Astrometry with the Hubble Space Telescope: A Parallax of the Fundamental Distance Calibrator RR Lyrae*

We present an absolute parallax and relative proper motion for the fundamental distance scale calibrator � Cep. We obtain these with astrometric data from FGS 3, a white-light interferometer on the Hubble Space Telescope (HST). Utilizing spectrophotometric estimates of the absolute parallaxes of our astrometric reference stars and constrainingCep and reference star HD 213307 to belong to the same association (Cep OB6), we findabs = 3.66 � 0.15 mas. The larger than typical astrometric residuals for the nearby astrome- tric reference star HD 213307 are found to satisfy Keplerian motion with P = 1.07 � 0.02 yr, a perturbation and period that could be due to an F0 V companion � 7 mas distant from and � 4 mag fainter than the pri- mary. Spectral classifications and VRIJHKT2M and DDO51 photometry of the astrometric reference frame surroundingCep indicate that field extinction is high and variable along this line of sight. However the extinction suffered by the reference star nearest (in angular separation and distance) toCep, HD 213307, is lower and nearly the same as forCep. Correcting for color differences, we find hAVi = 0.23 � 0.03 for � Cep and hence an absolute magnitude MV = � 3.47 � 0.10. Adopting an average V magnitude, hVi = 15.03 � 0.03, for Cepheids with log P = 0.73 in the large Magellanic Cloud (LMC) from Udalski et al., we find a V-band distance modulus for the LMC, mM = 18.50 � 0.13, or 18.58 � 0.15, where the lat- ter value results from a highly uncertain metallicity correction. These agree with our previous RR Lyr HST parallax-based determination of the distance modulus of the LMC.