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Astron. Astrophys. 356, 913-928 (2000)

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5. Rapid variations

5.1. Photometry

The analysis of prewhitened V magnitude data over the period interval from 0.0 to 2.0 d in several critical data subsets (Hipparcos data, data from HJD 2446500-800 which combine American, European and Asian observations, and whole-night series obtained in 1998 and 1999) confirmed the presence of a 0[FORMULA]2997 period reported by Hubert & Floquet (1998) as the best one. A PDM search for sinusoidal variations over the whole body of the V-magnitude data prewhitened for the long-term changes and the consecutive least-squares sinusoidal fit led to the following linear ephemeris:


the full amplitude being about 0[FORMULA]03. The phase diagram is presented in Fig. 7. Also shown here are the 0[FORMULA]03 normals from the Hvar 1999 observations when the data were obtained in longer series during 7 observing nights. The sampling in these nights represent the best coverage for the 0[FORMULA]3 period. Data from each night are connected by a line. One can see that a good phase coherence is observed on most but not all nights. A PDM search aimed at the detection of non-sinusoidal changes detected three other possible periods, near 0[FORMULA]727, 0[FORMULA]899 and 1[FORMULA]199. All four detected periods and their corresponding frequencies are listed in Table 8. It is seen that only the 0[FORMULA]727 period is independent one. The other two are integer multiples of the period of 0[FORMULA]2997.

[FIGURE] Fig. 7. Prewhitened individual V magnitudes of 60 Cyg plotted vs. phase of the 0[FORMULA]2997 period (upper panel). Note that the magnitude range is smaller for the Hvar 1999 data (middle panel). Measurements from individual nights are connected by lines. To characterize the observational scatter inherent to the data, we show in the bottom panel the plot of all individual observations of the check star HD 199479 over the same magnitude range as all variable-star data.


Table 8. Possible rapid periods detected in prewhitened V photometry of 60 Cyg

5.2. Analysis of line profile variability

As can be seen from Table 3 our observational material consists of 15 reasonably long night series. Most of them (11) come from blue spectra containing either He I 4388 Å or 4471 Å line or both.

5.2.1. Time series analysis of lpv

We have used the same method as Gies and Kullavanijaya (1988) in the sense that we have scanned the series of line profiles, and applied Fourier Transform with the CLEAN algorithm on each scan to obtain power (amplitude). However, we calculated power spectra for the time series, pixel by pixel (about 6.7 km s-1 ), while Gies and Kullavanijaya (1988) used velocity grid spacing of 4 km s-1 . The same authors then summed the power across the velocity axis of the periodogram (weighted by the residual absorption line depth at each velocity point). We have only summed the power obtained in each scan (Fig. 8).

[FIGURE] Fig. 8. Power spectra for He I 4388 Å line normalized to the minimum variance given by the summation of all CLEANed periodograms obtained in 1996 campaign.

The velocity phase (Fig. 9) is determined with the least-squares sinusoid fitting which gives a better restoration of amplitudes and phases.

[FIGURE] Fig. 9. Phase variation [FORMULA]/[FORMULA] as function of position across the profile of helium line 4388 Å for the frequency [FORMULA]=1.89 c d-1.

Periods shorter than 2 hours ([FORMULA]=12 c d-1) and longer than the total duration of the observing run in 1996, [FORMULA] 8 days ([FORMULA]=0.13 c d-1) could not be detected. The period search, based on the least-squares sinusoid fitting was carried out over these limits in frequency, with a constant step in frequency of less than one hundredth of the lower limit of [FORMULA], following Kambe et al. (1990). Both He I 4471 Å and 4388 Å line profiles obtained in 1994, 1996 and 1997 campaigns were analysed. In most cases the signal with the highest power corresponded to the frequency [FORMULA]=1.89 c d-1. In Fig. 8 we present detailed results for the He I 4388 Å line obtained in 1996. Most of the other peaks are aliases of the frequencies [FORMULA]=1.89 c d-1 and [FORMULA]=3.34 c d-1 (see Sect. 5.1). The phase variation as a function of the wavelength across the same helium line profile is shown in Fig. 9.

