The Lutz-Kelker bias in trigonometric parallaxes

Abstract

The theoretical prediction that trigonometric parallaxes suffer from a statistical effect has become topical again now that the results of the Hipparcos satellite have become available. This statistical effect, the so-called Lutz-Kelker bias, causes observed parallaxes to be too large. This has the implication that inferred distances, and hence inferred luminosities are too small. Published analytic calculations of the Lutz-Kelker bias indicate that the inferred luminosity of an object is, on average, 30 per cent too small when the error in the parallax is only 17.5 per cent. Yet, this bias has never been determined empirically. In this paper we investigate whether there is such a bias by comparing ground-based measurements with the best Hipparcos parallaxes. We find that there is indeed a large bias with an average and scatter comparable to predictions. We propose a simple method to correct for the LK bias, and apply it successfully to a subsample of our stars. We then analyse the sample of the 26 `best' Cepheids used by Feast & Catchpole to derive the zero-point of the period-luminosity relation. The final result is based on the 20 fundamental mode pulsators and leads to a distance modulus to the Large Magellanic Cloud - based on Cepheid parallaxes - of 18.56+/-0.08, consistent with previous estimates.