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 Å. We find that pulsational radial velocity amplitude determined over a broad wavelength range (≈ 100 Å) depends on the spectral region that is examined and can be as high as 60 m s at 5600 Å and as low as 7 m s in the 5900 Å region. RV measurements of individual spectral lines can show higher amplitudes than results obtained using a “broad-band” measurement that includes many spectral lines. 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◦ 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. We have estimated that this acoustic node is located above an optical depth log τ < −4.5 and below the level where the Nd III lines are formed. We also suspect that there may be a second atmospheric node in the lower atmosphere below, or at log τ ≃ −0.9 and close to continuum formation level. 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 ≈ 165◦ outof-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◦ phase difference as well as the broader width (by a factor of two) of one of the Gaussian components of the phase distribution. We also found evidence for phase variations as a function of effective Lande g-factors. This may be the influence of magnetic field and magnetic intensification effect on depths of spectral lines formation and that magnetic field is controlling the pulsations. Our RV measurements for 33 Lib suggest that we are seeing evidence of vertical structure to the oscillations as well as the influence of the distribution of elements on the stellar surface. We suggest and briefly discuss a new semi-empirical tomographic procedure for monoand multi-mode roAp stars that will use acoustic cross-sections obtained on different chemical elements and different pulsation modes for restoring the abundance and acoustic profiles throughout the stellar atmosphere and across the stellar surface.