The RR Lyrae Period-Luminosity Relation. I. Theoretical Calibration

We present a theoretical calibration of the RR Lyrae period-luminosity (PL) relation in the UBVRIJHK Johnsons-Cousins-Glass system. Our theoretical work is based on calculations of synthetic horizontal branches (HBs) for several different metallicities, fully taking into account evolutionary effects besides the effect of chemical composition. Extensive tabulations of our results are provided, including convenient analytical formulae for the calculation of the coefficients of the period-luminosity relation in the different passbands as a function of HB type. We also provide "average" PL relations in IJHK, for applications in cases where the HB type is not known a priori; as well as a new calibration of the M_V - [M/H] relation. These can be summarized as follows: M_I = +0.471 - 1.132 log P + 0.205 log Z, M_J = -0.141 - 1.773 log P + 0.190 log Z, M_H = -0.551 - 2.313 log P + 0.178 log Z, M_K = -0.597 - 2.353 log P + 0.175 log Z, and M_V = +2.288 + 0.882 log Z + 0.108 (log Z)^2.