A first core is a first hydrostatic object formed in the course of dynamical contraction of a molecular cloud core. Since the inflow pattern changes drastically before and after the first core formation, it is regarded as a milestone in the star formation process. In order to identify the first core from a mapping observation, the features expected for the first core are studied for CS rotation transitions at radio wavelengths. The non-LTE radiation transfer is calculated for the results of radiation magnetohydrodynamical simulations of the contraction of the magnetized molecular cloud core in rotation (Tomida et al. 2010a). We use the Monte-Carlo method to solve the non-LTE radiation transfer in a nested grid hierarchy. In the first core phase, an outflow arises from the vicinity of the first core due to the twisted magnetic field amplified by the rotation motion of the contracting gas disk. The disk and outflow system has several characteristic observational features: (i) in the pole-on view, relatively opaque lines indicate asymmetry in the emission lines in which the blue side is stronger than the red side (an infall signature of the envelope); (ii) in the edge-on view, the disk has a signature of simultaneous rotation and infall, i.e., the integrated intensity of the reaching side is brighter than that of the receding side and the gradient in the intensity-weighted velocity is larger in the reaching side; (iii) the observed outflow indicates rotation around the rotation axis. The size of the outflow gives the approximate age after the first core is formed, since the outflow is not expected for the earlier runaway isothermal collapse phase.Comment: Publ. Astron. Soc. Japan Vol.63 No.5 (2011 Oct. issue) in pres
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