M

where the weights Wm are functions of em.

If the light curve analysis provides p with standard error e < em without considering p^, the values pm will have little effect as their weights are small and they are typically not numerous. In the opposite case, e > em, they may have a strong effect. Part of the reason, in this case with large e, is that the standard errors of other light curve parameters could also be large due to correlations. In this case, use of the external estimations pmo and their standard errors, em, has a correlation-reducing influence on the overall light curve solution. As an example of a parameter-observable relation, we consider the mass ratio, q, in a detached binary. For detached binaries, q is strongly correlated with the Roche potentials. In this case, all is fine if the radial velocity curves are made part of a simultaneous least-squares analysis. However, in many publications, q is just fixed to a value q+ found in other publications. By contrast, exploitation of the parameter-observable relation and (5.1.8), the published q+ value and its standard error em+ are consistently embedded into the analysis.

Another interesting case has not yet been considered in light curve analysis. In Sect. 5.2.2 we discuss whole-curve fitting as an alternative to traditional times-of-minima analysis for deriving an EB ephemeris. With introduction of the observable Tm and its parameter counterpart T£, the observed times of minima, T^, could be made an integral part of the analysis with Tbeing a function of the ephemeris parameters T0 (time of conjunction), P0 (period at reference epoch), dP/dt (period time derivative), and in principle the other orbital parameters.

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