Astron. Astrophys. 337, 393-402 (1998)

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

In the following subsections we present a description of the light- and colour curves of the selected objects. It is very well known that the light variability of  Cygni variables, including hypergiants and LBVs, consists of several components, viz. the pseudo-periodical microvariations, the S Dor phases, and the ever present stochastic noise (for a detailed discussion, see Sterken et al. 1997). The stochastic-noise component-but also the occurrence of numerous gaps in the long-term light curve-sometimes hinders the graphical rendering, especially when all data points of the light curve are being connected by lines. However, our experience from previous studies indicates that it is extremely convenient to present parts of the light curves by full lines to help the eye see the variations clearly. We have, therefore, drafted lines representing the best polynomial fit (polynomials have the property to follow smooth minima and maxima without enforcing a harmonic function to the data). As to the pseudo-periodic character of the light curves (revealed, in the first place, by their visual effect) we prefer to use the term cycle instead of period since the latter term somehow involves a much higher degree of regularity than the former.

3.1. R 85 = HDE 269321, B5 Iae

During the uvby and VBLUW photometric campaigns R 85 appeared to be variable with a total range of 0:m 31, which is exceptionally large for an  Cyg variable of this spectral type (see Fig. 13 in van Genderen et al. 1992).

Fig. 1 shows the light curve 1983-1994, including the V observations of the VBLUW system transformed to () and the colour indices , and . The light curve () stretching over almost a dozen years shows a strongly oscillating trend of which the waves show a wide variety in duration (15-400 d) and amplitude (0:m 03-0:m 20). A small part, between JD 244 5900 and JD 244 6500 (1984-1986), is characterized by a long-term oscillation with two maxima with a time interval of roughly 400 d and an amplitude of (partially dashed curve in Fig. 2, obtained by polynomial fits to all data). Colours tend to be red in the maxima and blue in the minima. Thus, this episode probably can be considered as a "normal S Dor phase", the shorter one of the two types of SD phases identified by van Genderen et al. (1997a). Short-term micro-oscillations with amplitudes of are superimposed (fitted continuous curves in Fig. 2), and five approximate times of maximum can be recognised, which yield an average cycle length of (if we assume that the data span eight cycles).

Fig. 1. The complete light curve of R 85 ( for the Walraven system) and colour curves for the interval 1983-1994.

Fig. 2. A portion of the light and colour curves of R 85 as a function of JD-244 0000, based on uvby photometry (in magnitudes) showing an oscillation (probably a "normal SD phase") of d (upper, partially broken curve). Bright and blue are up. The solid lines that illustrate the long-term trend are polynomial fits to all data ( degree in and in the colour indices, see text). The short-term microvariations in are also represented by  degree polynomials.

During other time intervals the light curve looks completely different from this portion. The most surprising part, between 1987 and 1991, is shown in Fig. 3, incidentally including all VBLUW datapoints. The 400 d oscillation is not visible. This part starts with a large-amplitude ascending branch () lasting d and showing a few small bumps. Then the oscillations tend to occur on a decreasing time scale and range till about JD 244 8240-that is, from 180 d to 15 d and to -while the average brightness decreases. The stretches of solid line in Fig. 3 clearly illustrate that there is a change in the cyclic pattern. Note that the apparently-single wave (cycle length about 190 d) which is seen in 1988-1989 could very well be a double or triple wave (with cycle length d or d for the components).

Fig. 3. A portion of the light curve of R 85 as a function of JD-244 0000, based on VBLUW (o) and uvby () photometry. The fitted lines are  degree polynomial fits.

Thereafter, in the time interval 1991-1994, the time scales and amplitudes of the oscillations, often only partly covered by observations (therefore the light curve is not shown), amount to 1-3 months and , respectively. Due to gaps in time and the relatively large scatter, the precise behaviour of the colour curves is unknown. So far, R 85 is the most peculiar  Cyg variable known. The possible reason for this peculiarity will be made clear below. Fig. 4 shows, as an example, the detailed colour variations in the VBLUW system for four cycles.

Fig. 4. A portion of the light and colour curves of R 85 in the VBLUW system relative to the comparison star in intensity scale as a function of JD-244 0000. Bright and blue are up.

A period search of the light-curve data shown in Fig. 1 was carried out using Fourier analysis in the frequency range 0-0.1 cd^-1, and the resulting spectral window and amplitude spectrum are given in Fig. 5. The spectral window shows the annual cycle at 0.002745 cd^-1 ( d). An interesting peak in the amplitude spectrum occurs at cd^-1 ( d) with, at distances of  0.0027 cd^-1, the annual cycle aliases 0.01469 cd^-1 and 0.00927 cd^-1, corresponding to d and d, respectively. The 400 d cycle (seen in Fig. 2, in Table 3) is also present (0.0025 cd^-1). A simultaneous sine fit with both frequencies yields a calculated light curve that looks like the one in Fig. 1 (see Fig. 6), but reduces the overall standard deviation by only 25% (the calculated curve does not follow the strong amplitude changes). Alternatively, we have performed a simultaneous sine fit using and the d alias of , which does not yield any improvement in terms of goodness of fit. The resulting parameters are given in Table 3. It is clear that the Fourier spectrum of R 85 cannot be unambiguously solved.

