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Astron. Astrophys. 362, 189-198 (2000)

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5. Discussion

5.1. The SPBs behaviour

With its B3 IV spectral type, [FORMULA] Her lies in the SPBs instability trip (e.g. Gautschy & Saio 1996). Several other observed SPBs characteristics, as listed by North & Paltani (1994), confirm this statement. First, the presence and stability over a time scale of years of at least three frequencies is pointed out: [FORMULA] and [FORMULA] in between 1990-1993 (Hipparcos), [FORMULA] and [FORMULA] in 1985-1987. Second, the amplitude in the Hipparcos [FORMULA] filter is larger than that measured in the [FORMULA] filter, while no significant phase lag is observed between the two. Finally, the 4 proposed frequencies are in the range of observational and theoretical criteria. Thus, the present study confirms that [FORMULA] Her should be classified as an SPB star variable.

5.1.1. Ephemeris

From above, Hipparcos data provide a good value of the main frequency: [FORMULA] c.d-1. Using it as a starting value, an ephemeris has been computed for all spectroscopic observations between 1983 and 1995:


where [FORMULA] is the calculated date of heliocentric radial velocity maxima after E cycles. [FORMULA] d is the resulting period, corresponding to the more precise value of [FORMULA] c.d-1 This new value of [FORMULA] is very close to that obtained with Hipparcos, being within the error bars. Table 5 gives the mean value of the radial velocity maxima epoch for each observation sets, and the difference [FORMULA] between [FORMULA] and the maximum computed with the ephemeris. The ephemeris fits reasonably well all the spectroscopic observations, with a 0.50 d rms. It is compatible with all photometric observations, since the date of mean luminosity maxima of the 1987 observations and the Hipparcos ones are separated by 488.978 cycles, which implies a 3.48765 d (0.28673 c.d-1) photometric period.


Table 5. Epoch of observed heliocentric radial velocity maxima and [FORMULA] values [d] computed for each spectroscopic data sets

5.1.2. The phase-lag

The phase-lag, defined as the difference between the epoch of maximum luminosity and that of maximum radial velocity, has been computed with two different methods using the period given by the ephemeris:

  • comparison of mean luminosity maxima epoch with the ephemeris given above. This method leads, for the Spain and both Hipparcos data sets, to a phase-lag of respectively 0.659, 0.639 and 0.634 P, where P is the main pulsation period

  • comparison of the nearly simultaneous spectroscopic and photometric data obtained in 1987. The phase-lag here is 0.845 P

It should be noted that the second method is not as accurate as the first one since we added uncertainties on each maxima determination. Therefore, and because Hipparcos data are the most suitable for SPB stars, the phase-lag value must be around 0.64 P for [FORMULA] Her. This value, the first one obtained for an SPB star, differs significantly from reported values concerning pulsating stars on each side of the SPBs instability strip: 0.25 P for the [FORMULA] Cephei stars, and 0.5 P for the classical instability strip. However, other observations, involving simultaneous photometric and spectroscopic data, are needed to confirm this result.

5.1.3. The amplitudes

The pulsation amplitudes show important variations during the last 10 years. In spectroscopic data, the amplitude associated with the [FORMULA] frequency has dropped from 2.76 km s-1 in 1985-1987 to 1.08-1.36 km s-1 in 1993-1995 (Table 3). The same phenomenon occurred to the amplitude associated with the [FORMULA] frequency which has decreased by a factor of 2 during the same epoch.

However, this result should be treated with caution, since both the lines used to derive the velocity and the resolution of the different data sets are not the same. In particular, the larger dispersion noted in the 80's data may be enhanced as a bias in the corresponding amplitude.

Because the photometric data concern different filters, nothing can be said over the 1987-1993 period. However, due to their long time basis, a crude study of the Hipparcos data was undertaken. The data corresponding to each filter were binned with 15 points in each subset. Then, a sine-fit using the [FORMULA] frequency was computed on each subset, providing the evolution of the photometric amplitude with time. The general observed trend is an increase of the photometric amplitude (Fig. 11), in both filters.

[FIGURE] Fig. 11. Evolution of the amplitude of the sine-fit computed with the [FORMULA] frequency in the [FORMULA] Hipparcos filter. Horizontal bars represent the window containing the 15 points, while vertical bars represent the [FORMULA] error on the amplitude value

Thus it appears that the amplitude associated with [FORMULA] shows opposite variations on time-scale of years. However, observations are neither homogeneous enough nor well spread in time to follow the amplitude evolution over 10 years.

A similar phenomenon has also been observed for the SPB star 53 Per. For this latter, the amplitude associated with one of the two main frequencies increases regularly while the other remains constant (Chapellier et al. 1998). This phenomenon could be quite frequent among the SPB stars, since it is detected in the two best monitored stars of this class.

Furthermore, the amplitude ratios ([FORMULA]) associated with [FORMULA] and [FORMULA] are very different. Using the 1987 data, the values 950 and 430 km s-1.mag-1 are respectively obtained. A plausible interpretation is that the two modes have a different [FORMULA] degree, as mentioned, for [FORMULA] Cephei stars, by Cugier et al. (1994).

5.2. The short time scale behaviour

The [6-8] c.d-1 frequency range can be related to p-modes of a typical [FORMULA] Cephei star with a low mass (Chapellier et al. 1987). Using the available measures of [FORMULA] Her in the Genova photometric system together with the adequate calibration (North & Nicolet 1990), the parameters of the star are ([FORMULA])=([FORMULA]). Thus, from these parameters [FORMULA] Her lies within the SPBs instability strip and just below the tip of the [FORMULA] Cep instability strip as shown by Pamyatnykh (1999). However, Dziembowski et al. 1993 and Gautschy & Saio (1996) ruled out, in this HR diagram region, the existence of p-modes due to a too rapid variation of the lagrangian pressure perturbation within the driving zone: they are only excited in the more luminous stars. Following these studies, only high-order g-modes should be excited in a 7 [FORMULA] (and below) B-star. Hence, the detection of high frequencies in such a low mass star is puzzling. But as shown by Pamyatnykh (1999), the extension of the instability strip for these stars depends mainly on metallicity but also on the overshooting, which causes the effective red-edge of the [FORMULA] Cephei stars to be cooler.

Conversely, the high frequencies, in the [15-25] c.d-1 range, are still not understood. Obviously, more observations are needed to confirm their reality.

Another interesting point is the apparent instability of these high frequencies motions. This variability may be due to a transient phenomenon. Such an hypothesis, concerning the [FORMULA]-Cephei pulsation type, has already been invoked for the B2.5 IV star 53 Psc, where a relatively large frequency (10.4 c.d-1) has sometimes been detected (Jerzykiewicz & Sterken 1990).

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Online publication: October 30, 19100