5.2.2. Analyses of local RVs measured at specified line depths

As mentioned in Sect. 2.1 the local RV can be used for the study of lpv. The analysis of local RVs was primarily based on the He I 4471 Å and 6678 Å lines. He I 4471 Å could be measured in all blue spectra while He I 6678 Å was taken together with H[FORMULA] spectrum in most cases. Two sets of specified line depth of the continuum level for measurement of local RV were selected. He I 4471 Å: 0.96, 0.94, 0.92, 0.90, and 0.88, He I 6678 Å: 0.99, 0.985, 0.98, 0.975, 0.965, and 0.96. The RVs at these intensities were measured on both sides of the lines profile in all available spectra.

The analysis of the local RVs for the He I 4471 Å and He I 6678 Å lines proceeded in the following way: First, we inspected the variation of local RVs vs. time - see Figs. 10 and 11. It is obvious that there is a secular variation, undoubtedly related to a secular change of the width of the He I line. Notably, this affects the red wing of the profile more than the blue one. This secular variation implies that even the He lines are not purely photospheric and are affected by a contribution from circumstellar matter. This, of course, strongly complicates any interpretation of similar spectra. For instance, one cannot use the He lines to a reliable determination of the projected rotational velocity or effective temperature of the star.

[FIGURE] Fig. 10. The time plots of local RVs of the He I 4471 Å line of 60 Cyg at intensities of 0.92 (circles) and 0.88 (diamonds) measured on the blue and red wings of the profile. A gradual narrowing of the line is seen.

[FIGURE] Fig. 11. The time plots of local RVs of the He I 6678 Å line of 60 Cyg at intensity 0.965. Symbols used: squares - OND,filled circles - DAO, filled triangles - OHP.

To proceed further, we prewhitened the local velocities for the secular changes and analysed them for periodicity over the range from 0.25 to 5 d using Stellingwerf 's (1978) phase-dispersion minimization technique. It turned out that the best fit was obtained for frequencies close to 0.94 and 1.88 c d-1, in accordance with the results found by other techniques. Using the new program Period98 by Sperl (1998), we calculated least-squares fits of individual local RVs for both periods allowing for a simultaneous calculation of ten harmonic frequencies. It turned out that for all parts of the line profile, the longer period of 1[FORMULA]0647 gives a better fit to the data than the shorter one. The same is also true for the bisector RVs derived as the mean values of the local RVs measured at the same line intensity on the blue and red wings of the profile. A less certain finding is that it appears as if the outer wings of the profile would vary with a slightly longer period than the line core. If real, such an effect could reflect, for instance, the differential rotation of the star/envelope. Further tests of this exciting possibility on more extended series of spectrograms is, therefore, very desirable.

In Fig. 12 we compare the RV variation of the blue and red wing of the He I 4471 Å line with phase of the 1[FORMULA]0647 period for two different line depths. It is clearly seen that the blue and red wing vary essentially in phase , although the amplitude of the variation is decreasing systematically towards the line edges (the same is also seen from the Period98 fits). Given this, we therefore calculated the mean value of the residual local RVs at different levels for each spectrum and used this quantity to improve the value of the period by a least-square fit with Period98. We found a value of 1[FORMULA]0647393. The phase plot for this period and the mean residual RV for the He I 4471 Å line is shown in Fig. 13. The difference between the two maxima and minima is seen there.

[FIGURE] Fig. 12. The local RVs of He I 4471 Å measured at two different intensities and prewhitened for secular changes, plotted vs. phase of the 1[FORMULA]064739 period. The empty and filled circles denote the RVs from the blue and red wing, respectively.

[FIGURE] Fig. 13. The mean of all residual He I 4471 Å local RVs, measured at different line intensities at both wings and prewhitened for secular changes, vs. phase of the best-fit 1[FORMULA]0647393 period.

Although the time distribution of the available He I 4471 line profiles is not ideal, we also calculated the PDM periodogram of the mean RVs plotted in Fig. 13. This periodogram is shown in Fig. 14. One can see that the deepest minima correspond to the family of frequencies associated with the 1[FORMULA]0647 period.

