1. How to Measure Evolution in Fundamental Constants of Physics Using Large Telescopes Chris Churchill (Penn State) Evolution in the Fine Structure Constant  = (  z -  0 )/  0  = e 2 /hc

2. John Webb (UNSW) - Analysis; Fearless Leader Steve Curran (UNSW)- QSO (mm and radio) obs. Vladimir Dzuba (UNSW)- Computing atomic parameters Victor Flambaum (UNSW)- Atomic theory Michael Murphy (UNSW)- Spectral analysis John Barrow (Cambridge)- Interpretations Fredrik T Rantakyrö (ESO)- QSO (mm) observations Chris Churchill (Penn State) - QSO (optical) observations Jason Prochaska (Carnegie Obs.)- QSO (optical) observations Arthur Wolfe (UC San Diego)- QSO optical observations Wal Sargent (CalTech) - QSO (optical) observations Rob Simcoe (CalTech) - QSO (optical) observations Juliet Pickering (Imperial)- FT spectroscopy Anne Thorne (Imperial)- FT spectroscopy Ulf Greismann (NIST)- FT spectroscopy Rainer Kling (NIST)- FT spectroscopy Webb etal. 2001 (Phys Rev Lett 87, 091391)

3. 49 Systems ; 0.5 < z < 3.5 ; 28 QSOs  x 10 -5 (4.1  )

4. Intrinisic QSO Emission/Absorption Lines

5. H I (Lyman-  ) 1215.67

6. C IV 1548, 1550 & Mg II 2796, 2803

8. The “alkali doublet method” Resonance absorption lines such as CIV, SiIV, MgII are commonly seen at high redshift in intervening gas clouds. Bethe & Salpeter 1977 showed that the     of alkali-like doublets, i.e transitions of the sort are related to  by which leads to   Note, measured relative to same ground state

9. But there is more than just The doublets… there are other transitions too!

10. In addition to alkali-like doublets, many other more complex species are seen in quasar spectra. Note we now measure relative to different ground states EcEc EiEi Represents different FeII multiplets The “Many-Multiplet method” - using different multiplets and different species simultaneously - order of magnitude improvement Low mass nucleus Electron feels small potential and moves slowly: small relativistic correction High mass nucleus Electron feels large potential and moves quickly: large relativistic correction

11. Relativistic shift of the central line in the multiplet Procedure 1. Compare heavy (Z~30) and light (Z<10) atoms, OR 2. Compare s p and d p transitions in heavy atoms. Shifts can be of opposite sign. Illustrative formula: E z=0 is the laboratory frequency. 2 nd term is non-zero only if  has changed. q is derived from relativistic many-body calculations. K is the spin-orbit splitting parameter. Numerical examples: Z=26 (s p) FeII 2383A:   = 38458.987(2) + 1449x Z=12 (s p) MgII 2796A:   = 35669.298(2) + 120x Z=24 (d p) CrII 2066A:   = 48398.666(2) - 1267x where x =  z  0  2 - 1 MgII “anchor”

12. High-z (1.8 – 3.5) Low-z (0.5 – 1.8) FeII MgI, MgII ZnII CrII FeII Positive Mediocre Anchor Mediocre Negative SiIV

13. Low-z vs. High-z constraints:  /  = -5×10 -5 High-z Low-z

14. Current results:

15. Possible Systematic Errors 1.Laboratory wavelength errors 2.Heliocentric velocity variation 3.Differential isotopic saturation 4.Isotopic abundance variation (Mg and Si) 5.Hyperfine structure effects (Al II and Al III ) 6.Magnetic fields 7.Kinematic Effects 8.Wavelength mis-calibration 9.Air-vacuum wavelength conversion (high-z sample) 10.Temperature changes during observations 11.Line blending 12.Atmospheric dispersion effects 13.Instrumental profile variations

16. ThAr lines Quasar spectrum Using the ThAr calibration spectrum to see if wavelength calibration errors could mimic a change in  Modify equations used on quasar data: quasar line:  =   (quasar) + q 1 x ThAr line:  =   (ThAr) + q 1 x   (ThAr) is known to high precision (better than 0.002 cm -1)

