Radial Velocity Variations in Pulsating Ap Stars. II. 33 Librae

We present precise relative radial velocity (RV) measurements for the rapidly oscillating Ap (roAp) star 33 Librae measured from high resolution data spanning the wavelength interval 5000--6200 A. We find that pulsational radial velocity amplitude determined over a broad wavelength range (~100 A) depends on the spectral region that is examined and can be as high as 60 m/s at 5600 A and as low as 7 m/s in the 5900 A region. RV measurements of individual spectral lines can show even higher RV amplitudes. The acoustic cross-sections of the atmosphere, i.e. the phase and amplitude of the pulsations, as a function of optical depth is found for spectral lines of Ca, Cr, Fe, La, Ce, Gd, Er and Nd. This analysis shows that pulsation phase is variable through the atmosphere and that Nd III lines pulsate almost 180 degrees out-of-phase with those of Nd II features and are formed significantly higher in the stellar atmosphere. This conclusively establishes the presence of at least one radial node to the pulsations in the upper stellar atmosphere. The histogram of pulsational phases for all individual spectral feature shows a bi-modal Gaussian distribution with 17% of the lines having a pulsational phase approximatels 165 degrees out-of-phase with most other spectral lines. This is also consistent with the presence of a radial node in the stellar atmosphere. The accumulation of phase due to a running wave component can explain the 165 degree phase difference as well as the broader width (by a factor of two) of one of the Gaussian components of the phase distribution.