Annu. Rev. Astron. Astrophys. 1996. 34: 511-550
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2.5. The Field RR Lyraes

Although the Magellanic Clouds are known to be rich in variable stars, the published literature on field RR Lyraes is remarkably sparse. The Harvard Surveys were not deep enough to measure stars as faint as 19th magnitude. While there are 17 bright foreground RR Lyraes in the Hodge & Wright (1967) LMC, and 46 stars with periods less than 1d in the Hodge & Wright (1977) SMC Atlas, most of these are foreground variables or possible bright members of the anomalous Cepheid population in the SMC.

The first major survey for RR Lyrae variables was done by Thackeray and collaborators (see Thackeray & Wesselink 1953), who found cluster variables in NGC 121 in the SMC and in NGC 1466 in the LMC and near NGC 1978 in the LMC. Graham (1975, 1977) initiated the first modern survey in the regions surrounding NGC 1783 in the LMC and NGC 121 in the SMC. Kinman et al (1991) summarize the major studies of field RR Lyraes in the LMC. As of 1991, there were 122 field RR Lyraes known, almost all in the two fields surrounding NGC 1783 and NGC 2210 in the inner regions of the LMC. In total, 4.3 square degrees have been thoroughly searched in the LMC, with most of this area in regions more than 5 kpc from the center of the LMC where the variable density is low. Kinman et al (1991) have fit a King model to the density distribution in the six LMC fields, and they estimate that the total number of LMC field RR Lyraes is ~ 10,000.

The MACHO group (Alcock et al 1993) is monitoring 41 square degrees of the LMC and 15 square degrees of the SMC for microlensing by objects in the halo of the Milky Way. A by-product of this survey is an extensive catalog of RR Lyrae variables in the areas surveyed. This catalog is probably complete except near the cores of the larger clusters. Alcock et al (1996) have published an initial review of their LMC RR Lyrae catalog, where they announce the discovery of 7902 LMC RR Lyraes in the innermost, densest regions (11 square degrees), based on light curve data with 250 individual observations per star over a 400-day observing cycle. Some basic properties of the LMC RR Lyrae population from this first reconnaissance of the data are: 1. The surface density of RR Lyraes in the central LMC regions is a factor of two higher than the Kinman et al (1991) estimate; 2. the mean period of the RRab variables is 0.583 days; 3. the mean metallicity based on the period-amplitude relationship and spectral observations is [Fe/H] = -1.7; 4. the period-amplitude relation for 500 randomly chosen LMC RR Lyraes is skewed to amplitudes lower than 1 magnitude, unlike the case for Milky Way RR Lyraes; and 5. about 1% of the variables may be second-overtone pulsators with < P > = 0.281d.

The Alcock et al results on the mean metallicities of the RR Lyraes are similar to previous metallicity measurments for field variables. Using image tube spectra, Butler et al (1982) derived [Fe/H] = -1.4. Hazen & Nemec (1992), Walker (1989a), from the period-amplitude relation for the RR Lyraes in the clusters NGC 1783, NGC 2210, and NGC 2257 and their surrounding fields, measured mean abundances of [Fe/H] = -1.3, -1.8, and -1.8, respectively. The mean cluster RR Lyrae abundance from Table 1 (weighted by number of variables) is [Fe/H] = -1.8.

Both the Butler et al and Alcock et al metallicity studies are based on spectral data of rather poor quality by modern standards. With so many RR Lyraes with accurate periods and phases cataloged from the MACHO study, now is the time to consider a major new effort to study the abundance (and velocity) distribution of the RR Lyraes in the LMC, before the phase predictions are compromised by intrinsic period changes and period errors in the catalog.

