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.