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Astron. Astrophys. 322, 751-755 (1997)

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3. Determination of the correction functions

A sample of Cepheids was selected from the atlas of classical Galactic Cepheids published by Wisniewski & Johnson (1968 ), representing a range in periods, amplitudes and shapes of light curves. The figures of the atlas are shown relative to an arbitrary zero point in magnitude. The mean smooth curves drawn through the BVRI data points of the Cepheids of Table 1 were read off in steps of 0.05 phase units. These measurements provided a reliable estimate of the intensity means expressed in magnitudes. The V amplitude and the phase at [FORMULA] were also read from the plot. To align the V light curves of the chosen Cepheids in phase, each set of readings m([FORMULA]) of the same variable was shifted by the amount [FORMULA] ([FORMULA]). Correction values [FORMULA] were calculated for the transfers [FORMULA], [FORMULA] and [FORMULA] according to Eqs. (1) to (3).


Table 1. Characteristics of the Cepheid sample

The result is illustrated in Fig. 1 and corresponds very well with the expected pattern. The four Cepheids with normal light curves closely follow a mean relation the scatter of which is getting smaller from B to I. Some of the data points obtained from [FORMULA] Gem deviate significantly from the average because of the highly symmetrical light curves of that star. The effect is most pronounced in the phase interval 0.6 [FORMULA] 0.8. The secondary hump in the light curve of W Gem shows up prominently in the range 0.2 [FORMULA] 0.3. As the majority of Cepheid light curves are asymmetric (e.g., Schaltenbrand & Tammann 1971 ; Moffett & Barnes 1985 ) with only minor secondary humps, the adopted correction function (broken line in Fig. 1) disregards the irregular deviations from the mean relation. Table 2 lists values of the adopted correction functions [FORMULA], [FORMULA], and [FORMULA]. From these one can reconstruct the individual functions by interpolation. Quantitatively the term [FORMULA] [FORMULA] can be as large as [FORMULA] 0.25 mag for a Cepheid with an amplitude of 1.0 mag.

[FIGURE] Fig. 1. The correction function for B (panel a), R (b) and I (c) as a function of phase. Different symbols are used to distinguish between the Cepheids: SU Cyg (squares), [FORMULA] Cep (stars), W Gem (diagonal crosses), [FORMULA] Gem (crosses), Y Oph (circles), T Mon (triangles). The mean relation does not take into account the outlying points due to W Gem (secondary bump on the visual light curve) and [FORMULA] Gem (highly symmetric light curve).


Table 2. Adopted correction values for B, R, and I as a function of phase

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998