In this paper , we extend the calculations conducted previously in the stellar regime ( Chabrier , 2001 ) to determine the brown dwarf initial mass function in the Galactic disk .
We perform Monte Carlo calculations taking into account the brown dwarf formation rate , spatial distribution and binary fraction .
Comparison with existing surveys seems to exclude a power-law mass function as steep as the one determined in the stellar regime below 1 M _ { \odot } , i.e . dn / dm \propto m ^ { -1.5 } , and tends to favor a more flatish behaviour .
Although a power-law mass function in the substellar regime can not be excluded by present day observational constraints , a form dn / dm \propto m ^ { -1 } , i.e . dn / d \log m = constant , seems to be an upper limit .
Comparison with methane-dwarf detections tends to favor an eventually decreasing form like the lognormal or the more general exponential distributions determined in the previous paper .
We calculate predicting brown dwarf counts in near-infrared color diagrams and brown dwarf discovery functions for various types of mass functions and formation rates , and for different binary distributions .
Based on these diagnostics , future large deep field surveys should be able to determine more precisely the brown dwarf mass function and to provide information about the formation of star-like objects - stars and brown dwarfs - along the Galactic history .
These calculations yield the presently most accurate determination of the brown dwarf census in the Galactic disk .
The brown dwarf number density is comparable to the stellar one , n _ { BD } \simeq n _ { \star } \simeq 0.1 pc ^ { -3 } , showing that the star formation process in the disk extends well into the substellar regime .
The corresponding brown dwarf mass density , however , represents only about 10 % of the stellar contribution , i.e . \rho _ { BD } \hbox { \hbox { $ < $ } \kern - 8.0 pt \lower 4.3 pt \hbox { $ \sim$ } } 5.0 \times 10 % ^ { -3 } M _ { \odot } pc ^ { -3 } .
Adding up the local stellar density determined in the previous paper , we obtain the density of star-like objects , stars and brown dwarfs , in the solar neighborhood \rho _ { \odot } \approx 5.0 \times 10 ^ { -2 } M _ { \odot } pc ^ { -3 } .