1. 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 June 24, Columbus Symposium Tomoharu Oka, Keio University

2. H 3 + and CO are complementary n(CO)  n H N(C) → M n(H 3 + )  n H 0 N(H 3 + ) → L · ζ CO high n low T J = 0, 1, 2, 3 H 3 + low n high T (3,3), (2,2) N(CO) ~ 10 18-19 cm -2 v = 2←0 μ 2-0 = 0.00651 Debye N(H 3 + ) ~ 10 15-16 cm -2 v = 1←0 μ 1-0 = 0.158 Debye

3. H 3 + and CO Discriminate Clouds Oka et al. ApJ 632, 882 (2005)Geballe & Oka ApJ 709, L70 (2010) Expanding molecular ring Kaifu, Kato, Iguchi, Nature (1972) Scoville, ApJ, 175, L127 (1973) α

4. Disagreement between IR and Radio

5. Optical Depth: Central in Linear Analysis 13 C, 18 O, 17 O Non-linearity arises in two ways 1)Line-formation W λ → N(CO) 2)Thermalization Radiation trapping

6. Sobolev High Velocity Gradient Method V. V. Sobolev Moving Envelopes of Stars (1947) G. B. Rybicki Escape Probability Methods (1984) Escape probability

7. Collisional and radiative processes Detailed balance Steady State 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 H2H2H2H2

8. Polynomial fitting is dangerous Cubic spline FMM n(1)/n(0)

9. Some combinations are more useful n(1)/n(0)n(3)/n(2) Spiral arms Galactic C.