Electron-impact rotational excitation of H 3 + : relevance for thermalization and dissociation Alexandre Faure* Laurent Wiesenfeld* & Jonathan Tennyson.

Electron-impact rotational Electron-impact rotational excitation of Hexcitation of H33

++: relevance : relevance for thermalization and for thermalization and

dissociationdissociation

Alexandre FaureAlexandre Faure**Laurent Wiesenfeld* Laurent Wiesenfeld* & Jonathan & Jonathan

TennysonTennyson##

*Laboratoire d’Astrophysique de Grenoble, France*Laboratoire d’Astrophysique de Grenoble, France##University College LondonUniversity College London

Electron-molecule collisionsElectron-molecule collisions Rotational excitation of molecules by Rotational excitation of molecules by

electron-impact is very efficient:electron-impact is very efficient:

– k(e) k(e) ~ ~ 1010-6 -6 cmcm33ss-1-1

By comparison:By comparison:

– k(H, Hk(H, H22) ) ~ ~ 1010-10 -10 cmcm33ss-1-1

Electrons are the dominant exciting Electrons are the dominant exciting partners as soon as:partners as soon as:

– n(e)/nn(e)/n(H) >(H) > 1010-4 -4

HH33++ in the diffuse ISM in the diffuse ISM

Unexpected high Unexpected high abundance of Habundance of H33

++ in in diffuse cloudsdiffuse clouds

Three uncertain key Three uncertain key parameters: kparameters: kee, n(e) , n(e) and and

Observations Observations suggest suggest – n(e)/n(Hn(e)/n(H22) ) ~ 4 10~ 4 10-4-4

– high CR ionization high CR ionization rate (rate ( ~ ~ 1010-15-15ss-1-1))

Laboratory and space spectra of H3+,

from McCall et al. Nat. 2003

HH33++ toward the galactic toward the galactic

centercenter Large column Large column

densities in the (3, densities in the (3, 3) metastable state3) metastable state

Very low column Very low column densities in the (2, densities in the (2, 2) state 2) state

Provide evidence ofProvide evidence of– high high TT ( (~~ 250 K) 250 K)– low low nn ( (~ 100 cm~ 100 cm-3-3))– high high (> 10 (> 10-15-15ss-1-1))

H3+ and CO spectra toward GCS3-2,

from Oka et al. ApJ 2005

Rotation and DR Rotation and DR measurementsmeasurements

HH33++ internal excitation internal excitation

known to influence DR known to influence DR rate measurementsrate measurements

Influence of electron-Influence of electron-impact excitation? impact excitation?

Rotational cooling and Rotational cooling and heating by electrons heating by electrons observed at TSR (talk observed at TSR (talk by A. Wolf)by A. Wolf)

DR rate coefficients, from Lammich et al. 2005

CRYRING (McCall et al. 2003)

TSR, short storage time

TSR, long storage time

Electron-impact Electron-impact (de-)excitation(de-)excitation

Experiments extremely difficult

Vibrational excitation: negligible at relevant temperatures (first threshold at 0.3 eV)

Rotational excitation: standard theory is the long-range Coulomb-Born approximation (Chu & Dalgarno 1974, Chu 1975)

However, short-range forces are crucial! (Rabadán et al. 1998, Faure & Tennyson 2001)

The The RR-matrix method-matrix method

Internal region :exchange, correlation(adapt quantum chemistry codes)

External region :Multipolar potential(adapt electron-atom codes)

electron

R-matrix sphere

internal region

external region

Electron-HElectron-H33++ calculations calculations

HH33++ wavefunction taken from wavefunction taken from RR-matrix -matrix

calculations of Faure & Tennyson (2002)calculations of Faure & Tennyson (2002)

Ground-state quadrupole: 0.914 eaGround-state quadrupole: 0.914 ea0022 (close to (close to

0.9188 ea0.9188 ea0022 calculated by Meyer et al. 1986) calculated by Meyer et al. 1986)

Scattering model includes four target states, Scattering model includes four target states, viavia CI expansion.CI expansion.

Continuum functions represented by Gaussian-Continuum functions represented by Gaussian-type basis functions with type basis functions with ll4 (Faure et al. 4 (Faure et al. 2002).2002).

Resonances in good agreement with Orel’s Resonances in good agreement with Orel’s resultsresults

Rotational excitation Rotational excitation calculationscalculations

H3+ is taken at its equilibrium geometry

The adiabatic nuclei rotation (ANR) method (sudden approximation) is employed

Cross sections are expressed as a partial wave expansion with high partial waves deduced from long range approximations

Excitation cross sections are corrected (forced to zero) near threshold (Morrison & Sun 1995)

Rotational cross sections Rotational cross sections and selection rules and selection rules

Cross sections Cross sections computed from 10 meV computed from 10 meV to 10 eVto 10 eV

Entirely dominated by Entirely dominated by short range interactionsshort range interactions

Selection rules:Selection rules: J=(0), 1, 2, (3, …) J=(0), 1, 2, (3, …) – Ortho Ortho para forbidden para forbidden K=0, (3)K=0, (3)

J=1, 2 comparable in J=1, 2 comparable in magnitudemagnitude

Faure & Tennyson JPB 2002

Rate coefficientsRate coefficients

Rates obtained from Rates obtained from 100 to 10,000K100 to 10,000K

No dipole and large No dipole and large rotational thresholds:rotational thresholds:

