Calculating the infrared spectra of hot astrophysical molecules

SELAC, May 2005

Jonathan Tennyson

University College London

Layers in a star: the Sun

Spectrum of a hot star: black body-like

Infra red spectrum of an M-dwarf star

Cool stellar atmospheres: dominated by molecular absorption

BrownDwarf

M-dwarf

The molecular opacity problem

(m)

Cool stars: T = 2000 – 4000 KThermodynamics equilibrium, 3-body chemistryC and O combine rapidly to form CO.

M-Dwarfs: Oxygen rich, n(O) > n(C)H2, H2O, TiO, ZrO, etc also grains at lower T

C-stars: Carbon rich, n(C) > n(O) H2, CH4, HCN, C3, HCCH, CS, etc

S-Dwarfs: n(O) = n(C) Rare. H2, FeH, MgH, no polyatomics

Also (primordeal) ‘metal-free’ starsH, H2, He, H, H3

+ only at low T

Also sub-stellar objects:CO less important

Brown Dwarfs: T ~ 1500 KH2, H2O, CH4

T-Dwarfs: T ~ 1000K‘methane stars’

How common are these?Deuterium burning test using HDO?

Burn D only

No nuclear synthesis

Modeling the spectra of cool stars

• Spectra very dense – cannot get T from black-body fit.• Synthetic spectra require huge databases > 106 vibration-rotation transitions per triatomic molecule• Sophisticated opacity sampling techniques.• Partition functions also important

Data distributed by R L Kururz (Harvard), seekurucz.harvard.edu

Physics of molecular opacities:Closed Shell diatomics

CO, H2, CS, etc

Vibration-rotation transitions.

Sparse: ~10,000 transitions

Generally well characterized by lab data and/or theory

(H2 transitions quadrupole only)

HeH+

Physics of molecular opacities:Open Shell diatomics

TiO, ZrO, FeH, etc

Low-lying excited states.

Electronic-vibration-rotation transitions

Dense: ~10,000,000 transitions (?)

TiO now well understood using mixture of

lab data and theory

Physics of molecular opacities:Polyatomic molecules

H2O, HCN, H3+, C3, CH4, HCCH, etc

Vibration-rotation transitions

Very dense: 10,000,000 – 100,000,000

Impossible to characterize in the lab

Detailed theoretical calculations

Computed opacities exist for: H2O, HCN, H3+

Ab initio calculationof rotation-vibrationspectra

The DVR3D program suite: triatomic vibration-rotation spectraPotential energy

Surface,V(r1,r2,)

Dipole function (r1,r2,)

J Tennyson, MA Kostin, P Barletta, GJ Harris

OL Polyansky, J Ramanlal & NF Zobov

Computer Phys. Comm. 163, 85 (2004).

www.tampa.phys.ucl.ac.uk/ftp/vr/cpc03

Potentials: Ab initio or Spectroscopically determined

H3+

H2OH2S

HCN/HNCHeH+

Molecule considered at high accuracy

Partition functions are important

Model of cool, metal-free magnetic white dwarf WD1247+550 by Pierre Bergeron (Montreal)

Is the partition function of H3+ correct?

Partition functions are important

Model of WD1247+550 using ab initio H3+ partition function

of Neale & Tennyson (1996)

HCN opacity, Greg Harris

High accuracy ab initio potential and dipole surfaces Simultaneous treatment of HCN and HNC Vibrational levels up to 18 000 cm-1

Rotational levels up to J=60 Calculations used SG Origin 2000 machine 200,000,000 lines computed Took 16 months

Partition function estimates suggest 93% recovery of opacity at 3000 K

Ab initio vs. laboratory

HNC bend fundamental (462.7 cm-1).

•Q and R branches visible.

•Slight displacement of vibrational band centre (2.5 cm-1).

•Good agreement between rotational spacing.

•Good agreement in Intensity distribution.

Q branches of hot bands visible.Burkholder et al., J. Mol. Spectrosc. 126, 72 (1987)

GJ Harris, YV Pavlenko, HRA Jones & J Tennyson, MNRAS, 344, 1107 (2003).

Importance of water spectra

Other• Models of the Earth’s atmosphere• Major combustion product (remote detection of forest fires,

gas turbine engines)

• Rocket exhaust gases: H2 + ½ O2 H2O (hot) • Lab laser and maser spectra

Astrophysics• Third most abundant molecule in the Universe (after H2 & CO)

• Atmospheres of cool stars• Sunspots• Water masers• Ortho-para interchange timescales

Sunspots Image from SOHO : 29 March 2001

Molecules on the Sun

T=5760KDiatomicsH2, CO, CH, OH,CN, etc

SunspotsT=3200KH2, H2O,CO, SiO

Sunspot

lab

Sunspot: N-band spectrum

L Wallace, P Bernath et al, Science, 268, 1155 (1995)

