Calibration of Stellar Luminosity Using High-Precision Parallaxes

Utilization of sub-milliarcsecond trigonometric parallaxes shifts the classical problem of calibration of stellar parameters to a new level of complexity. Derivation of stellar luminosity from the parallaxes is not a straightforward task with a number of statistical effects, such as Malmquist bias, to be taken into account. Different methods are to be used in order to derive parameters of luminosity function depending on nature of an underlying stellar sample. It is also demonstrated how biases in luminosity may influence calibration relations between absolute magnitude and other stellar physical parameters, such as metallicity, pulsation period, etc. It is emphasized that any combination of astrometric parameters, mainly parallaxes, and astrophysical ones must be handled carefully to avoid or reduce statistical effect, which otherwise may seriously affect following astrophysical applications.