Southern Infrared Proper Motion Survey III: Constraining the mass function of low mass stars

The stellar mass function is one of the fundamental distributions of stellar astrophysics. Its form at masses similar to the Sun was found by Salpeter (1955) to be a power-law $m^{-\alpha}$ with a slope of $\alpha=1.35$. Since then the mass function in the field, in stellar clusters and in other galaxies has been studied to identify variation due to environment and mass range. Here we use results from previous papers in the SIPS series to constrain the mass function of low mass stars (0.075M$_\odot$$<$m$<0.2_\odot$). We use simulations of the low mass local stellar population based on those in Deacon & Hambly (2006) to model the results of the SIPS-II survey (Deacon & Hambly, 2007). We then vary the input parameters of these simulations (the exponent of the mass function $\alpha$ and a stellar birthrate parameter $\beta$) and compare the simulated survey results with those from the actual survey. After a correction for binarity and taking into account potential errors in our model we find that $\alpha=-0.62\pm0.26$ for the quoted mass range.