This study well confirms the presence of two shocks during one pulsation cycle in BW Vul. Dynamically, the "basic" shock (outward-shock) is due to a wave propagating from the subphotosphere, probably initiated by the iron -mechanism recently found in these stars. The velocity jump is between 80-100 km.s-1 depending on the night. Considering a sound speed of about 15 km.s-1 within the Si iii/H line formation regions, this leads to a Mach number around 5-7. It should be noted that the infalling motion is almost finished when the outward shock occurs during the first night, while during the second night, the velocity jump is again around 40 km.s-1. This shock gives an appreciable outward impulsion to the atmosphere, which is not physically detached from the "unperturbed" photosphere, contrary to the Odgers' scenario (1955) The atmosphere then follows a ballistic motion until it falls back. When the increasing density decelerates the layers, it appears a positive velocity gradient between the bottom and the top of the atmosphere, caused by the increasing density of the gas. When the velocity gradient is large enough, the wave front breakes into an infalling shock for the observer. The maximum front velocity is quite large (between 120-180 km.s-1 depending on the night). Thus, during its final acceleration phase (), its Mach number is close to 8-12, i.e. this shock is hypersonic contrary to the outward shock. This interpretation is opposite to the one given by Crowe & Gillet (1989) who invoked a second -mechanism. Finally, due to inertia, the atmosphere bounces on the photosphere and falls back again until complete damping: this explains the stillstand. It should also be noted that turbulence may play a non-negligeable role which may contribute to line broadening.
This scenario is based on a pure mechanical consideration. However, as noticed by a few authors (e.g. Young et al. 1981), effects of radiative transfer due to changes in the continuous opacity can lead to erroneous interpretations of atmospheric motions. Furthermore, Moskalik & Buchler (1994), using a full self-consistent hydrodynamic model of BW Vul, show that a unique shock wave, originating at the bottom of the He+ zone, is present during a pulsation cycle and causes the stillstand. This shock produces a sudden jump in the optical depth which contributes to the formation of the apparent discontinuity. However, although the amplitude of their radial velocity curve is correct, the stillstand has a velocity of about -100 km.s-1 in the stellar rest frame, which has never been observed for this star.
A future interesting test would be to synthetize line profiles along one cycle using a self-consistent pulsating atmospheric model such as the one developed by Fokin (1992) for RR Lyrae stars. This would represent the next step of this work.
© European Southern Observatory (ESO) 1998
Online publication: October 21, 1998