17. ThAr calibration results:

18. Atmospheric dispersion effects:

19. Atmospheric dispersion results: Pre-rotator Post-rotator Rotator

20. Isotopic ratio evolution:

21. Isotopic ratio evolution results: Isotope

22. Correcting for both systematics: Rotator + Isotope

23. Conclusions and the next step 1.~100 Keck nights; QSO optical results are “clean”, i.e. constrain a directly, and give ~6s result. Undiscovered systematics? If interpreted as due to a, a was smaller in the past. 2.3 independent samples from Keck telescope. Observations and data reduction carried out by different people. Analysis based on a RANGE of species which respond differently to a change in alpha: (Churchill: MgII/FeII); (Prochaska: dominated by ZnII, CrII, NiII); (Sargent: all the above others eg AlII, SiII). 3.Work for the immediate future: (a) 21cm/mm/optical analyses. (b) UVES/VLT, SUBARU data, to see if same effect is seen in independent experiments; (c) new experiments at Imperial College to verify laboratory wavelengths;

24. The position of a potential interloper “X” Suppose some unidentified weak contaminant is present, mimicking a change in alpha. Parameterise its position and effect by d  : MgII line generated with N = 10 12 atoms/cm 2 b = 3 km/s Interloper strength can vary Position of fitted profile is measured

25. Parameters describing ONE absorption line b (km/s)  1+z) rest N (atoms/cm 2 ) 3 Cloud parameters: b, N, z “Known” physics parameters: rest, f, 

26. Cloud parameters describing TWO (or more) absorption lines from the same species (eg. MgII 2796 + MgII 2803 A) z b bN Still 3 cloud parameters (with no assumptions), but now there are more physics parameters

27. Cloud parameters describing TWO absorption lines from different species (eg. MgII 2796 + FeII 2383 A) b(FeII) b(MgII) z(FeII) z(MgII) N(FeII) N(MgII) i.e. a maximum of 6 cloud parameters, without any assumptions

28. However… T is the cloud temperature, m is the atomic mass So we understand the relation between (eg.) b(MgII) and b(FeII). The extremes are: A: totally thermal broadening, bulk motions negligible, B: thermal broadening negligible compared to bulk motions,

29. We can therefore reduce the number of cloud parameters describing TWO absorption lines from different species: b Kb z N(FeII) N(MgII) i.e. 4 cloud parameters, with assumptions: no spatial or velocity segregation for different species

30. How reasonable is the previous assumption? FeII MgII Line of sight to Earth Cloud rotation or outflow or inflow clearly results in a systematic bias for a given cloud. However, this is a random effect over and ensemble of clouds. The reduction in the number of free parameters introduces no bias in the results

31. Numerical procedure:  Use minimum no. of free parameters to fit the data  Unconstrained optimisation (Gauss-Newton) non- linear least-squares method (modified version of VPFIT,  explicitly included as a free parameter);  Uses 1 st and 2 nd derivates of    with respect to each free parameter (  natural weighting for estimating  ;  All parameter errors (including those for  derived from diagonal terms of covariance matrix (assumes uncorrelated variables but Monte Carlo verifies this works well)

32. We model the complex profiles as multiple clouds, using Voigt profile fitting (Lorentzian + Gaussian convolved) Free parameters are redshift, z, and  Lorentzian is natural line broadening Gaussian is thermal line broadening (line of sight)

33. 1.Zero Approximation – calculate transition frequencies using complete set of Hartree-Fock energies and wave functions; 2.Calculate all 2 nd order corrections in the residual electron- electron interactions using many-body perturbation theory to calculate effective Hamiltonian for valence electrons including self-energy operator and screening; perturbation V = H-H HF. This procedure reproduces the MgII energy levels to 0.2% accuracy (Dzuba, Flambaum, Webb, Phys. Rev. Lett., 82, 888, 1999) Dependence of atomic transition frequencies on  Important points: (1) size of corrections are proportional to Z 2, so effect is small in light atoms; (2) greatest precision will be achieved when considering all relativistic effects (ie. including ground state)

34. Wavelength precision and q values

35. Line removal checks:

36. Removing MgII2796: Post-removal Pre-removal Line Removal

37. Removing MgII2796: Post-removal Pre-removal Line Removal

38. Number of systems where transition(s) can be removed Transition(s) removed Pre-removal Post-removal