Abstract
AbstractThe 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.
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