## 6. The phase factorsTable 5 gives our main results which are the normal points for all 28 groups. The table gives the color (index 1..4 is uvby), the phase factor and its mean error, the phase and the magnitude and its mean error. For groups 1, 23 and 28 the phase factor could not be derived directly so for color y the estimates from the table above were used. A statistical "analysis of variance" shows that the values in
Table 5 can
Fig. 3 shows the phase factors and from Table 5. The quite independent values in y and b obtained by two different photomultipliers seem to support each other and indicate a structure with three maxima. The observed phase factors are too large to be explained by an effect of small errors in rotational phases in the subtracted magnitudes (dy/dP=1.0 mag/rev at max., with errors 0.01 in P it only may explain 10% of the phase factors). In Fig. 4 the 1983 lightcurve at phase angle =1.84 is compared with the 1994 curve at phase at nearly the same aspect. The V magnitudes in 1983 are interpolated from table 8 in Astron. Nachr. 306 (1985) 246 and the figure gives c=(V(1983)-y(1994))/ . Due to undetermined constants in V and y (resulting in values ) the phase factor can only be determined apart from a constant. We note, however, the three maxima around 0.2, 0.5 and 0.8 and the two minima 0.4 and 0.65.
The phase factor variation found earlier is confirmed and the more numerous data now available seem to indicate the presence of three maxima in the phase factor curve. Let us assume that the non-linear phase curve y(G, ) depends on a slope parameter G(P) which is a function of rotational phase P and assume that for all and the difference ) is a monotonous function of . Then all phase factor curves dy/d are similar in the sense that if for a given we have then the same relation should be valid for all values of This means that the phase factor curves should have extrema at the same rotational phases. We note from figs. 3 & 4 that local minima occur at 0.35 and 0.75, maxima at 0.55 and 0.9. The two minima are, however switched, that is primary and secondary are interchanged when compared with Fig. 3 in Kristensen & Gammelgaard (1993). In both y and b minimum occur at phase 0.37 rev and maximum at 0.91. The average value of differs from the constant =0.0909 mag/deg found by the Fourier series in Table 4. The two quantities refer to different averages, one integrates all phase and the other one only a part where the higher values around phase 0 is excluded. © European Southern Observatory (ESO) 1997 Online publication: June 5, 1998 |