Alcock et al (1996) provide some interpretation for the mean characteristics of the field RR Lyrae population. They argue that the excess of small-amplitude fundamental pulsators (RRb-type variables), the mean period of the RRab variables, and the "transition period" between the fundamental (RRab) and first overtone (RRc) pulsators imply that the HB stars are evolving from the red of the instability strip blueward. An underlying red horizontal branch in such a metal-poor population of variables may indicate that this population is not ancient but somewhat younger, something we have already seen in the HB characteristics of the LMC clusters. We note, however, that trends seen in mean properties of RR Lyraes in Galactic globular clusters are based on stars in a given cluster where all objects have the same age and metallicity. Interpreting the same mean properties in a population that almost certainly has a wide range in metallicity and possibly in age is problematical.

In the SMC, there have been two major surveys. Graham (1975) discovered 75 RR Lyrae stars in 1.3 square degrees surrounding NGC 121, and Smith et al (1992) surveyed 1.3 square degrees surrounding NGC 361, finding 22 definite and 20 probable RR Lyraes. The metallicity of the RR Lyraes is [Fe/H] = -1.6 from the period-amplitude relationship given by Smith et al and -1.8 from the spectra of three field stars (Butler et al 1982). Both estimates are quite uncertain.

Little work has been done on the kinematics of the RR Lyrae populations. The only quoted attempt to measure the velocity dispersion of the LMC RR Lyraes was made by Freeman a decade ago (Freeman 1996), who derived a dispersion of ~ 50 km s-1. This result, if confirmed by modern data, is quite remarkable because, although it corresponds to the expected dispersion of a kinematical halo, it also disagrees with the LMC old cluster kinematics as discussed above. It should be noted that because RR Lyraes can have velocity amplitudes well in excess of 50 km s-1, it is very important to have good phases in order to determine accurate corrections to the gamma velocities.

With accurate photometry, the mean magnitudes of the RR Lyraes can be used to derive the distance, tilt, and reddening of the LMC; to measure the relative distances between the Clouds; and to check the consistency of the RR Lyrae and the Cepheid distance scales. To date, however, there are only a few fields with relatively high-quality (error in magnitude < 0.05 mag) photometric zero points. In the LMC, three fields have adequate photometry: the NGC 2210 field (Hazen & Nemec 1992), the NGC 1466 field (Kinman et al 1991), and the NGC 2257 field (Walker 1989a). The mean B magnitudes, corrected for the presumed reddening, are 19.56, 19.55, and 19.29, respectively. In the SMC, the mean B magnitude for the NGC 121 field is 19.95, and for NGC 361 it is 19.91. Evidently the difference in mean RR Lyrae magnitude between the Clouds is ~ 0.45 (if we ignore the small difference in mean reddening to the Clouds), but accurate photometry in more fields across both Clouds are needed to reduce the uncertainty in this result to below 0.1 magnitudes. A final complication is that parts of the SMC are very extended along the line of sight (Mathewson et al 1986). Some of the fields discussed in Kinman et al (1991) have reasonably accurate relative photometry but need modern zero points.

In principle, the spread in magnitudes in a given field can be used to derive the line-of-sight depth in the galaxy, but two effects limit the usefulness of this statistic. The first effect is that Galactic globular clusters apparently have a natural dispersion in RR Lyrae luminosities, presumably due to evolution from the zero-age HB. For instance, 33 variables in M15 (Bingham et al 1984) give a dispersion of 0.15 mag, and 35 variables in M3 (Sandage 1981) give 0.07 mag, implying a natural dispersion in magnitude of about 0.1. The second effect is that, in a population with a range in abundances, there should be a natural range in luminosities due to the variation of MV as a function of [Fe/H]. Although the precise level of this variation is controversial, it is roughly 0.2-0.3 mag per dex in [Fe/H] (Sandage & Cacciari 1990).

