PERIOD LUMINOSITY METALLICITY RELATIONS, PULSATION MODES, ABSOLUTE MAGNITUDES, AND DISTANCES FOR POPULATION-II VARIABLE-STARS

Period-luminosity-metallicity (P-L-[Fe/H]) relations are presented for RR Lyrae stars, Pop. II Cepheids, anomalous Cepheids and SX Phe stars pulsating in the fundamental (F) and first-overtone (H) modes. The relations were derived by fitting regression lines to the observed pulsation periods and mean B, V, and K magnitudes of over 1200 stars in approximately 40 stellar systems. Analysis of covariance methods, which allow the simultaneous computation of more than one P-L-[Fe/H] relation, were used to estimate the slopes and intercepts. Of the 24 possible P-L-[Fe/H] relations for the four kinds of stars, two pulsation modes, and three passbands considered here, 18 relations have been derived-the others could not be derived because of a lack of photometry in one or more of the three passbands. The slopes for the F and H pulsators were tested for departures from equality for all types of stars and passbands; the results suggest that the observations are consistent with the assumption that, for each kind of star (except possibly the Pop. II Cepheids), the P-L-[Fe/H] relations for the F and H pulsation modes are parallel but vertically offset, with a family of lines corresponding to a range of metallicities. Pulsation modes and absolute magnitudes are presented for the non-RR Lyrae variable stars considered in the analysis, and distances are estimated for the program clusters. It is well established from previous studies that the P-L relations for RR Lyrae stars are approximately flat for the B passband, and have a Slope DELTAM(K)/DELTAlogP approximately -2.4 for the K passband. We recover these slopes, and find that the P-L-[Fe/H] relation in V has an intermediate slope, DELTAM(V)/DELTAlog P = -0.52 +/- 0.11. A similar dependence of slope on pass band is seen for classical Cepheids [see Madore & Freedman, PASP, 103, 933 (1991)]. The available B,V photometry for approximately 40 of the known globular cluster Cepheids are found to be consistent with Arp's [AJ, 60, 1 (1955)] assumption that Pop. II Cepheids pulsate in the F and H modes (and not in the F mode only, as has been often assumed). The estimated slopes of the corresponding P-L-[Fe/H] relations are DELTAM(B)/DELTAlog P = -1.69 +/- 0.05 and DELTAM(V)/DELTAlog P = -1.93 +/- 0.05, with a separation between the F and H modes of 0.59 mag in B, and 0.45 mag in V. As in the case of the RR Lyrae stars the redder passband has the steeper slope. We find that 15 of the 21 short-period BL Her Cepheids (P less-than-or-equal-to 8 days) appear to be H pulsators, while 15 of the 19 W Vir Cepheids (12 less-than-or-equal-to P less-than-or-equal-to 30 days) appear to be F pulsators. The period-amplitude (P-A(B)) diagram suggests that at a given period the first-overtone pulsators have larger amplitudes than the fundamental mode pulsators. For the Anomalous Cepheids the estimated P-L-[Fe/H] relations have slopes DELTAM(B)/DELTAlogP = -3.20 +/- 0.18, and DELTAM(V)/DELTAlogP = -3.13 +/- 0.28. The offsets between the F and H mode relations are 0.68 and 0.66 mag in B and V, respectively. The estimated P-L-[Fe/H] relations in B and V for the SX Phe stars have slopes DELTAM(B)/DELTAlog P = -2.66 +/- 0.52 and DELTAM(V)/DELTAlog P = -2.56 +/- 0.54, and the F and H relations are separated by 0.34 and 0.29 mag in B and V, respectively. These relations are consistent with the observed period ratio for the double-mode star SX Phe. In a period-amplitude diagram the longest period SX Phe stars have the largest amplitudes, with no dependence on metallicity. The (B - V)0 color range of the SX Phe stars is from 0.12 to 0.29.