Radial velocity variations in pulsating Ap stars – II. 33 Librae

ABSTRACT

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 the 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⁻¹ at 5600 Å and as low as 7 m s⁻¹ 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 are 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 features shows a bimodal Gaussian distribution with 17 per cent of the lines having a pulsational phase ≈165° 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° phase difference as well as the broader width (by a factor of 2) of one of the Gaussian components of the phase distribution.

We also found evidence for phase variations as a function of effective Landég-factors. This may be the influence of magnetic field and magnetic intensification effect on depths of spectral line formation and shows that the 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 mono- and multimode 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.