– Excitation rates Excitation rates generally peak above generally peak above 1,000K, at about 101,000K, at about 10-7 -7

cmcm33ss-1-1

– Deexcitation rates Deexcitation rates increase slightly below increase slightly below 1,000K 1,000K

Faure & Tennyson MNRAS 2003

Comparison with Comparison with DR rate coefficients DR rate coefficients

Latest measurements Latest measurements with rotationally cold with rotationally cold HH33

++::– k(23K)=2.6 10k(23K)=2.6 10-7 -7 cmcm33ss-1-1 – k(300K)=6.8 10k(300K)=6.8 10-8 -8 cmcm33ss-1-1

Two possible regimes:Two possible regimes:– Rotational cooling Rotational cooling

important below 100Kimportant below 100K– Rotational heating Rotational heating

important above 100Kimportant above 100KMcCall et al. PRA 2004

Thermalization of HThermalization of H33++ in in

spacespace Centrifugal distorsion Centrifugal distorsion

causes « forbidden » causes « forbidden » transitions: transitions: J=0, 1 J=0, 1 K=3 K=3

Spontaneous Spontaneous emission times emission times comparable to comparable to collision intervalscollision intervals

Nonthermal rotational Nonthermal rotational distribution expected distribution expected (Oka & Epp 2004)(Oka & Epp 2004)

Forbidden rotational transitions, from Pan & Oka

ApJ 1986

Reactive collisions with HReactive collisions with H22

In contrast to standard neutral collisions, In contrast to standard neutral collisions, collisions between Hcollisions between H33

++ and H and H22 are reactive: are reactive:

HH33++ + H + H22 (H (H55

++)* )* H H33++ + H + H22

Random selection rules: ortho/para Random selection rules: ortho/para conversion is allowedconversion is allowed

Langevin potential: rates expected to lie Langevin potential: rates expected to lie between between 10between between 10-10 -10 cmcm33ss-1-1 and 10 and 10-9 -9 cmcm33ss-1-1

Rigorous quantum (or even classical) Rigorous quantum (or even classical) calculations greatly needed!calculations greatly needed!

Thermalization by HThermalization by H22 (Oka & Epp (Oka & Epp

2004)2004) Collision rates based Collision rates based

on Langevin rate and on Langevin rate and detailed balancedetailed balance

Steady state Steady state approximation:approximation:– Lifetime Lifetime ~ 10~ 109 9 ss– Collision time ~ 10Collision time ~ 107 7 ss

Results consistent Results consistent with observations forwith observations for– T T ~ 250K ~ 250K – n(Hn(H22) ~ 100cm) ~ 100cm-3-3

Population ratios and Tex as a function

of n(H2) and T, from Oka & Epp 2004

Thermalization by e-impact?Thermalization by e-impact? The electron effect is estimated by Oka & Epp to The electron effect is estimated by Oka & Epp to

be 2 orders of magnitude less than that of Hbe 2 orders of magnitude less than that of H22::

– k(e)/k(Hk(e)/k(H22) ~ 10) ~ 1022

– n(e)/n(Hn(e)/n(H22) ~ 10) ~ 10-4-4

However, it is not unreasonable to assume:However, it is not unreasonable to assume:

– k(e)/k(Hk(e)/k(H22) ~ 10) ~ 1033 , i.e. k(H , i.e. k(H22) ~ 10) ~ 10-10 -10 cmcm33ss-1-1

– n(e)/n(Hn(e)/n(H22) ~ 10) ~ 10-3-3, i.e. high ionization rate , i.e. high ionization rate

In such conditions, might electrons compete with In such conditions, might electrons compete with neutrals?neutrals?

Steady-state approximationSteady-state approximation Solve the rate equation:Solve the rate equation:

Ortho/para conversion Ortho/para conversion forbidden:forbidden:– Initial n(1, 0)/n(1, 1) is Initial n(1, 0)/n(1, 1) is

crucialcrucial

The steady state The steady state solution is NOT solution is NOT compatible with compatible with observations! observations! Population ratios as a function

of T and n(e)

Obs ~ 0.7!

Obs ~ 0.5!

n(e)

Time dependent approach?Time dependent approach?

However, steady state However, steady state approximation is NOT approximation is NOT valid:valid:

– t(lifetime)t(lifetime)~3 10~3 1088 s s– t(steady-state)>10t(steady-state)>1099 s s

Proper modelling Proper modelling needs inclusion of needs inclusion of rates for:rates for:– formation (Hformation (H22

+++H+H22))

– destruction (Hdestruction (H33+++ e)+ e)

Level populations as a function of time

for T=300K, n(e)=5 10-2 cm-3

t(lifetime)

ConclusionsConclusions

Electron-impact rotational (de)excitation rates Electron-impact rotational (de)excitation rates of Hof H33

++ are comparable in magnitude to the DR are comparable in magnitude to the DR rate at 300K, i.e. about rate at 300K, i.e. about 1010-7 -7 cmcm33ss-1-1

Ortho-para conversion is collisionally forbiddenOrtho-para conversion is collisionally forbidden We now provide rotational rates for all allowed We now provide rotational rates for all allowed

transitions up to (5, 4) from 100 to 10,000Ktransitions up to (5, 4) from 100 to 10,000K Future works:Future works:

– Modelling of HModelling of H33++ thermalization by electrons in thermalization by electrons in

spacespace– Modelling of HModelling of H33

++ cooling and heating by electrons in cooling and heating by electrons in storage ringsstorage rings

– Isotopologs of HIsotopologs of H33++