The Inverse Problem of Statistical Determination of the Total Number, Luminosity Function, and Brightness Variability Characteristics of T Tau Type Stars in Stellar Aggregates

Abstract

Based on four observations of a stellar aggregate which are fairly widely separated in time, the possibility of estimating the total number of irregularly variable stars in it is demonstrated. The inverse problem of recovering the luminosity function of the stellar aggregate from the averaged brightnesses of its members is formulated. The problem of finding the brightness distribution function is examined under the assumption that the variabilities of the stars are a stationary random process. Detailed photometric data on the stars in two “pictures” of the aggregate which are fairly widely separated in time are used as initial information.