On the sensitivity of the cepheid period-luminosity relation to variationsof metallicity

Predictions are made of the effect of variations in the [Fe/H] metallicity on the zero point of the Cepheid period-luminosity relation in bolometric, B, V, and I magnitudes. Theoretical evolutionary tracks in the H-R diagram, computed by three independent groups at Geneva, Padua, and Basel, are comb ined with the positions of the blue and red edges of the instability strip in the relevant H-R diagrams to give the predicted P-L relations for [Fe/H] metallicities of 0.0, -0.4, -0.7, -1.3, and -1.7. The predictions are base d on the pulsation equation, P(M, L, T-e, Z, Y), calculated at the points w here the tracks of a given mass for each metallicity intersect the instabil ity strip in the H-R diagrams. New model atmospheres and synthetic spectra are computed giving sets of gri ds of the bolometric corrections and B-V, V-R, R-I, and V-I colors for temp eratures between 7500 and 5000 It, gravities between log g = 3.0 and log g = 0.75, and metallicities between [Fe/H] = 0.0 and [Fe/H] = -1.7. Interpola tion in the grids at the relevant temperatures, gravities, and metallicitie s of the Cepheid instability strip give theoretical P-L relations on the Ca pe Cousins BVI photometric system at the blue and red edges of the strip. T he metallicity dependence of the P-L relations, read at P = 10 days, are dM /d[Fe/H] = 0.00 mag dex(-1) in M(bol), +0.03 mag dex(-1) in B, -0.08 mag de x(-1) in V, and -0.10 mag dex(-1) in I in the sense that lower metallicitie s mean brighter magnitudes in B and fainter ones in V and I. Similar depend encies are found at P = 31.6 days. Confirmation that the zero points of the Cepheid P-L relations are not stee per functions of [Fe/H] than the theoretical values derived here is found b y comparing the distance moduli of the LMC, the SMC, and IC 1613 based on t he P-L relation for Galactic Cepheids ([[Fe/H]] = 0) with the distance modu li determined for these galaxies using RR Lyrae variables with the steep ab solute magnitude-metallicity calibration of M,(RR)= 0.30[Fe/H] + 0.94. Appl ying this bright calibration, based on the Oosterhoff-Arp-Preston (OAP) met allicity effect, to the RR Lyrae variables in the LMC, the SMC, and IC 1613 gives individual distance moduli that agree to within 0.10 mag with the Ce pheid distance moduli for [Fe/H] = 0 for each galaxy, confirming that no me tallicity dependence of the Cepheid P-L relation can be detected at this le vel with the present observational data if the bright RR Lyrae hi ([Fe/H]) calibration is used. Using the stated calibrations with the Cepheid data from the literature giv es the distance modulus of the LMC to be (m - M)(0) = 18.57. The modulus fo r the SMC, corrected for the mild metallicity effect derived here, reconcil es the deviant individual B, V, and I moduli to within +/-0.01 mag, giving (m - M)(0) = 18.94 for the SMC.