[FIGURE] Fig. 14. The PDM periodogram of the mean of all residual He I 4471 Å local RVs, measured at different line intensities at both wings and prewhitened for secular changes, calculated for the (10,4) bin/cover structure using Stellingwerf 's (1978) method.

The fact that the local RVs at different levels vary at phase is notable since it shows that the apparent RV changes are not caused by the passing subfeatures, moving from the blue to the red wing of the profiles. In general the RV behaviour of 60 Cyg reminds the RV changes of [FORMULA] CMa. As demonstrated by Baade (1984), the amplitude of the periodic RV variations of [FORMULA] CMa with a period of 1[FORMULA]37 is largest at the line centre.

The results for the He I 6678 Å confirm the long-term variability of the width of the line (see Fig. 11). On the other hand, we were not able to derive similar diagrams for all He I 6678 Å lines as it was possible for He I 4471 Å (Figs. 12 and 13). This is probably due to intrinsic noise originating from the presence of variable emission component to the line. A radial velocity curve mimicking that one shown in Fig. 12 was only obtained for data from 1994 campaign (see upper panel in the Fig. 15) when the amplitude of the lpv was very strong. The results from 1997 are much less convincing (the lower panel in the same figure).

[FIGURE] Fig. 15. The local RVs of He I 6678 Å measured at intensity 0.965 plotted vs. phase of the 1[FORMULA]0647393 period. The upper panel represents the results from 1994, while in bottom we show velocities obtained in 1997. Different symbols denotes different night series.

5.2.3. Residual analysis

Residuals formed by subtracting the mean night profile from each spectrum are shown for the nights August 5-6, 1994 - Fig. 16, July 8-9, 1996 - Fig. 17, and July 14, 1997 - Fig. 18, respectively. Absorption features moving from blue to red across the He I 4471 Å are clearly seen. The measured velocities of the features marked with letters are plotted versus the phase of 0.2997029-day period for three seasons in Fig. 19. This figure shows good correspondence of the emission and absorption bumps over the interval of three years. This may suggest that the structures are controlled with the 0.3-day period found also in the photometric and probably in the spectroscopic data (see the Sects. 5.1 and 5.2.1). The scatter of individual points is due to the fact that the bumps are not well defined, namely in 1996 and 1997 seasons. We can estimate that the acceleration is about 1900 km s-1 d-1. The residual analysis could not be performed for He I 6678 Å line because the difference spectra were much more noisy, probably influenced by the variation of the emission component present in the line. The He I 4388 Å line was observed in 1996 and 1997 when the contrast on the He I 4471 Å residuals was much lower. The only Balmer line, for which we have enough observational data to construct residual spectra, is the H[FORMULA] line. However, the weakness of the traveling sub-features in 60 Cyg (bumps in the He I 4471 Å line are at one percent of the continuum level), combined with the strong and variable H[FORMULA] emission, presence of (also variable) telluric lines and with the difficulty to define the continuum reliably enough over the range of H[FORMULA] makes such an attempt hopeless.

[FIGURE] Fig. 16. Residuals obtained by subtracting the nightly mean profile from the individual profiles in the vicinity of the He I 4471 Å line during 5-6 August 1994 (HJD 49570.5). The residuals are identified by fraction of HJD on their right side. Moving bumps are indicated by letters.

[FIGURE] Fig. 17. The same as in Fig. 16 but for the night 8-9 July 1996 (HJD 50273.5).

[FIGURE] Fig. 18. The same as in Fig. 16 but for the night 14 July 1997 (HJD 50643.7).

[FIGURE] Fig. 19. Acceleration of moving bumps displayed in Figs. 16,  17, and 18. The data are folded with the 0.3-day period (see Sect. 5.1). Symbols used: filled symbols - absorption, open symbols - emission bumps; 1994 data - circles, 1996 data - squares, and 1997 data - triangles. Note that there is a good agreement between the corresponding types of bumps over the interval of three years.

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Online publication: April 17, 2000