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Calibration of the Mass-Luminosity Relation Using Trigonometric Parallaxes. I

Published online by Cambridge University Press:  12 April 2016

William F. Van Altena ,
Terrence M. Girard  and
John T. Lee
William F. Van Altena
Affiliation:
Yale Astronomy Department, P.O. Box 6666, New Haven, CT 06511, USA
Terrence M. Girard
Affiliation:
Yale Astronomy Department, P.O. Box 6666, New Haven, CT 06511, USA
John T. Lee
Affiliation:
Yale Astronomy Department, P.O. Box 6666, New Haven, CT 06511, USA

Abstract

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The calibration of luminosities using trigonometric parallaxes introduces well-known errors that are a function of the ratio of the parallax error to the parallax, when the sample is chosen from stars with measured parallaxes larger than some minimum parallax. In this paper it is shown that similar errors are also introduced into the mass axis of the mass-luminosity relation (MLR) and can result in a biased MLR. The bias is shown to be related to the Lutz-Kelker correction to the absolute magnitude, as extended by Hanson for the case of selection effects in the data sample. The size of the correction in the mass axis is substantial and for the case of a uniform distribution in space, it can amount to a multiplicative factor of 1.17 in the mass for a ten sigma (σ/π = 0.10) parallax and a factor of 1.62 for a five sigma (σ/π = 0.20) parallax.

Type
Classical Methods, Catalogs, & Databases
Information
International Astronomical Union Colloquium , Volume 135: Complementary Approaches to Double and Multiple Star Research , 1992 , pp. 276 - 283
Copyright
Copyright © Astronomical Society of the Pacific 1992

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