Astronomical spectroscopy Lecture 1: Hydrogen and the Early Universe

1. Astronomical spectroscopyLecture 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 The molecular opacity problem M-dwarf l (mm)

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) 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

8. 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

10. 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

11. Physics of molecular opacities:Closed Shell diatomics HeH+ CO, H2, CS, etc Vibration-rotation transitions. Sparse: ~10,000 transitions Generally well characterized by lab data and/or theory (H2 transitions quadrupole only)

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 H2O, HCN, H3+, C3, CH4, HCCH, NH3, 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+

14. Ab initio calculation of rotation-vibration spectra

15. 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)

16. Potentials:Ab initioorSpectroscopically determined

17. Molecule considered at high accuracy H3+ H2O (HDO) H2S HCN/HNC HeH+

18. 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?

19. Partition functions are important Model of WD1247+550 using ab initio H3+ 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 • 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

24. 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

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

26. 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).

27. 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).

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

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

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

31. 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/ • 50,000 processor hours. • Wavefunctions > 0.8 terabites • 221,100 energy levels (all to J=50, E = 30,000 cm-1) 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

33. Raw spectra from DVR3D program suite

34. Energy file: N J sym n E/cm-1 v1 v2 v3 J Ka Kc

35. Transitions file:Nf Ni Aif 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 CO2, 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) Planetary nebula NGC3132 • Photoionisation important • Molecular ions • Hot (T ~ 1000 K) but • Not thermodynamic equilibrium • Electron collisions • Optical pumping

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

44. Rotational excitation of molecular ions: Astrophysical importance Photon dominated regions (PDRs) Electron density, ne ~ 10-4 n(H2) Rotational excitation cross section selectron > 105smolecule Radiative lifetime < mean time between collisions Therefore: Observed emissions proportional to selectron 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 DJ = 1 excitations possible Only DJ = 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. Rotational excitation of molecular ions Have considered HeH+, CH+, NO+, CO+, H2+, HCO+ Find J=2-1 emissions should be observable for HeH+ and others Working on H3+ and H3O+ A. Faure and J. Tennyson, Mon. Not. R. astr. Soc., 325, 443 (2001)

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