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Astron. Astrophys. 332, 857-866 (1998)

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3. The light- and colour curves, the period analysis

3.1. R 99 = HDE 269445, Ofpe/WN9

R 99 was found to be variable with a total range of [FORMULA], which is abnormally large for such an early spectral type (see Fig. 13 in van Genderen et al. 1992). Fig. 1 shows an example of the light and colour curves (in log intensity scale) as a function of Julian Date during two months in 1990. Sometimes a W measurement is missing because of a bad reading. The error bars represent twice the mean error per datapoint.

[FIGURE] Fig. 1. A portion of the light and colour curves of R 99 relative to the comparison star in log intensity scale as a function of JD - 2440000. Bright and blue are up. Error bars are twice the mean error.

The time scale of the variations lies between 2 and 10 d (see below). Stahl et al. (1984) found light variations of [FORMULA] within two weeks of monitoring. The large range in the colours is peculiar: about 40% of the range in V (Fig. 1), compare with R 103 (Fig. 7), R 123 (Fig. 11) and R 128 (Fig. 12).

Like most [FORMULA]  Cyg variables, the brightness amplitude of R 99 in general show a progressive increase to shorter wavelengths. However, there are exceptions: simultaneous with the peaks in V and [FORMULA], there are dips in [FORMULA] and [FORMULA], e.g. around JD 244 8170 and JD 244 8197. Thus, light ranges in L and U are significantly smaller than in B. More quantitative and qualitative information can be obtained by combining this inspection with two-colour diagrams. Fig. 2 shows two of these as an example (with blue up and to the right). In the upper diagram B and W are compared to U. When [FORMULA] is blue, [FORMULA] is red, thus, W often has a smaller range than U. However, this is not always the case (which can also be identified in the colour curves) considering the relatively large scatter and the small slope of the regression line.

[FIGURE] Fig. 2. Two-colour diagrams of R 99. Blue is up and to the right. Error bars are twice the mean error.

In the lower diagram L and U ranges are compared to B. The regression line indicates that the L and U ranges are more or less equal. Whether they are larger or smaller than B ranges can be deduced when combined with diagrams including V and [FORMULA].

Fig. 3 shows that the star also exhibits brightness variations of [FORMULA] on a long time-scale as evidenced by magnitudes ([FORMULA]) and colours [FORMULA] collected from the literature by Stahl et al. (1984) and by Stahl & Wolf (1987) and completed with those of the present paper. The time-scale is of the order of 30 y and the colour becomes red in the maximum suggesting an S Dor phase (mainly caused by a temporary expansion of the stellar radius and a decrease of the temperature, and sometimes also partly by an increase of the stellar-wind density). More specifically, Fig. 3 suggests that R 99 exhibits a VLT-SD (Very Long-Term S Dor) cycle. This is one of the two types of SD phases identified by van Genderen et al. (1997a, b). Thus, the suggestion by Stahl et al. (1984) that R 99 and Ofpe/WN9 stars in general (e.g. Pasquali et al. 1997a, b) are related to LBVs is reinforced. We consider R 99 a real LBV, but subject to one type of SD phase only and, because of the low amplitude, not very spectacular.

[FIGURE] Fig. 3. The long time-scale light and colour variation of R 99 representing a VLT-SD cycle.

A period search was carried out using Fourier analysis of the V and B data in the frequency range 0.08-0.5 cycles per day (cd-1), and the resulting amplitude spectrum and spectral window for V are given in Fig. 4. The strongest amplitude occurs at 0.479 [FORMULA] ([FORMULA] d), with nearby 1 cycle per year aliases. Another strong amplitude is at 0.1003 [FORMULA] ([FORMULA] d)

[FIGURE] Fig. 4. Amplitude spectrum (top) and spectral window (bottom) for V measurements of R 99.

Fig. 5 shows, for the 2.088 d period, the light and colour curves [FORMULA] and [FORMULA] (showing a clear cyclic behaviour). The other periods near 2 d show some more scatter. Note the difference in position of the maxima in [FORMULA] and [FORMULA]. A weak cyclicity in [FORMULA] is present, but with a larger (intrinsic) scatter than in [FORMULA]. No cyclicity is present in [FORMULA] when folded with the periods around 2 d because of an intrinsic scatter three times larger than in the other colours. This points to an additional variability in the W passband independent from the 2.088 d period.

[FIGURE] Fig. 5. The phase diagrams of R 99 folded with P = 2.088 d. Bright and blue are up. Error bars are twice the mean error.

The phase diagram for the 9.98 d period shows no cyclic behaviour in the colours whatsoever with the exception of [FORMULA], which is a most surprising result (Fig. 6). Furthermore, this colour runs in antiphase with V which means that on those occasions when W has a smaller range than U (see discussion on Fig. 2) it is modulated by a 9.98 d period.

