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Astron. Astrophys. 338, 1031-1040 (1998)

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6. Conclusions

From an analysis of the long-term photometry of HD 81410 we find that two prominent spot groups, well-separated in effective longitudes, were present on its surface most of the time, as indicated by the presence of two light minima; probably there are two preferred effective longitudes about which spots are usually formed. The migration of the phase of the light minimum usually observed in RS CVn stars is lacking in the case of HD 81410 suggesting that the effective latitude of the spots is in synchronous rotation with the binary orbit.

The light curve of HD 81410 evolves drastically rather fast. During 1988 the light curve changed from being of double minima to single minimum and back to double minima. The deeper minimum, however, remained anchored more or less at the same phase, between [FORMULA] and [FORMULA], through out. The colors are found to vary in phase with the light variation in the sense that the star is redder at light minimum. During 1971-85 the brightness at light maximum remained more or less constant around 0.20 mag below the maximum ever observed, where as the brightness at light minimum monotonically increased from 1971 till 1987, by more than 0.5 mag. The largest V amplitude observed is 0.45 mag and the smallest 0.05 mag. The total range in brightness (difference between the brightest [FORMULA] and faintest [FORMULA]) observed is around 0.70 mag, and is similar to that seen in other active RS CVn systems, like, II Peg. There is an indication that at amplitudes larger than 0.20 mag an increase in amplitude results from a decrease in the brightness at light minimum.

We find that for a reasonable level of spot coverage it is essential that in active RS CVn systems, like, DM UMa, II Peg, HD 81410, etc., the spots should extent well-beyond [FORMULA]in latitude at least at certain epochs, and the photosphere-spot temperature difference should be more than 1000 K. The spread in the maximum amplitudes in V observed in DM UMa, HD 81410, II Peg and HD 12545 is only around 0.25 mag. If these objects show at least spread of about [FORMULA] in the inclination of their rotational axes, assuming similar levels of spot activity in all these stars, it is tempting to conclude that the longitudinal asymmetry in the distribution of spots, which causes the observed light modulation, is largely restricted to within around [FORMULA] latitudes in these objects. A strong support for such a possibility comes from a consideration of the total ranges of rotational periods quoted for several spotted stars from long-term photometry in conjunction with the variation of rotational period with latitude in the Sun.

The investigation of synthetic light curves also shows that the effects of limb-darkening in the amplitudes and shapes of colour curves depend on the exact distribution of spots on the stellar surface. It is found that when the spots have a larger extension in longitudes than in latitudes the limb-darkening effects are negligibly small and the colour variations produced are entirely caused by the temperature effects.

A modified version of the spot modeling program developed by Mohin & Raveendran (1992) was applied to synthetic light curves in UBVRI due to an equatorial band of spots covering [FORMULA] longitude. The single-spot assumption is found to give a poor approximation to the light and colour curves whereas the two-spot approximation is found to give acceptable fits to the synthetic light and colour curves. Those corresponding to the three- and four-spot assumptions are mutually indistinguishable and excellently reproduce the synthetic data. Interestingly, the spot temperatures derived in all the cases are close to the assumed input value, and show only a spread of about 150 K. The results clearly indicate that if there are more than one prominent spot group the light curve could still show a single well-defined minimum, and hence the migration of the phase of light minimum may not represent a true migration of a spot or spot group because the apparent shift in the phase of the light minimum may be arising from a change in the relative strengths of the various spot groups.

We have modeled a series of eight light curves of HD 81410 which gave the standard deviation of fit comparable to the scatter in the light curve. It is found that the maximum temperature difference between the spots and the photosphere is around 1400 K in HD 81410. The spot temperature derived is comparatively higher (around 4500 K) when the light curve has a shallow minimum. This implies that during such epochs the spots are spread out over a wider region on the stellar surface, both longitudinally and latitudinally, and hence the circular spot approximation for the spot group forces the equivalent spots to include a larger region of the unspotted photospheric region also. As the number of spots is increased in the modeling, it is found that the spots shift closer to the equator indicating that spots are most likely distributed about the equator, and therefore the solutions which indicate polar spots are the result of limiting the number of spots in the modeling to a few.

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© European Southern Observatory (ESO) 1998

Online publication: September 17, 1998