Formal aspects of the model calculations

The prime requirement for a good fit is - apart from its astrophysical viability - that the O-C curve, i.e. the difference between the observations and the model light curve, should consist of randomly distributed data. In the lower frames of Figs. 1 and 2 the O-C curves of Models 1.1, 1.2 and 2.1, respectively, are shown.

It is obvious that the O-C curves of Model 1 show considerable structure, indicating a less than ideal model fit. The observed minimum is deeper than the calculated one, yielding positive O-C values. The opposite is true for the maximum; in particular in the case of Model 1.2 which predicts an unobserved shallow secondary minimum. But also at phases intermediate between maximum and minimum correlated residuals are clearly present.

In order to quantify the statistical deviations of the O-C values from a purely random distribution, a formal R-statistics analysis (Bruch [1999]) was undertaken. For Model 1.1, R=0.157 (for 651 data points). The corresponding R-probability (i.e. the statistical probability for completely random data scattered around 0 to have an even smaller value of R, or - somewhat loosely spoken - the probability for correlations to be present in the residuals) is R_R=0.99998. Model 1.2 yields an R-probability even closer to 1. Thus, the formal analysis confirms the visual impression that from a purely statistical point of view Model 1 does not lead to a good fit to the observations.

This is different for Model 2.1. In this case the O-C curve does not show systematic deviations from a random distribution. The R-probability is P_R0.20 which is in excellent agreement with the hypothesis of the absence of correlated residuals. Therefore, statistically, Model 2.1 is completely satisfactory. The same holds true for Model 2.2. The R-probability remains close to P_R=0.20 for 0.19 <= q <= 5.7. Only very close to the borders of this range P_R starts to increase reaching a value of P_R~0.9 at the edges.

These positive results open another way to determine confidence ranges which may be more realistic than the formal errors quoted in Table 4. We modified each parameter (keeping all other parameters fixed) until the R-probability for the residuals reaches P_R=0.90, indicating a significant correlations between the residuals and thus systematic differences between data and fit. The corresponding ``90% confidence ranges'' for the parameters are also quoted in Table 4. In some cases the parameters assumed unphysical values before P_R=0.90 was reached. Then, the physically sensible limit enters the table. This applies in particular to the upper boundary of the Roche-lobe filling factor. Larger values lead to an over-contact configuration (but note that in contrast to Model 1 this is not wholly impossible in the present case because the temperatures of the components are similar!). Although these confidence ranges might be somewhat more realistic than the formal errors they must still be regarded as lower limits because they do not take into account correlations between parameters: The effect of modifying one parameter could be neutralized by corresponding modifications of one or more other parameters, permitting wider parameter ranges.

This last point becomes particularly evident regarding the large range of permitted values for the mass ratio when a contact configuration is adopted. As was argued in Sect. 5.2 not the entire range of statistically acceptable values of q makes sense physically, but only values of q<~1. To be definite, we limit the subsequent discussion to two particular values, namley q=1.0 (Model 2.2.1) and q=0.5 (Model 2.2.2). The corresponding confidence ranges for the free parameters in Model 2.2 are listed in Table 5.

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Table 5: Parameter confidence ranges for Model 2.2

	q=1.0	q=0.5
inclination i	64.8 ... 66.6	66.4 ... 68.1
temperature T2	41800 ... 48900	41040 ... 48350

Finally, we note that the phase shift Delta Phi for both, Model 1 and Model 2, is well compatible with 0 within the confidence or error range. Therefore, there is no need to revise the zero-point of the ephemeris given in Sect. 4. The contribution of third light - 0 for Model 1, and expressed in Table 4 in fractions of the total system brightness at phase 0.25 for Model 2 - is vanishingly small, suggesting that the subtraction of nebular light was even more successful than could be expected. But since there is always the specter of parameter correlations we tried to find solutions with a larger (positive or negative) contribution of third light. However, these attempts did not meet success.