Distance errors and the stellar luminosity function

Abstract

A study of the stellar luminosity function in the region of the north galactic pole is described. The method is based on photometric parallaxes derived from the V-I colour index. A complete sample of stars is defined with I≤16, V> 13, V-l> 1.5 and within 130 pc of the Sun. JHK photometry is obtained for stars with V-I> 2.9 to check the V-I calibration and exclude contamination by giants. It is demonstrated that application of the classical Malmquist bias derives an incorrect luminosity function. A detailed discussion is given of the effects of Malmquist-type biases on luminosity functions and a method presented which effectively deconvolves the observed luminosity function to determine the intrinsic luminosity function. The method is applied to the data in the north galactic pole sample. The derived main sequence luminosity function is in good agreement with other determinations based on the method of photometric parallaxes, showing a clear peak at Mv~ + 11.5 to +12 and a well-defined decrease thereafter to Mv = + 15. Fainter than Mv, = + 15, the luminosity function is not defined by the present study.