  The abundance of brown dwarfs (BDs) in young clusters is a diagnostic of star
formation theory. Here we revisit the issue of determining the substellar
initial mass function (IMF), based on a comparison between NGC1333 and IC348,
two clusters in the Perseus star-forming region. We derive their mass
distributions for a range of model isochrones, varying distances, extinction
laws and ages, with comprehensive assessments of the uncertainties. We find
that the choice of isochrone and other parameters have significant effects on
the results, thus we caution against comparing IMFs obtained using different
approaches. For NGC1333, we find that the star/BD ratio R is between 1.9 and
2.4, for all plausible scenarios, consistent with our previous work. For IC348,
R is between 2.9 and 4.0, suggesting that previous studies have overestimated
this value. Thus, the star forming process generates about 2.5-5 substellar
objects per 10 stars. The derived star/BD ratios correspond to a slope of the
power-law mass function of alpha=0.7-1.0 for the 0.03-1.0Msol mass range. The
median mass in these clusters - the typical stellar mass - is between
0.13-0.30Msol. Assuming that NGC1333 is at a shorter distance than IC348, we
find a significant difference in the cumulative distribution of masses between
the two clusters, resulting from an overabundance of very low mass objects in
NGC1333. Gaia astrometry will constrain the cluster distances better and will
lead to a more definitive conclusion. Furthermore, ratio R is somewhat larger
in IC348 compared with NGC1333, although this difference is still within the
margins of error. Our results indicate that environments with higher object
density may produce a larger fraction of very low mass objects, in line with
predictions for brown dwarf formation through gravitational fragmentation of
filaments falling into a cluster potential.
