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4. Results

The results of the light curve analysis in a "compressed" form are presented in Table 2 (click here) (single spot model) and Table 3 (click here) (double spot model). The tables contain parameters of the system evaluated through an analysis of individual light curves, numerated in accordance with Table 1 (click here). The errors in parameter estimation originated from the nonlinear least-squares method on which the inverse problem method is based. They are just formal and do not represent a real accuracy of the evaluation of the parameters. Especially, in evaluation of the spotted area size and latitude the real errors are probably larger than mentioned. This may be explained by the lack of a method for estimating the spot latitude and dimensions on the basis of the light curve analysis. Namely, for a given orbit inclination, light curve modulations produced by a smaller spotted area at a lower latitude or by a larger spotted area at a higher latitude are similar. This gives rise to errors in the spot-latitude and spot size estimation. In well-defined light curves the real spot size and latitude errors approximately estimated amount to tex2html_wrap_inline1866 and tex2html_wrap_inline1868. The errors can be larger in light curves insufficiently covered by observations.

  figure316
Figure 2: Solutions obtained by analysing the light curves of SV Cam within the framework of the Roche model with one and two spotted areas: Left - Quality of fitting (S) and basic sistem parametrs (F1,2, T2, i) obtained by analysing the individual light curves; Right - spotted area parametres (tex2html_wrap_inline1088, tex2html_wrap_inline1090 and tex2html_wrap_inline1086) and (tex2html_wrap_inline1088, tex2html_wrap_inline1090) spot positions during the period 1973-1981

On the basis of the results presented in Tables 2 (click here) and 3 (click here), and from Fig. 2 (click here)a, it is evident that the double spot model yields a better fit (lesser tex2html_wrap_inline1882. In this case, the basic system parameters are approximately constant for the whole set of the analysed light curves (see Figs. 2 (click here)b-d). This means that for the entire observational period the changes in the light curve form can be almost completely explained by changes in the position and size of the spotted areas. Certain variability can be noticed in temperature of the secondary, with the minimum value in light curve No. 15. A comparatively small depth of the secondary minimum of this light curve, probably indicates a real phenomenon. The variations of the orbit inclination are within the accuracy limits of the evaluation of this parameter.

In the case of the single spot model, the fit obtained is somewhat poorer, whereas the basic system parameters obtained by analysing the individual light curves show stronger variations about a mean value (see Table 2 (click here) and Fig. 2 - left column). We consider this case as less reliable, to the point of being possibly excluded.

The change of active-region parameters over the analysed observational period is suitable to be presented on plots. Such a presentation is given in Fig. 2 (click here) (right column), for a single and double spot model. The spot migration in longitude during the analysed period is shown in Fig. 2e. In the double spot model differences in spot longitudes in opposite stellar hemispheres can be noticed.

The spotted areas appear at high latitudes, near the polar regions (Fig. 2f). In the single spot model, for all light curves one obtains a spotted area on the upper stellar hemisphere, at sufficiently high latitudes tex2html_wrap_inline1884. In the case of the double spot model, the tex2html_wrap_inline1886 larger spotted area is on the upper stellar hemisphere, near the polar region (latitudes tex2html_wrap_inline1888). The tex2html_wrap_inline1890 smaller spotted area is on the lower sttelar hemisphere, with latitudes in the interval tex2html_wrap_inline1892. During the analysed period, the angular distance beetwen the centres of these two spotted areas is in the interval tex2html_wrap_inline1894 to tex2html_wrap_inline1896 in longitude and tex2html_wrap_inline1898 to tex2html_wrap_inline1900 in latitude. The mean values of these distances amount to tex2html_wrap_inline1902 and tex2html_wrap_inline1904.

The size of spotted area can be an indicator of the system's activity. Based on the obtained results (Fig. 2 (click here)g) one can say that the system during 1973 showed a significant activity. During 1974 the activity decreased. Therefore, for light curve No. 10, obtained in late 1974, one finds minimum dimensions of the spotted areas. After this, there is a fast increase in the activity. In 1976 it reaches a lower level again, at which it remains with smaller changes till the end of 1980. It seems that then a new significant increase in the activity took place. Then the activity increases again. Unfortunately, the data available are not sufficiently dense in time to study the activity in more detail. A clear cyclicity in the system's activity is not noticeable.

In the framework of the obtained solutions for both models it is possible to see a correlation between the latitude, (Fig. 2f) and size (Fig. 2g) of spotted areas. The large spotted area, near the stellar polar regions corresponds to an enhanced activity of the system.

During the analysed period, (tex2html_wrap_inline1906)-postions of the spotted area are grouped within active longitude and latitude sectors (Fig. 2h). For the single spot model they are in the intervals tex2html_wrap_inline1908 and tex2html_wrap_inline1910 of longitude, and in tex2html_wrap_inline1912 of latitude respectively. In the case of the double spot model the active longitude belts for tex2html_wrap_inline1886 spot in the intervals tex2html_wrap_inline1916 and tex2html_wrap_inline1918 are less prominent, but more prominent for tex2html_wrap_inline1890 spot in the tex2html_wrap_inline1922 and tex2html_wrap_inline1924 ones. The latitudes are concentrated within the sectors tex2html_wrap_inline1926 - (tex2html_wrap_inline1886 spot) and tex2html_wrap_inline1930 - (tex2html_wrap_inline1890 spot). Due to a selection effect it is possible that a more extensive observational material would correct this result to some extent.

Photometric effects of the spots with longitudes about tex2html_wrap_inline1934 and tex2html_wrap_inline1936 would be observable from the depth and shape of the light curve minima and partialy from the rest part of the light curve, which is not covered by eclipses. So, masking by eclipses does not explain the noticeable scarcity of these spots.

The obtained fit of the observed light curves (LCO) by the synthetic ones (LCC) following from the inverse problem solutions based on the single and double spot model are shown in Fig. 3 (click here). In order to easily follow the obtained solutions, the light curves are noted by ordinal numbers (No) in accordance with the ones applied in Tables 1 (click here), 2 (click here) and 3 (click here). Substantial differences in the quality of fits obtained by using single (dashed line) and double spot models (solid line) can be noticed in some light curves.

  figure364
Figure 3: Observed (LCO) and final synthetic (LCC) light curves of SV Cam obtained by solving the inverse problem within the framework of the Roche model with one (dashed line) and two (solid line) spotted areas

Figure 4 (click here) (double spot model) shows the view of the system obtained on the basis of the parameters estimated by analysing the corresponding light curves. The numeration of the figures corresponds to the ordinal number of the analysed light curves. The figures were made by using the programme (Djurasevic 1991). Thanks to such plots, one can see a view of a CB system at a noted orbital phase, chosen in such a way that the spots are visible.

  figure371
Figure 4: The view of the CB SV Cam at corresponding orbital phase with parameters obtained by solving the inverse problem


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