On the sensitivity of the cepheid period-luminosity relation to variations of 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 combined 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 based on the pulsation equation, P(M, L, T-e, Z, Y), calculated at the points where the tracks of a given mass for each metallicity intersect the instability strip in the H-R diagrams. New model atmospheres and synthetic spectra are computed giving sets of grids of the bolometric corrections and B-V, V-R, R-I, and V-I colors for temperatures 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. Interpolation in the grids at the relevant temperatures, gravities, and metallicities of the Cepheid instability strip give theoretical P-L relations on the Cape Cousins BVI photometric system at the blue and red edges of the strip. The 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 dex(-1) in V, and -0.10 mag dex(-1) in I in the sense that lower metallicities mean brighter magnitudes in B and fainter ones in V and I. Similar dependencies are found at P = 31.6 days. Confirmation that the zero points of the Cepheid P-L relations are not steeper functions of [Fe/H] than the theoretical values derived here is found by comparing the distance moduli of the LMC, the SMC, and IC 1613 based on the P-L relation for Galactic Cepheids ([[Fe/H]] = 0) with the distance moduli determined for these galaxies using RR Lyrae variables with the steep absolute magnitude-metallicity calibration of M,(RR)= 0.30[Fe/H] + 0.94. Applying this bright calibration, based on the Oosterhoff-Arp-Preston (OAP) metallicity 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 Cepheid distance moduli for [Fe/H] = 0 for each galaxy, confirming that no metallicity dependence of the Cepheid P-L relation can be detected at this level 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 gives the distance modulus of the LMC to be (m - M)(0) = 18.57. The modulus for the SMC, corrected for the mild metallicity effect derived here, reconciles the deviant individual B, V, and I moduli to within +/-0.01 mag, giving (m - M)(0) = 18.94 for the SMC.