Atmospheric temperature structure in the RoAp stars

Master Thesis


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University of Cape Town

The rapidly oscillating Ap (roAp) stars are a sub-group of the chemically peculiar stars of class 2 (CP2), which are characterised by peculiar spectra and anomalously strong lines of Sr, Cr, Eu and other rare earth elements. They have strong global dipole magnetic fields with effective strengths of up to a few thousand gausses. Stars showing these phenomena cover the spectral range B8p to F0 V-IV. About 20 years ago rapid non-radial pulsations were discovered in the coolest members of the CP2 group, namely the roAp stars. These pulsations are due to high over-tone, low degree p modes with periods between 5.6 and 15 minutes. Since then, studies of these rapid oscillations have revealed a lot of information about these stars. The eigenfrequency spectra of roAp stars can potentially reveal information such as their rotation periods, rotational inclinations, magnetic geometries, internal magnetic field strengths, radii, masses, luminosities and ages. Matthews et al. (1990, 1996) suggested a technique to empirically determine the T(Ƭ) relation for roAp stars. This technique involves comparing the pulsation amplitudes obtained from multi-colour photometry to the ones calculated from black-body pulsator models (assuming dipole mode pulsations). This comparison yielded limb-darkening coefficients which were used to determine T(Ƭ) in a way similar to what was done for the sun. Matthews et al. based their idea on the observed fact that pulsation amplitudes of roAp stars drop sharply with increasing wavelength. They thus explained this sharp decline of amplitude with wavelength in terms of the strongly wavelength dependent limb-darkening. The initial aim of this thesis was to investigate the technique proposed by Matthews et al., and to apply it to a number of roAp stars. However, when a linearised expression for the variation of the pulsation amplitude with wavelength, limb-darkening, inclination of the pulsation axis α, and ΔT/T₀ (where ΔT is the polar pulsational temperature semi-amplitude and T₀ is the atmospheric temperature) was derived, it was discovered that limb-darkening is too small an effect to account for the observed amplitudes. The result is based on the Wien approximation and uses the Planck function to represent intensity. Therefore, limb-darkening cannot be measured from the amplitude vs wavelength data. This analysis and the results thereof are reported in this thesis. Numerical models based on realistic treatment of the intensity spectra (obtained from model atmospheres) are used to confirm and refine the analytical results. The linearised expression mentioned above suggests that an important factor that explains the sharp decline of amplitude with wavelength is the variation of the ratio ΔT/T₀ with wavelength. Therefore, if the T(Ƭ) structure of a star is known a priori (from model atmospheres), the variation of ΔT with wavelength can be determined. This new technique, together with the variation of opacity with wavelength in the atmospheres of roAp stars, is applied to HD 134214:, HD 137949, HD 128898, HD 101065 and HR 3831 to determine ΔT cos α as a function of atmospheric depth. HR 3831 was observed at various rotation phases to investigate the effect of rotation on the derived ΔT cos α vs atmospheric depth relation. Preliminary results on this are included in this thesis. Bibliography: pages 107-113.