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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