November 6, 2010 MWAM 2010 University of Illinois1 The ortho:para ratio of H 3 + in diffuse molecular clouds Kyle N. Crabtree, Nick Indriolo, Holger Kreckel, Brian A. Tom, and Benjamin J. McCall

November 6, 2010 MWAM 2010 University of Illinois2 H 3 +, Interstellar Chemistry, and Astrophysics Starting point for complex gas-phase chemistry Use as an astrophysical probe: –Gas density at the galactic center –Imaging of Jupiter’s polar aurorae –Interstellar cosmic ray ionization rate –Interstellar temperature Starting point for complex gas-phase chemistry Use as an astrophysical probe: –Gas density at the galactic center –Imaging of Jupiter’s polar aurorae –Interstellar cosmic ray ionization rate –Interstellar temperature

November 6, 2010 MWAM 2010 University of Illinois3 H 3 + Spectroscopy R(1,0) Å R(1,1) u Å R(1,1) l Å

November 6, 2010 MWAM 2010 University of Illinois4 H 3 + as an Interstellar Thermometer Observed R(1,0) and R(1,1) u /R(1,1) l lines  n(1,0), n(1,1)  T(H 3 + ) Analogous to T 01, derived from UV observations of H 2 J=0 (para) and J=1 (ortho) levels Observed R(1,0) and R(1,1) u /R(1,1) l lines  n(1,0), n(1,1)  T(H 3 + ) Analogous to T 01, derived from UV observations of H 2 J=0 (para) and J=1 (ortho) levels

November 6, 2010 MWAM 2010 University of Illinois5 Temperature in Diffuse Molecular Clouds Diffuse molecular clouds: diffuse clouds with most hydrogen in molecular form. Survey of diffuse molecular clouds: – ~ 70 K (N = 66) 1 – ~ 30 K (N = 18) 2 Only 2 are in common: ζ-Per and X-Per Recent observations (N. Indriolo) have extended this number to 5 Diffuse molecular clouds: diffuse clouds with most hydrogen in molecular form. Survey of diffuse molecular clouds: – ~ 70 K (N = 66) 1 – ~ 30 K (N = 18) 2 Only 2 are in common: ζ-Per and X-Per Recent observations (N. Indriolo) have extended this number to 5 1 B. D. Savage et al., ApJ, (1977), 216, 291, B. L. Rachford et al., ApJ, (2002), 577, 221, B. L. Rachford et al., ApJS, (2009), 180, N. Indriolo et al., ApJ, (2007), 671, B. D. Savage et al., ApJ, (1977), 216, 291, B. L. Rachford et al., ApJ, (2002), 577, 221, B. L. Rachford et al., ApJS, (2009), 180, N. Indriolo et al., ApJ, (2007), 671, 1736.

November 6, 2010 MWAM 2010 University of Illinois6 Temperature Discrepancy ζ-Per X-Per HD HD HD T(H 3 + ) T 01 Which of these represents the “true” kinetic temperature? T 01 Why is there more p-H 3 + than expected for the temperature?

November 6, 2010 MWAM 2010 University of Illinois7 Chemistry of H 3 + Formation: 1.H 2 + cosmic ray  H e - (slow) 2.H H 2  H H (fast) Thermalization H H 2  H 2 + H 3 + Destruction: H e -  H 2 + H or 3H Nuclear spin dependence? Formation: 1.H 2 + cosmic ray  H e - (slow) 2.H H 2  H H (fast) Thermalization H H 2  H 2 + H 3 + Destruction: H e -  H 2 + H or 3H Nuclear spin dependence?

