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Cosmological Evolution of the Fine Structure Constant

Cosmological Evolution of the Fine Structure Constant. a = e 2 /hc. Da = ( a z - a 0 )/ a 0. Chris Churchill (Penn State). In collaboration with: J. Webb, M. Murphy, V.V. Flambaum, V.A. Dzuba, J.D. Barrow, J.X. Prochaska, & A.M. Wolfe. Your “Walk Away” Info.

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Cosmological Evolution of the Fine Structure Constant

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  1. Cosmological Evolutionof the Fine Structure Constant a = e2/hc Da = (az-a0)/a0 Chris Churchill (Penn State) In collaboration with: J. Webb, M. Murphy, V.V. Flambaum, V.A. Dzuba, J.D. Barrow, J.X. Prochaska, & A.M. Wolfe

  2. Your “Walk Away” Info • 49 absorption cloud systems over redshifts 0.5–3.5 toward 28 QSOs compared to lab wavelengths for many transitions • 2 different data sets; • low-z (Mg II, Mg I, Fe II) • high-z (Si II, Cr II, Zn II, Ni II, Al II, Al III) • Find Da/a = (–0.72±0.18) × 10-5 (4.1s) (statistical) • Most important systematic errors are atmospheric dispersion (differential stretching of spectra) and isotopic abundance evolution (Mg & Si; slight shifting in transition wavelengths) • Correction for systematic errors yields stronger a evolution

  3. Executive Summary • History/Motivations • Terrestrial and CMB/BBN • QSO Absorption Line Method • Doublet Method (DM) & Results • Many-Multiplet Method (MM) & Results • Statistical and Systematic Concerns • Concluding Remarks

  4. Classes of Theories • Multi-dimensional and String Theories • Scalar Theories • Varying Speed of Light Theories Unification of quantum gravity with other forces… Couples E+M to cosmological mass density… Attempts to solve some cosmological problems…

  5. Varying Speed of Light Theories Motivation is to solve the “flatness” and “horizon” problems of cosmology generated by inflation theory (Barrow 1999). Lc2, where L is the cosmological constant, acts as a “stress”. Changes in c convert the L energy density into radiation (Barrow & Magueijo 2001) Theory allows variation in a to be ~10-5H0 at redshift z=1, and ~10-4H0 at z=1000 (near time of recombination). Magnitude of evolution is proportional to ratio of radiation to matter density.

  6. Varying Speed of Light Theories a(z)/a(BBN) redshift, z Theory allows variation in a to be ~10-5H0 at redshift z=1, and ~10-4H0 at z=1000 (near time of recombination). Magnitude of evolution is proportional to ratio of radiation to matter density.

  7. QSO Absorption Lines (history) QSO absorption line methods can sample huge time span Savedoff (1965) used doublet separations of emission lines from galaxies to search for a evolution (first cosmological setting) Bahcall, Sargent & Schmidt (1967) used alkali-doublet (AD) separations seen in absorption in QSO spectra.

  8. Intrinisic QSO Emission/Absorption Lines

  9. H I (Lyman-a) 1215.67

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

  11. We require high resolution spectra…

  12. Interpreting those cloud-cloud separations….

  13. Spectrum of multi-cloud Mg II system (z=1.32)

  14. And, of course… The Weapon. Keck Twins 10-meter Mirrors

  15. The High Resolution Echelle Spectrograph (HIRES)

  16. 2-Dimensional Echelle Image Dark features are absorption lines

  17. Electron Energy and Atomic Configuration A change in a will lead to a change in the electron energy, D, according to where Z is the nuclear charge, |E| is the ionization potential, j and l are the total and orbital angular momentum, and C(l,j) is the contribution to the relativistic correction from the many body effect in many electron elements. Note proportion to Z2(heavy elements have larger change) Note change in sign as j increases and C(l,j) dominates

  18. The “Doublet Method” ex. Mg IIll2796, 2803 Si IVll1393, 1402 A change in a will lead to a change in the doublet separation according to where (Dl/l)z and (Dl/l)0 are the relative separations at redshift z and in the lab, respectively. Dl 2796 2803

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

  20. Example of a Si IV system at z=2.53 used in the a analysis of Murphy et al (2001)

  21. Si IV Doublet Results: Da/a = –0.51.3 ×10-5 (Murphy et al 2001)

  22. The “Many-Multiplet Method” The energy equation for a transition from the ground state at a redshift z, is written Ez = Ec + Q1Z2[R2-1] + K1(LS)Z2R2+ K2(LS)2Z4R4 Ec= energy of configuration center Q1, K1, K2 = relativistic coefficients L = electron total orbital angular momentum S = electron total spin R = az/a0 Z = nuclear charge

  23. wz = w0 + q1x + q2y A convenient form is: wz= redshifted wave number w0 = rest-frame wave number q1, q2 = relativistic correction coefficients for Z and e- configuration x = (az/a0)2 - 1 y = (az/a0)4 - 1 Mg II 2803 Mg II 2796 Fe II 2600 Fe II 2586 Fe II 2382 Fe II 2374 Fe II 2344

  24. w Shifts for Da/a ~ 10-5 Anchors & Data Precision A precision of Da/a ~ 10-5 requires uncertainties in w0 no greater than 0.03 cm-1 (~0.3 km s-1) Well suited to data quality… we can centroid lines to 0.6 km s-1, with precision going as 0.6/N½ km s-1 Typical accuracy is 0.002 cm-1, a systematic shift in these values would introduce only a Da/a ~ 10-6

