Because of our relatively low spectral resolution, we compare our observations with Gray's line bisector data by fitting observed line profiles to an expansion in terms of orthogonal (Hermite) functions. To obtain an accurate comparison, we model the emergent line profiles from rotating and pulsating stars, taking the instrumental point spread function into account. We describe this modeling process in detail. We find no evidence for line profile or strength variations at the radial velocity period in either 51 Peg or in Tau Boo. For 51 Peg, our upper limit for line shape variations with 4.23-day periodicity is small enough to exclude with 10 sigma confidence the bisector curvature signal reported by Gray & Hatzes; the bisector span and relative line depth signals reported by Gray (1997) are also not seen, but in this case with marginal (2 sigma) confidence. We cannot, however, exclude pulsations as the source of 51 Peg's radial velocity variation, because our models imply that line shape variations associated with pulsations should be much smaller than those computed by Gray & Hatzes; these smaller signals are below the detection limits both for Gray & Hatzes' data and for our own. Tau Boo's large radial velocity amplitude and v*sin(i) make it easier to test for pulsations in this star. Again we find no evidence for periodic line-shape changes, at a level that rules out pulsations as the source of the radial velocity variability. We conclude that the planet hypothesis remains the most likely explanation for the existing data.

44 pages, 19 figures, plain TeX, accepted to ApJS (companion to letter astro-ph/9712279)