1. Astronomical spectroscopy Lecture 1: Hydrogen and the Early Universe Jonathan Tennyson Department of Physics and Astronomy Helsinki University College London December 2006

2. Astronomical Spectroscopy Lecture 1: Hydrogen and the Early Universe Lecture 2: Molecules in harsh environments Lecture 3: The molecular opacity problem

3. Layers in a star: the Sun

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

5. Infra red spectrum of an M-dwarf star

6. Cool stellar atmospheres : dominated by molecular absorption Brown Dwarf M-dwarf The molecular opacity problem (  m)

7. 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) H 2, H 2 O, TiO, ZrO, etc also grains at lower T C-stars: Carbon rich, n(C) > n(O) H 2, CH 4, HCN, C 3, HCCH, CS, etc S-Dwarfs: n(O) = n(C) Rare. H 2, FeH, MgH, no polyatomics Also (primordeal) ‘metal-free’ stars H, H 2, He, H , H 3 + only at low T

8. Also sub-stellar objects: CO less important Brown Dwarfs: T ~ 1500 K H 2, H 2 O, CH 4 T-Dwarfs: T ~ 1000K ‘methane stars’ How common are these? Deuterium burning test using HDO? Burn D only No nuclear synthesis

10. Modeling the spectra of cool stars Spectra very dense – cannot get T from black-body fit. Synthetic spectra require huge databases > 10 6 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

11. Physics of molecular opacities: Closed Shell diatomics CO, H 2, CS, etc Vibration-rotation transitions. Sparse: ~10,000 transitions Generally well characterized by lab data and/or theory (H 2 transitions quadrupole only) HeH +

12. 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

13. Physics of molecular opacities: Polyatomic molecules H 2 O, HCN, H 3 +, C 3, CH 4, HCCH, NH 3, 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: H 2 O, HCN, H 3 +

14. Ab initio calculation of rotation-vibration spectra

15. The DVR3D program suite : triatomic vibration-rotation spectra Potential energy Surface,V(r 1,r 2,  ) Dipole function  (r 1,r 2,  ) 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

16. Potentials: Ab initio or Spectroscopically determined

17. H 3 + H 2 O (HDO) H 2 S HCN/HNC HeH + Molecule considered at high accuracy

18. Partition functions are important Model of cool, metal-free magnetic white dwarf WD1247+550 by Pierre Bergeron (Montreal) Is the partition function of H 3 + correct?

19. Partition functions are important Model of WD1247+550 using ab initio H 3 + partition function of Neale & Tennyson (1996)

20. 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 2006 edition uses observed energy levels

21. 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)

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

23. 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: H 2 + ½ O 2 H 2 O (hot) Lab laser and maser spectra Astrophysics Third most abundant molecule in the Universe (after H 2 & CO) Atmospheres of cool stars Sunspots Water masers Ortho-para interchange timescales

24. Sunspots Image from SOHO : 29 March 2001 Molecules on the Sun T=5760K Diatomics H 2, CO, CH, OH, CN, etc Sunspots T=3200K H 2, H 2 O, CO, SiO

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

26. 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 – K a = n a or J – K c = n c, 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).

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

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

29. Spectroscopically determined water potentials ReferenceYear  vib /cm -1 N vib E max /cm -1 Hoy, Mills & Strey19722142513000 Carter & Handy1987 2.422513000 Halonen & Carrington1988 5.355418000 Jensen1989 3.225518000 Polyansky et al (PJT1)1994 0.64018000 Polyansky et al (PJT2)1996 0.946325000 Partridge & Schwenke1997 0.334218000 Shirin et al2003 0.1010625000  mportant to treat vibrations and rotations

30. Viti & Tennyson computed VT2 linelist: Partridge & Schwenke (PS), NASA Ames New study by Barber & Tennyson (BT2) Computed Water opacity Variational nuclear motion calculations High accuracy potential energy surface Ab initio dipole surface

31. 50,000 processor hours. Wavefunctions > 0.8 terabites 221,100 energy levels (all to J=50, E = 30,000 cm  ) 14,889 experimentally known 506 million transitions (PS list has 308m) >100,000 experimentally known with intensities  Partition function 99.9915% of Vidler & Tennyson’s value at 3,000K New BT2 linelist Barber et al, Mon. Not. R. astr. Soc. 368, 1087 (2006). http://www.tampa.phys.ucl.ac.uk/ftp/astrodata/water/BT2/

32. Comparison with Experimental Levels BT2AMES Agreement:% Within 0.10 cm -1 48.759.2 Within 0.33 cm -1 91.485.6 Within 1 cm -1 99.292.6 Within 3 cm -1 99.996.5 Within 5 cm -1 100.097.0 Within 10 cm -1 100.098.1 Number of Experimental Levels: 14,889

