RR Lyrae variables: visual and infrared luminosities, intrinsic colours and kinematics

We use US Naval Observatory CCD Astrograph Catalogue (UCAC4) proper motions and Wide-Field Infrared Survey Explorer (WISE) W1-band apparent magnitudes and intensity means for almost 400 field RR Lyrae variables to determine the parameters of the velocity distribution of the Galactic RR Lyrae population and constrain the zero-points of the metallicity-< M-V >, period-metallicity-< M-Ks >-band and period-metallicity-< M-W1 >-band luminosity relations via statistical parallax. We find the mean velocities of the halo- and thick-disc RR Lyrae populations in the solar neighbourhood to be [U-0(Halo), V-0(Halo), W-0(Halo)] = (-7 +/- 9, -214 +/- 10, -10 +/- 6) km s(-1) and [U-0(Disc), V-0(Disc), W-0(Disc)] = (-13 +/- 7, -37 +/- 6, -17 +/- 4) km s(-1), respectively, while the corresponding components of the velocity-dispersion ellipsoids are [sigma V-R(Halo), sigma V-phi (Halo), sigma V-theta(Halo)] = (153 +/- 9, 101 +/- 6, 96 +/- 5) km s(-1) and [sigma V-R(Disc), sigma V-phi (Disc), sigma V-theta(Disc)] = (46 +/- 7, 37 +/- 5, 27 +/- 4) km s(-1), respectively. The fraction of thick-disc stars is estimated at 0.22 +/- 0.03. The corrected infrared period-metallicity-luminosity relations are < M-Ks > = -0.769 + 0.088[Fe/H] -2.33 log P-F and < M-W1 > = -0.825 + 0.088[Fe/H] -2.33 log P-F and the optical metallicity-luminosity relation [Fe/H]-< M-V > is < M-V > = + 1.094 + 0.232[Fe/H] with a standard error of +/- 0.089, implying a Large Magellanic Cloud distance modulus of 18.32 +/- 0.09, a solar Galactocentric distance of 7.73 +/- 0.36 kpc and M31 and M33 distance moduli of DMM31 = 24.24 +/- 0.09 (D = 705 +/- 30 kpc) and DMM33 = 24.36 +/- 0.09 (D = 745 +/- 31 kpc), respectively. Extra-galactic distances calibrated with our RR Lyrae star luminosity scale imply a Hubble constant of similar to 80 km s(-1) Mpc(-1). Our results suggest marginal prograde rotation for the population of halo RR Lyraes in the Milky Way.