how to measure evolution in fundamental constants of physics using large telescopes
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How to Measure Evolution inFundamental Constants of Physics
Using Large Telescopes
Chris Churchill(Penn State)
Evolution in the Fine Structure Constant
= (z-0)/0
= e2/hc
John Webb (UNSW) - Analysis; Fearless LeaderSteve Curran (UNSW) - QSO (mm and radio) obs.Vladimir Dzuba (UNSW) - Computing atomic parametersVictor Flambaum (UNSW) - Atomic theoryMichael Murphy (UNSW) - Spectral analysisJohn Barrow (Cambridge) - InterpretationsFredrik T Rantakyrö (ESO) - QSO (mm) observationsChris Churchill (Penn State) - QSO (optical) observations Jason Prochaska (Carnegie Obs.) - QSO (optical) observationsArthur Wolfe (UC San Diego) - QSO optical observationsWal Sargent (CalTech) - QSO (optical) observationsRob Simcoe (CalTech) - QSO (optical) observationsJuliet Pickering (Imperial) - FT spectroscopyAnne Thorne (Imperial) - FT spectroscopyUlf Greismann (NIST) - FT spectroscopyRainer Kling (NIST) - FT spectroscopy
Webb etal. 2001 (Phys Rev Lett 87, 091391)
49 Systems ; 0.5 < z < 3.5 ; 28 QSOs
x 10-5 (4.1)
Intrinisic QSO Emission/Absorption Lines
H I (Lyman-) 1215.67
C IV 1548, 1550 & Mg II 2796, 2803
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
:
:
2
1
221
2
)(
Note, measured relative to same ground state
2/12
2/12
2/32
2/12
PS
PS
But there is more than justThe doublets… there are
other transitions too!
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
Ec
Ei
Represents differentFeII multiplets
The “Many-Multiplet method” - using different multiplets and different species simultaneously - order of magnitude improvement
Low mass nucleusElectron feels small potential and moves slowly: small relativistic correction
High mass nucleusElectron feels large potential and moves quickly: large relativistic correction
Relativistic shift of the central line in the multiplet
Procedure1. 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:
1qEE2
0
z0zz
Ez=0 is the laboratory frequency. 2nd term is non-zero only if has changed. q is derived from relativistic many-body calculations.
)S.L(KQq K is the spin-orbit splitting parameter.
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) - 1267xwhere x = z02 - 1 MgII “anchor”
High-z (1.8 – 3.5) Low-z (0.5 – 1.8)
FeII
MgI, MgII
ZnII
CrII
FeIIPositiveMediocre
Anchor
MediocreNegative
SiIV
Low-z vs. High-z constraints:
/ = -5×10-5High-z Low-z
Current results:
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
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) + q1x
ThAr line: = (ThAr) + q1x
(ThAr) is known to high precision (better than 0.002 cm-1)
ThAr calibration results:
Atmospheric dispersion effects:
Atmospheric dispersion results:
Pre-rotator Post-rotator
Rotator
Isotopic ratio evolution:
Isotopic ratio evolution results:
Isotope
Correcting for both systematics:
Rotator + Isotope
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;
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 withN = 1012 atoms/cm2
b = 3 km/s
Interloper strength can vary
Position of fitted profile is measured
Parameters describing ONE absorption line
b (km/s)
1+z)rest
N (atoms/cm2)
3 Cloud parameters: b, N, z
“Known” physics parameters: rest, f,
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
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
However…
bobserved2 b b
kT
mcons tthermal bulk
2 2 2tan
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,
b MgIIm Fe
m Mgb FeII Kb FeII( )
( )
( )( ) ( )
b MgII b FeII( ) ( )
We can therefore reduce the number of cloud parameters describing TWO absorption lines from different species:
bKb
z
N(FeII)N(MgII)
i.e. 4 cloud parameters, with assumptions: no spatial or velocity segregation for different species
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
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 1st and 2nd 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)
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)
1. Zero Approximation – calculate transition frequencies using complete set of Hartree-Fock energies and wave functions;
2. Calculate all 2nd 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-HHF.
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 Z2, so effect is small in light atoms;(2) greatest precision will be achieved when considering all relativistic effects (ie. including ground state)
Wavelength precision and q values
Line removal checks:
Removing MgII2796: Post-removal Pre-removal
Line Removal
Removing MgII2796: Post-removal Pre-removal
Line Removal
Number of systems where transition(s) can be removed
Transition(s) removed
Pre-removalPost-removal
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