  25. Advantages/Strengths of the MM Method • Inclusion of all relativistic corrections, including ground states, provides an order of magnitude sensitivity gain over AD method • In principle, all transitions appearing in QSO absorption systems are fair game, providing a statistical gain for higher precision constraints on Da/a compared to AD method • Inclusion of transitions with wide range of line strengths provides greater constraints on velocity structure (cloud redshifts) • (very important) Allows comparison of transitions with positive and negative q1 coefficients, which allows check on and minimization of systematic effects

  26. Possible Systematic Errors • Laboratory wavelength errors • Heliocentric velocity variation • Differential isotopic saturation • Isotopic abundance variation (Mg and Si) • Hyperfine structure effects (Al II and Al III) • Magnetic fields • Kinematic Effects • Wavelength mis-calibration • Air-vacuum wavelength conversion (high-z sample) • Temperature changes during observations • Line blending • Atmospheric dispersion effects • Instrumental profile variations

  27. Isotopic Abundance Variations There are no observations of high redshift isotopic abundances, so there is no a priori information Focus on the “anchors” Observations of Mg (Gay & Lambert 2000) and theoretical estimates of Si in stars (Timmes & Clayton 1996) show a metallicity dependence We re-computed Da/a for entire range of isotopic abundances from zero to terrestrial. This provides a secure upper limit on the effect.

  28. Correction for Isotopic Abundances Effect low-z Data Corrected Uncorrected This is because all Fe II are to blue of Mg II anchor and have same q1 sign (positive) Leads to positive Da/a For high-z data, Zn II and Cr II are To red of Si II and Ni II anchors and have opposite q1 signs

  29. Atmospheric Dispersion Causes an effective stretching of the spectrumwhich mimics a non-zero Da/a a = pixel size [Å] , d = slit width arcsec/pix, Dψ = angular separation of l1 and l2 on slit, θ = angle of slit relative to zenith Blue feature will have a truncated blue wing! Red feature will have a truncated red wing! This is similar to instrumental profile distortion, effectively a stretching of the spectrum

  30. Correction for Atmospheric Distortions Effect low-z Data Corrected Uncorrected This is because all Fe II are to blue of Mg II anchor and have same q1 sign (positive) Leads to positive Da/a For high-z data, Zn II and Cr II are To blue and red of Si II and Ni II anchors and have opposite q1 signs

  31. Summary of MM Method • 49 absorption clouds systems over redshifts 0.5 to 3.5 toward 28 QSOs compared to lab wavelengths for many transitions • 2 different data sets; • low-z (Mg II, Mg I, Fe II) • high-z (Si II, Cr II, Zn II, Ni II, Al II, Al III) • Find Da/a = (–0.72±0.18) × 10-5 (4.1s) (statistical) • Most important systematic errors are atmospheric dispersion (differential stretching of spectra) and isotopic abundance evolution (Mg & Si; slight shifting in transition wavelengths) • Correction for systematic errors yields stronger a evolution

  32. Da/a = (–0.72±0.18) × 10-5 (4.1s) (statistical)

  33. Hot off the Press Preliminary (yet confident) Findings… Now have a grand total of 138 systems due to adding the HIRES data of Sargent & Simcoe! Find Da/a = (–0.65±0.11) × 10-5 (6s) (statistical) What We Need: The Future Same and new systems observed with different instrument and reduced/analyzed by different software and people. Our plans are to get UVES/VLT and HRS/HET spectra in order to reproduce the HIRES/Keck results

  34. Multi-dimensional Unification Quantization of gravitational interactions… Evolution of scale size of extra dimensions drives variability of coupling constants in the 4-dimensional subspace of Kaluza-Klein and superstring theories a, aweak, astrong, vary as inverse square of dimension scale In M theory (all string theories are limiting cases), only the gravitational force acts in higher dimensions, while weak, strong, and electromagnetic act in 3 dimensional space (Arkani-Hamed 1998; Horava & Witten 1996) Measures of variation in a, aweak, astrong, constrains these theoretical scenarios

  35. Scalar Theories Bekenstein (1982) introduced a scalar field that produces a space-time variation in electron charge (permittivity of free space). Reduces to Maxwell’s theory for constant a. Variation in a coupled to matter density and is therefore well suited for astronomical testing (Livio & Stiavelli 1998). Requires assumptions- there is no single self-consistent scalar field theory incorporating varying a; theoretical limits must all be quoted in conjuction with theoretical framework Bekenstein’s assumptions: covariance, gauge invariance, causality, time reversal of E+M, Robertson-Walker metric; Livio & Stiavelli depends on evolution of H and He mass fractions …

  36. Terrestrial and Laboratory Constraints Clock rates based upon ultra-stable oscillators with relativistic corrections scaling as Za2 Prestage, Robert, & Maleki (1995) used H-maser and Hg+ to constrain Da/a< 1.4 ×10-14 Non-cosmological environment nor detailed theory of space-time variation Note that this is at z=0 in Earth’s gravity field… Oklo phenomenon- natural fission reactor in Gabon, W Africa, occurred 1.8 Bya Shlyakher (1976) and Damour & dyson (1996) used 150Sm isotope to constrain Da/a< 1.2 ×10-7 Note that this is at z~0.1, is in Earth’s gravity field, and is model dependent…

  37. Early Universe (CMB and BBN) (implications) A different value of a would change: • The electromagnetic coupling at time of nucleosynthesis (z~108-109). Assuming a scales with p-n mass difference, 4He abundance yields Da/a < 9.9 ×10-5 (Kolb et al 1986) However, electromagnetic contribution to p-n mass difference is very uncertain • The ionization history of the universe, either postponing (smaller a) or delaying (larger a) the redshift of recombination (z~1000). This would alter the ratio of baryons to photons and the amplitude and position of features in the CMB spectrum (Kujat & Scherrer 2000)

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