3.6 Future Needs and Directions

There are numerous improvements possible in the detection and use of Cepheid variables that have been made possible by new detectors, fast computing hardware, and reduction software. In this section we will discuss some of the more important developments. Madore and Freedman (1985) were the first to discuss possible procedural changes in the way Cepheids are used to determine distances. They correctly point out that Cepheid periods have traditionally been determined to precisions far greater than required for distance estimation and suggested an expedient technique for estimating periods based on photometry obtained at two phases. Their method attempts to exploit the rate of brightness decline on the descending branch of the lightcurve which is correlated with period. Unfortunately, the first application of this technique by Cook et al. (1986) on Cepheids in M101 was not encouraging (although it should be recognized that this is the most distant object in which a search has yet been attempted).

There are a number of ways in which Cepheid searches can be streamlined and improved. The first involves the acquisition of observations. In more distant galaxies, only the longer period Cepheids are going to be detected. A convenient breakpoint in terms of total numbers and brightness occurs at a period of 10 days. If observations are obtained across three consecutive dark runs (at intervals of two or three days), there will be practically no ambiguity in period for 10-20 and 40 day Cepheids. In Figure 5, the window function for 8 nights of observing spread over three dark runs is shown. Note how little aliasing occurs for periods between 10 and 20 days. (The 30 day alias is difficult to avoid if dark time is required!) Since the frequency distribution of Cepheids is heavily weighted toward shorter periods, the selected dates can be chosen to ensure a high success rate in period determinations. A similar case can be made for more distant galaxies where the less common 40-50 day Cepheids will be the targets of choice.

Figure 5. The power in the ``window function'' for eight nights spread over three consecutive dark runs. The actual sequence of days used was 0, 4, 8, 29, 33, 36, 56, and 63. The power near 30 days is difficult to avoid if the dark time is required!

Period determination has a long and well-documented history. (For a very readable overview, see Fullerton 1986). We offer few new insights here. Suffice it to say that the use of small numbers of observations demands signal-to-noise ratios of at least 10. One bad point can completely skew a period determination. While some discrimination is possible by examination of colors, there is no substitute for good data. The most generally useful and easily implemented algorithm for Cepheid period searches is to search the data phased with a range of trial periods for minimum ``string-length''.

The bandpasses of choice for ground-based observations with CCDs are V and R. The R bandpass occurs near the peak sensitivity of most currently used CCDs. While the V bandpass falls at a slightly less sensitive wavelength than R, most chips have still lower quantum efficiencies at B. Furthermore, Cepheids are typically a half magnitude brighter (or more) at V than B, leading to higher S/N photometry with the same exposure. The amplitude of variation decreases to the red of R, but so does the quantum efficiency of CCDs. A further detriment to photometry at the longest optical wavelengths is night sky emission by OH^- radicals, which is much stronger at I than at R. Since the V - R color still provides good discrimination between types of variable stars, the R bandpass is the better long wavelength choice for CCD detectors.

Cepheid variables are likely to remain the most precise distance indicators in the near-field for a considerable time to come. They are far brighter than RR Lyrae stars and can be detected and characterized in a reasonable number of nights if optimum scheduling is allowed. The greatest distance to which they can be used is determined more by image size (seeing plus optical quality) than by photon statistics, at present (due to crowding). As 8-10-m-class telescopes become available and high-resolution imaging techniques improve we can expect the limit for Cepheid distances to be pushed out at least as far as the spirals in Virgo. In fact, the search for Cepheids in Virgo cluster galaxies has already begun with a study in NGC 4571 by Pierce et al. (1992). Near-infrared space-based (NIC) measurements may well be able to detect the longest-period Cepheids in more distant galaxies.