Cosmological Evolution
of 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
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 Da/a = (–0.72±0.18) × 10-5 (4.1s)
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 a evolution
(statistical)
Executive Summary
1.
2.
3.
4.
5.
6.
7.
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
Classes of Theories
• Multi-dimensional and String Theories
Unification of quantum gravity with other forces…
• Scalar Theories
Couples E+M to cosmological mass density…
• Varying Speed of Light Theories
Attempts to solve some cosmological problems…
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.
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.
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.
Intrinisic QSO Emission/Absorption Lines
H I (Lyman-a) 1215.67
C IV 1548, 1550 & Mg II 2796, 2803
We require high resolution spectra…
Interpreting those cloud-cloud separations….
Spectrum of multi-cloud Mg II system (z=1.32)
And, of course… The Weapon.
Keck Twins
10-meter Mirrors
The High Resolution Echelle Spectrograph (HIRES)
2-Dimensional Echelle Image
Dark features are absorption lines
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
The “Doublet Method”
ex. Mg II ll2796, 2803
Si IV ll1393, 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
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)
Example of a Si IV system at z=2.53 used
in the a analysis of Murphy et al (2001)
Si IV Doublet Results: Da/a = –0.51.3 ×10-5
(Murphy et al 2001)
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
Z = nuclear charge
R = az/a0
A convenient form is:
wz = w0 + q1x + q2y
wz = redshifted wave number
w0 = rest-frame wave number
q1, q2 = relativistic correction coefficients for Z and e- configuration
x = (az/a0)2 - 1
Mg II 2803
Mg II 2796
Fe II 2600
Fe II 2586
Fe II 2382
Fe II 2374
Fe II 2344
y = (az/a0)4 - 1
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
w Shifts for Da/a ~ 10-5
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 Da/a 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
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
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.
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
Atmospheric Dispersion
Causes an effective stretching
of the spectrum which mimics
a non-zero Da/a
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
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
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
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 Da/a = (–0.72±0.18) × 10-5 (4.1s)
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 a evolution
(statistical)
Da/a = (–0.72±0.18) × 10-5 (4.1s)
(statistical)
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