| Summary: | Anyone seeking to understand the physical processes of star formation must make reference to the spectrum of masses (mass function) produced by such processes. The low mass end of this mass function in particular is poorly constrained. The two leading environments in which to measure the mass function are in open clusters and star forming regions and in the solar neighbourhood. Studies of some star forming regions claim to constrain the mass function down to a few tens of Jupiter masses. However the validity of results in young clusters and star forming regions has been called into question, with the accuracy of the evolutionary models that all studies are based on being considered debatable at young ages. Hence a study in the field, where there is a spread of ages, provides a useful, possibly more robust, method for measuring the mass function. Low mass stars and brown dwarfs in the field are usually identified by either infrared surveys or by proper motion surveys. Here these techniques are combined for the first time to produce an infrared proper motion survey. This has produced a sample of over 7000 low mass objects with proper motions greater than 0.1"/yr . It has also found several common proper motion binary systems and SIPS1259-4336, an M8.5 dwarf within l0pc. This sample on its own will not yield a constraint on the mass function. In the field the range of ages and the luminosity evolution of objects leads to the mass function being intertwined with the stellar birthrate. Here this problem is dealt with by detailed simulations. By drawing ages from a birthrate and masses from a mass function, simulated objects can have space positions, velocities and absolute magnitudes assigned using a simple model of the Galaxy, evolutionary models of low mass objects and empirical relations. These can then be converted into observables and passed through a survey selection mechanism. By varying the underlying birthrate and mass function the effect these have on the survey results can be found. These results can then be compared with those of the actual survey to constrain the mass function and birthrate. Here the mass function parameter α is found to be 0.66 ± 0.44 in the range O.2M⊙ > m > O.O75M⊙, that the birthrate parameter β is -0.01 ± 0.10 and that the space density of objects in the mass range O.O9M⊙ < m < O.1M⊙ is 0.0053 ± 0.0002 /pc³. It should be noted that due to noise in the probability surface, the constraint on β should be treated with caution. Finally the results of the future infrared surveys by UKIDSS are simulated and the potential constraints that could be set by them outlined.
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