A Preliminary Calibration of the Rr Lyrae Period–luminosity Relation at Mid-Infrared Wavelengths: Wise Data

Using time-resolved, mid-infrared data from the Wide-field Infrared Survey Explorer ( WISE ) and geometric parallaxes from the Hubble Space Telescope for four Galactic RR Lyrae variables, we derive the following Population II period–luminosity (PL) relations for the WISE [ W 1], [ W 2], and [ W 3] bands at 3.4, 4.6, and 12 μm, respectively: The slopes and the scatter around the fits are consistent with a smooth extrapolation of those same quantities from previously published K -band observations at 2.2 μm, where the asymptotic (long-wavelength) behavior is consistent with a period–radius relation with a slope of 0.5. No obvious correlation with metallicity (spanning 0.4 dex in [Fe/H]) is found in the residuals of the four calibrating RR Lyrae stars about the mean PL regression line.