Observational Identification of First Cores:
Non-LTE Radiative Transfer Simulation
TOMISAKA, Kohji & TOMIDA, Kengo(NAOJ)

written as JνJJ 0 , where h is the Plank constant.
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 gasdisk.
The disk and outﬂow system has several characteristic
observational features (Fig. 2): (i) relatively opaque lines
indicate asymmetry in the emission lines in which theblue side is stronger than the red side (an infall signatureof the envelope); (ii) in the edge-on view, the disk has
a signature of simultaneous rotation and infall, i.e., theintegrated intensity of the approaching side is brighter
than that of the receding side and the gradient in theintensity-weighted velocity is larger in the approachingside; (iii) the observed outﬂow indicates rotation aroundthe rotation axis. The size of the outﬂow gives the approximate age after the ﬁrst core is formed, since theoutﬂow is not expected for the earlier runaway isothermal collapse phase
The reason why the mirror symmetry is broken in therotating infall disk is understood as follows. This assymmetry arises due to the self-absorption. Since thetemperature decreases outwardly, the emission from theportion near the tangential point is absorbed by foreground rotating inﬂow gas. In this conﬁguration, velocity diﬀerence between gases which contribute emission
and absorption is larger for approating side rather thanreceding side of rotation.

A ﬁrst core is a ﬁrst hydrostatic object formed in thecourse of dynamical contraction of a molecular cloudcore. Since the inﬂow pattern changes drastically before and after the ﬁrst core formation, it is regarded asa milestone in the star formation process. Although theﬁrst core was predicted by Larson in 1969[1], this has notbeen conﬁrmed by observation yet. In order to identify
the ﬁrst core from a mapping observation, the features
expected for the ﬁrst core are studied for CS rotationtransitions at radio wavelengths[3]. The non-LTE radiation transfer is calculated for the results of radiation magnetohydrodynamical simulations of the contraction of themagnetized molecular cloud core in rotation [2]. Figure
1 indicates the structure at the age of τ = 6.45 × 102 yr
after the ﬁrst core formation.

Figure 1: Density and velocity (left) and temperature(right) distributions. In this 140-AU scale map showsthat a ﬁrst core forms r < 30AU and an outﬂow is ejectedvertically. Inﬂowing gas is essentially isothermal with atemperature of T ' 10K, while the ﬁrst core has highertemperature.
We use the Monte-Carlo method to solve the nonLTE radiation transfer in a nested grid hierarchy.
Balance equation between radiative excitaion, inducedemission, spontaneous deexcitaion, collisional excitation and deexcitation is solved, coupled with the radiation transfer equation. Denoting the number density of the J level (energy level E(J))∑ as nJ , we0canwrite
thebalanceequation
asn=J
J 0 6=J RJJ∑00nR(J=0,1,···,J),
whereRJ Jmax
JJ 0J 0 6=J J
represents{ the transition probability from J to J 0= AJJ 0 + BJJ 0 JνJJ 0 + nCJJ 0 for J > J 0 ,as RJJ 0= BJJ 0 JνJJ 0 + nCJJ 0
for J < J 0 ,where AJJ 0 and BJJ 0 represent Einstein’s coeﬃcients,
the former being the coeﬃcient for spontaneous emission
and the latter the coeﬃcient for absorption (J < J 0 ) andinduced emission (J > J 0 ). CJJ 0 is the collisional transition rate from J to J 0 for collisions with H2 molecules
whose density is denoted by n. The average intensity ofradiation with a frequency of ν = [E(J 0 ) − E(J)]/h is

Figure 2: Expected distribution of the integrated intensityof the CS J = 2−1 (left) and J = 7−6 (right) emissions. The
integrated intensities are shown with false color and intensityweighted mean velocity (first moment) is shown in white contour lines. This shows the edge-on view.

References[1] Larson, R. B. 1969, MNRAS, 145, 271[2] Tomida, K., Tomisaka, K., Matsumoto, T., Ohsuga,K., Machida, M.N., & Saigo, K., 2010, ApJ, 714, L58[3] Tomisaka, K. & Tomida, K.: 2011, PASJ, 63, 1151

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