Key points are not available for this paper at this time.
We estimate the initial mass function (IMF) for star formation at the bottom of the mass sequence by measuring the number of low-luminosity companions to white dwarfs. A histogram of the number of companions versus luminosity indicates that the IMF is flat or increasing with decreasing stellar mass down to, at least, 0.1 M⊙. We show that GD 165B has the same proper motion as the white dwarf GD 165A. Thus, the former is the coolest and lowest luminosity dwarf star ever imaged and may be a brown dwarf, although most recent theoretical models would position it as a transition object at the very bottom of the main sequence (M ~ 0.075 M⊙). If our observations and those of Henry & McCarthy of stars near Earth do not suffer from serious selection effects, then the luminosity function of low-mass objects drops precipitously near MK ~ 10. If present theoretical models of low-mass stars are correct, then this drop implies a rapid decline in the IMF at about 0.08 M⊙.
Zuckerman et al. (Sat,) studied this question.