Transcript 10ColumbusCO.ppt

Linear Analysis of Infrared CO Spectra
Takeshi Oka
Department of Astronomy and Astrophysics
and Department of Chemistry,
The Enrico Fermi Institute, University of Chicago
Han Xiao
Department of Statistics, University of Chicago
Tom Geballe
Gemini Observatory
Chris Morong
Department of Chemistry, University of Chicago
Tomoharu Oka, Keio University
June 24, Columbus Symposium
H3+ and CO are complementary
6
n(CO)  nH
n(H3+)  nH0
10
N(C) → M
H2
5
10
4
10
3
10
N(H3+) → L· ζ
2
10
CO
1
10
H
0
10
n(X)
-1
10
-2
10
-3
CO high n low T J = 0, 1, 2, 3
10
+
H3
-4
10
+
C
-5
10
H3
+
low n high T (3,3), (2,2)
-6
10
-7
10
-8
10
Diffuse Clouds
Dense Clouds
-9
10
6
10
5
10
4
10
3
2
10
10
1
10
0
10
n(H)
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
-1
10
H3+ and CO Discriminate Clouds
Expanding molecular ring
Oka et al. ApJ 632, 882 (2005)
Kaifu, Kato, Iguchi, Nature (1972)
Scoville, ApJ, 175, L127 (1973)
Geballe & Oka ApJ 709, L70 (2010)
Disagreement between IR and Radio
Optical Depth: Central in Linear Analysis
13C, 18O, 17O
Non-linearity arises in two ways
1) Line-formation
2) Thermalization
Wλ → N(CO)
Radiation trapping
Sobolev High Velocity Gradient Method
V. V. Sobolev Moving Envelopes of Stars (1947)
G. B. Rybicki Escape Probability Methods (1984)
Escape probability
1 I 1  e
  
 I

Collisional and radiative processes
Steady State
dnJ
0
dt

1
2J  3
1
1
2J 1
1




AJ 1, J 1  2 B ( J 1) / T  nJ 1   AJ 1, J

A
1

n

A
nJ 1

J
,
J

1
J
J
,
J

1
2 B ( J 1) / T
2 BJ / T
2 BJ / T


e

1
2
J

1
e

1
e

1
2
J

1
e

1





  k J ', J nJ '  k J , J ' nJ nH 2
CO J’
H2
CO J
H2
J'
k J ' J
E  EJ '
2J  1

exp(  J
)
k J  J ' 2 J ' 1
kT
Detailed balance
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)
Polynomial fitting is dangerous
n(1)/n(0)
Cubic spline
FMM
Some combinations are more useful
n(1)/n(0)
n(3)/n(2)
Galactic C.
Spiral arms