THE ASTRONOMICAL JOURNAL    VOLUME 108, NUMBER 1, PAGE 222            JULY 1994

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

                                JAMES M. NEMEC

 Department of Astronomy, University of Washington, Seattle, Washington 98195
and Program in Astronomy, Washington State University, Pullman, Washington 99164
                       Electronic mail: nemec@das.nrc.ca

                            AMANDA F. LINNELL NEMEC

        International Statistics & Research Corporation, Brentwood Bay,
                       British Columbia, Canada V8M 1R3
                   Electronic mail: anemec@galaxy.gov.bc.ca

                                THOMAS E. LUTZ

 Program in Astronomy, Washington State University, Pullman, Washington 99164
                   Electronic mail: tlutz@beta.math.wsu.edu


                                   ABSTRACT
    
    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
    ~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 kind 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 Delta M(K)/Delta log P ~ -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, Delta M(V)/Delta log P = -0.52 +/- 0.11.  A similar
    dependence of slope on passband is seen for classical Cepheids [see
    Madore & Freedman, PASP, 103, 933 (1991)].  The available B,V
    photometry for ~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 often been assumed).  The estimated slopes of the corresponding
    P-L-[Fe/H] relations are Delta M(B)/Delta log P = -1.69 +/- 0.05 and
    Delta M(V)/Delta log 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 <= 8 days) appear to
    be H pulsators, while 15 of the 19 W Cir Cepheids (12 <= P <= 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 Delta
    M(B)/Delta log P = -3.20 +/- 0.18, and Delta M(V)/Delta log P = -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 Delta M(B)/Delta log P =
    -2.66 +/- 0.52 and Delta M(V)/Delta log 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.