[FIGURE] Fig. 6. The phase diagrams of R 99 folded with P = 9.98 d. Bright and blue are up. Error bars are twice the mean error.

Considering R 99's pure emission-line spectrum in the optical region (Walborn 1982; Bohannan & Walborn 1989), Stahl et al. (1984) suggested that it has a luminous disk. It is possible that the modulation has something to do with variations in the physics of a disk, but a second stellar pulsation mode is also a possibility.

3.2. R 103 = HDE 269546 = -68 82, B3 Ip

R 103 appears to be variable with a maximum light range of [FORMULA], which is rather high compared with [FORMULA]  Cyg variables of the same spectral type (see Fig. 13 in van Genderen et al. 1992). There are no firm indications that R 103 is variable on a long time-scale (Thackeray 1974). The photometric data obtained by Walraven & Walraven (1977) made somewhere between 1958 and 1963, and by van Genderen et al. (1982) made in 1979, are practically equal to those listed in Table 2 (note that the [FORMULA] in the last reference should be read as -0.008 and not as -0.08).

Fig. 7 shows the light and colour curves (in log intensity scale) as a function of Julian Date during two months in 1990/91. The error bars represent twice the average mean error. The time-scale of the variations is of the order of a few weeks. The search for the period was made between 10 d and 50 d. Fig. 8 gives the amplitude and window spectrum for the V data. The highest peak in the amplitude spectrum is at 0.0419 [FORMULA] ([FORMULA] d), with adjacent 1 cycle per year aliases. The phase diagram for this best period displays a scatter of [FORMULA]   [FORMULA] around the mean curve which itself has an amplitude of [FORMULA]. Only the colour curve [FORMULA] shows a significant cyclic behaviour of [FORMULA] amplitude, blue at maximum light and red at minimum light, which is normal for [FORMULA]  Cyg variables. It is impossible to say anything about the physical reality of the other periods.


[FIGURE] Fig. 7. A portion of the light and colour curves of R 103 relative to the comparison star in log intensity scale as a function of JD - 2440000. Bright and blue are up. Error bars are twice the mean error.

[FIGURE] Fig. 8. Amplitude spectrum (top) and spectral window (bottom) for V measurements of R 103

3.3. R 123 = HD 37836 = -69 201 = S 124, Bpec

R 123 appears to be variable with a maximum light amplitude of [FORMULA], which is abnormally high for such an early B type supergiant (see Fig. 13 in van Genderen et al. 1992).

Stahl et al.'s (1984) compilation of photometric data between 1960 and 1984 showed a total range of [FORMULA], hovering between [FORMULA] and [FORMULA]. The magnitude [FORMULA] = 10.47 (December 1984, Stahl & Wolf 1987), the average magnitude of the present paper [FORMULA] = 10.61 and the Hipparcos magnitude (for 1989-1993) Hp = 10.55 ([FORMULA] -van Leeuwen et al. 1998) fits very well in this sequence. (It must be noted that the Hipparcos light curve looks like a scatter diagram and no cyclicity is evident, contrary to the data discussed below. Nearby faint field stars may have contaminated the Hipparcos photometry).

The light curve of R 123 V clearly demonstrates that R 123 exhibits at least two types of variation: a long time-scale one ([FORMULA] y) with a range of [FORMULA]   [FORMULA] and, superimposed on it, [FORMULA]  Cyg-type variations with a time-scale of a few days and an amplitude of [FORMULA]   [FORMULA].

Before we describe the search for periods, it is of interest to discuss first the historical photometric behaviour of R 123. Compilations by Thackeray (1974) for observations between 1834 and 1974 and by Stahl et al. (1984) for observations between 1959 and 1984 (to which we can add the one by van Genderen 1970, made in 1966) demonstrate that the star was [FORMULA]   [FORMULA] brighter in the 19th century. Thus, R 123 is also subject to a third type of variablility on a time scale of at least a few decades to one century.

A period search in the domain 0.003-0.1 [FORMULA] was carried out; see Fig. 9 for the corresponding V -amplitude spectra. A strong (double) peak occurs in the amplitude spectrum at 0.0025 ([FORMULA] d) and 0.0036 [FORMULA] ([FORMULA] d)(note that the highest peak in the spectral window is at 0.00288 [FORMULA] or [FORMULA] d). Some lesser peaks appear, but the most prominent time-scale of R 123's photometric variations is obviously [FORMULA] d. In order to choose which of these periods gives the best phase diagram we used the period search program of Sterken (1977), which is based on a sine curve fit to the data. The period with the highest correlation coefficient (r = 0.630) then appears to be 292 d [FORMULA] 20 d. Our data partly cover three such cycles in a row.

