On the Use of Trigonometric Parallaxes for the Calibration of Luminosity Systems: Theory

Abstract

Trumpler and Weaver (1953) discuss a systematic error which they attribute to the process of selecting stars by a lower limit in parallax values. The systematic error is introduced because, on the average, the observed parallaxes are larger than the true parallaxes. We demonstrate that the same type of systematic effect exists for all stars with observed trigonometric parallaxes. The problem is treated analytically and can be put in a dimensiouless form. The size of the systematic error depends only upon the ratio oH0 where 0 is the standard deviation of irO, the observed parallax. Corrections are obtained which are to be applied to absolute magnitudes derived from trigonometric parallaxes. The corrected absolute magnitudes are the proper values to use in luminosity calibrations.