Theoretical insights into the RR lyrae K-band period-luminosity relation

Theoretical constraints on the K-band period-luminosity (PLK) relation of RR Lyrae stars are presented, based on updated non-linear convective pulsation models that are computed for several values of stellar mass, luminosity and metallicity. We show that for each given metal content the predicted PLK is marginally dependent on uncertainties of the stellar mass and/or luminosity. Then, by considering the RR Lyrae masses suggested by evolutionary computations for the various metallicities, we state that the predicted infrared magnitude MK over the range 0.0001 < Z < 0.02 is given by the relation M-K = 0.568 - 2.071 log P + 0.087 log Z - 0.778 log L/L-., with a rms scatter sigma (K) = 0.032 mag. Therefore, by allowing the luminosities of RR Lyrae stars to vary within the range covered by current evolutionary predictions for metal-deficient (0.0001 < Z < 0.006) horizontal branch models, we eventually find that the infrared period-luminosity-metallicity (PLZ(K)) relation is M-K = 0.139 - 2.071 (log P + 0.30) + 0.167 log Z, with a total intrinsic dispersion of sigma (K) = 0.037 mag. As a consequence, the use of such a PLZ(K) relation should constrain the infrared distance modulus of field and cluster RR Lyrae variables within +/-0.04 mag, provided that accurate observations and reliable estimates of the metal content are available. Moreover, we show that the combination of K and V measurements can supply independent information on the average luminosity of RR Lyrae stars, thus yielding tight constraints on the input physics of stellar evolution computations. Finally, for globular clusters with a sizable sample of first overtone (RRv) variables, the reddening can be estimated by using the PLZK relation together with the predicted M-v-log P relation at the blue edge of the instability strip (Caputo et al. 2000).