Assigning a spectrum with 50 lines per cm-1

1. Make ‘trivial’ assignments (ones for which both upper and lower level known experimentally)

2. Unzip spectrum by intensity 6 – 8 % absorption strong lines 4 – 6 % absorption medium 2 – 4 % absorption weak < 2 % absorption grass (but not noise)

3. Variational calculations using ab initio potential Partridge & Schwenke, J. Chem. Phys., 106, 4618 (1997) + adiabatic & non-adiabatic corrections for Born-Oppenheimer approximation

4. Follow branches using ab initio predictions branches are similar transitions defined by

J – Ka = na or J – Kc = nc, n constant

Only strong/medium lines assigned so far

OL Polyansky, NF Zobov, S Viti, J Tennyson, PF Bernath & L Wallace, Science, 277, 346 (1997).

Sunspot

lab

Assignm

entsSunspot: N-band spectrum

L-band, K-band & H-band spectra also assignedZobov et al, Astrophys. J., 489, L205 (1998); 520, 994 (2000); 577, 496 (2002).

Assignments using branches

Ab initio potentialLess accurate but extrapolate well

J

Err

or /

cm-1

Determined potentialSpectroscopically

Variational calculations:

Accurate but extrapolate poorly

ObservedLudwigJorgensen

Miller & Tennyson

Spectrum of M-dwarf star TVLM 513

Water opacities

HRA Jones, S Viti, S Miller, J Tennyson, F Allard & PH Hauschildt (1996)

Viti & Tennyson computed VT2 linelist:All vibration-rotation levels up to 30,000 cm-1

Giving ~ 7 x 108 transitionsSimilar study by Partridge & Schwenke (PS), NASA AmesNew study by Barber & Tennyson (BT1/BT2)

Computed Water opacity• Variational nuclear motion calculations

• High accuracy potential energy surface

• Ab initio dipole surface

Spectroscopically determined water potentials

Reference Year vib/cm-1 Nvib Emax /cm-1

Hoy, Mills & Strey 1972 214 25 13000

Carter & Handy 1987 2.42 25 13000

Halonen & Carrington 1988 5.35 54 18000

Jensen 1989 3.22 55 18000

Polyansky et al (PJT1) 1994 0.6 40 18000

Polyansky et al (PJT2) 1996 0.94 63 25000

Partridge & Schwenke 1997 0.33 42 18000

Shirin et al 2003 0.10 106 25000

mportant to treat vibrations and rotations

Emission spectra of comet 153P/Ikeya-Zhang (C/2002 C1)

N. Dello Russo et al, Icarus, 168, 186 (2004) & Astrophys. J., 621, 537 (2005)Gives rotational temperaturesRotational temperatures & ortho/para ratios

Solarpumping

Emissionlines

Water in Mira

Cooler than sunspot, but what is T?

vr = 92 km s-1

NovaV838 MonExplodedFeb 2002

DPK Banerjee, R.J. Barber, N.K. Ashok & J. Tennyson, Astrophys. J. Lett (submitted).

Water assignments using variational calculations

• Long pathlength absoption (T = 296K) 9000 - 27000 cm-1

Fourier Transform and Cavity Ring Down

• Laboratory emisson spectra (T =13001800K) 400 – 6000 cm-1

• Absorption in sunspots (T = 3200 K) N band, L band, K band, H band 10-12m 3 m 2 m 1.4 m

30000 new lines assigned

Dataset of 13500 measured H216O energy levels

J. Tennyson, N.F. Zobov, R. Williamson, O.L. Polyansky & P.F. Bernath,J. Phys. Chem. Ref. Data, 30, 735 (2001).

New: lab torch spectra (T ~ 3000 K) from Bernath. 100 000+ lines.

Bob Barber

Greg Harris

Theoretical Atomic and Molecular Physics and Astrophysics

Accuracy better than 1cm1 • Adiabatic or Born-Oppenheimer Diagonal Correction (BODC)

• Non-adiabatic corrections for vibration and rotation

• Electronic (kinetic) relativistic effect

• Relativistic Coulomb potential (Breit effect)

• Radiative correction (Lamb shift or qed)

Can BO electronic structure calculations be done this accurately?

Variational rotation-vibration calculations with exact kinetic energy operator accurate to better than 0.001 cm1

mode Eobs / cm-1 BO +Vad

011 2521.409 0.11 0.24 100 3178.290 1.30 0.40 020 4778.350 0.00 0.50 022 4998.045 0.30 0.64 111 5554.155 1.40 0.50

1 2992.505 1.46 0.36 2 2205.869 0.47 0.25 3 2335.449 +0.47 0.14

1 2736.981 1.04 0.28 2 1968.169 +0.58 0.11 3 2078.430 0.74 0.18

Ab initio vibrational band origins

H2D+

H3+

D2H+

mode Eobs / cm1 BO +Vad v nuc

011 2521.409 0.11 0.24 +0.056 100 3178.290 1.30 0.40 +0.025 020 4778.350 0.00 0.50 +0.020 022 4998.045 0.30 0.64 +0.010 111 5554.155 1.40 0.50 0.000

1 2992.505 1.46 0.36 0.020 2 2205.869 0.47 0.25 0.050 3 2335.449 +0.47 0.14 +0.090

1 2736.981 1.04 0.28 +0.001 2 1968.169 +0.58 0.11 +0.023 3 2078.430 0.74 0.18 0.004

Ab initio vibrational band origins

H2D+

H3+

D2H+

O.L. Polyansky and J. Tennyson, J. Chem. Phys., 110, 5056 (1999).

