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3.2 Method

The traditional path to a Cepheid-based distance to a galaxy has involved the following steps: (1) acquisition of plate material at several epochs; (2) discovery of variables; (3) magnitude estimates; (4) determination of periods; (5) estimation of mean magnitudes and colors on a standard system; (6) correction for absorption and distance estimate (given an absolute calibration).

A common feature of many of the earliest surveys for extragalactic Cepheids was the acquisition of huge numbers of plates. For instance, Hubble (1929) obtained 350 plates of M31 over 18 years - 270 of which were of one field. From this only 40 confirmed Cepheid variables were identified. It is clear that such a large number of plates is not required to extract a reasonable distance estimate to a galaxy, particularly if photometric errors are sufficiently small that variability is obvious from only a few measurements.

The process of blinking plates is extremely tedious and inefficient. The earlier searches made up for inefficiency with plate area, but even with this advantage, sometimes only a handful of Cepheids were identified and characterized. For typical Cepheid lightcurve amplitudes, only about 20% of the variables will be detected by blinking one plate pair under ideal conditions. Hence, large numbers of plate pairs need to be blinked to assure the largest sample of variables. Since modern detectors can obtain photometry of much higher precision, an automated means of selecting variables for further study is obviously desirable.

It is not widely appreciated how difficult it was to obtain accurate photometry of extragalactic Cepheids from photographic plates. The variables were most often superimposed on a nonuniform and crowded background. Furthermore, photoelectrically-calibrated standards were rarely available on the same plate. These problems were dealt with in the most efficient way possible at the time. Typically, plates of a nearby standard field were taken on the same night as the program plates, with identical exposures, and developed at the same time. Then, local standards in the variable fields were established by comparing the stellar images on both plates by eye. This procedure attempted to use the ability of the eye to compensate for the differences in background and crowding, since iris photometry could not be trusted in such situations. A recent example of the use of this technique for M33 is found in Sandage (1983).

Increasing the quality of the photometry dramatically reduces the number of observations required to unambiguously determine the correct period. The large numbers of plates used in early studies were also necessary to combat a combination of poor photometry and aliasing introduced by scheduling. (Even so, 270 plates was a little extreme!) In the best case of ideal scheduling and high S/N photometry only about 8 epochs are required, as demonstrated by Cook et al. (1986). While it might seem that so few epochs might not sample the light curve adequately, this is not true for detected variables. To be discovered, the photometry must have sampled a significant fraction of the light-curve amplitude.

The difficulties in setting up a magnitude system have been mentioned above. While the zero-point and scale of the chosen system are unimportant for establishing a period, they are critical to the distance determination. For CCD detectors used to date, the field of view has usually been too small to contain enough stars free from background and crowding. Hence, one of the major difficulties encountered in establishing local standards has been applying aperture corrections to magnitudes derived from profile-fitting at small radii. For frames of NGC 2403 and M81, Freedman and Madore (1988) estimated the aperture-correction uncertainty as ± 0.07 mag. Fortunately, the recent availability of large format CCD detectors should alleviate this problem considerably.

Once mean magnitudes and colors are in hand, it is necessary to estimate the correction for absorption. With only two colors, it is not possible to estimate the reddening for individual stars and hence the most common expedient has been to adopt a global reddening correction. Properly calibrated CCD photometry permits the mean reddening to be estimated from the upper main sequence, since these stars are the precursors of Cepheids and are found in the same regions. Another approach, described in Freedman (1988b), is to ``slide fit'' the P-L relations for different bandpasses to match the P-L relation for a calibrating object such as the LMC. The trend in zeropoint differences may then be used to estimate the differences in mean absorption between the two objects by fitting a universal extinction curve. Obviously, the onus on the calibration then falls on the LMC where individual corrections for reddening are possible.

The actual distance must be obtained by appealing to a more local calibration. The most trusted existing calibration technique is that obtained from cluster main sequence fitting. The largest part of the systematic error in determining distances to external galaxies still lies in the Galactic calibration. The reasons for this will be discussed in Sec. 3.5.

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