Statistical Parallaxes and the fundamental distance scale – II. Application of the maximum likelihood technique to RR Lyrae and Cepheid Variables

The statistical parallax technique of Paper I is used to derive an absolute magnitude of <f>\\\,=\\,1.0\±0.25\\,</f> for the set of 59 high <it>S</it> RR Lyrae stars of Clube & Jones. Taken in conjunction with the kinematical properties of RR Lyrae variables and other field stars, this magnitude leads to the following values for the principal galactic constants: <f>${R}₀\\,\\\,7\± 1\\,,\\,A\\,\\\,16\± 3\\,\\,⁻¹\\,⁻¹,B\\,\ -20\± 5\\,\\,⁻¹\\,⁻¹\\,\\,{\θ}₀\\,\\\,250\± 40\\,\\,⁻¹$</f> The technique is also applied to Wielen's set of 45 Cepheids and no correction of the galactic Cepheid distance scale based on cluster members is found to be necessary. These sets of results are consistent if, as has been shown elsewhere, the kinematic model used to analyse the motions of young stars takes account of radial motions in the Galaxy. The distances to the Magellanic Clouds given by RR Lyraes and Cepheids are in conflict however. Although the evidence suggesting a general similarity of halo RR Lyraes in our Galaxy and the Magellanic Clouds is not absolutely conclusive, it is suggested that the conflict may be resolved by use of a colour term in the P–L–C relation for Cepheids which is much less than that adopted by Sandage & Tammann. Our conclusions are in general accord with recent proposals seeking to increase the Hubble constant to around 80 km s–1 Mpc–1