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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 Constraints • QSO Absorption Line Method • Doublet Method (DM) & Results • Many-Multiplet Method (MM) & Results • Statistical and Systematic Concerns • Concluding Remarks

  4. Very Brief History Milne (1935, 1937) and Dirac (1937) postulate that the gravitation constant, G, varied with time. Dirac’s “Large Number Hypothesis” led to theoretical work, development of scalar-tensor generalizations of Einstein’s general relativity (Brans & Dicke 1961) Jordon (1937, 1939) considers other coupling constants Landau (1955) proposes variations in a connected to renormalization in quantum electrodynamics (QED) Modern theories unify gravity with other forces…

  5. Multi-dimensional Unification Quantization of gravitational interactions… Early attempts invoke (4+D)-dimensional curved space-times similar to Kaluza-Klein scenario for E&M + gravity a, aweak, astrong, vary as inverse square of dimension scale Evolution of scale size of extra dimensions drives variability of these coupling constants in the 4-dimensional subspace of Kaluza-Klein and superstring theories Cosmological variation of a may proceed at different rates at different points in space-time (Barrow 1987; Li & Gott 1998)

  6. Multi-dimensional Unification 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) Testing for variation in a, aweak, astrong, tests these theoretical scenarios Was believed scale length of higher dimensions was Plank scale, 10-33 cm, but can be as large as 0.01 mm; this would modify gravity at scales smaller than this size!

  7. 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). Also can be applied to other coupling constants. All require assumptions- there is no single self-consistent scalar field theory incorporating varying a; theoretical limits must all be quoted in conjuction with theoretical framework Self-consistency relations for M theory require Da/a2 ~ DG/G

  8. 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 2000) • Two benefits: • prevents L from dominating during the radiation epoch • links cosmological acceleration (Perlmutter et al 1998) to a varying a Theory allows variation in a to be ~10-5 H0 at redshift z=1, and for L to dominate today and produce acceleration. The factor of 10-5 comes from the ratio of radiation to matter density today.

  9. 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…

  10. 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) or delaying (larger) 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)

  11. QSO Absorption Lines (history) 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. QSO absorption line methods can sample huge time span Wolfe, Brown, & Roberts (1976) used AD method for the strong Mg II doublet (ll2796,2803 Å) This method has become increasing popular, but until the advent of very high resolution data and 10-meter telescopes, it has been less than conclusive, Da/a = (2±7) ×10-5

  12. So… what are QSO absorption lines?

  13. And… What do we mean by “high resolution”?

  14. Interpreting those cloud-cloud separations….

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

  16. The High Resolution Echelle Spectrograph (HIRES)

  17. 2-Dimensional Echelle Image Dark features are absorption lines

  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

  19. Example spectrum of this Mg II system (z=1.32)

  20. We model the complex profiles as multiple clouds, using Voigt profile fitting (Lorentzian + Gaussian convolved) to obtain component redshifts (velocities). Lorentzian is natural line broadening Gaussian is thermal line broadening (line of sight)

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

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

  23. The “Many Multiplet Method” 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

  24. 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 Z = nuclear charge R = az/a0

  25. 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 2796 Mg II 2803 Fe II 2600 Fe II 2586 Fe II 2382 Fe II 2374 Fe II 2344

  26. 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

  27. 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

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

  29. 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

  30. 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.

  31. 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 blue and red of Si II and Ni II anchors and have opposite q1 signs

  32. 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

  33. 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

  34. 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

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