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

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

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 Brown Dwarf M-dwarf The molecular opacity problem (  m)

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

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

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

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 +

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 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 +

Ab initio calculation of rotation-vibration spectra

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).

Potentials: Ab initio or Spectroscopically determined

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

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

Partition functions are important Model of WD using ab initio H 3 + 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 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

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: 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

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

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 – 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).

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).

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

Spectroscopically determined water potentials ReferenceYear  vib /cm -1 N vib E max /cm -1 Hoy, Mills & Strey Carter & Handy Halonen & Carrington Jensen Polyansky et al (PJT1) Polyansky et al (PJT2) Partridge & Schwenke Shirin et al  mportant to treat vibrations and rotations

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

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 % of Vidler & Tennyson’s value at 3,000K New BT2 linelist Barber et al, Mon. Not. R. astr. Soc. 368, 1087 (2006).

Comparison with Experimental Levels BT2AMES Agreement:% Within 0.10 cm Within 0.33 cm Within 1 cm Within 3 cm Within 5 cm Within 10 cm Number of Experimental Levels: 14,889

E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+00 Raw spectra from DVR3D program suite

ABC D EFGH IJK Energy file : N J sym n E/cm -1 v 1 v 2 v 3 J K a K c

E E E E E E E E E E E E E E-03 Transitions file: N f N i A if 12.8 Gb Divided into 16 files by frequency For downloading

S.A. Tashkun, HiRus conference (2006)

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

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?

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  m indicates the presence of warm, gaseous CO along the line of sight. van Dishoeck et al

Photon dominated region (PDR)

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

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

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

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

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

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

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

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