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Astron. Astrophys. 333, 125-140 (1998)

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5. Cyclic V / R variability

[FORMULA] is variable at virtually all times. It is perhaps the most pronounced on the ascending branch of the emission strength curve of an outburst (Sect.  4.3) and seen best in the strong He i lines such as those at [FORMULA] 5876, 6678, and 7065 Å. However, only during three, maybe four, minor bursts covered sufficiently well by our observations and one in data published by Baade (1991) have we been able to detect some temporal regularity in this behaviour.

5.1. HEROS data

For the strongest and best observed small outburst (32 HEROS spectra during 5 nights) around MJD 50 232, a time series analysis using Scargle's (1982) method in the range from 0 to 4 c/d indicates a fixed time scale of [FORMULA] days well above a [FORMULA] detection limit. The peak-to-peak amplitude is [FORMULA] around unity (Fig. 7, lower panel). This variability is also visible in the emission of [FORMULA] where not only the peak height but also the position of the edges of the emission is varying with the same period. Phase diagrams for [FORMULA] and the He i lines are shown in Fig. 7, lower panel.

For the other well-observed (25 HEROS spectra during 6 nights) small outburst around MJD 50 223 the time scale is significantly different. During this event the same analysis technique as above reveals a period of [FORMULA] days with a lower amplitude of [FORMULA] around unity (Fig. 7, upper panel). No significant hydrogen [FORMULA] -variability was detected during this phase; this might be due to the lower amplitude. For a third minor outburst on MJD 50 246 the phase coverage is not good enough to allow a reliable time series analysis (9 spectra during 2 nights). However, the variability has a similar time scale and a high amplitude. Fig. 9 compares the power spectra corresponding to the first two events to the power spectrum of all HEROS data.

[FIGURE] Fig. 7. The rapid variability of the [FORMULA] -ratio of He i [FORMULA] 5876 (Box), He i [FORMULA] 6678 ([FORMULA]), and He i [FORMULA] 7065 ([FORMULA]) during the minor bursts from MJD 50 219 to 50 225 (top) and from MJD 50 232 to 50 237 (bottom). The data have been folded with periods of 0.593 days (top) and 0.622 days (bottom), respectively. In the lower panel the [FORMULA] -ratio is also shown for [FORMULA] (bullet)

5.2. Boller&Chivens data

A simple MIDAS procedure was written which automatically fits a second order polynomial to the continuum between 4820 and 4910 Å and one Gaussian each to the broad absorption and the two emission components of H [FORMULA]. Although both the full width at half maximum (FWHM) and the separation of the two emission components exceed the nominal width of a spectral resolution element by no more than 30% and their peak heights amount to only 10 [FORMULA] 5% of the local continuum, the fitting procedure seriously diverged in less than 5-10% of all spectra. The results proved to be fairly robust against modifications of the initial guesses. Since, furthermore, the parameters derived from `upper' and `lower' spectra agree well, the large number of spectra and the high temporal sampling provide for a meaningful time series analysis (TSA).

The period search in the Boller&Chivens spectra was performed with the analysis-of-variance (AOV; Schwarzenberg-Czerny 1989) and Scargle's (1982) method implemented in the MIDAS TSA package (Schwarzenberg-Czerny, 1993; ESO-Midas, 1995). The analysis covers the frequency range from 0 to 10 c/d within which the window spectrum virtually consists of nothing but strong features at 0, 1, and 2 c/d. Albeit the two methods yielded essentially the same results, the effects of the daily aliasing of the window spectrum turned out to be much less disturbing in the AOV statistics. Therefore, the results reported below rest mainly on the AOV method. Results on other quantities measured in the B&C data, such as the radial velocity of different absorption lines, are reported in Paper II.

Of the parameters fitted to the emission components, the FWHM, the peak height (in units of the continuum), and the radial velocity were subjected to a separate TSA for the absorption and the violet and red component. Only the results of the period search in the radial velocities (RVs) of the emission peaks were negative, with a crude detection limit of 10 [FORMULA] (peak to peak). The positive detections are as follows:

  1. The height of the violet peak varies with a cycle time of 0.576 d.
  2. The red peak height varies cyclically with [FORMULA] = 0.571 d but in antiphase with respect to the violet peak.
  3. The FWHM of the violet peak varies with a cycle time of 0.571 d and is in phase with the variability in height of the violet peak.
  4. The variability of the red FWHM has a cycle length of 0.569 d but is in antiphase with the violet FWHM.
  5. The velocity of the underlying broad absorption line also varies cyclically, the cycle time being 0.583 d.