November 6, 2010 MWAM 2010 University of Illinois8 H 3 + Formation 1.H 2 + cosmic ray  H e - (slow) 2.H H 2  H H (fast) Reaction Collision Fraction Branching Fraction  p-H 3 + p-H 3 + Fraction p-H p-H 2 (p2)2(p2)2 1(p2)2(p2)2 p-H o-H 2 (p 2 ) (1-p 2 )2/3(2/3) (p 2 ) (1-p 2 ) o-H p-H 2 (1-p 2 ) (p 2 )2/3(2/3) (1-p 2 ) (p 2 ) o-H o-H 2 (1-p 2 ) 2 1/3(1/3)(1-p 2 ) 2 Total(1/3) + (2/3)p 2

November 6, 2010 MWAM 2010 University of Illinois9 “Nascent” p-H 3 + Fraction (p 3 )

November 6, 2010 MWAM 2010 University of Illinois10 Thermalization: H H 2 “identity” “hop” “exchange” H5+H5+ H5+H Branching fractions: S id, S hop, and S exch α ≡ S hop /S exch (0.5?) Selection Rules Branching fractions: S id, S hop, and S exch α ≡ S hop /S exch (0.5?) Selection Rules Does the steady state of this reaction give a thermal ortho:para H 3 + ratio at low temperature?

November 6, 2010 MWAM 2010 University of Illinois11 Bimolecular Reactive Equilibrium (BRE) n(H 2 )/n(e - ) ~ 10 4 ; k(H 2,H 3 + )/k DR ~ /10 -7 ~ H 3 + sees ~100 collisions with H 2 during its lifetime Assume steady state [p-H 3 + ] is determined by nuclear-spin-changing collisions with H 2 : Express in terms of p-H 3 + fraction (p 3 ): n(H 2 )/n(e - ) ~ 10 4 ; k(H 2,H 3 + )/k DR ~ /10 -7 ~ H 3 + sees ~100 collisions with H 2 during its lifetime Assume steady state [p-H 3 + ] is determined by nuclear-spin-changing collisions with H 2 : Express in terms of p-H 3 + fraction (p 3 ): o-H p-H 2  p-H o-H 2

November 6, 2010 MWAM 2010 University of Illinois12 Nuclear Spin Rate Coefficients ParameterValue(s) T rot 10 K T coll K S id S hop 0-1 S exch 0-1 k oooo k ooop k oopo k oopp k opoo k opop k oppo k oppp k pooo k poop k popo k popp k ppoo k ppop k pppo k pppp f (T,S id,  )

November 6, 2010 MWAM 2010 University of Illinois13 p 3 vs. p 2 Determination T rot = 10 K Choose S id, α

November 6, 2010 MWAM 2010 University of Illinois14 p 3 vs. p 2 Determination T coll p2p2

November 6, 2010 MWAM 2010 University of Illinois15 BRE Results S id = 0.9 S id = 0.1

November 6, 2010 MWAM 2010 University of Illinois16 BRE Results

November 6, 2010 MWAM 2010 University of Illinois17 Steady State Model Include nuclear spin dependent formation and destruction reactions: k e,o = o-H 3 + DR k e,p = p-H 3 + DR x e = Electron fraction (1.5 x ) f = Molecular fraction (0.9) x e = Electron fraction (1.5 x ) f = Molecular fraction (0.9)

November 6, 2010 MWAM 2010 University of Illinois18 Steady State: DR Rates Equal

November 6, 2010 MWAM 2010 University of Illinois19 Steady State: DR Rates Equal

November 6, 2010 MWAM 2010 University of Illinois20 Steady State: Theoretical 1 DR Rates p-H 3 + DR 10x faster than o-H dos Santos et al., J. Chem. Phys. (2007), 127,

November 6, 2010 MWAM 2010 University of Illinois21 Steady State: DR Only

November 6, 2010 MWAM 2010 University of Illinois22 Conclusions H 3 + ortho:para ratio in diffuse molecular clouds likely governed by competition between thermalization (H 3 + -H 2 collisions) and destruction by DR with electrons H H 2 reaction based on microcanonical statistical model– quantum scattering calculations and experimental measurements needed State-selective DR measurements of H 3 + also needed to verify/invalidate model H 3 + ortho:para ratio in diffuse molecular clouds likely governed by competition between thermalization (H 3 + -H 2 collisions) and destruction by DR with electrons H H 2 reaction based on microcanonical statistical model– quantum scattering calculations and experimental measurements needed State-selective DR measurements of H 3 + also needed to verify/invalidate model

November 6, 2010 MWAM 2010 University of Illinois23 Acknowledgements McCall group Takeshi Oka Steve Federman Brian Rachford McCall group Takeshi Oka Steve Federman Brian Rachford