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