Large-area mapping at 850 microns. II. Analysis of the clump distribution in the ρ Ophiuchi molecular cloud

We present results from a survey of the central 700 arcmin² region of the ρ Ophiuchi molecular cloud at 850 μm using the Submillimeter Common-User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope. Using the clump-finding procedure developed by Williams et al., we identify 55 independent objects and compute size, flux, and degree of central concentration. Comparison with isothermal, pressure-confined, self-gravitating Bonnor-Ebert spheres implies that the clumps have internal temperatures of 10-30 K and surface pressures P/k = 10^6-7 K cm^-3, consistent with the expected average pressure in the ρ Ophiuchi central region, P/k ∼ 2 × 10⁷ K cm^-3. The clump masses span 0.02-6.3 M⊙ assuming a dust temperature Td ∼ 20 K and a dust emissivity κ850 = 0.01 cm² g^-1. The distribution of clump masses is well characterized by a broken power law, N(M) ∝ M^-α, with α = 1.0-1.5 for M > 0.6 M⊙ and α = 0.5 for M ≤ 0.6 M⊙, although significant incompleteness may affect the slope at the lower mass end. This mass function is in general agreement with the ρ Ophiuchi clump mass function derived at 1.3 mm by Motte et al. The two-point correlation function of the clump separations is measured and reveals clustering on size scales r < 3 × 10⁴ AU with a radial power-law exponent γ = 0.75.