Introduction

The star BWVul has the largest amplitude (about 200 km.s^-1) among the known $\beta$Cephei stars. This class is found to be destabilized by a $\kappa$-mechanism acting in the metal opacity bump, near $T \sim 2\,10^{5}$K (e.g. Cox et al. [1992], Dziembowski & Pamyatnykh [1993]). However, this usually leads to relatively small amplitude (of the order of 20km.s^-1) with slow line profile variations, often interpreted in terms of non-radial modes. On the contrary, BWVul presents a complex velocity curve, with two discontinuities during each pulsation cycle, surrounding a nearly constant velocity phase called stillstand. These two abrupt velocity changes are followed by a phase of line doubling, while at other phases the profiles remain more or less symmetric.

Physically, a line doubling phenomenon is associated with either a non-radial mode (linear theory) or a shock wave (non-linear theory). Non-radial modes for BWVul have already been invoked (Kubiak [1978], Odell [1981]). However, the moment method (Aerts [1996]), based on the linear pulsation theory as the above studies, favored a radial mode, instead of a non-radial one, (Aerts et al. [1995]) which cannot reproduce a line doubling. Conversely, a shock wave propagation can induce such a profile as suggested by Schwarzschild ([1954]) for WVirginis stars.

First, Odgers ([1955]) invoke for BW Vul an upper atmosphere accelerated by non-linear radial pulsations, involving a shock wave which impulsively separates this layer from the photosphere, becoming a shell. When the shell falls back, a decrease in its optical thickness occurs, allowing to see the ``static'' photosphere: two line components are thus present, one being at the systemic velocity, the other one being redshifted. The origin of the same shocks is different for Crowe & Gillet ([1989]). Indeed, in their scenario, there are two $\kappa$-mechanism acting: the one associated to the first discontinuity involves the propagation of a shock wave, coming from the inner part of the star, which appears during the infalling motion of the atmosphere. The other one, as in the case of Odgers ([1955]), deals with the impulsion mechanism, and concerns the second discontinuity.

Other explanations have been proposed as well. Young et al. ([1981]) suggest that a stationary layer is generated during the infalling atmospheric motion by the strong temperature and gas pressure increases. Thus a line doubling phenomenon appears. Recently, using a nonlinear pulsational model, Moskalik & Buchler ([1994]) found that the stillstand is caused by an outward propagating shock which originates at the bottom of the HeII ionization zone. The consecutive strong compression provokes a sudden jump of the Rosseland-mean opacity which contributes to the formation of an apparent discontinuity in the observed radial velocities. Nevertheless, their solution shows that the stillstand is at a radial velocity of -100km.s^-1 in the stellar rest frame while it is now well established by accurate spectral observations that it is close to a zero velocity.

These pictures are not equivalent, and it is the aim of this paper to try to select the best model. The observations are described in Sect.2 and the line doubling phenomena are discussed in Sect.3. The origin of the two shock waves and the sketch of the cycle are proposed in Sect.4. Finally, some concluding remarks are given in Sect.5.