J Ka Kc J Ka Kc Eobs / cm-1 BO +Vad v nuc + KNBO

3 2 1 3 2 2 2225.501 0.385 0.245 0.062 0.044

3 2 1 2 0 2 2448.627 0.521 0.259 0.011 0.076

2 2 0 2 2 1 2208.417 0.435 0.242 0.050 0.068

2 2 1 2 0 2 2283.810 0.521 0.239 +0.030 0.059

2 2 0 1 0 1 2381.367 0.573 0.250 +0.008 0.060

3 3 1 2 1 2 2512.598 0.647 0.250 +0.075 0.099

2 0 2 3 1 3 2223.706 0.418 0.163 +0.050 +0.068

2 2 1 3 1 2 2242.303 0.753 0.151 +0.140 +0.095

2 1 2 2 2 1 2272.395 0.420 0.168 +0.035 +0.099

2 2 0 2 1 1 2393.633 0.320 0.162 +0.140 +0.087

3 3 1 3 2 2 2466.041 0.224 0.164 +0.190 +0.080

3 3 1 2 2 0 2596.960 0.185 0.177 +0.167 +0.077

3 3 0 2 2 1 2602.146 0.203 0.172 +0.167 +0.080

2

3

H2D+ : ab initio spectra

Obs / cm1 5Z1 6Z1 CBS2 CBS+CV3

(010) 1594.75 2.99 2.30 0.32 +0.48 (020) 3155.85 4.22 2.38 0.79 +1.16(030) 4666.73 6.30 3.24 1.52 +2.05(040) 6134.01 9.81 5.54 2.74 +3.20(050) 7542.44 14.70 9.19 4.72 +4.82 (101) 7249.82 +12.51 +10.76 +9.32 5.35 (201) 10613.35 +18.72 +16.46 +13.97 7.47(301) 13830.94 +25.72 +22.81 +18.74 8.97 (401) 13805.22 +32.56 +28.92 +23.06 10.17(501) 19781.10 +40.72 +35.96 +28.68 10.72[104]all 22.84 19.74 16.567.85

Ab initio calculations for water

1 MRCI calculation with Dunning’s aug-cc-pVnZ basis set2 Extrapolation to Complete Basis Set (CBS) limit3 Core—Valence (CV) correction

OL Polyansky, AG Csaszar, J Tennyson, P Barletta, SV Shirin, NF Zobov, DW Schwenke & PJ KnowlesScience, 299, 539 (2003)

BO / cm1 +BODC1 + Non-adiabatic

v nuc2 diag3 full4

(010) 1597.60 0.46 0.19 0.06 0.07 (020) 3157.14 0.94 0.38 0.12 0.15(100) 3661.00 0.55 0.46 0.72 0.70 (030) 4674.88 1.43 0.55 0.18 0.23(110) 5241.83 0.16 0.65 0.77 0.76 (040) 6144.64 2.00 0.71 0.23 0.30(120) 6784.56 0.23 0.83 0.83 0.84(200) 7208.80 1.25 0.88 1.39 1.37 (002) 7450.86 1.47 0.90 1.47 1.57(050) 7555.62 2.71 0.84 0.28 0.32

Born-Oppenheimer corrections for water

1 Born-Oppenheimer diagonal correction using CASSCF wavefunction2 Non-adiabatic correction by scaling vibrational mass, V

3 Two parameter diagonal correction4 Full treatment by Schwenke (J. Phys. Chem. A, 105, 2352 (2001).)

J. Tennyson, P. Barletta, M.A. Kostin, N.F.Zobov, and O.L. Polyansky, Spectrachimica Acta A, 58, 663 (2002).

Ab initio predictions of water levelsIsotopomer N(levels) J(max) / cm

H216O 9426 20 1.17

H217O 669 12 0.28

H218O 2460 12 0.65

D216O 2807 12 0.71

HD16O 1976 12 0.47All water 17338 20 0.95

Rotational non-adiabatic effects very important

Residual sources of error

• Basis set convergence of MRCI:

need extrapolated 7Z• Full CI: contributes ~ 1 cm at 25,000 cm (?)• Surface fitting: 346 points computed,

need 1000 points, reduce by ~ 0.2 cm

• Full inclusion of non-adiabatic effects

up to 25,000 cm-1