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Molecular spectroscopy for exoplanets: II - Jonathan Tennyson

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Brave new worlds
May 29-June 03, 2016 – Lake Como School of Advanced Studies

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Molecular spectroscopy for exoplanets: II - Jonathan Tennyson

  1. 1. Jonathan Tennyson University College London Brave New Worlds Lake Como, June 2016 Molecular spectroscopy for exoplanets: II
  2. 2. Molecular spectroscopy for exoplanets Lecture 1 Molecular spectroscopy: basics Lecture 2 for astronomy/exoplanets
  3. 3. Lyman bands Werner bands Electronic transitions in H2
  4. 4. Spectrum of ζ Oph showing rotational lines of X 1 Σg + (υ" = 0) → B 1 Σu + (υ' = 4,5) transitions in the Lyman bands of H2. (L. Spitzer, Jr. and E. B. Jenkins, Ann. Rev. Astron. Astrophys., 1975, 13, 133.) Notation: (v’,v”) ie (upper vib state, lower vib state)
  5. 5. Spectroscopy of H2 • There is a lot of hydrogen in the Universe! • No dipole allowed rotational or ro-vibrational transitions • Undergoes quadrupole transitions instead • VERY weak (about factor of 10-9 ) • New selection rules: ∆J = +2 S –branch ∆J = 0 Q –branch ∆J = -2 O –branch
  6. 6. Jupiter’s aurorae: electronic emission from H2
  7. 7. Infrared emission from shocked-heated H2 in the Orion molecular cloud: transitions in the υ = 2 → υ = 1 and υ = 1 → υ = 0 bands. (N. S. Scoville, D. N. B. Hall, S. G. Kleinmann & S. T. Ridway, 1982, Astrosphys. J., 253, 136.)
  8. 8. The infrared spectrum of Uranus is dominated by lines of the fundamental rotation-vibration band of H2. In addition to the bright emission lines, which are labeled, pressure-broadened S(1), S(0) and Q(1) absorption of H can be seen.
  9. 9. Spectra of molecular of hydrogen Lyman & Werner bands Vib-Rot Rotations 21 cm line
  10. 10. Molecules in magnetic fields Zeeman effect: “weak” field B ∆E = M µB gJ B Where µB is Bohr Magneton, quantum of magnetic effects J is total angular momentum (not just rotation) M is projection of J along B, -J < M < J in steps of 1 (2J+1) values gJ is Lande g-factor Small for closed shell species eg H2O, CH4, etc Significant for open shell eg TiO, VO, C2, etc
  11. 11. Splitting in a weak magnetic field Transitions: extra selection rule ∆M = -1,0,+1 (not 0 0) Svetlana V Berdyugina, & SK Solanki, A+A, 385 (2002) 701
  12. 12. Cool atmospheres: dominated by molecular absorption Brown Dwarfs M-dwarf The molecular opacity problem Exoplanets? M Dwarf Planet Marley & Leggett (2008)
  13. 13. 1 2 3 4 5 6 7 8 9 10 0.01 0.1 1 10 100 1000 10000 100000 1000000 Intensity/[cm/mole] wave length / µm 1500K 1200K 900K 600K 300K Absorption spectra of 14 NH3: Temperature effect hc N e TQ e SI AkThc kTE 3)4( ~8 ]1[ )( )if()if( 0 if 3 /~ / if i πε νπν− − −←=←
  14. 14. Methane, CH4
  15. 15. Temperature-dependent colours of methane
  16. 16. Exoplanet spectroscopy do’s + don’t’s Do: •Use HITRAN for models of earth-like planets •Give a proper attribution of spectroscopic data Don’t: •Use HITRAN if T > 400 K •Cite HITRAN when your data comes from elsewhere
  17. 17. •5 year project from May 2011 •Provide data for all molecular transitions important for exoplanet atmospheres •Methodology: first principles quantum mechanical calculations, informed by experiment J Tennyson and S.N. Yurchenko, MNRAS, 425, 21 (2012).
