THE EFFECTS OF UNRESOLVED BINARY STARS ON THE DETERMINATION OF THE STELLAR MASS FUNCTION

We quantify the effect of unresolved binary stars on the stellar luminosity function that results from a given mass function. It is such that previous studies have significantly underestimated the numbers of low-mass stars. If we assume that both component masses of a binary system are chosen independently from the same mass function, unresolved binary systems can account for the difference between the shapes of those luminosity functions deduced from photographic samples and that deduced from nearby stars with trigonometric parallaxes. The best results are obtained if all 'stars' are binary systems with two hydrogen-burning components. A mass function composed of two power-law segments represents a good solution if its index decreases appreciably below about half a solar mass. When extrapolated to zero mass this mass function contributes at most 20 per cent to the Oort limit. The minimum number of binary systems consistent with both luminosity functions lies between 43 and 56 per cent of stellar objects.