  We have obtained moderate-resolution (R=800-1200) K-band spectra for ~100
stars within and surrounding the cloud core of rho Oph. We have measured
spectral types and continuum veilings and have combined this information with
results from new deep imaging. The IMF peaks at about 0.4 M_sun and slowly
declines to the hydrogen burning limit with a slope of ~-0.5 in logarithmic
units (Salpeter is +1.35). Our lower limits on the numbers of substellar
objects demonstrate that the IMF probably does not fall more steeply below the
hydrogen burning limit, at least down to ~0.02 M_sun. We then make the first
comparison of mass functions of stars and pre-stellar clumps (Motte, Andre, &
Neri) measured in the same region. The similar behavior of the two mass
functions in rho Oph supports the suggestion of Motte et al. and Testi &
Sargent that the stellar mass function in young clusters is a direct product of
the process of cloud fragmentation. After considering the effect of extinction
on the SED classifications of the sample, we find that ~17% of the rho Oph
stars are Class I, implying ~0.1 Myr for the lifetime of this stage. In spectra
separated by two years, we observe simultaneous variability in the Br gamma
emission and K-band continuum veiling for two stars, where the hydrogen
emission is brighter in the more heavily veiled data. This behavior indicates
that the disk may contribute significantly to continuous K-band emission, in
contrast to the proposal that the infalling envelope always dominates. Our
detection of strong 2 micron veiling (r_K=1-4) in several Class II and III
stars, which should have disks but little envelope material, further supports
this proposition.
