Mid-Infrared Period--Luminosity Relations of RR Lyrae Stars Derived from the AllWISE Data Release

Abstract: We use photometry from the recent AllWISE Data Release of the Wide-field In-frared Survey Explorer (WISE) of 129 calibration stars, combined with prior distances obtained from the established $M_V-$[Fe/H] relation and Hubble Space Telescope trigonometric parallax, to derive mid-infrared period--luminosity relations for RR Lyrae pulsating variable stars. We derive relations in the W1, W2, and W3 wavebands (3.4, 4.6, and 12 {\mu}m, respectively), and for each of the two main RR Lyrae sub-types (RRab and RRc). We report an error on the period--luminosity relation slope for RRab stars of 0.2. We also fit posterior distances for the calibration catalog and find a median fractional distance error of 0.8 per cent.