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Cosmological Evolution of the Fine Structure Constant

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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. - PowerPoint PPT Presentation
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Cosmological Evolution of the Fine Structure Constant Chris Churchill (Penn State) = e 2 /hc = ( z - 0 )/ 0 In collaboration with: J. Webb, M. Murphy, V.V. Flambaum, V.A. Dzu J.D. Barrow, J.X. Prochaska, & A.M. Wolfe
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Page 1: Cosmological Evolution of the  Fine Structure Constant

Cosmological Evolutionof the

Fine Structure Constant

Chris Churchill(Penn State)

= e2/hc = (z-0)/0

In collaboration with: J. Webb, M. Murphy, V.V. Flambaum, V.A. Dzuba,J.D. Barrow, J.X. Prochaska, & A.M. Wolfe

Page 2: Cosmological Evolution of the  Fine Structure Constant

Your “Walk Away” Info

1. 49 absorption cloud systems over redshifts 0.5–3.5 toward 28 QSOs compared to lab wavelengths for many transitions

2. 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)

3. Find = (–0.72±0.18) × 10-5 (4.1) (statistical)

4. Most important systematic errors are atmospheric dispersion (differential stretching of spectra) and isotopic abundance evolution (Mg & Si; slight shifting in transition wavelengths)

5. Correction for systematic errors yields stronger evolution

Page 3: Cosmological Evolution of the  Fine Structure Constant
Page 4: Cosmological Evolution of the  Fine Structure Constant

Executive Summary

1. History/Motivations2. Terrestrial and CMB/BBN 3. QSO Absorption Line Method4. Doublet Method (DM) & Results5. Many-Multiplet Method (MM) & Results6. Statistical and Systematic Concerns7. Concluding Remarks

Page 5: Cosmological Evolution of the  Fine Structure Constant

Classes of Theories

Attempts to solve some cosmological problems…

• Multi-dimensional and String Theories

• Scalar Theories (varying electron charge)

• Varying Speed of Light Theories

Unification of quantum gravity with other forces…

Couples E+M to cosmological mass density…

Page 6: Cosmological Evolution of the  Fine Structure Constant

Varying Electron Charge Theories

Variation occurs over matter dominated epoch of the universe.

(Barrow etal 2001)

Page 7: Cosmological Evolution of the  Fine Structure Constant

Varying Speed of Light Theories

Motivation is to solve the “flatness” and “horizon” problems of cosmology generated by inflation theory (Barrow 1999, Moffat 2001).

Theory allows variation in to be ~10-5H0 at redshift z=1. Evolution is proportional to ratio of radiation to matter density.

Page 8: Cosmological Evolution of the  Fine Structure Constant

Last scattering vs. z CMB spectrum vs. l

CMB Behavior and ConstraintsSmaller delays epoch of last scattering and results in first peak at larger scales (smaller l) and suppressed second peak due to larger baryon to photon density ratio.

Solid (=0); Dashed (=-0.05); dotted (=+0.05)

Battye etal (2000)

Page 9: Cosmological Evolution of the  Fine Structure Constant

BBN Behavior and Constraints

D, 3He, 4He, 7Li abundances depend upon baryon fraction, b.

Changing a changes b by changing p-n mass difference and Coulomb barrier.

Avelino etal claim no statistical significance for a changed from neither the CMB nor BBN data.

They refute the “cosmic concordance” results of Battye etal, who claim that =-0.05 is favored by CMB data.

Avelino etal (2001)

Page 10: Cosmological Evolution of the  Fine Structure Constant

QSO absorption line methods can sample huge time span

Savedoff (1965) used doublet separations of emission lines from galaxies to search for evolution (first cosmological setting)

Bahcall, Sargent & Schmidt (1967) used alkali-doublet (AD) separations seen in absorption in QSO spectra.

QSO Absorption Lines (history)

Page 11: Cosmological Evolution of the  Fine Structure Constant

Intrinisic QSO Emission/Absorption Lines

Page 12: Cosmological Evolution of the  Fine Structure Constant

H I (Lyman-) 1215.67

Page 13: Cosmological Evolution of the  Fine Structure Constant

C IV 1548, 1550 & Mg II 2796, 2803

Page 14: Cosmological Evolution of the  Fine Structure Constant
Page 15: Cosmological Evolution of the  Fine Structure Constant
Page 16: Cosmological Evolution of the  Fine Structure Constant

We require high resolution spectra…

Page 17: Cosmological Evolution of the  Fine Structure Constant
Page 18: Cosmological Evolution of the  Fine Structure Constant

Interpreting those cloud-cloud separations….

Page 19: Cosmological Evolution of the  Fine Structure Constant

And, of course…

Keck Twins10-meter Mirrors

The Weapon.

Page 20: Cosmological Evolution of the  Fine Structure Constant

The High Resolution Echelle Spectrograph (HIRES)

Page 21: Cosmological Evolution of the  Fine Structure Constant

2-Dimensional Echelle Image

Dark features are absorption lines

Page 22: Cosmological Evolution of the  Fine Structure Constant

Electron Energy and Atomic Configuration

A change in will lead to a change in the electron energy, , 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

Page 23: Cosmological Evolution of the  Fine Structure Constant

The “Doublet Method” ex. Mg II 2796, 2803

A change in will lead to a change in the doublet separation according to

where ()z and ()0 are the relative separations at redshift z and in the lab, respectively.

