The Luminosity and Mass Functions at the Bottom of the Main Sequence.

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We present infrared K-band photometry of complete samples of VLM candidates constructed from IIIaF and IVN plates in ten fields (270 degrees(2) ) taken as part of the POSSII and UKSRC surveys. Using the I--K colours so meaured and recent improvements in the main sequence bolometric corrections and colour-magnitude relations for these stars, we estimate a bolometric luminosity function which extends to MBol = 13.75. Combining this data with a photographic luminosity function for more luminous stars, we find significant evidence for a luminosity function decreasing towards these luminosities. We also find that our data are consistent with the results of studies based on the Nearby Star sample, when those data are presented as a bolometric luminosity function. We convert our observed LF into the form of a mass function, which extends with reasonable statistics to 0.08M\solar\ -- the H-burning minimum mass. We find significant evidence for features in the mass function at these masses. Specifically, the mass function `turns over' at ~ 0.25M\solar, goes through a local minimum at ~ 0.15M\solar, and seems to increase again below 0.1M\solar\ -- none of these features are predicted by any of the current theories of star formation. Lastly, the mass density we observe just above the H-burning minimum mass makes it difficult to envisage brown dwarfs contributing significant quantities of missing mass without invoking either a mass function in this region significantly steeper than that seen for main sequence stars, or an extremely low cut-off mass to the mass function.

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