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 [W1], [W2], and [W3] bands at 3.4, 4.6, and 12 μm, respectively: M_([W1]) = −2.44(±0.95) × log(P) − 1.26(±0.25) σ = 0.10 M_([W2]) = −2.55(±0.89) × log(P) − 1.29(±0.23) σ = 0.10 M_([W3]) = −2.58(±0.97) × log(P) − 1.32(±0.25) σ = 0.10. 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