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The Arizona Radio Observatory CO Mapping Survey of Galactic Molecular Clouds. VI. The Cep OB3 Cloud (Cepheus B and C) in CO J=2-1, (CO)-C-13 J=2-1, and CO J=3-2We present (1) new fully sampled maps of CO and (CO)-C-13 J = 2-1 emission and CO J = 3-2 emission toward the molecular clouds Cep B and C, associated with the Cep OB3 association; (2) a map of extinction, A(V), derived from IR colors of background stars; and (3) the distribution of young stellar objects (YSOs) over the same field as the molecular maps. An LTE analysis of the CO and (CO)-C-13. maps yields the distribution of molecular column densities and temperatures. Substantial variations are evident across the clouds; smaller subregions show correlations between molecular properties and dust extinction, consistent with a picture of outer photodissociation regions with a layer of CO-dark molecular gas, a CO self-shielded interior, and an inner cold dense region where CO is largely depleted onto grains. Comparing the distribution of YSOs with molecular gas surface density shows a power-law relation very similar in slope to that for the giant molecular cloud associated with the H II region Sh2-235 from a previous paper in this series that employed the same methodology. We note the presence of several compact, isolated CO emission sources in the J = 3-2 maps. The gas temperature and (CO)-C-13. velocity dispersion yield a map of the sonic Mach number, which varies across the cloud but always exceeds unity, confirming the pervasiveness of supersonic turbulence over length scales greater than or similar to 0.1 pc (the map resolution). We also compute a J = 2-1 CO X-factor that varies with position but is, on average, within. 20% of the Galactic average derived from CO J = 1-0 observations.