1. Introduction and statement of the problem
The (HST) has now begun to provide the long hoped for Cepheid distances to galaxies as remote as 25 Mpc, [ ]. Cepheids have been discovered with HST before repair in IC 4182 and NGC 5253 as the first two galaxies in the calibration program to determine the absolute magnitudes at maximum of type Ia supernovae (Sandage et al. 1992, 1994; Saha et al. 1994, 1995; Sandage & Tammann 1993; Tammann & Sandage 1995). There also have been reports of Cepheid discoveries in M81 (Freedman et al. 1994a), and M101 (Kelson et al. 1996). After repair of the HST, Cepheids have been discovered in M100 (Freedman et al. 1994b, Ferrarese et al. 1996), to be used primarily as a contributor to the recalibration of the Tully-Fisher relation to find its intrinsic dispersion. Large numbers of Cepheids have now also been found in NGC 4536, NGC 4496A, and NGC 4639 (Saha et al. 1996 a, b, 1997; Sandage et al. 1996) as part of an ongoing program of SNe Ia calibration. Furthermore, Cepheids have been found in NGC 3368 (Tanvir et al. 1995), NGC 925 (Silbermann et al. 1996), NGC 3351 (Phelps et al. 1995), and NGC 4414 (Turner et al. 1995) - the latter three as part of the HST Key Project on the Extragalactic Distance Scale.
It is of central importance in all this work to determine the apparent distance modulus of each galaxy in at least two different effective wavelengths so as to estimate the internal reddening, either differential from Cepheid to Cepheid, or general across the Cepheid area. Without such a reddening determination, any individual distance modulus will be in contention, and the primary purposes to which a distance is to be used will be compromised. Hence, Cepheid period-luminosity relations are required in a minimum of two photometric bands, well separated in effective wavelength.
Due to the extreme pressure on HST telescope time, Time Allocation Committees have always taken a minimalist approach in their assignment of the amount of telescope time. The time eventually assigned has always been insufficient to obtain complete Cepheid light curves in two wavelength bands. In view of this, it has become necessary to devise methods to obtain the required mean magnitudes in a particular passband (such as I) from scattered observations in that band when complete light curves, properly phased, exist in some other band such as V.
In our papers on IC 4182, NGC 5253, NGC 4536, NGC 4496A, and NGC 4639 we have used a method devised early in the work on IC 4182 to accomplish this conversion of scattered individual I magnitudes to . We use the phased V light curve as a template, suitably reduced in amplitude to account for the smaller amplitude in I than in V. The purpose of this note is to present the method, to give templates for conversion of scattered data in the B, R, and I band passes to the mean values , , and , and to assess the accuracy of the method.
Our method differs from the solution by Freedman (1988, her Fig. 5) for the same problem. She derived and adopted fixed amplitude ratios for light curves in as 1.00 : 0.67 : 0.44 : 0.34 using the multicolor photometry of Galactic Cepheids given by Wisniewski & Johnson (1968). In her demonstration she used the B light curve as a template by reducing its amplitude by the appropriate amplitude ratio to match the amplitude of the light curve in any other band pass. In doing that, the well known phase shift as a function of wavelength, discovered by Stebbins (1945) from his six color photometry of Delta Cephei, is encountered over part of the light curves, generally on the falling branch. However, the phase shift is not constant over the cycle, often approaching zero on the rising branch.
Freedman adopts average phase lags of 0.03 at V, 0.07 at R, and 0.10 at I relative to B, and applies these average lags to all phases. The precept of her method is that the entire light curve in the fiducial band, after squeezing in amplitude and shifting in phase by the appropriate amount for the bandpass, is a good representation of the unknown light curve at all phases. Freedman states that the resulting mean magnitudes obtained by averaging several individual determinations is accurate to mag.
It is to be emphasized that from a physical point of view Freedman's constant phase shift correction is incorrect. The method would be precise if there was no color change with phase. However, it is known that the photospheric temperature of the Cepheids varies with phase, being hottest near maximum light. Because of the observed color change with phase, a squeezed and shifted template will not fit precisely the light curve in another bandpass, shown first by Stebbins' six-color data for Delta Cephei.
It is this lack of automorphism between the squeezed and shifted curves due to the color variation that prompted us to seek the different solution set out in the next section. The detailed correction table and our adopted template curves to convert B, R, and I magnitudes to , , and are in x 3. Application of the method is in x 4. Comparison of the accuracies of the method presented here with that of Freedman is made in x 5.
© European Southern Observatory (ESO) 1997
Online publication: June 5, 1998