The abundance of brown dwarfs

The amount of mass contained in low-mass objects is investigated anew. Instead of using a mass–luminosity relation to convert a luminosity function to a mass function, I predict the mass-luminosity relation from assumed mass functions and the luminosity functions of Jahreiss &Wielen (1997) and Gould, Bahcall & Flynn (1997). Comparison of the resulting mass–luminosity relations with data for binary stars constrains the permissible mass functions. If the mass function is assumed to be a power law, the best fitting slope lies either side of the critical slope, α = −2, below which the mass in low-mass objects is divergent, depending on the luminosity function adopted. If these power-law mass functions are truncated at 0.001M⊙, the contribution to the local density from stars lies between 0.016 and 0.039M⊙ pc , in conformity with the mass density that has been inferred dynamically from stars in the Hipparcos Catalogue. If the mass function is generalized from a power law to a low-order polynomial in log(M), the mass in stars with M < 0.1M⊙ is either negligible or strongly divergent, depending on the order of the polynomial adopted.