  18. 18. Theoretical solution Paul Dirac (1929): The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known… ….the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble For molecular spectra: Solve time-independent Schrodinger Equation
  19. 19. Ab initio calculationsAb initio calculations DMS PES Variational calculations Rovibrational wavefunctions Rovibrational energies Intensities (Einstein Aif) Line list Refinement Method: Spectrum from the “first-principles”
  20. 20. How to compute a line list: Step 1: electronic structure calculation Solve electronic structure problem on a grid of points using Quantum Chemistry code eg MOLPRO e.g. Diatomic such NaCl
  21. 21. How to compute a line list: Step 1: electronic structure calculation At the same time compute the dipole moment µ(R) at each geometry -
  22. 22. How to compute a line list: Step 2: ab initio potential energy surface (curve) Fit electronic structure points to a functional form
  23. 23. How to compute a line list: Step 3: solve the nuclear motion problem Variational solution: Level (closed shell diatomic) Duo (open shell diatomic) DVR3D (triatomics) TROVE (polyatomics) AngMol (larger systems) Gives set of ro-vib energy levels
  24. 24. How to compute a line list: Step 4: compare with experiment Compare ab initio levels with measured ones
  25. 25. How to compute a line list: Step 5: Fit new potential to observed levels Gives spectroscopically-determined potential
  26. 26. How to compute a line list: Step 6: solve the nuclear motion problem Variational solution: Final energy levels
  27. 27. How to compute a line list: Step 7: Compute transition frequencies List of transitions
  28. 28. How to compute a line list: Step 8: compute Einstein A coefficients Final line list stored as .states file with all energies, quantum numbers, ets .trans file with i, f, Aif New release of ExoMol database: J Tennyson et al, J Mol Spectrosc (in press), arXiv:1603.05890
  29. 29. Ab initio calculationsAb initio calculations DMS PES Variational calculations Rovibrational wavefunctions Rovibrational energies Intensities (Einstein Aif) Line list Refinement Method: Spectrum from the “first-principles”
  30. 30. Shayesteh et al 2007 MOLPRO Line list: MgH Potential energy curve Dipole moment curve Line list: 6690 lines, Nmax=60 Solve for the motion of the nuclei MOLPRO REFINED Ab initio: solve for motion of electrons B Yadin et al, MNRAS 425, 34 (2012) LEVEL 8.0 R. Le Roy, Waterloo, Canada
  31. 31. Line list: CaO Solve for the motion of the nuclei New program duo SN Yurchenko et al, Comp Phys Comms 202, 262 (2016) Potential energy Dipole moment REFINED Khalil et al (2011) SN Yurchenko et al, MNRAS 456, 4524 (2016) Line list: 22 M lines
  32. 32. Dipole moment TROVE: Yurchenko, Thiel, Jensen PH3 Potential energy Tunneling motion neglected Solve for the motion of the nuclei Line list: 16.8 billion transitions for T up to 1500 K TROVE HITRANJPL Ab initio PES [CCSD(T)/aug-cc-pV(Q+d)Z] Refined using lab spectra R. I. Ovsyannikov et al. J. Chem. Phys 129, 044309 (2008). Ab initio: CCSD(T)/aug-cc-pVTZ S.N. Yurchenko et al. J. Mol. Spectrosc 239, 71 (2006). TROVE JPL HITRAN First principles Predictions of tunnelling being investigated C Sousa-Silva, MNRAS, 446, 2337 (2015).
  33. 33. 1x10 -30 1x10 -28 1x10 -26 1x10 -24 1x10 -22 1x10 -20 1x10 -20 1x10 -22 1x10 -24 1x10 -26 1x10 -28 1x10 -30 1 2 3 4 5 6 7 8 9 10 HITRAN wavelength, µm Intensity(cm/molecule) ExoMol Dipole moment TROVE Yurchenko, Thiel, Jensen CH4 9D surface 130 000 geometries Potential energy Ab initio 10 electrons Ground electronic state Three 9D surfaces 130 000 geometries Solve for the motion of the nuclei Line list: 9.8 Billion transitions MOLPRO CCSD(T)-f12/QZ MOLPRO CCSD(T)-f12/QZ Ab initio: solve for motion of electrons 10to10 SN Yurchenko & J Tennyson, MNRAS 440, 1649 (2014)
