3 Used methods

3.1 Mass/inclination procedure

The radial velocities derived from the Si II profiles were already used in Paper I for the determination of the orbits of the spectroscopic binaries. The derived orbital elements and estimations for M₁ and R₁ are used here to put constraints on the orbital inclination angle i and the mass M₂ of the secondary by using what we will call the "mass/inclination procedure''. For each choice of i, M₂ is derived from the mass function f(M). Subsequently, the radius R₂ of a main-sequence secondary is estimated and herefrom the semi-major axis a_1,2 of the relative orbit. In some cases, restrictions on i, and hence on M₂  can be found by expressing that the periastron distance has to be larger than the sum of the two radii R₁+R₂. Moreover, the absence of eclipses and the single-lined character provide us an upper limit of respectively i and M₂. Note that for double-lined binaries, exact values of i and M₂ can be derived when an estimation of M₁ is available.

3.2 Frequency procedure

We used what we will call the "frequency procedure'' to determine the intrinsic frequencies in the final data-sets. We calculated the first three normalised velocity moments <v>, <v²>, and <v³> of the individual Si II lines (see Aerts et al. 1992). During analysis, we generally focussed on the moments of the deepest Si II line, except if blending effects occurred. Since we are dealing with B stars, we focussed on the B-filter of the Geneva photometric system. For every star, we subsequently analysed data-sets with increasing frequency resolution $\Delta\nu_{\rm win}$, which we define as the half-width at half-max (HWHM) of the central peak of the window function.

Three frequency search algorithms were combined: Stellingwerf's PDM-algorithm (Stellingwerf 1978), the modified Scargle periodogram (Horne & Baliunas 1986), and the CLEAN-algorithm (Roberts et al. 1987). We restrict ourselves to discuss the modified Scargle periodograms in the text below. To judge upon the reality of the different occurring frequency peaks in the periodograms, we used both the "false alarm probability'' (FAP, Scargle 1981) and a "S/N-criterion'' (Breger et al. 1993). The noise-level of a periodogram is empirically defined as the average amplitude in an oversampled spectrum surrounding the suspected frequency, where the sampling interval is $\Delta\nu = \frac{1}{20T}$ with T the total time-span of the considered data-set (Handler et al. 1996). Alvarez et al. (1998) showed that the 99% confidence level can be reproduced fairly well by taking 3.7 times the noise-level for multi-site data of p-mode pulsators. To check its applicability to single-site data of g-mode pulsators, the amplitude-level corresponding to a FAP of 1% and to 3.7 times the noise-level (hereafter "3.7 S/N-level'') are indicated respectively by a dashed and a dotted line on every shown modified Scargle periodogram.

If more than one intrinsic frequency is present in the data, we used subsequent prewhitening with sinusoidal models. The frequency analysis is stopped when all the frequency peaks are below the 1% FAP-level and/or the 3.7 S/N-level and/or when we were not able to distinguish between different candidate frequencies. The residual standard deviation $\sigma _{\rm res}$ is compared to the level of mean error of the observations $\sigma _N$ to judge upon the possibility of having more intrinsic frequencies than the ones retained from our analysis.

Afterwards, the observed amplitudes A_i, phases $\phi_i$, and their corresponding standard errors, are determined for all the accepted frequencies $\nu_i$ by fitting the data with a superposition of sinusoidal models of the form $A_i \sin[2\pi (\nu _i t + \phi _i)]$, where t = HJD - 2450000. For the higher order moments, the appropriate interaction terms are also taken into account (see Mathias et al. 1994). In the following, A_U,..., A_G denote the observed photometric amplitudes of respectively the Geneva U, ..., G data (same notations as in Aerts 2000), $A_{\rm H_{\rm p}}$ the observed photometric amplitude of the HIPPARCOS $H_{\rm p}$ data, and $\{AA\}$, $\{CC,DD\}$ and $\{EE,FF,RST\}$ the observed moment amplitudes of respectively the <v>, <v²> and <v³> data (same notations as in Aerts 1996).