A new tool to study the wave propagation: the Van Hoof effect

P. Mathias - D. Gillet

Received April 21; accepted May 7, 1993

Abstract:

Discovered in 1953 in the beta Cephei star beta CMa, the Van Hoof effect, defined as a phase lag of hydrogen compared to metal lines, has often been considered as a detail in the study of these stars. However, thanks to modern detectors, it is now possible to get well-defined velocity curves, and hence to start a serious study of this phenomenon, interpreted as the time propagation of the pulsation wave through the atmosphere. We present a new method for the detection of the Van Hoof effect with the use of velocity curves. Thus, and contrary to the other methods, only the phase lag due to the pure variation differences is taken into account. We considere the case of a small amplitude star (alpha Lupi) and that of a large amplitude star (BW Vulpeculae). We observe that, for both stars, the Van Hoof effect is also present between metal lines.
Thanks to the quasi-sinusoidal velocity curves presented by alpha Lupi, the time propagation of the waves between several elements has been determined with an excellent accuracy (about 1s). Using an atmospheric model and the contribution functions of the considered absorption profiles, the location of the line forming regions have been determined. Hence, the velocity of the outward pulsation wave at each altitude has been deduced. By comparison with the sound velocity, it is shown that in the deepest observed photospheric layers, the wave velocity is quite supersonic while the shock wave strongly dissipates when it reaches the outermost photosphere.
For BW Vulpeculae, the velocity curves show that the phase lag happens during each atmospheric acceleration. But, due to a well-marked line doubling phenomenon, the velocity curves are not so accurately determined, and the propagation time is only measured within a factor 2. The results obtained do not seem to be consistent with the use of a single layer atmospheric model. This means that a more realistic approach, based on a pulsating atmosphere taking into account the occurence of shocks, is required for the largest amplitude beta Cephei star.

Keywords: Shock waves -- Stars: atmospheres -- Stars: variables: alpha Lupi -- Stars: variables: BW Vulpeculae

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