1. 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

2. To Earth CIV SiIVCIISiII Ly  em Ly  forest Lyman limit Ly  NV em SiIV em CIV em Ly  em Ly  SiII quasar Quasars: physics laboratories in the early universe

3. 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

4. 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

5. 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)

6. 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. Q ~ 10K 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”

7. Advantages of the new method 1. Includes the total relativistic shift of frequencies (e.g. for s-electron) i.e. it includes relativistic shift in the ground state (Spin-orbit method: splitting in excited state - relativistic correction is smaller, since excited electron is far from the nucleus) 2. Can include many lines in many multiplets JiJi JfJf (Spin-orbit method: comparison of 2-3 lines of 1 multiplet due to selection rule for E1 transitions - cannot explore the full multiplet splitting) 3. Very large statistics - all ions and atoms, different frequencies, different redshifts (epochs/distances) 4. Opposite signs of relativistic shifts helps to cancel some systematics.

8. Wavelength precision and q values

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

10. Biggest shifts are around 300 m/s. Doppler searches for extra-solar planets reach ~3 m/s at similar spectral resolution (but far higher s/n).

11. Low-z vs. High-z constraints: High-z Low-z

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

14. J.K. Webb, Department of Astrophysics and Optics, School of Physics, UNSW

15. 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, 

16. 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

17. 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

18. 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,

19. 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

20. 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

21. 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)

22. Low redshift data: MgII and FeII (most susceptible to systematics)

23. Low-z MgII/FeII systems:

24. High-z damped Lyman-  systems:

25. Current results:

29. Potential systematic effects Laboratory wavelength errors: New mutually consistent laboratory spectra from Imperial College, Lund University and NIST Data quality variations: Can only produce systematic shifts if combined with laboratory wavelength errors Heliocentric velocity variation: Smearing in velocity space is degenerate with fitted redshift parameters Hyperfine structure shifts: same as for isotopic shifts Magnetic fields: Large scale fields could introduce correlations in  for neighbouring QSO site lines (if QSO light is polarised) - extremely unlikely and huge fields required Wavelength miscalibration: mis-identification of ThAr lines or poor polynomial fits could lead to systematic miscalibration of wavelength scale Pressure/temperature changes during observations: Refractive index changes between ThAr and QSO exposures – random error Line blending: Are there ionic species in the clouds with transitions close to those we used to find  Instrumental profile variations: Intrinsic IP variations along spectral direction of CCD? “Isotope-saturation effect” (for low mass species)  Isotopic ratio shifts: Very small effect possible if evolution of isotopic ratios allowed  Atmospheric dispersion effects: Different angles through optics for blue and red light – can only produce positive  at low redshift

30. 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)

31. ThAr calibration results:

33. 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;

34. Metal absorption Over 60 000 data points! Quasar Q1759+75 H absorption H emission C IV doublet C IV 1550ÅC IV 1548Å QSO absorption lines:  A Keck/HIRES doublet Separation   2

35.  y/y = -1×10 -5

36. 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

37. d       log 10 [N(X)f X /N(MgII)] The strength of a potential interloper “X” Interloper strength described by logN(X)f X. Parameterise strength relative to strength of “host” line (e.g. MgII): log 10 [N(X)f X /N(MgII)] Monte-Carlo simulation: vary interloper strength (y-axis) and , measure  plausible range of parameters for strength and position of and potential interloper Photoionization equilibrium calculations: an exhaustive search for possible candidates (atomic species only) using “CLOUDY” to derive list of weak transitions, any element, any ionization….. No atomic interloper candidates were found for any species