Systematics of RR Lyrae statistical parallax. III. Apparent magnitudes and extinctions

We sing the praises of the central limit theorem. Having previously removed all other possible causes of significant systematic error in the statistical-parallax determination of RR Lyrae absolute magnitudes, we investigate systematic errors from two final sources of input data: apparent magnitudes and extinctions. We find corrections due to each of about 0.05 mag, i.e., about half the statistical error. However, these are of opposite sign and so approximately cancel out. The apparent-magnitude system that we previously adopted from Layden et al. was calibrated to the photoelectric photometry of Clube & Dawe. Using Hipparcos photometry and archival modern ground-based photometry, we show that the Clube & Dawe system is about 0.06 mag too bright. Extinctions were previously based on the map of Burstein & Heiles, which was constructed from H I maps. We argue that extinctions should rather be estimated using the new map of Schlegel, Finkbeiner, & Davis based on COBE and IRAS measurements of dust emission. This substitution increases the mean estimated extinction by about 0.05 mag, primarily because of a difference in the zero point of the two maps. Our final estimate for the absolute magnitude is M-V = 0.77 +/- 0.13 at [Fe/H] = -1.60 for a pure sample of 147 halo RR Lyrae stars, or M-V = 0.80 +/- 0.11 at [Fe/H] = -1.71 if we incorporate kinematic information from 716 nonkinematically selected non-RR Lyrae stars from Beers gr Sommer-Larsen. These are 2 and 3 sigma fainter than recent determinations of M-V based on main-sequence fitting of clusters using Hipparcos measurements of subdwarfs by Reid and Gratton et al. Since statistical parallax is being cleared of systematic errors and since the probability of a more than 2 sigma statistical fluctuation is less than 1/20, we conclude that these brighter determinations may be in error. In the course of these three papers, we have corrected six systematic errors whose absolute values total 0.20 mag. Had these, contrary to the expectation of the central limit theorem, all lined up one way, they could have resolved the conflict in favor of the brighter determinations. In fact, the net change was only 0.06 mag.