1 / 45

Calculating the infrared spectra of hot astrophysical molecules

Calculating the infrared spectra of hot astrophysical molecules. Jonathan Tennyson University College London. SELAC, May 2005. Layers in a star: the Sun. Spectrum of a hot star: black body-like. Infra red spectrum of an M-dwarf star.

wren
Download Presentation

Calculating the infrared spectra of hot astrophysical molecules

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Calculating the infrared spectra of hot astrophysical molecules Jonathan Tennyson University College London SELAC, May 2005

  2. Layers in a star: the Sun

  3. Spectrum of a hot star: black body-like

  4. Infra red spectrum of an M-dwarf star

  5. Cool stellar atmospheres: dominated by molecular absorption Brown Dwarf The molecular opacity problem M-dwarf l (mm)

  6. Cool stars: T = 2000 – 4000 K Thermodynamics equilibrium, 3-body chemistry C 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’ stars H, H2, He, H-, H3+ only at low T

  7. Also sub-stellar objects: CO less important Brown Dwarfs: T ~ 1500 K H2, H2O, CH4 T-Dwarfs: T ~ 1000K ‘methane stars’ How common are these? Deuterium burning test using HDO? Burn D only No nuclear synthesis

  8. 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), see • kurucz.harvard.edu

  9. 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+

  10. 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

  11. 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+

  12. Ab initio calculation of rotation-vibration spectra

  13. The DVR3D program suite: triatomic vibration-rotation spectra 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 Potential energy Surface,V(r1,r2,q) Dipole function m(r1,r2,q)

  14. Potentials:Ab initioorSpectroscopically determined

  15. Molecule considered at high accuracy H3+ H2O H2S HCN/HNC HeH+

  16. 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?

  17. Partition functions are important Model of WD1247+550 using ab initio H3+ partition function of Neale & Tennyson (1996)

  18. 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

  19. 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)

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

  21. Importance of water spectra • Astrophysics • Third most abundant molecule in the Universe • (after H2 & CO) • Atmospheres of cool stars • Sunspots • Water masers • Ortho-para interchange timescales • 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

  22. Sunspots T=3200K H2, H2O, CO, SiO T=5760K Diatomics H2, CO, CH, OH, CN, etc Molecules on the Sun Sunspots Image from SOHO : 29 March 2001

  23. Sunspot: N-band spectrum Sunspot lab L Wallace, P Bernath et al, Science, 268, 1155 (1995)

  24. Assigning a spectrum with 50 lines per cm-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).

  25. Sunspot: N-band spectrum Sunspot Assignments lab L-band, K-band & H-band spectra also assigned Zobov et al, Astrophys. J.,489, L205 (1998); 520, 994 (2000); 577, 496 (2002).

  26. Variational calculations: Assignments using branches Spectroscopically Determinedpotential Accurate but extrapolate poorly Error / cm-1 Ab initio potential Less accurate but extrapolate well J

  27. Spectrum of M-dwarf star TVLM 513 HRA Jones, S Viti, S Miller, J Tennyson, F Allard & PH Hauschildt (1996) Water opacities Observed Ludwig Jorgensen Miller & Tennyson

  28. Computed Water opacity • Variational nuclear motion calculations • High accuracy potential energy surface • Ab initio dipole surface Viti & Tennyson computed VT2 linelist: All vibration-rotation levels up to 30,000 cm-1 Giving ~ 7 x 108 transitions Similar study by Partridge & Schwenke (PS), NASA Ames New study by Barber & Tennyson (BT1/BT2)

  29. Spectroscopically determined water potentials Important to treat vibrations and rotations

  30. Emission spectra of comet 153P/Ikeya-Zhang (C/2002 C1) Emission lines Solar pumping N. Dello Russo et al, Icarus, 168, 186 (2004) & Astrophys. J., 621, 537 (2005) Rotational temperatures & ortho/para ratios Gives rotational temperatures

  31. Water in Mira vr = 92 km s-1 Cooler than sunspot, but what is T?

  32. Nova V838 Mon Exploded Feb 2002

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

  34. Water assignments using variational calculations • Long pathlength absoption (T = 296K) 9000 - 27000 cm-1 Fourier Transform and Cavity Ring Down • Laboratory emisson spectra (T =1300-1800K) 400 – 6000 cm-1 • Absorption in sunspots (T = 3200 K) N band, L band, K band, H band 10-12 mm 3 mm 2 mm 1.4 mm • 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.

  35. Bob Barber Greg Harris Theoretical Atomic and Molecular Physics and Astrophysics

  36. Accuracy better than 1cm1 • 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 cm-1

  37. Ab initio vibrational band origins 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 n1 2992.505 1.46 0.36 n2 2205.869 0.47 0.25 n3 2335.449 +0.47 0.14 n1 2736.981 1.04 0.28 n2 1968.169 +0.58 0.11 n3 2078.430 0.74 0.18 H3+ H2D+ D2H+

  38. Ab initio vibrational band origins mode Eobs / cm-1 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 n1 2992.505 1.46 0.36 0.020 n2 2205.869 0.47 0.25 0.050 n3 2335.449 +0.47 0.14 +0.090 n1 2736.981 1.04 0.28 +0.001 n2 1968.169 +0.58 0.11 +0.023 n3 2078.430 0.74 0.18 0.004 H3+ H2D+ D2H+ O.L. Polyansky and J. Tennyson, J. Chem. Phys., 110, 5056 (1999).

  39. H2D+ : ab initio spectra 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 n2 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 n3

  40. Ab initio calculations for water • Obs / cm1 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 • 13805.22 +32.56 +28.92 +23.06 -10.17 • (501) 19781.10 +40.72 +35.96 +28.68 -10.72 • s[104]all 22.84 19.74 16.567.85 1 MRCI calculation with Dunning’s aug-cc-pVnZ basis set 2 Extrapolation to Complete Basis Set (CBS) limit 3 Core—Valence (CV) correction OL Polyansky, AG Csaszar, J Tennyson, P Barletta, SV Shirin, NF Zobov, DW Schwenke & PJ Knowles Science,299, 539 (2003)

  41. Born-Oppenheimer corrections for water BO / cm1 +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 1 Born-Oppenheimer diagonal correction using CASSCF wavefunction 2 Non-adiabatic correction by scaling vibrational mass, mV 3 Two parameter diagonal correction 4 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).

  42. Ab initio predictions of water levels Isotopomer N(levels) J(max) s / cm-1 H216O 9426 20 1.17 H217O 669 12 0.28 H218O 2460 12 0.65 D216O 2807 12 0.71 HD16O 1976 12 0.47 All water 17338 20 0.95 Rotational non-adiabatic effects very important

  43. Residual sources of error • Basis set convergence of MRCI: need extrapolated 7Z • Full CI: contributes ~ 1 cm-1 at 25,000 cm-1(?) • Surface fitting: 346 points computed, need 1000 points, reduce s by ~ 0.2 cm-1 • Full inclusion of non-adiabatic effects up to 25,000 cm-1

More Related