John Webb (UNSW)
- Analysis; Fearless Leader
Steve Curran (UNSW)
- QSO (mm and radio) obs.
Vladimir Dzuba (UNSW)
- Computing atomic parameters
Victor Flambaum (UNSW)
- Atomic theory
Michael Murphy (UNSW)
- Spectral analysis
John Barrow (Cambridge)
- Interpretations
Fredrik T Rantakyrö (ESO)
- QSO (mm) observations
Chris Churchill (Penn State)
- QSO (optical) observations
Jason Prochaska (Carnegie Obs.)
- QSO (optical) observations
Arthur Wolfe (UC San Diego)
- QSO optical observations
Wal Sargent (CalTech)
- QSO (optical) observations
Rob Simcoe (CalTech)
- QSO (optical) observations
Juliet Pickering (Imperial)
- FT spectroscopy
Anne Thorne (Imperial)
- FT spectroscopy
Ulf Greismann (NIST)
- FT spectroscopy
Rainer Kling (NIST)
- FT spectroscopy
Quasars: physics laboratories in the
early universe
quasar
To Earth
Lyman limit
Lya
Lyb
SiII CII SiIV
SiII CIV
Lyaem
Lybem
NVem
SiIVem
CIVem
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 l1, l2 of alkali-like doublets, i.e transitions of the sort
l1 :
l2 :
2
S1 / 2 2 P3 / 2
2
S1 / 2  P1 / 2
2
are related to a by
l1  l2 l

 a 2 which leads to
l
l
l2
l1
 a  ( l )

a
2l
Note, measured relative to
same ground state
The “Many-Multiplet method” - using different
multiplets and different species simultaneously order of magnitude improvement
E
i
Ec
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
Low mass nucleus
Electron feels small
potential and moves
slowly: small relativistic
correction
Represents different
FeII multiplets
High mass nucleus
Electron feels large
potential and moves
quickly: large relativistic
correction
Dependence of atomic transition frequencies on a
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 electronelectron 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)
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)
Procedure
1. 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.
E

E
z
z 0
Illustrative formula:
 a
 q  z
 a 0


  1


2
Ez=0 is the laboratory frequency. 2nd term is non-zero only if a has
changed. q is derived from relativistic many-body calculations.
Relativistic shift of the
q  Q  K (L.S )
central line in the multiplet
Numerical examples:
K is the spin-orbit splitting
parameter. Q ~ 10K
Z=26 (s
p) FeII 2383A: w0 = 38458.987(2) + 1449x
Z=12 (s
p) MgII 2796A: w0 = 35669.298(2) + 120x
Z=24 (d
p) CrII 2066A: w0 = 48398.666(2) - 1267x
where x = (az/a0)2 - 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
Jf
Ji
(Spin-orbit method: comparison of 2-3 lines of 1
multiplet due to selection rule for E1 J i  J f  1
transitions - cannot explore the full multiplet splitting)
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:
Low-z (0.5 – 1.8)
High-z (1.8 – 3.5)
ZnII
FeII
SiIV
FeII
Positive
Mediocre
Anchor
Mediocre
Negative
CrII
MgI, MgII
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).
High-z
Low-z vs. High-z
Low-z
constraints:
a/a = -5×10-5
Low-z
High-z
Low-z vs. High-z constraints:
J.K. Webb, Department of Astrophysics and Optics, School of Physics, UNSW
Parameters describing ONE absorption line
3 Cloud parameters:
b, N, z
b (km/s)
N (atoms/cm2)
“Known” physics
parameters: lrest, f, G...
(1+z)lrest
Cloud parameters describing TWO (or
more) absorption lines from the same
species (eg. MgII 2796 + MgII 2803 A)
N
b
b
z
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)
i.e. a maximum
of 6 cloud
parameters,
without any
assumptions
N(FeII)
N(MgII)
z(FeII)
z(MgII)
However…
b
2
observed
b
2
thermal
b
2
bulk
2kT

 cons tan t
m
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(MgII)  m(Fe) b(FeII)  Kb(FeII)
(
m(Mg)
)
B: thermal broadening negligible compared to
bulk motions, b(MgII)  b(FeII)
We can therefore reduce the number of cloud
parameters describing TWO absorption lines
from different species:
b
Kb
N(FeII)
N(MgII)
z
i.e. 4 cloud
parameters, with
assumptions: no
spatial or velocity
segregation for
different species
How reasonable is the previous assumption?
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.
FeII
MgII
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) nonlinear least-squares method (modified version of
VPFIT, a/a explicitly included as a free parameter);
 Uses 1st and 2nd derivates of c2 with respect to each
free parameter ( natural weighting for estimating
a/a);
 All parameter errors (including those for a/a
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-a 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 a/a 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 a/a?
 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 a/a at low redshift
Using the ThAr calibration spectrum to see if wavelength
calibration errors could mimic a change in a
ThAr lines
Quasar spectrum
Modify equations used on quasar data:
quasar line: w = w0(quasar) + q1x
ThAr line: w = w0(ThAr) + q1x
w0(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;
QSO absorption lines:
 A Keck/HIRES doublet
H emission
2
Separation

a
H absorption
Quasar Q1759+75
Over 60 000 data points!
C IV doublet
Metal absorption
C IV 1548Å
C IV 1550Å
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 dl, l:
MgII line generated with
N = 1012 atoms/cm2
b = 3 km/s
Interloper strength can vary
Position of fitted profile is
measured
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 interloper
strength (y-axis) and l, measure l
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