Luminosity functions for K giant stars derived from the two-micron sky survey.

Description of a method for determining either the space density or the luminosity function from star counts covering large areas of sky. Space density is assumed to vary only in the direction perpendicular to the galactic plane. The method extends that derived for use with the star counts in the Selected Areas by allowing for an integration over a wide and continuous range of galactic latitudes, and is therefore applicable to surveys where the number of stars per square degree is small but the area surveyed is an appreciable fraction of the sky. The catalog (IRC) produced from the 2-micron sky survey at Caltech is such a survey. Application of the method to a selection of IRC stars dominated by K giants shows that if these stars obey Oort's determination of their normalized space density perpendicular to the galactic plane than the dispersion of their 2.2-micron luminosity distribution must be large - i.e., on the order of plus or minus 1.0 min within a single spectral subtype. This result is in accord with conclusions recently set forth by Jung (1970).