Fig. 5. Spectral window (top) and amplitude spectrum (bottom) for V measurements of R 85.

Fig. 6. Two-frequency fit with parameters from Table 3 (solution I).

Table 3. Overview of the results of the period search. Amplitudes A (in mag) and phase (in degrees, phase zero corresponds to JD=2440000. Roman numbers indicate different possible solutions.).

The changes in colour during the microvariations over the whole dataset and in the two photometric systems appear to be so diverse, that no systematic behaviour of the colours can be noticed: sometimes they are blue in the maxima, sometimes they are red. It is as if we are dealing here with a mix of the two types of microvariations. Indeed, if the individual cycles are scrutinized, we get the impression that both types of microvariations for LBVs, identified by van Genderen et al. (1997b), are operating here together, like in HR Car during a short time interval. The conclusion was that both types of microvariations are probably caused by different instability mechanisms. If the time scale amounts to 100 d, the colours are red in the maxima, if 100 d, the colours are blue in the maxima. They are called the "100 d-type" (for large range LBVs appearing at the upper half of the SD cycle) and " Cyg-type" microvariations (for large range LBVs appearing at the lower half of the SD cycle), respectively.

The mix as exhibited by R 85 is no surprise since its temperature, according to its spectral type, is about 14 000 K and the estimated temperature boundary for the switch from one type of oscillation to the other presumably lies between 10 000 K and 15 000 K. The peculiarity of the overall light curve, noted above, is now understandable.

Also striking is the relatively large range of the colour variations, especially in and (Fig. 4). Quantitative parameters to characterize the size of the light and colour variations of  Cyg variables are the "maximum light amplitude" or MLA, and the "" for the four colour variations (for definitions, see van Genderen et al. 1989, 1990, 1992).

For R 85 they are too large for normal  Cyg stars, e.g. the MLA amounts to 0.122 in intensity scale (0:m 31). They are of the same order as for the B9 Ia⁺ LBV/hypergiant HD 168607 = V4029 Sgr (van Genderen et al. 1992). The relative lack of secondary features on top of the micro-oscillations is another characteristic shared with other LBVs.

A phenomenon which also strongly favours an LBV-classification is that R 85 shows a weak S Dor-activity on a time scale of decades if scattered observations during the last few decades are examined: colours are redder when the star is bright and bluer when faint. This has been convincingly established by Stahl et al. (1984) who made a compilation of values from the literature. Fig. 7 shows the plot of this compilation, completed with the data of the present paper by taking averages of sub-sets of observations. The indices were transformed to and then to by using the data sets where Walraven and Strömgren photometry was obtained simultaneously. The long-term variation has a time scale of more than 30 y with a light range of 0:m 3, thus very similar to the LBV R 99 (Paper I). The colour behaves as it should for an SD-activity. We believe that this represents the longer one of the two types of SD phases identified by van Genderen et al. (1997a,b) in other LBVs, viz. the VLT (Very Long-Term)-SD phase. Part of the maximum and the subsequent decline of the VLT-SD cycle can be seen in more detail in the light curve of Fig. 1 (1983-1994). The colour index clearly shows the blueing trend during the decline.

Fig. 7. The long-term light and colour variation of R 85.

3.2. R 110 = HDE 269662, B9 I:eq - G

The main results of the VBLUW and uvby monitoring campaigns have been discussed by van Genderen et al. (1997b) in combination with scattered observations dating back to 1957 and which were mainly collected for the study of the SD-activity on time scale of decades.

We discuss here the detailed photometry related to the microvariations. The star is an LBV which reached a maximum early 1993 (JD 244 9000) with .

The detailed light curves show a micro-oscillating behaviour on top of the ongoing SD-activity. These oscillations are smooth and have various amplitudes and time scales: 0:m 02 to 0:m 10 and 50 d to 100 d, respectively. Fig. 8 shows the light curve based on part of the uvby and all VBLUW observations made more or less simultaneously. The colour behaviour for these oscillations is often blue in the maxima and red in the minima. Sometimes the colours behave in the opposite way, sometimes they stay constant. The remainder of the uvby data show large gaps in the sequences which prevent a proper insight in time scales and colour behaviour (though a Fourier analysis does confirm the possible presence of a cd^-1 frequency, see also the right panel of Fig. 8).

Fig. 8. The detailed light curve of R 110 based on all available VBLUW (o) and part of the uvby () photometry made simultaneously. Dates mark the beginning of the year. Full lines are polynomial fits.

According to the time scales, the position close to or in the maximum of the SD cycle and the fact that the temperature is lower than 10 000 K, one would expect microvariations exclusively of the 100 d-type, which is obviously not the case.

3.3. R 42 = HD 7099, B2.5 I

During the VBLUW photometric campaign R 42 appeared to be variable with a total amplitude of 0:m 19 (0.076 in intensity scale), which is higher than for normal  Cyg variables of the same spectral type (see Fig. 13 in van Genderen et al. 1992) and more appropriate for LBVs.