Do we resolve the depth in either of the Clouds? In the SMC, 34 RR Lyraes near NGC 121 (Graham 1975) have a dispersion of 0.12 mag in B, whereas near NGC 361, the data in Smith et al (1992) imply a dispersion of 0.19 mag for 17 stars with periods greater than 0.4 days. We may be marginally resolving a real depth in the SMC near NGC 361, but it is surprising that the dispersion is not much larger since NGC 361 lies close to the central body of the SMC where the Cepheid studies imply a line-of-sight depth of 15 to 20 kpc (Mathewson et al 1986, Caldwell & Coulson 1986). In the LMC we find the following dispersions: 0.16 mag for 55 stars in the NGC 1783 field (Graham 1977), 0.16 mag for 28 stars with periods longer than 0.4d in the NGC 2210 field (Hazen & Nemec 1992), and 0.17 mag for 13 RRab variables near NGC 2257 (Nemec et al 1985, new zero points in Walker 1989a). Little can be said about the LMC depth with these data.

The distances to the Magellanic Clouds, the absolute magnitudes of the Population I Cepheid variables and the Population II RR Lyrae stars, the [Fe/H]-absolute magnitude relation for RR Lyrae stars, the ages of globular clusters, and the value of the Hubble Constant are all interrelated. It is beyond the scope of this review for us to try to provide best values for each of these parameters. We can, however, recapitulate the problems that occur when certain values are adopted. These problems will show that substantial fundamental work is still needed before local distance calibrators are on a firm footing.

If we assume that the LMC distance modulus (m-M)0 = 18.55, based on the Cepheid distance scale (Feast and Walker 1987, Walker 1992c), the absolute magnitude of LMC and of SMC RR Lyraes follows. For the LMC field variables near NGC 2210, NGC 2257, and NGC 1866, we calculate the dereddened mean V to be < V > = 19.0 (Walker 1989a, 1995, Hazen & Nemec 1992 with a transformation from B to V). The resultant absolute magnitude of MV = 0.45 is identical to that found for the LMC cluster RR Lyraes (see Walker 1992c, 1993a).

The results for the SMC seem to be in mild discord with the LMC result. If we use the mean B magnitudes for the NGC 121 and NGC 361 fields given above, along with the mean B magnitude of 19.91 for the four variables in NGC 121 (Walker & Mack 1988), and deredden the NGC 361 field by E(B-V) = 0.06 (Smith et al 1992), and the NGC 121 field by 0.04, we find < B > = 19.75. With an SMC Cepheid distance modulus of 18.8 (Feast and Walker 1987) and a B-V of 0.3 for the typical RR Lyrae, we derive an absolute V magnitude of ~ 0.65 for the SMC RR Lyraes. The NGC 121 field, at least, is in the portion of the SMC that has a small line-of-sight depth. Although no evidence for the depth of the SMC is seen in these small RR Lyrae samples, it is clear that the sample should be enlarged.

An interesting test of the relative photometry of the Cepheids and the RR Lyraes is to measure relative magnitudes of these types of stars in the same fields. One possible field is near the young, Cepheid-rich cluster NGC 1866, where Welch and Stetson (1993), Walker (1995) have discovered a total of four field RR Lyraes.

Are the absolute V magnitudes of 0.45 or of 0.65 the expected values for metal-poor RR Lyraes? A number of authors have attempted to derive the metallicity-absolute magnitude relation for RR Lyraes. If we use the average relation given in Sandage and Cacciari (1990), and the relations of Carney et al (1992), and Layden et al (1996), we find MV = 0.7 at [Fe/H] = -1.7. The LMC RR Lyraes would be brighter than this relation by 0.25 magnitudes, while the SMC RR Lyraes would be consistent with this Galactic calibration. Sandage (1993) has argued for a steeper slope in the relation, which makes the LMC RR Lyraes consistent with his calibration, and the SMC RR Lyraes inconsistent. Careful calibration of extant large samples of RR Lyraes in both Clouds is clearly of paramount importance, as is the discovery and photometry of metal-rich Magellanic Cloud RR Lyraes discussed above. We do note that an absolute magnitude of 0.45 for Galactic RR Lyraes does affect the calibration of globular cluster ages (Walker 1992c), and the value of the Hubble constant (van den Bergh 1996).

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