1. Optical Zeeman Spectroscopy of the (0,0) bands of the B 3  -X 3  and A 3  -X 3  Transitions of Titanium Monoxide, TiO Wilton L. Virgo, Prof. Timothy C. Steimle and Prof. John M. Brown Ap. J. 628, 2005 July 20

2. Zeeman Spectroscopy of TiO: Dual Purpose Magnetic “g” factors are useful in unraveling the nature of electronic states of metal containing molecules. –Analyze electronic state composition and provide evidence for mixing between states. Optical Zeeman effect of TiO is used to probe ambient stellar magnetic fields. –Experimentally determine magnetic tuning rates of molecular energy levels.

3. TiO Stokes V Spectrum of Sunspot S.V. Berdyugina et. al. A&A 364, L101 2000 3000G Calc. Stokes V Profile of  (0,0) R 3 (10) line with magnetic field strengths.5-3.5kG TiO  (0,0) R 3 band head in a sunspot Dashed: Observed Solid: Calculated

4. Origin of the Stokes V Spectrum Profiles calculated for low-J lines of Q branch in  ’(B 3  -X 3  )

5. Zeeman Effect in Diatomic Molecules: Berdyugina’s Astrophysical Model m L = -  B g L L, m S = -  B g S S Magnetic dipole moment operator is a sum of terms directly proportional to angular momentum operators: In principle, Zeeman effect can be predicted a priori from field free eigenvalues and eigenvectors given the g-values: 1. Only diagonal terms in J included 2. Predicts linear field dependence 3. g S, g L fixed to 2.002 and 1.0 4.  and  are rigorously good Berdyugina et. al. A&A 412, 513 (2003), A&A 385, 701 (2002).

6. Modeling the Zeeman Effect in TiO: Sophisticated Effective Hamiltonian Approach 1. Spin-orbit and rotational mixing significant in metal species 2. Evident in large  -doubling in B 3  state of TiO Key difference from astrophysical model: Accounts for both linear and non-linear field dependence by including off diagonal in J matrix elements Eff. Hamiltonian absorbs effects of other states into the g parameters Makes allowance for all possible admixtures of electronic states Adjustable g parameter values glean insight into the perturbations

7. Laser Ablation and Molecular Beam Production

8. High-Resolution Spectrometer Electromagnet Optical Zeeman Spectroscopy

9. Electromagnet for Zeeman Spectroscopy (56G-1.2kG)

10. Electronic Transitions of TiO

11. Zeeman Spectra: R 11 (1)  (A 3  2 -X 3  1 )

12. Zeeman Spectra: Q 11b (1) (0,0)  ’(B 3  0 - X 3  1 ) Feature

13. ‘Stick’ Spectra of Q 11b (J)  ’(B 3  0 - X 3  1 ) Branch A) Berdyugina model with only diagonal (in J) matrix elements and fixed g-factors B) Steimle model w/off diagonal  J=+/-1 matrix elements and determined g-factors

14. Results: Zeeman Fitting Parameters

15. Conclusion #1: Chemistry g L values indicate that C 3  is reasonable candidate for state that interacts strongly with both A 3  and B 3 . C~A and C~B satisfy rules for S.O. mixing –C 3  state differs by one spin-orbital from A 3  and B 3  states A 3 ,B 3  : 8  2 3  4 1  1 4  1 C 3  : 8  2 3  4 1  1 10  1 –C 3  state differs from A 3  and B 3  states by one unit of orbital angular momentum.

16. Conclusion #2: Astrophysics Significant  -doubling in B 3  0 state requires inclusion of  J=+/-1 matrix elements. Strong off-diagonal J interaction will impose a non-linear response to magnetic field in the low-J lines. Fitted g-factors necessary to reproduce experimental observations. Unexpected by current astrophysical model.

17. Thank You Funding provided by NSF Experimental Physical Chemistry