Mathematics of Statistical Parallax and the Local Distance Scale
Abstract
We present a mathematical analysis of the statistical parallax method. The method yields physical insight into the maximumlikelihood determinations of the luminosity and velocity distribution and enables us to conduct a vigorous Monte Carlo investigation into various systematic effects. We apply our analytic formalism to the RR Lyrae sample of Layden et al. The velocity distribution of RR Lyrae stars is highly nonGaussian, with kurtoses K_\pi = 2.04, K_\theta = 3.22 and K_z = 4.28 in the three principal directions, but this has almost no effect on either the best fit or the uncertainty of the luminosity determination. Indeed, our principal result is that the statistical parallax method is extremely robust in the face of all systematic effects that we considered. Our analysis, applied to the Layden et al. RR Lyrae sample, strictly confirms the majority of their results. The mean RR Lyrae absolute magnitude is M_V = 0.75 +/ 0.13 at the mean metallicity of the sample <[Fe/H]> = 1.61, compared to M_V = 0.71 +/ 0.12 obtained by Layden et al. Most of the difference is due to Malmquist bias which was not considered in previous studies. We also analyze a semiindependent nonkinematically selected sample of stars with metallicities at the [Fe/H] <= 1.5 taken from Layden et al. and Beers & SommerLarsen and obtain M_V = 0.79 +/ 0.12 at <[Fe/H]> = 1.79. Additionally, this analysis yields measurements of the radial bulk motion (4 +/ 10 km/s) and vertical bulk motion (0 +/ 6 km/s) of the halo relative to the Local Standard of Rest.
 Publication:

arXiv eprints
 Pub Date:
 March 1997
 arXiv:
 arXiv:astroph/9703140
 Bibcode:
 1997astro.ph..3140P
 Keywords:

 Astrophysics
 EPrint:
 Analytic results unchanged, minor changes in numerical results, paper restructured, new analysis of nonkinematically selected sample confirms main result, discussion section expanded