Securing the data for an analysis of the long-term light changes often represents a big problem because most photoelectric measurements, although of superior accuracy, cover just limited time intervals. The situation is better in the case of the photographic surveys but photographic emulsions are being changed occasionally. On the other hand, monitoring of many variable stars, organized by associations of observers, has made long series of data available. These observations are mostly visual but since they come from a large number of observers, the objectivity of the features of the light curve can be assessed. Visual data, if treated carefully, can be very useful for analysis of long-term activity. [30, Percy et al. (1985)] and [32, Richman et al. (1994)] discussed the advantages of using visual data and evaluated their accuracy. They found that although the typical error of a single visual observation is about 0.2 mag a much better accuracy of 0.02 mag can be achieved by averaging the data. This accuracy is quite sufficient for analyses of large-amplitude variable stars as V Sge.
Most visual data used in this analysis were obtained from the American Association of Variable Star Observers (AAVSO) International database [25, (Mattei 1996).] The original file contained about 25000 measurements, covering the years 1961-1995. The coverage is so dense that strings of multiple observations are sometimes available for a single night. The interval covered by the AAVSO observations was extended by inclusion of a part of the data from the Association Francaise des Observateurs d'Etoiles Variables (AFOEV) extending the coverage back to the years 1934-1944 (see also Paper I). The negative, unreliable and several largely deviating observations were rejected. As was revealed by HPSP, the contribution of the orbital modulation (the reflection effect and mainly the primary eclipse) can be appreciable mainly at the epochs when the system is in its low state. The course of the long-term changes is more clearly defined when this modulation is suppressed by rejecting the data inside the phase interval 0.9-1.1 (the primary eclipse - see also Paper I). The orbital phase of each observation was calculated using the ephemeris of HPSP since it plausibly satisfies the data in the analysed interval [38, (Smak 1995).] We note, however, that the remaining orbital modulation can still contribute to the scatter (see Fig. 7 in HPSP). The data within the phases 0.1-0.9 were binned into one-day means. The main reason for doing this was that the numbers of observations largely differ for both the respective nights and segments. It would introduce a bias into the statistical analysis. Binning into one-day means is very helpful here because we are interested in the activity on the time scale longer than one day. Moreover, these one-day means were found to display the course of most variations very well.
Table 1 includes the average number of observations in the one-day mean and the coverage of the light curve (number of one-day means divided by the length of the interval in days) in the respective segments, which are defined below. We can see that most points in the light curve were constructed from multiple observations. We should note that this definition of coverage is of great importance for rapid changes. Inspection of densely populated parts of the light curve shows that the brightness variations, analysed here, occur on the time scale of at least several days, or even weeks, therefore only the seasonal gaps are likely to affect the light curve. If only the seasonal gaps are considered, then the coverage is as high as 40 to 65 percent even in the worst case (segment S0).
The accuracy of the one-day means can be assessed from the scatter of the out-eclipse data. We determined the standard deviations for the means, computed from at least two observations. Typical standard deviation and rms error of a one-day mean during an interval of relatively flat light curve are about 0.15 mag and 0.09 mag, respectively, but one should bear in mind that the error includes both observational inaccuracies and intrinsic variations (mainly the orbital modulation). Another way to assess the reliability of the visual light curve is a comparison with photoelectric observations. We show the one-day visual means with superposed photoelectric observations, obtained by HPSP, in Fig. 1. It can be seen that the observations obtained out of eclipse by both methods are in good agreement and that the visual data give a good description of the long-term variations. We found that a slight systematic shift of the photoelectric data by 0.2 mag(V), applied also in Fig. 1, improves the match. This effect may be explained by slightly different passbands of the V filter and the eye. We will therefore abbreviate the brightness determined from the visual data as mag.
|Figure 1: Comparison of the AAVSO visual data (one-day means) with the out-eclipse photoelectric observations, obtained by HPSP. See Sect. 2 for details|
The CCD observations in the high state by [33, Robertson et al. (1997)] show occasional rapid dips with an amplitude about 1 mag(V) and duration at most 10 days. However, we will concentrate just on the long-term changes which of course are clearly visible in a series of visual data, not to overinterpret the visual data and work with the noise.
|Figure 2: The light curve of V Sge, constructed from the AAVSO one-day means of observations, displayed on the condensed time scale and covering the years 1961-1995. The respective segments, discussed in the text, are marked by S1-S7|
Copyright The European Southern Observatory (ESO)