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

Theoretical constraints on the K-band period-luminosity (PLK) relation of R R Lyrae stars are presented, based on updated non-linear convective pulsati on models that are computed for several values of stellar mass, luminosity and metallicity. We show that for each given metal content the predicted PL K is marginally dependent on uncertainties of the stellar mass and/or lumin osity. Then, by considering the RR Lyrae masses suggested by evolutionary c omputations for the various metallicities, we state that the predicted infr ared 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 scat ter sigma (K) = 0.032 mag. Therefore, by allowing the luminosities of RR Ly rae stars to vary within the range covered by current evolutionary predicti ons for metal-deficient (0.0001 < Z < 0.006) horizontal branch models, we e ventually find that the infrared period-luminosity-metallicity (PLZ(K)) rel ation is M-K = 0.139 - 2.071 (log P + 0.30) + 0.167 log Z, with a total int rinsic dispersion of sigma (K) = 0.037 mag. As a consequence, the use of su ch a PLZ(K) relation should constrain the infrared distance modulus of fiel d and cluster RR Lyrae variables within +/-0.04 mag, provided that accurate observations and reliable estimates of the metal content are available. Mo reover, we show that the combination of K and V measurements can supply ind ependent information on the average luminosity of RR Lyrae stars, thus yiel ding tight constraints on the input physics of stellar evolution computatio ns. 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 inst ability strip (Caputo et al. 2000).