The abundance of brown dwarfs |
| |
| Authors: | James Binney |
| |
| Institution: | Theoretical Physics, University of Oxford, Oxford, OX1 3NP |
| |
| Abstract: | 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 and Gould, Bahcall & Flynn. 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 0.001 M⊙, the contribution to the local density from stars lies between 0.013 and 0.10 M⊙ pc?3 depending on the mass at which the mass function is normalized and the adopted value of α . Recent dynamical estimates of the local mass density rule out stellar mass densities above ～0.05 M⊙ pc?3. Hence, power laws steeper than α =?2 that extend down to 0.001 M⊙ are allowed only if one adopts an implausible normalization of the mass function. If the mass function is generalized from a power law to a low-order polynomial in log( M ), the mass in stars with M <0.1 M⊙ is either negligible or strongly divergent, depending on the order of the polynomial adopted. |
| |
| Keywords: | stars: luminosity function mass function |
|
|