  34. 34. A. Campargue et al. / Icarus 219 (2012) 110–128 CH4: spectrum is very complex hc N e TQ e SI AkThc kTE 3)4( ~8 ]1[ )( )if()if( 0 if 3 /~ / if i πε νπν− − −←=←
  35. 35. 0 5 10 15 20 25 30 35 40 45 50 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000 220000 Number of eigenvalues N J Matrix dimension (F symmetry) CH4 diagonalization: Size of the problem LAPACK (DSYEV) DARW IN SCALAPACK (PDSYEV) COSMOS II/DARW IN Acknowledgment: Andrey Kaliazin Dirac/COSMOS SGI: Jan Wilson, Simon Appleby Cheng Liao
  36. 36. 0 5 10 15 20 25 30 35 40 45 50 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000 220000 Number of eigenvalues N J Matrix dimension (F symmetry) CH4 diagonalization: Size of the problem 2.5 hours 15 hours 6 hours 16 nodes = 1 DARWIN socket
  37. 37. 0 5 10 15 20 25 30 35 40 45 50 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000 220000 Number of eigenvalues N J Matrix dimension (F symmetry) CH4 diagonalization: Size of the problem 4 hours 64 cores 9 hours 144 cores 11 hours 160 cores 6 hours 96 cores COMSOS II DARWIN
  38. 38. CH4
  39. 39. CH4
  40. 40. CH4
  41. 41. CH4
  42. 42. 3.86783374E-18 1.63418438E-17 ~350000 lines ~ 1010 lines Absorption spectra of CH4: from experimental line list
  43. 43. T 4.5 Observed (SpeX@IRTF) VSTAR spectra of the T4.5 brown dwarf: a “methane dwarf” Cushing ,Rayner, Vacca (2005) VSTAR STDS CH4 (empirical) VSTAR ExoMol CH4 (10to10) SN Yurchenko, J Tennyson, J Bailey, MDJ Hollis, G Tinetti, PNAS, 111, 9379 (2014) 2MASS 0559-14
  44. 44. 4.5 million CPUh DiRAC HPC (COSMOS and Darwin) and about 6 months of the human time
  45. 45. Molecular spectra for atmospheric species • Line positions • Line intensities • Line profile Measured very accurately Often measured to only 5 – 10% Voigt profile + As stored in databases such as HITRAN: earth’s atmosphere, 296 K ExoMol: exoplanets, brown dwarfs, cool stars, up to 3000 K CDMS/JPL: ISM, long wavelength only, up to ~100 K
  46. 46. 12 FACTORS: ab initio dipole moments
  47. 47. Dipole moment of water at equilibrium . Contribution Value (a.u.) Uncertainty (a.u.) Nonrelativistic, all electron 0.7310 0.0005 Relativistic correction −0.0017 0.0001 Vibrational averaging 0.0001 0.0001 Final value for the ground-state dipole 0.7294 0.0006 Experimental value (Clough et al, 1973) 0.7296 0.0002 L. Lodi, R.N. Tolchenov, J. Tennyson, A.E. Lynas-Gray, S.V. Shirin, N.F. Zobov, O.L. Polyansky, A.G. Csaszar, J. van Stralen & L. Visscher, J. Chem. Phys., 128, 044304 (2008) Also L. Lodi, J. Tennyson and O.L. Polyansky, J. Chem. Phys., 135, 034113 (2011)
  48. 48. : OL Polyansky, K Bielska, M Ghysels, L Lodi, NF Zobov, JT Hodges & J Tennyson, Phys Rev Letts 114, 243001 (2015) High-Accuracy CO2 Line Intensities Determined from Theory and Experiment (30013 – 00001) 6200 – 6258 cm-1
  49. 49. CO2 (20012 - 00001) band near 2 µm Theory New measurements J Brunzendorf et al (Braunschweig) Agree within 0.35%
  50. 50. Calculating transition dipoles and intensities S = |< i | µ | f >|2 = | |2 < i | initial wavefunction | f > final wavefunction µdipole moment Intensity α to dipole squared I (T) Role of the wavefunction?
  51. 51. Published in MNRAS I.BeH, MgH, CaH II.SiO III.HCN/HNC IV.CH4 V.NaCl, KCl VI.PN VII. PH3 VIII. H2CO IX.AlO X.NaH XI.HNO3 XII. CS XIII. CaO XIV. SO2 XV. H2S XVI. HOOH XVII. SO3 (Virtually) Complete •H2 18 O, H2 17 O •H3 + •SH, AlH •H2 16 O •NO, NS •CrH In progress •TiO •C3 •PH, PO, PS •TiH •MnH •NaO Hot line lists Planned •NH3 •MgO •NiH •FeH • C2H4 • SiH • HCCH • CH3Cl • SiH4 • Larger hydrocarbons
  52. 52. www.worldscibooks.com/physics/7574.html About the first edition “The best book for anyone who is embarking on research in astronomical spectroscopy” Contemporary Physics (2006) Published 2011

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