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 re lations were derived by fitting regression lines to the observed pulsa tion periods and mean B, V, and K magnitudes of over 1200 stars in app roximately 40 stellar systems. Analysis of covariance methods, which a llow 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-t he 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 w ere tested for departures from equality for all types of stars and pas sbands; the results suggest that the observations are consistent with the assumption that, for each kind of star (except possibly the Pop. I I Cepheids), the P-L-[Fe/H] relations for the F and H pulsation modes are parallel but vertically offset, with a family of lines correspondi ng to a range of metallicities. Pulsation modes and absolute magnitude s 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 L yrae 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 inter mediate slope, DELTAM(V)/DELTAlog P = -0.52 +/- 0.11. A similar depend ence of slope on pass band is seen for classical Cepheids [see Madore & Freedman, PASP, 103, 933 (1991)]. The available B,V photometry for a pproximately 40 of the known globular cluster Cepheids are found to be consistent with Arp's [AJ, 60, 1 (1955)] assumption that Pop. II Ceph eids 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 mod es 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 t he 21 short-period BL Her Cepheids (P less-than-or-equal-to 8 days) ap pear to be H pulsators, while 15 of the 19 W Vir Cepheids (12 less-tha n-or-equal-to P less-than-or-equal-to 30 days) appear to be F pulsator s. The period-amplitude (P-A(B)) diagram suggests that at a given peri od the first-overtone pulsators have larger amplitudes than the fundam ental mode pulsators. For the Anomalous Cepheids the estimated P-L-[Fe /H] relations have slopes DELTAM(B)/DELTAlogP = -3.20 +/- 0.18, and DE LTAM(V)/DELTAlogP = -3.13 +/- 0.28. The offsets between the F and H mo de relations are 0.68 and 0.66 mag in B and V, respectively. The estim ated 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 ma g in B and V, respectively. These relations are consistent with the ob served period ratio for the double-mode star SX Phe. In a period-ampli tude diagram the longest period SX Phe stars have the largest amplitud es, with no dependence on metallicity. The (B - V)0 color range of the SX Phe stars is from 0.12 to 0.29.