2. Seeing the trees in the forest Group meeting 10 December 2007 Ruth Buning, Wim Ubachs, Michael Murphy, Lex Kaper

3. Has changed on a cosmological timescale?

4. Empirical search for a change in  Compare H 2 spectra of different epochs: Compare H 2 spectra of different epochs: QSO 12 Gyr ago Lab today 90-112 nm ~275-350 nm

7.  /  and spectrum H 2 Recent finding, based on 76 lines in 2 QSO absorbers: Recent finding, based on 76 lines in 2 QSO absorbers: Accurately calculated Lab: 5 x 10 -9 QSO: (2-10) x 10 -7 4σ4σ

8. The QSO absorption sample >2300 HI absorption systems >2300 HI absorption systems ~600 DLA’s ~600 DLA’s 14 H 2 absorption systems (~15%) 14 H 2 absorption systems (~15%) 6 useful 6 useful 4 high-quality spectra 4 high-quality spectra Q0405: 37 lines at z abs =2.59 Q0405: 37 lines at z abs =2.59 Q0347: 39 lines at z abs =3.02 Q0347: 39 lines at z abs =3.02 J2123: ~50 lines at z abs =2.06 from Prochaska, Keck J2123: ~50 lines at z abs =2.06 from Prochaska, Keck Q2348: ~20 lines at z abs =2.43 observed aug. 07, VLT Q2348: ~20 lines at z abs =2.43 observed aug. 07, VLT

9. Aug. ’07 observations

10. Aug. ’07 observations: data

11. Blue CCD chip Red CCD chip 1Red CCD chip 2 Lyman-  of quasar emission z emis =3.0236 C IV emission DLA at z abs =2.615 H 2 region z abs =2.426 DLA at z abs =2.93 DLA at z abs =2.426

12. Spectrum Q2348 DLA at z abs =2.615 DLA at z abs =2.426 H 2 region Ly  at z abs =2.615 Lyman limit  at z abs =2.93

13. L0R0 line of H 2 > 7 velocity components

14. Aug. ’07 observations: data Archival data: Archival data: –Total exposure time 4.5 hr –R = 47,000 –SNR = ~11 August: August: –Total exposure time 19.25 hr –R = 55,000 –SNR = ~25

15. J2123 spectrum (Keck/HIRES, Prochaska) H 2 region Resolution 103,000 ; z abs =2.0593

17. Spectrum analysis: line profile Natural line profile: Lorentz Natural line profile: Lorentz FWHM FWHM

18. Spectrum analysis: line profile Doppler/thermal broadening: Gauss Doppler/thermal broadening: Gauss Turbulence: Gauss with Turbulence: Gauss with Instrument profile Instrument profile

19. Spectrum analysis: line profile Voigt profile = Lorentz * Gauss Voigt profile = Lorentz * Gauss

20. Spectrum analysis: line profile 3 free parameters: 3 free parameters: –z -> position –N -> depth –b -> width Input: Input: –lab wavelengths –oscillator strengths –damping coefficients –mass Physical properties in space Molecular data

21. Spectrum analysis: line profile Multiple lines: Multiple lines: –1 z for each velocity component –1 N for each ‘species’ (J0, J1, J2, etc.) –1 b for each velocity component –Connected via molecular data Difficulties: Difficulties: –Physical conditions in space unknown –Uncertainties in molecular data –Ly  forest

23. HD?

25. Astronomy letters, 2001

26. Conclusions QSO H 2 spectra for  /  determination QSO H 2 spectra for  /  determination –Q0347: 37 lines –Q0405: 39 lines –Q2348: ~20 lines –J2123: ~50 lines HD absorption in J2123 HD absorption in J2123 –Include in  /  analysis –Lab wavelengths –> K coefficients Working on analysis

28. Kueyen

29. Aug. ’07 observations: The Instrument

30. UVES: Ultraviolet – Visual Echelle Spectrograph

31. 300-500 nm 420-1100 nm

32. Spectrum quality Resolving power R=  Resolving power R=  –slitwidth SNR SNR –brightness/sky background –seeing –airmass –total exposure time

33. J2123 spectrum H2H2 Ly 

35. Energy levels in a diatomic molecule Electronic Electronic Vibrationalv Vibrationalv RotationalJ RotationalJ

36. Representation of the energy levels Rotation: Rotation: Vibration: Vibration: (Rigid rotor) (Nonrigid rotor) (Harmonic oscillator) (Anharmonic oscillator)

37. Dunham representation Energies derived from Schrödinger equation and general potential function Energies derived from Schrödinger equation and general potential function These contain the parameters  e and B e, which are mass-dependent These contain the parameters  e and B e, which are mass-dependent

38. The sensitivity coefficients Dependence of transition wavelengths (or energies) on  quantified by sensitivity coefficients: Dependence of transition wavelengths (or energies) on  quantified by sensitivity coefficients: E and dE/dµ derived from Dunham expansion: E and dE/dµ derived from Dunham expansion:

39. The H 2 data Available lab data: Available lab data: –Lyman (B-X): v’=0-18, v’’=0 –Werner (C-X): v’=0-4, v’’=0 –J between 0 and 5