Testing substellar MF models

Theoretical predictions (e.g. Burrows et al. 1997; Chabrier et al. 2000) of the temperature and luminosity of very low mass objects as a function of age have become much more secure over the last few years with the incorporation of non-gray atmospheric models and dust. These advances are timely, since we can now predict, with some confidence, the infrared absolute magnitudes and colours of very low mass objects. This is of course pivotal in the derivation of the mass function from observables.

The UKIDSS Large Area Survey (LAS) will find large numbers of brown dwarfs, but to measure the mass function we need to survey clusters. First, all the objects found will be at a known distance so that the luminosity function is easy to derive. Second, to derive the mass function we need to know the age of the brown dwarfs concerned to correct for cooling. To test our assumptions about cooling, and the universality of the mass function, we should look at clusters with a range of ages. We would also like to test the universality of the mass function with respect to metallicity.

In order to provide estimates of the numbers of BDs expected in our proposed surveys, we have used the two model forms, power-law and log-normal, along with data from the Pleiades (e.g. Martin et al. 1998; Hambly et al. 1999b). For power-law MFs we assume alpha=2.35 for m>0.5M(sun); alpha=1.5 for 0.5>m/M(sun)>0.1; and the plausible values alpha=+1, 0, -1 for m<0.1M(sun). For the log-normal, we assume a shape extrapolated from that measured in Hambly et al. (1999b) - see Figure 4.1. In each case, the MFs are normalised to give the total mass estimated for each cluster in Table 4.1 (see Technical requirements).