To within the errors, all these periods are indistinguishable.

For the peak heights, only a relatively minor part of the total power is accounted for by the periods stated, and none of the variations should be considered to be truly periodic. But the reality of the repetitive behaviour is indisputable in all 4 cases whereas we regard the differences between the quasi-periods as insignificant. Fig. 8 shows the data folded with [FORMULA] = 0.583 d, which is derived from the RVs of the broad absorption component and probably the most reliable. It clearly illustrates the pronounced cyclic [FORMULA] variability of the H [FORMULA] emission. (In the phase diagram for the B&C data MJD = 0.0 has been arbitrarily chosen as the epoch of phase zero, irrespective of the period.)

[FIGURE] Fig. 8. The trend-corrected cyclic variability of the H [FORMULA] emission in the Boller&Chivens spectra folded with a period of 0.583 d (Sect.  5.2). Shown is the product of the peak height (in units of the continuum) and the FWHM (in Å) of the violet (top) and the red (bottom) component, respectively. For details see Sect.  5.2

The length of the [FORMULA] cycles in the Boller&Chivens spectra is quite similar to those found at other epochs with HEROS (Sect.  5.1). Since furthermore the prominence of rapid cyclic [FORMULA] variability seems to be linked to the outburst activity, the H [FORMULA] observations suggest that the observing run with the Boller&Chivens spectrograph fell into an outburst of µ Cen. This is also supported by the preliminary periodic ephemeris for the outbursts which was derived from a time series analysis of stellar and circumstellar lines (Rivinius et al., 1998b).

5.3. Previous CAT/CES data

Only the profiles of He i [FORMULA] 6678 obtained on April 1-5, 9, and 10, 1986 (Baade, 1991) were studied in more detail because only in them significant [FORMULA] variations were visible, especially during April 1-5. After a re-analysis of the 71 spectra from these five nights, a cycle length of about 0.69 days became apparent for the [FORMULA] variability. The corresponding power spectrum is presented in Fig. 9.

[FIGURE] Fig. 9. Power spectra of He i [FORMULA] 6678 during the bursts described in Sect.  5. Contours in each panel mark areas of constant power (in arbitrary units) as a function of radial velocity (w.r.t. the star's systemic velocity) and frequency. They were derived by Fourier analyzing the flux in narrow slices of the line profile. From left to right are shown (i) the burst during April 1986 found in Baade's (1991) CAT/CES data (Sect.  5.3), (ii) the burst detected in the 1995 B&C observations (Sect.  5.2; since He i [FORMULA] 6678 was not covered by these data, He i [FORMULA] 4471 is used instead), (iii) the burst on MJD 50 223 and (iv) the one on MJD 50 232, both observed in 1996 with HEROS (Sect.  5.1), and, for comparison, (v) the power spectrum of all HEROS spectra from 1995 to 1997. The first four panels display enhanced power in the range 1.4-1.7 c/d and at the RVs of the emission components. These features correspond to the cyclic [FORMULA] variability during outbursts Sect. 5. The fifth panel does not contain significant power at these frequencies because the proportion of HEROS spectra taken during outbursts is very small compared to the whole dataset. Finally, the features at [FORMULA] c/d and somewhat lower radial velocities are due to the photospheric variability (cf. Paper II). Note that for the CAT/CES data and the burst on MJD 50 232 (panels i and iv, respectively) the blue power peak is stronger than the red one at [FORMULA] c/d

Like for the Boller&Chivens spectra (Sect.  5.2), the similarity of the time scales and the correlation between the occurrence of [FORMULA] variability and outbursts (Sect.  5) suggest that also the CAT/CES spectra of April 1-5, 1986 were obtained during an outburst. In fact, this is again (cf. Sect.  5.2) confirmed by the preliminary periodic ephemeris described and explained by Rivinius et al. (1998b) for the times of outbursts. The few contemporaneous H [FORMULA] profiles and their extreme [FORMULA] variability are reminiscent of those observed by Baade et al. (1988) during the 1987 February outburst. But the phase of the initial sharp rise of the emission strength seems to have been just missed.

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Online publication: April 15, 1998