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3. Brief summary of the observed properties of cepheid variables

At the time of this writing, Cepheids have now been surveyed for and discovered in over two dozen galaxies. Including surveys of the Magellanic Clouds, light curves for approximately 3,000 Cepheids have been obtained. Over 1,100 Cepheids are known in each of the Magellanic Clouds. These numbers are rapidly increasing as additional galaxies are being surveyed with the HST, and as the MACHO survey for microlensing in fields toward the Large Magellanic Cloud (Cook 1996) progresses.

Cepheids are high-luminosity, radially-pulsating, variable stars. Their spectral types range from early F to late K (see Code 1947; Kraft 1960); while their intrinsic brightnesses at visual wavelengths range from -2 > MV > -7 mag making them ideal candidates for distance indicators on Galactic and extragalactic scales. The periods of Population I classical Cepheids range from approximately 2 to over 100 days. Cepheids are characterized by their distinctive light curves having a rapid rise to maximum light, followed by a slower linear decline to minimum light. Due to their variability, they are easily isolated, identified and classified. Below a period of about 9 days (e.g., Bohm-Vitense 1994) Cepheids are observed to pulsate in both the fundamental, in addition to the first harmonic (overtone) mode. But perhaps most importantly for the distance determinations, detailed stellar pulsation models of these objects indicate that we understand the basic physics underlying their luminosities, colors and periods. In this regard, Cepheids appear to stand alone in the extragalactic distance scale; however, we shall argue in this series of lectures that there is a second, fully complementary path using the brightest Population II red giant stars that has similar accuracy and precision to the Population I Cepheid route.

Although Cepheids exhibit strong correlations between their periods, luminosities and colors, the amplitudes of Cepheids do not appear to correlate with other observables. Rather, examples of Cepheids having amplitudes from 0.4 to about 1.5 mag in the V band can be found at almost all periods, with the greatest upper bound on the amplitudes occurring preferentially around 25-30 days (e.g., see Schaltenbrand & Tammann 1970). On the other hand, for an individual Cepheid, the monochromatic amplitude is observed to decrease toward redder wavelengths (see Figures 1 and 2). As a practical matter, the large amplitudes at bluer wavelengths suggest that Cepheid searches should be carried out at shorter wavelengths (Freedman, Grieve &Madore 1985; Madore & Freedman 1991).

Finally, in searching for Cepheid variables, it is useful to know their frequency relative to other types of variables of comparable luminosity. Averaging over the discovery statistics for complete surveys in fields published before the launch of HST, for the SMC, LMC, M31 and NGC 300, Madore & Freedman (1985) found that more than 70% of all variables reported are classical Cepheids, 16% are irregular variables, 5% are Mira-type long-period variables, 7% are eclipsing variables, and the remaining 2% are W Virginis stars.

Figure 1 Figure 1. Variations of amplitude and phase for a typical Galactic Cepheid as a function of increasing wavelength. Note the monotonic drop in amplitude, the progression toward more symmetric light variation, and the phase shift of maximum toward later phases, all with increasing wavelength.

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