Precise Empirical Determination of Metallicity Dependence of Near-infrared Period-Luminosity Relations for RR Lyrae Variables

RR Lyrae variables are excellent population II distance indicators thanks to their well-defined period-luminosity relations (PLRs) at infrared wavelengths. We present results of near-infrared (NIR) monitoring of Galactic globular clusters to empirically quantify the metallicity dependence of NIR PLRs for RR Lyrae variables. Our sample includes homogeneous, accurate, and precise photometric data for 964 RR Lyrae variables in 11 globular clusters covering a large metallicity range ($Δ\textrm{[Fe/H]}\sim2$~dex). We derive $JHK_s$ band period-luminosity-metallicity (PLZ) and period-Wesenheit-metallicity (PWZ) relations anchored using 346 Milky Way field RR Lyrae stars with {\it Gaia} parallaxes, and simultaneously solved for independent distances to globular clusters. We find a significant metallicity dependence of $\sim0.2$~mag/dex in $JHK_s$ band PLZ and PWZ relations for RR Lyrae stars independent of the adopted metallicity scale. The metallicity coefficients and the zero-points of the empirical PLZ and PWZ relations are in excellent agreement with the predictions from the horizontal branch evolution and pulsation models. Furthermore, RR Lyrae based distances to our sample of globular clusters are also statistically consistent with other independent measurements in the literature. Our recommended empirical $JHK_s$ band PLZ relations are also provided for RR Lyrae based distance measurements.