Low-mass star formation and the initial mass function in the ρ Ophiuchi cloud core

We have obtained moderate-resolution (R = 800-1200) K-band spectra for similar to 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. Using the latest evolutionary tracks of D'Antona & Mazzitelli to interpret the M-R diagram for rho Oph, we infer ages ranging between 0.1 and 1 Myr for the class II and III sources (i.e., those that have emerged from their natal cocoons). A few stars may be slightly older. The initial mass function (IMF) peaks at about 0.4 M. and slowly declines to the hydrogen-burning limit with a slope of similar to-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 similar to 0.02 M.. The derived IMF is consistent with previous findings that the rho Oph IMF is roughly flat from 0.05 tol M.. The exact shape of the mass function remains a function of the theoretical evolutionary tracks and, at the lowest masses, the conversion from spectral types to effective temperatures. We then make the first comparison of mass functions of stars and prestellar clumps 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. We have also studied the very young and often still embedded class I and hat-spectrum objects. After considering the effect of extinction on the SED classifications of the sample, we find that similar to 17% of the rho Oph stars are class I, implying similar to 0.1 Myr for the lifetime of this stage. In spectra separated by 2 yr, 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 mu m veiling (r(K) =1-4) in several class II and III stars, which should have disks but little envelope material, further supports this proposition. We also detect absorption features in the spectra of similar to 25% of class I and Bat-spectrum sources, demonstrating the feasibility of studying the photospheres of extremely young protostars.