic varia
tions in radial velocity.