Mid-infrared Period-Luminosity Relations of RR Lyrae Stars Derived from
  the WISE Preliminary Data Release
  Interstellar dust presents a significant challenge to extending
parallax-determined distances of optically observed pulsational variables to
larger volumes. Distance ladder work at mid-infrared wavebands, where dust
effects are negligible and metallicity correlations are minimized, have been
largely focused on few-epoch Cepheid studies. Here we present the first
determination of mid-infrared period-luminosity (PL) relations of RR Lyrae
stars from phase-resolved imaging using the preliminary data release of the
Wide-Field Infrared Survey Explorer (WISE). We present a novel statistical
framework to predict posterior distances of 76 well-observed RR Lyrae that uses
the optically constructed prior distance moduli while simultaneously imposing a
power-law PL relation to WISE-determined mean magnitudes. We find that the
absolute magnitude in the bluest WISE filter is M_W1 = (-0.421+-0.014) -
(1.681+-0.147)*log(P/0.50118 day), with no evidence for a correlation with
metallicity. Combining the results from the three bluest WISE filters, we find
that a typical star in our sample has a distance measurement uncertainty of
0.97% (statistical) plus 1.17% (systematic). We do not fundamentalize the
periods of RRc stars to improve their fit to the relations. Taking the
Hipparcos-derived mean V-band magnitudes, we use the distance posteriors to
determine a new optical metallicity-luminosity relation which we present in
Section 5. The results of this analysis will soon be tested by HST parallax
measurements and, eventually, with the Gaia astrometric mission.
