  The initial mass function (IMF) of the Arches cluster, which was formed a few
million years ago in the harsh environment of the Galactic center (GC), has
long been a target of interest to those who study the GC and the theory of star
formation. The distinct star-forming conditions in the GC might have caused the
cluster to have a shallower slope or an elevated lower mass cutoff in its IMF.
But its mass function has been revealed only down to 1-2 Msun (the lower limit
of resolved stars), and the low- end mass function of the Arches is still
unknown. To estimate the unresolved part of the Arches mass function, we have
devised a novel photometric method that involves the histogram of pixel
intensities in the observed image, which contains information on the
unresolved, faint stars. By comparing the pixel intensity histograms (PIHs) of
numerous artificial images constructed from model IMFs with the observed PIH,
we find that the best-fit model IMF for the Arches cluster has a cutoff mass
less than or similar to 0.1 Msun and a shape very close to that of the Kroupa
MF. Our findings imply that the IMF of the Arches cluster is similar to those
found in the Galactic disk.