There is a slight overlap with the Hipparcos photometry (1990-1993). During that time interval, the total amplitude amounted to 0:m 11 (van Leeuwen et al. 1998). There is no indication for a long-term trend within the last four decades: all magnitudes, starting with the one listed by Feast et al. (1960) until those obtained with Hipparcos, hover around = 10.95 with an amplitude less than 0:m 1. So, in that respect, R 42 is not an LBV.

Fig. 9 shows as an example a portion of the light and colour curves in the VBLUW system during five months in 1989. The colour variations are about twice as large as for other  Cyg variables of the same spectral type. The of the four colour indices (see Sect. 3.1) amount to 0.0026, 0.0035, 0.0058 and 0.0032, respectively (compare with Fig. 6 in van Genderen et al. 1990). In most cases the colours are blue in the maxima and red in the minima as expected. At first sight the time scales of the oscillations lie between 10 and 30 d, but it appears that longer time scale oscillations are hidden in the fluctuating brightness (see below).

Fig. 9. A portion of the light and colour curves of R 42 in the VBLUW system relative to the comparison star in intensity scale as a function of JD. Bright and blue are up.

A Fourier analysis in the frequency interval 0-0.10 cd^-1 was carried out on both data sets together (in the V band; the Hp magnitudes were transformed to V applying a small correction to the Hipparcos photometry [Table 2 of van Leeuwen et al. 1998]). Fig. 10 shows the resulting spectral window and amplitude spectrum. Weak amplitude peaks occur at 0.0078 cd^-1 (128 d) and 0.0224 cd^-1 (44.6 d), these frequencies could be real because they are present in both data sets separately, but they are embedded in strong noise.

Fig. 10. Spectral window (top) and amplitude spectrum (bottom) for V measurements of R 42.

The most surprising result is the duration of the longest cycle: if real, its length is unique among the early-type  Cyg variables (see Sect. 4.3). Fig. 11 is the phase diagram for 128 d and shows a visible cyclic behaviour in V (both data sets). The colour indices do not exhibit any significant cyclic behaviour.

Fig. 11. The V (log intensity) phase diagram of R 42 with d. Bright and blue are up.

A phase diagram folded with 44.6 d (the second best period for the V measurements) only shows a cyclic behaviour in , but then in phase with V as it should. We must stress, though, that the composite light curve based on the simultaneous fit of both periods does not reproduce the morphology of the light curve: the overall residual decreases by only 10%, and the resulting amplitudes are far too small (not exceeding 0:m 015) to combine to any large amplitude variations. We have, therefore, not included these results in Table 3.

3.4. R 45 = HD 7583,

During the VBLUW photometric campaign R 45 appeared to be variable with a total amplitude of 0:m 13 (0.052 in intensity scale) which is normal for an A-type hypergiant (see Fig. 13 in van Genderen et al. 1992). The Hipparcos observations were made directly after the campaign. The amplitude of the variations was of the same order (van Leeuwen et al. 1998). There is no significant long-term trend present when scattered observations within the last decades are considered.

Fig. 12 shows the complete light curve in V (1986-1993) for both data sets (^o for the Hipparcos data) relative to the comparison star and in intensity scale. The mean errors per data point vary between 0.001 and 0.004 in intensity scale. We applied a small correction to the Hipparcos data (Table 2 of van Leeuwen et al. 1998) and transformed them to the same scale as for the other set.

Fig. 12. The complete light curve in V of R 45 for 1986-1993 relative to the comparison star and in intensity scale. Bright is up (Hipparcos data o, our data ).

Fig. 13 shows a characteristic portion of the light and colour curves in the VBLUW system during five months in 1989. The curve is omitted because of low readings in the W channel. Colours are blue in the maxima and red in the minima which is normal for  Cyg variables. Also the amplitude of the colour variations is normal for this spectral type. The time scales of the oscillations is difficult to estimate, but lies in the order of 1-2 months.

Fig. 13. A portion of the light and colour curves of R 45 in the VBLUW system relative to the comparison star and in intensity scale as a function of JD-244 0000. Bright and blue are up, full lines are polynomial fits.

A Fourier analysis of the V data was carried out (both data sets together, the Hp magnitudes corrected by m [see Table 2 in van Leeuwen et al. 1998]) in the frequency range 0-0.10 cd^-1, and the resulting spectral window (top) and amplitude spectrum (bottom) are given in Fig. 14.

Fig. 14. Spectral window (top) and amplitude spectrum (bottom) for V measurements of R 45.

A strong peak in the window function at 0.0031 cd^-1 (322 d) corresponds with a strong peak in the amplitude spectrum, most likely representing the nearly-annual cycle. A nearby peak in the latter diagram at 0.0053 cd^-1 could be the half annual cycle. Other peaks lie at 0.0207 cd^-1 (48 d) and 0.037 cd^-1 (27 d), and there are many others that are only slightly lower. We conclude that the period search does not give unambiguous results.

© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998
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