linear analysis of infrared co spectra takeshi oka department of astronomy and astrophysics and...
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![Page 1: Linear Analysis of Infrared CO Spectra Takeshi Oka Department of Astronomy and Astrophysics and Department of Chemistry, The Enrico Fermi Institute, University](https://reader035.vdocuments.us/reader035/viewer/2022062518/56649d3b5503460f94a15cab/html5/thumbnails/1.jpg)
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
![Page 2: Linear Analysis of Infrared CO Spectra Takeshi Oka Department of Astronomy and Astrophysics and Department of Chemistry, The Enrico Fermi Institute, University](https://reader035.vdocuments.us/reader035/viewer/2022062518/56649d3b5503460f94a15cab/html5/thumbnails/2.jpg)
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
![Page 3: Linear Analysis of Infrared CO Spectra Takeshi Oka Department of Astronomy and Astrophysics and Department of Chemistry, The Enrico Fermi Institute, University](https://reader035.vdocuments.us/reader035/viewer/2022062518/56649d3b5503460f94a15cab/html5/thumbnails/3.jpg)
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
![Page 4: Linear Analysis of Infrared CO Spectra Takeshi Oka Department of Astronomy and Astrophysics and Department of Chemistry, The Enrico Fermi Institute, University](https://reader035.vdocuments.us/reader035/viewer/2022062518/56649d3b5503460f94a15cab/html5/thumbnails/4.jpg)
Disagreement between IR and Radio
![Page 5: Linear Analysis of Infrared CO Spectra Takeshi Oka Department of Astronomy and Astrophysics and Department of Chemistry, The Enrico Fermi Institute, University](https://reader035.vdocuments.us/reader035/viewer/2022062518/56649d3b5503460f94a15cab/html5/thumbnails/5.jpg)
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
![Page 6: Linear Analysis of Infrared CO Spectra Takeshi Oka Department of Astronomy and Astrophysics and Department of Chemistry, The Enrico Fermi Institute, University](https://reader035.vdocuments.us/reader035/viewer/2022062518/56649d3b5503460f94a15cab/html5/thumbnails/6.jpg)
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
![Page 7: Linear Analysis of Infrared CO Spectra Takeshi Oka Department of Astronomy and Astrophysics and Department of Chemistry, The Enrico Fermi Institute, University](https://reader035.vdocuments.us/reader035/viewer/2022062518/56649d3b5503460f94a15cab/html5/thumbnails/7.jpg)
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
![Page 8: Linear Analysis of Infrared CO Spectra Takeshi Oka Department of Astronomy and Astrophysics and Department of Chemistry, The Enrico Fermi Institute, University](https://reader035.vdocuments.us/reader035/viewer/2022062518/56649d3b5503460f94a15cab/html5/thumbnails/8.jpg)
Polynomial fitting is dangerous
Cubic spline FMM
n(1)/n(0)
![Page 9: Linear Analysis of Infrared CO Spectra Takeshi Oka Department of Astronomy and Astrophysics and Department of Chemistry, The Enrico Fermi Institute, University](https://reader035.vdocuments.us/reader035/viewer/2022062518/56649d3b5503460f94a15cab/html5/thumbnails/9.jpg)
Some combinations are more useful
n(1)/n(0) n(3)/n(2)
Spiral arms
Galactic C.
![Page 10: Linear Analysis of Infrared CO Spectra Takeshi Oka Department of Astronomy and Astrophysics and Department of Chemistry, The Enrico Fermi Institute, University](https://reader035.vdocuments.us/reader035/viewer/2022062518/56649d3b5503460f94a15cab/html5/thumbnails/10.jpg)