John Webb (UNSW) - Analysis; Fearless Leader Steve Curran (UNSW)- QSO (mm and radio) obs. Vladimir Dzuba (UNSW)- Computing atomic parameters Victor Flambaum.

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

To Earth

CIVSiIVCIISiII

Lyem

Ly forest

Lyman limit Ly

NVem

SiIVem

CIVem

Lyem

Ly SiII

quasar

Quasars: physics laboratories in the early universe

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

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

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)

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. Q ~ 10K

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”

Advantages of the new method

1. Includes the total relativistic shift of frequencies (e.g. for s-electron) i.e. it

includes relativistic shift in the ground state

(Spin-orbit method: splitting in excited state - relativistic correction is smaller, since excited electron is far from the nucleus)

2. Can include many lines in many multiplets

Ji

Jf

(Spin-orbit method: comparison of 2-3 lines of 1 multiplet due to selection rule for E1 transitions - cannot explore the full multiplet splitting)

1 fi JJ

3. Very large statistics - all ions and atoms, different frequencies, different

redshifts (epochs/distances)

4. Opposite signs of relativistic shifts helps to cancel some systematics.

Wavelength precision and q values

Low-z vs. High-z constraints:High-z (1.8 – 3.5) Low-z (0.5 – 1.8)

FeII

MgI, MgII

ZnII

CrII

FeIIPositiveMediocre

Anchor

MediocreNegative

SiIV

Biggest shifts are around 300 m/s. Doppler searches for extra-solar planets reach ~3 m/s at similar spectral resolution (but far higher s/n).

Low-z vs. High-z constraints:High-z Low-z

Low-z vs. High-z constraints:/ = -5×10-5High-z Low-z

J.K. Webb, Department of Astrophysics and Optics, School of Physics, UNSW

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)

Low redshift data: MgII and FeII (most susceptible to systematics)

Low-z MgII/FeII systems:

High-z damped Lyman- systems:

Current results:

Current results:

Current results:

Current results:

Potential systematic effects Laboratory wavelength errors: New mutually consistent laboratory spectra from Imperial College, Lund University and NIST Data quality variations: Can only produce systematic shifts if combined with laboratory wavelength errors Heliocentric velocity variation: Smearing in velocity space is degenerate with fitted redshift parameters Hyperfine structure shifts: same as for isotopic shifts Magnetic fields: Large scale fields could introduce correlations in for neighbouring QSO site lines (if QSO light is polarised) - extremely unlikely and huge fields required Wavelength miscalibration: mis-identification of ThAr lines or poor polynomial fits could lead to systematic miscalibration of wavelength scale Pressure/temperature changes during observations: Refractive index changes between ThAr and QSO exposures – random error Line blending: Are there ionic species in the clouds with transitions close to those we used to find Instrumental profile variations: Intrinsic IP variations along spectral direction of CCD? “Isotope-saturation effect” (for low mass species) Isotopic ratio shifts: Very small effect possible if evolution of isotopic ratios allowed Atmospheric dispersion effects: Different angles through optics for blue and red light – can only produce positive at low redshift

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:

ThAr calibration results:

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;

Metal absorption

Over 60 000 data points!

Quasar Q1759+75

H absorption

H emission

C IV doublet

C IV 1550ÅC IV 1548Å

QSO absorption lines: A Keck/HIRES doublet

Separation 2

y/y = -1×10-5

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

d

log 1

0[N

(X)f

X/

N(M

gII)

]

The strength of a potential interloper “X”

Interloper strength described by logN(X)fX. Parameterise strength relative to strength of “host” line (e.g. MgII): log10[N(X)fX/N(MgII)]

Monte-Carlo simulation: vary interloperstrength (y-axis) and , measure plausible range of parameters for strength and position of and potential interloper

Photoionization equilibrium calculations: an exhaustive search for possible candidates (atomic species only) using “CLOUDY” to derive list of weak transitions, any element, any ionization…..

No atomic interloper candidates were found for any species