The first steps of the extragalactic distance ladder

Recent distance determinations by means of the Cepheid period-magnitude relations are based on a true distance modulus of m-M=18.5 to the Large Magellanic Cloud. It has further been assumed that for the LMC Cepheids the average E(B-V)=0.10 and that the ratio of interstellar extinction A(V) in the visual to E(B - V), i.e., R(V), is 3.1. In order to determine the distance to the LMC with its lower than solar metallicity, it is also assumed that the period-magnitude relation is independent of metallicity. Here we reexamine the different assumptions, i.e., the reddening and distance to the LMC and to the Galactic Cepheids. We also study the dependence of the period-magnitude relations for different heavy element abundances. In that process we rediscuss the distances to the LMC, to M31 and the Small Magellanic Cloud. Adopting the theoretical result, that the period-luminosity relation is independent of metallicity, we derive for the V and B bands the dependence of the period-magnitude relations on Z. The use of these relations changes the determination of the interstellar extinction for the three M31 fields, studied by Freedman and Madore, and yields very good agreement for the distance moduli of the three fields; namely m-M=24.59+/-0.02, or (m-M)(M31)-(m-M)(LMC)=6.09+/-0.02, where the error limits refer only to the internal agreement for the three fields. We adopt a foreground reddening of E(B-V)=0.08 for M31 and estimate an average E(B-V)=0.18 for the LMC Cepheids. With a distance modulus to the Pleiades, m-M=5.57, we derive a distance modulus to the LMC of m-M=18.42+/-0.11, and m-M=18.84+/-0.1 for the SMC. These error limits are only estimates. We also point out a way to get a rough estimate about large metallicity differences of Cepheids observed in external galaxies. (C) 1997 American Astronomical Society.