Si IV 1393, 1402

2796 2803

Page 24: Cosmological Evolution of the  Fine Structure Constant

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

Page 25: Cosmological Evolution of the  Fine Structure Constant

We model the complex profiles as multiple clouds, usingVoigt profile fitting (Lorentzian + Gaussian convolved)

Free parameters are redshift, z, and

Lorentzian is natural line broadening Gaussian is thermal line broadening (line of sight)

Page 26: Cosmological Evolution of the  Fine Structure Constant

Si IV Doublet Results: = –0.51.3 ×10-5

(Murphy et al 2001)

Page 27: Cosmological Evolution of the  Fine Structure Constant

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 = z/

The energy equation for a transition from the ground state at a redshift z, is written

The “Many-Multiplet Method”

Page 28: Cosmological Evolution of the  Fine Structure Constant

A convenient form is: z = 0 + q1x + q2y

z = redshifted wave number

x = (z/0)2 - 1 y = (z/0)4 - 1

0 = rest-frame wave number

q1, q2 = relativistic correction coefficients for Z and e- configuration

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

Page 29: Cosmological Evolution of the  Fine Structure Constant
Page 30: Cosmological Evolution of the  Fine Structure Constant

Typical accuracy is 0.002 cm-1, a systematic shift in these values would introduce only a ~ 10-6

A precision of ~ 10-5 requires uncertainties in 0 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

Anchors & Data Precision Shifts for ~ 10-5

Page 31: Cosmological Evolution of the  Fine Structure Constant

Advantages/Strengths of the MM Method

1. Inclusion of all relativistic corrections, including ground states, provides an order of magnitude sensitivity gain over AD method

2. In principle, all transitions appearing in QSO absorption systems are fair game, providing a statistical gain for higher precision constraints on compared to AD method

3. Inclusion of transitions with wide range of line strengths provides greater constraints on velocity structure (cloud redshifts)

4. (very important) Allows comparison of transitions with positive and negative q1 coefficients, which allows check on and minimization of systematic effects

Page 32: Cosmological Evolution of the  Fine Structure Constant

Possible Systematic Errors

1. Laboratory wavelength errors2. Heliocentric velocity variation3. Differential isotopic saturation4. Isotopic abundance variation (Mg and Si)5. Hyperfine structure effects (Al II and Al III)6. Magnetic fields7. Kinematic Effects8. Wavelength mis-calibration9. Air-vacuum wavelength conversion (high-z sample)10. Temperature changes during observations11. Line blending12. Atmospheric dispersion effects13. Instrumental profile variations

Page 33: Cosmological Evolution of the  Fine Structure Constant

Isotopic Abundance Variations

There are no observations of high redshift isotopic abundances, so there is no a priori information

Focus on the “anchors”

We re-computed for entire range of isotopic abundances from zero to terrestrial. This provides a secure upper limit on the effect.

Observations of Mg (Gay & Lambert 2000) and theoretical estimates of Si in stars (Timmes & Clayton 1996) show a metallicity dependence

Page 34: Cosmological Evolution of the  Fine Structure Constant

Corrected Uncorrected

This is because all Fe II are to blue of Mg II anchor and have same q1 sign (positive)

Leads to positive

For high-z data, Zn II and Cr II areTo red of Si II and Ni II anchors and have opposite q1 signs

Correction for Isotopic Abundances Effect low-z Data

Page 35: Cosmological Evolution of the  Fine Structure Constant

a = pixel size [Å] , = slit width arcsec/pix,ψ = angular separation of and 2 on slit,θ = angle of slit relative to zenith

Atmospheric Dispersion

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

Causes an effective stretching of the spectrum which mimics a non-zero

Page 36: Cosmological Evolution of the  Fine Structure Constant

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

For high-z data, Zn II and Cr II areTo blue and red of Si II and Ni II anchors and have opposite q1 signs

Page 37: Cosmological Evolution of the  Fine Structure Constant

Summary of MM Method

1. 49 absorption clouds systems over redshifts 0.5 to 3.5 toward 28 QSOs compared to lab wavelengths for many transitions

2. 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)

3. Find = (–0.72±0.18) × 10-5 (4.1) (statistical)

4. Most important systematic errors are atmospheric dispersion (differential stretching of spectra) and isotopic abundance evolution (Mg & Si; slight shifting in transition wavelengths)

5. Correction for systematic errors yields stronger evolution

Page 38: Cosmological Evolution of the  Fine Structure Constant

= (–0.72±0.18) × 10-5 (4.1) (statistical)

Page 39: Cosmological Evolution of the  Fine Structure Constant

Soon to the PressPreliminary Findings…

Now have a grand total of 138 systems due to adding the HIRES data of Sargent et al.

Find = (–0.65±0.11) × 10-5 (6) (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 spectrain order to reproduce the HIRES/Keck results


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