[FIGURE] Fig. 9. Amplitude spectrum (top) and spectral window (bottom) for V measurements of R 123.

Fig. 10 shows the corresponding phase diagram for V, [FORMULA] and [FORMULA] (the scales of the latter two diagrams are twice as large as for V). The amplitude of the sketched curve amounts to 0.09 log intensity scale or [FORMULA]. The large scatter is mainly caused by the [FORMULA]  Cyg-type variations. The two colour curves clearly show a cyclic variation. They are blue in the light minimum and red in the light maximum, strongly suggesting an S Dor-variation. Most peculiar is the fact that the scatter in [FORMULA] (curve omitted) is twice that in [FORMULA] and [FORMULA], even slightly more than in [FORMULA] and without a cyclic variation (see further).

[FIGURE] Fig. 10. The phase diagram of R 123 in log intensity scale, folded with P = 292 d. Bright and blue are up. Error bars are twice the mean errors.

To search for [FORMULA]  Cyg-type variations with a much shorter period, all V and B datapoints were corrected for the three individual 292 d cycles. As zeropoints we used the V and B values -1.12 and -1.19, respectively, corresponding with the brightness at minimum light of the 292 d-cycle. Then, a new period search was made (with the algorithm of Sterken 1977), and yielded a most probable period [FORMULA] d. The phase diagram with this best period is shown in Fig. 11 for V, [FORMULA], [FORMULA] and [FORMULA].

[FIGURE] Fig. 11. The phase diagrams of the residuals of the 292 d cycles of R 123 folded with a period [FORMULA] d. The continuous and broken curves run through the observations of the first two and third 292 d-cycles, respectively. Bright and blue are up. Error bars are twice the mean error.

There is something very peculiar with the 3.91 d-colour variations: those for the observations belonging to the first and second cycle (continuous curve) of the 292 d-variation show a different phase dependence from those belonging to the third cycle (broken curve, observations after JD 244 8113). In additon, the mean colours are redder during the third 292 d-cycle. There is no significant difference between the three 292 d-cycles in V. Now it is also clear why the omitted [FORMULA] curve in the phase diagram folded with the 292 d-period (Fig. 10) showed such a large scatter: [FORMULA] shows the largest intrinsic colour range.

Because of this marked dichotomy we decided to repeat the search with the observations of the first and second 292 d-cycle separated from that of the third one. The result is that for the first two 292 d-cycles the 3.910 d (r = 0.638) period is by far more significant than the 1.344 d (r = 0.485) and 1.338 d (r = 0.478) periods. However, the reverse is the case for the third 292 d-cycle: 1.342 d (r = 0.711) is now the most significant one (note the small difference in the third decimal), 3.910 d (r = 0.662) is present again and a new period of 1.362 d (r = 0.523) appears.

Thus, it seems that the star has (at least) two types of short-period oscillations: sometimes 3.910 d is the dominant time-scale, here apparently during the first two 292 d-cycles, and at other times, here during the third 292 d-cycle, the 1.342 d oscillation is more prominent.

It is noteworthy that the colour curves of the 1.342 d period also show a substantial shift with respect to the light curve: they are nearly in antiphase, like in Fig. 11. Thus, red in the maxima and blue in the minima. This is quite exceptional for an [FORMULA]  Cyg-type variation. We cannot offer an explanation for the time dependence of the colours, amounting to 1-3%.

3.4. R 128 = HDE 269859 = -69 221, B2 Ia

R 128 varied with a total range of [FORMULA] (between 1983 and 1990), which is very large with respect to its spectral type (see Fig. 13 in van Genderen et al. 1992). According to the compilation of Stahl et al. (1984), R 128 varied over not less than [FORMULA] between 1969 and 1984, which is mainly due to a very faint magnitude obtained by Sterken (1980, pr. comm. to Stahl et al. 1984).

The time-scale of the variations is difficult to determine. The light curve looks rather chaotic with sharp peaks and dips, alternated by slow low-amplitude variations, on time-scales of a week to a month, respectively.

Fig. 12 shows an example of the light and colour curves (in log intensity scale) for the interval 1989-1990.

[FIGURE] Fig. 12. A portion of the light and colour curves of R 128 relative to the comparison star and in log intensity scale as a function of JD - 2440000. Bright and blue are up. Error bars are twice the mean error.

The amplitude spectrum is given in Fig. 13. The best period is 3.444 d, but the phase diagram is not convincing.

[FIGURE] Fig. 13. Amplitude spectrum (top) and spectral window (bottom) for V measurements of R 128.

Possibly, R 128 is subject to multi-periodicity and stochastic perturbations. In the colour curves [FORMULA] tends to be bluer in the maxima than in the minima which is normal for [FORMULA]  Cyg-type variations.

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© European Southern Observatory (ESO) 1998

Online publication: March 30, 1998
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