Optical Zeeman Spectroscopy of the (0,0) bands of the B3-X3 and A3-X3 Transitions of Titanium Monoxide, TiO

Wilton L. Virgo, Prof. Timothy C. Steimle and Prof. John M. Brown

Ap. J. 628, 2005 July 20

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.

TiO Stokes V Spectrum of SunspotS.V. Berdyugina et. al. A&A 364, L101 2000

3000G

Calc. Stokes V Profile of (0,0) R3(10) line with magnetic field strengths .5-3.5kG

TiO (0,0) R3 band head in a sunspot

Dashed: ObservedSolid: Calculated

Origin of the Stokes V Spectrum

Profiles calculated for low-J lines of Q branch in ’(B3-X3)

Zeeman Effect in Diatomic Molecules:Berdyugina’s Astrophysical Model

mL = -BgLL, mS = -BgSS

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 freeeigenvalues and eigenvectors given the g-values:

J JJ MnΛ S nΛ S J M m B

J ( / ( 1)B L SBM g g J J

1. Only diagonal terms in J included2. Predicts linear field dependence3. gS, gL fixed to 2.002 and 1.04. and are rigorously good

Berdyugina et. al. A&A 412, 513 (2003), A&A 385, 701 (2002).

Modeling the Zeeman Effect in TiO:Sophisticated Effective Hamiltonian Approach

1. Spin-orbit and rotational mixing significant in metal species2. Evident in large -doubling in B3 state of TiO

2 2

( .) g L g S

g μ S B S B g S B S B

L B z S B z

i il B x x y y l B

eff

e e

ZeeH

Key difference from astrophysical model:Accounts for both linear and non-linear field dependence byincluding off diagonal in J matrix elements

Eff. Hamiltonian absorbs effects of other states into the g parametersMakes allowance for all possible admixtures of electronic statesAdjustable g parameter values glean insight into the perturbations

Laser Ablation and Molecular Beam Production

Free JetExpansion

High-Resolution Spectrometer

Electromagnet

Optical Zeeman Spectroscopy

Electromagnet for Zeeman Spectroscopy (56G-1.2kG)

Electronic Transitions of TiOW

avenum

ber (c

m) x

10

-1-3

X3

B3

A3

E312.0

0.0

14.0

16.0

(D3

-band= 101ns

band= 4900 ns

C3

18.0

20.0

Zeeman Spectra: R11(1) (A32-X31)

Zeeman Spectra: Q11b(1) (0,0) ’(B30 - X31) Feature

‘Stick’ Spectra of Q11b(J) ’(B 30 - X31) Branch

A) Berdyugina model with only diagonal (in J) matrix elements and fixed g-factorsB) Steimle model w/off diagonal J=+/-1 matrix elements and determined g-factors

Results: Zeeman Fitting Parameters

State Fit A Fit BgL gL gl

A3 0.994(2) 0.994(2)B3 1.037(8) 1.035(8) -0.02(4)a

Std. dev. 18.9MHz 18.9MHza Consistent w/value predicted by Curl’s relationship:gl = -/2B = -.02

Conclusion #1: Chemistry

• gL values indicate that C3 is reasonable candidate for state that interacts strongly with both A3 and B3.

• C~A and C~B satisfy rules for S.O. mixing– C3 state differs by one spin-orbital from A3

and B3 states• A3,B3: 82341141

• C3: 823411101

– C3 state differs from A3 and B3 states by one unit of orbital angular momentum.

Conclusion #2: Astrophysics

• Significant -doubling in B30 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.

Thank YouFunding provided by NSF Experimental Physical Chemistry