linear analysis of infrared co spectra takeshi oka department of astronomy and astrophysics and...
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Linear Analysis of Infrared CO Spectra
Takeshi OkaDepartment of Astronomy and Astrophysics
and Department of Chemistry, The Enrico Fermi Institute, University of Chicago
Han XiaoDepartment of Statistics, University of Chicago
Tom GeballeGemini Observatory
Chris MorongDepartment of Chemistry, University of Chicago
June 24, Columbus Symposium
Tomoharu Oka, Keio University
H3+ and CO are complementary
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
n(X
)
10-1
100
101
102
103
104
105
106
n(H)
Dense Clouds Diffuse Clouds
H2
HCO
C+H3
+
n(CO) nH N(C) → M
n(H3+) nH
0 N(H3+) → L· ζ
CO high n low T J = 0, 1, 2, 3
H3+ low n high T (3,3), (2,2)
N(CO) ~ 1018-19 cm-2 v = 2←0 μ2-0 = 0.00651 Debye
N(H3+) ~ 1015-16 cm-2 v = 1←0 μ1-0 = 0.158 Debye
H3+ and CO Discriminate Clouds
Oka et al. ApJ 632, 882 (2005) Geballe & Oka ApJ 709, L70 (2010)
Expanding molecular ringKaifu, Kato, Iguchi, Nature (1972)Scoville, ApJ, 175, L127 (1973)
α
Disagreement between IR and Radio
Optical Depth: Central in Linear Analysis
13C, 18O, 17O
Non-linearity arises in two ways
1) Line-formation Wλ → N(CO)2) Thermalization Radiation trapping
Sobolev High Velocity Gradient MethodV. V. Sobolev Moving Envelopes of Stars (1947)G. B. Rybicki Escape Probability Methods (1984)
1 1I e
I
Escape probability
Collisional and radiative processes
' '
'
2 1exp( )
2 ' 1J J J J
J J
k E EJ
k J kT
Detailed balance
Steady State
1/21,/21,/)1(2,11/)1(2,1 1
1
12
12
1
11
1
1
12
32
1
11
JTBJJJJTBJJJTJBJJJTJBJJ n
eJ
JAn
eA
eJ
JAn
eA
0dt
dnJ
'
',',' 2J
HJJJJJJ nnknk
Green & Chapman, ApJS 37, 169 (1978)
D. R. Flower, J. Phys. B: At. Mol. Opt. Phys. 34, 2731 (2001)
Wernli, Valiron, Faure, Wiesenfeld, Jankowski, Swalewicz, A&A, 446, 367 (2006)
Schöier, van der Tak, van Dishoeck, Black, A&A 432, 369 (2005) LAMDA
Yang, Stancil, Balakrishnan, Forrey, J. Chem. Phys. 124, 104304 (2006)
CO J’
CO J
H2
H2
Polynomial fitting is dangerous
Cubic spline FMM
n(1)/n(0)
Some combinations are more useful
n(1)/n(0) n(3)/n(2)
Spiral arms
Galactic C.