Thomas E. Lutz

ON THE USE OF TRIGONOMETRIC PARALLAXES FOR THE CALIBRATION OF LUMINOSITY SYSTEMS: THEORY

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. Key words: luminosity calibration - systematic errors - trigonometric parallaxes

CALIBRATION OF THE WILSON-BAPPU EFFECT USING TRIGONOMETRIC PARALLAXES

Corrections are applied to the absolute magnitudes of the stars used by Wilson (1967) to account for the systematic error discussed by Lutz and Kelker (1973). Several methods of fifting straight lines to data are applied to this sample in an effort to determine the relation between Mv and log Wo. We conclude that this relation is best represented by the equation Mv = -17.13 log Wo + 30.74. Key words: K line - luminosity calibration - trigonometric parallaxes - fitting straight lines

THE EFFECT OF METAL ABUNDANCE ON K-LINE ABSOLUTE MAGNITUDES

The possible influence of variation in stellar metal abundance on K4ine absolute magnitudes is investigated. Using a small sample, a weak correlation is found between the difference in trigonometric and K-line absolute magnitudes, Mv, and [Fe/H]. However, larger samples, using ultra-violet excesses and CN anomalies, show no correlation. Luminosity-sensitive line ratios show better agreement between trigonometric and K-line absolute magnitudes when an abundance effect is assumed.