The Lutz-Kelker Paradox

Abstract

The Lutz-Kelker correction is intended to give an unbiased estimate for stellar parallaxes and magnitudes, but it is shown explicitly that it does not. This paradox results from the application of an argument about sample statistics to the treatment of individual stars, and involves the erroneous use of a frequency distribution in the manner of a probability density function considered as a Bayesian prior. It is shown that the Bayesian probability distribution for true parallax given the observed parallax of a selected star is independent of the distribution of other stars. Consequently the Lutz-Kelker correction should not be used for individual stars. This result has important implications for the RR Lyrae scale and for the interpretation of results from Gaia and Hipparcos. The Lutz-Kelker correction is a poor treatment of the Trumpler-Weaver bias which affects parallax limited samples. A true correction is calculated using numerical integration and confirmed by a Monte Carlo method.

To be printed in MNRAS, 5 pages, 2 figs, minor corrections

References in corpus (8)

• Astrometry with Hubble Space Telescope: A Parallax of the Fundamental Distance Calibrator delta Cephei
• Astrometry with Hubble Space Telescope: A Parallax of the Fundamental Distance Calibrator RR Lyrae
• Distance Scale Zero-Points from Galactic RR Lyrae Star Parallaxes
• The red clump absolute magnitude based on revised Hipparcos parallaxes
• Two estimates of the distance to the Galactic centre
• Bias in Absolute Magnitude Determination from Parallaxes
• Bias Properties of Extragalactic Distance Indicators.XI. Methods to Correct for Observational Selection Bias for RR Lyrae Absolute Magnitudes from Trigonometric Parallaxes Expected from the FAME Astrometric Satellite
• Calibration of RAVE distances to a large sample of Hipparcos stars

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