33. 1715470339003.8927003.799 2000.092 4.01E-032.78E-223.89E-04 6.71E-01 1303831179098.5307098.116 2000.415 1.56E-031.01E-221.41E-04 5.59E-01 17084604710486.1388485.481 2000.657 4.69E-021.12E-211.56E-03 7.84E+00 16077614510939.5328938.685 2000.848 4.83E-038.33E-231.16E-04 9.34E-01 161115154407.2212406.299 2000.922 2.77E-025.25E-207.34E-02 5.35E+00 060165054407.3552406.297 2001.058 3.26E-022.06E-202.88E-02 6.30E+00 14160404611384.2459383.183 2001.062 6.66E-038.35E-231.17E-04 1.86E+00 16078706010955.9148954.726 2001.188 1.69E-022.88E-224.03E-04 3.27E+00 071197096034.9924033.695 2001.297 7.29E-041.43E-222.00E-04 1.22E-01 151104507512912.87110911.526 2001.344 3.36E-021.40E-221.96E-04 7.68E+00 Raw spectra from DVR3D program suite

34. ABC D EFGH IJK 43432111508730.1369980211138 43433111518819.7739620401166 43434111528918.53621500211210 43435111538965.4961300211156 43436111548975.1451752001148 43437111559007.8688941011138 43438111569082.4138911201166 43439111579170.3438711011156 43440111589223.4441580021148 43441111599264.4898152001166 43442111609267.08831605011210 43443111619369.8877220211174 43444111629434.0025470401184 43445111639457.2726551011174 43446111649498.0127280021166 43447111659565.8900231201184 Energy file : N J sym n E/cm -1 v 1 v 2 v 3 J K a K c

35. 1448481461833.46E-04 1153091085207.42E-04 1960181984131.95E-04 703177031.13E-02 1491761501231.69E-04 81528787342.30E-01 80829782378.83E-04 2096722108762.51E-01 2070262032412.72E-04 1889721849711.25E-01 1524711533991.12E-02 39749374791.46E-07 10579158826.90E-05 34458356171.15E-03 Transitions file: N f N i A if 12.8 Gb Divided into 16 files by frequency For downloading

36. S.A. Tashkun, HiRus conference (2006)

37. Astronomical Spectroscopy Lecture 1: Hydrogen and the Early Universe Lecture 2: Molecules in harsh environments Lecture 3: The molecular opacity problem Merry Christmas

38. Master file strategy: Inclusion of Experimental (+ other theoretical) data Added to record. Data classified: Property of level  Energy File Experimental levels (already included) Alternative quantum numbers (local modes) Property of transition  Transition File Measured intensities or A coefficients Line profile parameters Line mixing as a third file? Location of partition sums?

39. Spectrum obtained with the Infrared Space Observatory toward the massive young stellar object AFGL 4176 in a dense molecular cloud. The strong, broad absorption at 4.27  m is due to solid CO 2, whereas the structure at 4.4- 4.9  m indicates the presence of warm, gaseous CO along the line of sight. van Dishoeck et al. 1996.

40. Photon dominated region (PDR)

41. Photon dominated regions (PDRs) Photoionisation important Molecular ions Hot (T ~ 1000 K) but Not thermodynamic equilibrium Electron collisions Optical pumping Planetary nebula NGC3132

43. Cernicharo, Liu et al, Astrophys. J., 483, L65 (1997).

44. Rotational excitation of molecular ions: Astrophysical importance Photon dominated regions (PDRs) Electron density, n e ~ 10  4 n(H 2 ) Rotational excitation cross section  electron > 10 5  molecule Radiative lifetime < mean time between collisions Therefore: Observed emissions proportional to  electron x column density Similar arguments hold for vibrational excitation

45. Rotational excitation of molecular ions: Theoretical models Standard model Dipole Coulomb-Born approximation Only considers (long-range) dipole interactions Only  J = 1 excitations possible Only  J = 1 emissions should be observed No experimental data available for electron impact rotational excitation of molecular ions Tests of this model performed with R-matrix calculations which explicitly include short-range electron-molecular ion interactions

49. Have considered HeH +, CH +, NO +, CO +, H 2 +, HCO + A. Faure and J. Tennyson, Mon. Not. R. astr. Soc., 325, 443 (2001) Working on H 3 + and H 3 O + Find J=2-1 emissions should be observable for HeH + and others Rotational excitation of molecular ions

50. Summary of results  J = 1  c Coulomb-Born model satisfactory  c Short range interactions important Find  c ~ 2 Debye  J = 2 Dominated by short range interactions Always important, can be bigger than  J = 1  J > 2 Determined by short-range interactions Usually small, but  J = 3 can be significant For light molecules (H containing diatomics), cross-sections need to energy modified near threshold

52. Comets Dirty snowballs which link our solar system with the ISM Comet Hale-Bopp

53. Molecules identified in comet Hale-Bopp Simple species H 2 O HDO CO CO 2 H 2 S SO SO 2 OCS CS NH 3 Molecular ions H 2 O + H 3 O + HCO + CO + Organic and similar HCN DCN CH 3 CN HNC HC 3 N HNCO C 2 H 2 CH 3 OCHO C 2 H 6 CH 4 NH 2 CHO CH 3 OH H 2 CO HCOOH H 2 CS Radicals OH CN NH 2 NH C 3 C 2