## 5. Comparison with Freedman's solutionEquation (4) differs fundamentally from the Freedman procedure
because all phase shift information is contained in the shape of the
Freedman's solution is where denotes the phase shifted by +0.07. We have made numerical experiments using both Eqs. (4) and (5) to assess the accuracy of each method. We have carried out Eq. (5) on the six Cepheids in Table 1 at each of the 20 phases, separated by 0.05 phase units, so as to construct correction curves as a function of phase for Eq. (5) as we did for Eqs. (1) to (3), shown as Fig. 1. We found that the Freedman squeeze and phase shift method is excellent, except during the phase interval of the rising branch. This was to be expected because of the way the non-isomorphism of the phase shifted curve manifests itself, as explained in x 1. However, the phase interval is small in which the large deviations occur in the Freedman solution. The problem typically is between phase 0.85 to 1.00. The deviations can produce an error as large as 0.3 mag in this phase interval. This part of the light curve must be avoided when using the Freedman method which does not take into account the color variation with phase. On the other hand, our method also has a moderately large scatter
of the individual points in Fig. 1 about the adopted mean
correction curve
To assess the accuracy directly we have selected 8 to 10 random
phases for the four normal Cepheids in Table 1 and have applied
both Eqs. (4) and (5) to the data to determine the individual
values at each phase. The result is shown in
Fig. 2. Plotted is the difference between the real
as known for each Cepheid in Table 1 using
the complete
The conclusion is that both methods are competitive, and that each
is capable of delivering the important data with
as few as four random epochs in © European Southern Observatory (ESO) 1997 Online publication: June 5, 1998 |