The near-infrared extinction law and limits on the pre-main-sequence population of the ρ Ophiuchi dark cloud

We describe new techniques to measure the near-infrared extinction law and to place limits on the pre-main-sequence stellar population of a dark cloud. We analyze JHK imaging data for the central 1 deg(2) of the rho Ophiuchi cloud core and show that nearly all stars projected onto regions of low CS intensity, I-CS less than or equal to 10 K km s(-1), are background stars. Most sources at larger CS intensities lie within cloud material. We use the background stars to derive the slope of the near-IR extinction law, EJ-H/EH-K = 1.57 +/- 0.03. This result is consistent with previous extinction laws but has a factor of 2-3 smaller uncertainty. The new rho Oph extinction law yields strong constraints on the number of previously undiscovered pre-main-sequence stars in the cloud, 46 +/- 11, and the number of previously undiscovered young stars with near-IR excesses, 15 +/- 4. Neither limit exceeds the number of known pre-mainsequence stars in the cloud, similar to 100. Thus, current samples of pre-main-sequence stars ale reasonably complete for K less than or equal to 14.