The LutzKelker 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 socalled LutzKelker 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 LutzKelker 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 groundbased 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 zeropoint of the periodluminosity 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.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 March 1998
 DOI:
 10.1046/j.13658711.1998.01409.x
 arXiv:
 arXiv:astroph/9801093
 Bibcode:
 1998MNRAS.294L..41O
 Keywords:

 Cepheid Variables;
 Magellanic Clouds;
 Hipparcos Satellite;
 Trigonometric Functions;
 Stellar Parallax;
 Statistical Analysis;
 Bias;
 Stellar Luminosity;
 Astronomy;
 STARS: DISTANCES;
 CEPHEIDS;
 MAGELLANIC CLOUDS;
 Astrophysics
 EPrint:
 MNRAS Letters in press