  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.
