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| - Pulsations in the atmosphere of the roAp star HD 24712 - II. Theoretical models
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| - We discuss pulsations of the rapidly oscillating Ap (roAp) star HD 24712 (HR 1217) based on non-adiabatic analyses taking into account the effect of dipole magnetic fields. We have found that all the pulsation modes appropriate for HD 24712 are damped, i.e. the κ-mechanism excitation in the hydrogen ionization layers is not strong enough to excite high-order p modes with periods consistent with observed ones, all of which are found to be above the acoustic cut-off frequencies of our models. The main (2.721 mHz) and the highest (2.806 mHz) frequencies are matched with modified l= 2 and 3 modes, respectively. The large frequency separation (≈68 μHz) is reproduced by models which lay within the error box of HD 24712 on the Hertzsprung-Russell diagram. The nearly equally spaced frequencies of HD 24712 indicate the small frequency separation to be as small as ≈0.5 μHz. However, the small separation derived from theoretical l= 1 and 2 modes is found to be larger than ∼3 μHz. The problem of equal spacing could be resolved by assuming that the spacings correspond to pairs of l= 2 and 0 modes; this is possible because magnetic fields significantly modify the frequencies of l= 0 modes. The amplitude distribution on the stellar surface is strongly affected by the magnetic field resulting in the predominant concentration at the polar regions. The modified amplitude distribution of a quasi-quadrapole mode predicts a rotational amplitude modulation consistent with the observed one. Amplitudes and phases of radial velocity variations for various spectral lines are converted to relations of amplitude/phase versus optical depth in the atmosphere. Oscillation phase delays gradually outward in the outermost layers indicating the presence of waves propagating outward. The phase changes steeply around log τ∼−3.5, which supports a T-τ relation having a small temperature inversion there.
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