1 Introduction

Many early-type B stars are known to show $\beta$ Cephei like pulsations, which are internally excited due to the $\kappa$-mechanism (e.g. Balona & Dziembowski 1999). Waelkens & Rufener (1983) searched for pulsations in photometric observations of close binaries containing early-B type stars, and concluded that for close binaries with periods shorter than that of $\alpha$ Vir (orbital period P=4.0 day, eccentricity e=0.15, pulsations in the primary, Smith 1985) no pulsations are detectable, and argued that in close binaries the tidal forces may suppress the $\beta$ Cephei pulsations.

In this paper we present spectroscopic detection of multi-frequency non-radial pulsations in the primary of the close binary $\psi ^2$ Ori (HD 35715, m_V=4.6 mag, B1III + B2V, P=2.5 day, e=0.05, Lu 1985). In a forthcoming paper (Schrijvers & Telting) on the close binary $\nu$ Cen (P=2.6 day, e=0.0) we report an extensive dataset disclosing similar multi-frequency non-radial pulsations. Both these binaries have orbital periods shorter than that of $\alpha$ Vir and have primaries that show $\beta$ Cephei like pulsations with intermediate values of the pulsational degree $\ell$, which could not have been detected photometrically by Waelkens & Rufener (1983).

For $\nu$ Cen and $\alpha$ Vir (Smith 1985) there is strong observational evidence that a low-degree (non-)radial mode has damped out. The variable-amplitude low-degree mode in $\nu$ Cen (Ashoka & Padmini 1992) which gave rise to a radial velocity amplitude of about 10 kms^-1 from 1985 to 1988, could not be detected in the high-quality data set, obtained in 1998, to be presented by Schrijvers & Telting. However, as only limited amounts of data of the above stars have been obtained, it is also possible that the apparent low-degree modes and their apparent dissapearance are both observational symptoms of complicated multimodal beating. Nevertheless, it is clear that the conclusion put forward by Waelkens & Rufener (1983) does not hold, but it is still unclear if the tidal forces in close binaries can cause the amplitudes of low-degree $\beta$ Cephei pulsations to damp out or become variable.

Figure 1: Left: five nights of data of the SiIII 4552, 4567, and 4574 line profiles. Top: mean of one night. Middle: overplotted spectra. Bottom: grey-scale representation of the spectra, with each spectrum offset according to acquisition time. Middle: same for the 4552 profile, but shifted to the velocity frame relative to the primary. The mean of all spectra is plotted in the top panel. Right: as middle frame, after prewhitening with the orbital frequency and its first four harmonics to filter out most of the variability caused by the moving profile of the secondary. In the grey-scale plots, moving bumps are clearly visible in the profiles of the primary.

Examples of other close binaries with early-B type components which have shown traces of pulsations are: $\lambda$ Sco, P=6.0 day, e=0.29, non-radial pulsations in primary (De Mey et al. 1997); $\beta$ Sco A, P=6.8, e=0.29, non-radial pulsations in secondary (Holmgren et al. 1997); $\eta$ Ori Aab, P=8.0 day, e=0.0, non-radial pulsations in secondary (De Mey et al. 1996); 16 Lac, P=12.1, e=0.047, radial and non-radial pulsations in primary (Chapellier et al. 1995). The case of $\epsilon$ Per, P=14 day, e=0.5, is an intriguing object with well-studied multi-periodic pulsations in the primary (Gies & Kullavanijaya 1988; Tarasov et al. 1995; De Cat et al. 2000).

For the above mentioned close binaries, which all have pulsating components with spectral types in the range of $\beta$ Cephei stars, another question is important: are the observed pulsations excited internally, or are they powered by the perturbing tidal forces? Witte & Savonije (1999) have shown that tidally excited g- and r-mode oscillations are a means to dissipate orbital energy at large rates, if the disturbing frequency coincides with a resonance frequency of the star. Hence, the study of tidally excited pulsations may have an impact on binary star evolution and on the dynamics of the central parts of globular clusters in which tidal captures of binary components take place.

To study these effects, the case of $\psi ^2$ Ori presents a well-observed system, with a history of orbit determinations of almost a century. This system is known to show rapid apsidal motion (e.g. Batten et al. 1978), and ellipsoidal variations (Percy 1969; Hutchings & Hill 1971; Waelkens & Rufener 1983; Jerzykiewicz 1984), and was labelled as a tentative $\beta$ Cephei variable by Hill (1967). The luminosity ratio of the primary and secondary is about 4.5 (Lu 1985). The Hipparcos parallax of $\psi ^2$ Ori is $2.3 \pm 0.9$ mas. Warren & Hesser (1978) list $\psi ^2$Ori as a member of subgroup 1a of the Orion OB1 association, which has a mean distance of $336 \pm 16$ pc and an age of $11.4 \pm 1.9$ Myr (De Zeeuw et al. 1999).

For the binary system $\psi ^2$ Ori, high-resolution time series showing non-radial pulsations have never been presented in the literature before. Of the stars with known $\beta$ Cephei pulsations in close binaries, $\psi ^2$ Ori is the system with shortest orbital period.

In Sect. 2 we present the data. In Sect. 3 we analyse the radial velocity of the two components of $\psi ^2$ Ori, and determine the geometry of the system. In Sect. 4 we determine and discuss the apsidal motion period of $\psi ^2$ Ori. In Sect. 5 we investigate the line profiles of the primary to derive some of the pulsational characteristics of the star. In Sect. 6 we discuss the possibility that the non-radial pulsations in $\psi ^2$ Ori are due to tidal perturbations.