Does the fine structure constant vary? A third quasar absorption sample consistent with varying α
ABSTRACT We report results from a third sample of quasar absorption line spectra from the Keck telescope which has been studied to
search for any possible variation of the fine structure constant, α. This third sample, which is larger than the sum of the
two previously published samples, shows the same effect, and also gives, as do the previous two samples, a significant result.
The combined sample yields a highly significant effect, Δα = (αz - α0 )/α0 = -0.57 ± 0.10 × 10-5, averaged over the redshift range 0.2 < z < 3.7. We include a brief discussion of small-scale kinematic structure in quasar
absorbing clouds. However, kinematics are unlikely to impact significantly on the averagednon-zeroΔα /α above, and we have
so far been unable to identify any systematic effect which can explain it. New measurements of quasar spectra obtained using
independent instrumentation and telescopes are required to properly check the Keck results.
[show abstract] [hide abstract]
ABSTRACT: We investigate the constraints on quintessence arising from both renormalisable and non-renormalisable couplings where the 5d Planck mass is around the TeV scale. The quintessence field vacuum expectation value is typically of order the 4d Planck mass while non-renormalisable operators are expected to be suppressed by the 5d Planck mass. Non-renormalisable operators are therefore important in computing the 4d effective quintessence potential. We then study the quantum corrections to the quintessence potential due to fermion and graviton loops. The tower of Kaluza-Klein modes competes with the TeV-scale cut-off, altering the graviton contribution to the vacuum polarization of quintessence. Nevertheless we show that, as in four dimensions, the classical potential is stable to such radiative corrections.11/2003;
arXiv:astro-ph/0210531v1 24 Oct 2002
Does the fine structure constant vary? A third quasar
absorption sample consistent with varying α
John K. Webb, Michael T. Murphy, Victor V. Flambaum, Stephen J.
School of Physics, University of New South Wales, Sydney, NSW 2052, Australia
Abstract. We report preliminary results from a third sample of quasar absorption
line spectra from the Keck telescope which has been studied to search for any possible
variation of the fine structure constant, α. This third sample, which is larger than the
sum of the two previously published samples, shows the same effect, and also gives,
as do the previous two samples, a significant result. The combined sample yields a
highly significant effect, ∆α/α = (αz− α0)/α0 = −0.57 ± 0.10 × 10−5, averaged
over the redshift range 0.2 < z < 3.7. We include a brief discussion of small-scale
kinematic structure in quasar absorbing clouds. However, kinematics are unlikely to
impact significantly on the averaged non-zero ∆α/α above, and we have so far been
unable to identify any systematic effect which can explain it. New measurements
of quasar spectra obtained using independent instrumentation and telescopes are
required to properly check the Keck results.
Keywords: line: profiles – instrumentation: spectrographs – methods: data analysis
– techniques: spectroscopic – quasars: absorption lines
1. Experimental status
Any variation in α ≡ e2/?c would cause shifts in the relative positions of
atomic resonance transitions. Astrophysical measurements permit tests
over cosmological time-scales through spectroscopy of high redshift gas
clouds seen in absorption against background quasars. Recently we
introduced a new method for the analysis of absorption systems seen in
optical quasar spectra (the “many multiplet method”). This technique
provides an order of magnitude increase in precision over the earlier
“alkali doublet” method for the same quality of data (Webb et al.,
1999; Dzuba et al., 1999b).
The many multiplet method compares wavelengths from many species,
exploiting the fact that the ground state levels have an enhanced sen-
sitivity, compared to excited levels, to any variation in α.
The dependence of the observed wavenumber, ωz, on α is most con-
laboratory wavenumber and ωzis the wavenumber in the rest-frame of
the absorber at the absorption redshift, z. α0is the present-day value
veniently expressed as ωz= ω0+ q
. ω0is the present-day
c ? 2008 Kluwer Academic Publishers. Printed in the Netherlands.
paper.tex; 2/02/2008; 1:11; p.1
of the fine structure constant and αz is the value at the absorption
The q coefficients quantify the relativistic correction for a particular
atomic mass and electron configuration. These coefficients have been
calculated using accurate many-body theory methods (Dzuba et al.,
1999b; Dzuba et al., 1999a; Dzuba et al., 2001; Dzuba et al., 2002).
The parameterization of ωzabove means that any uncertainties in the
numerical values of the q coefficients will not introduce an artificial
non-zero value of ∆α/α.
An important characteristic of the many-multiplet method is that
a given variation in α produces wavelength shifts for different species
which vary greatly in magnitude and which can be in opposite di-
rections. i.e. the q coefficients can be of opposite sign (for the same
species in some cases) and vary by up to two orders of magnitude in
numerical value (Figure 1). This latter effect can be understood in terms
of the atomic orbital properties and the way in which α effects them.
This characteristic enhances the power of the many-multiplet because
it helps to reduce the impact of any systematic effects in wavelength
calibration of the data. Since absorption clouds appear at all redshifts,
the observed transitions sample the entire observed wavelength range.
It is therefore hard to conceive a systematic error in the wavelength
calibration which could emulate the distinctive pattern of shifts caused
by a change in α, when a range of different transitions are included in
In order to exploit the enhanced sensitivity defined by the q val-
ues, new high precision laboratory measurements of ω0for the species
observed were carried out using Fourier transform spectrographs (Pick-
ering et al., 1998; Pickering et al., 2000; Griesmann and Kling, 2000).
Several experiments have been completed and new highly precise lab-
oratory wavelengths measured for 16 transitions. The improvement in
the accuracy of these wavelengths is 1−2 orders of magnitude compared
to the compilation of Morton (1991).
Three independent samples of Keck quasar spectra have now been
analysed, covering a broad redshift range. Two of these three samples
have been previously published. The first sample (Churchill and Vogt,
2001) used transitions in several Mgii and Feii multiplets in 30 quasar
absorbers. These data provided the first statistically significant effect
in the data which was consistent with a variation in α over the redshift
range 0.5 < z < 1.6 (Webb et al., 1999).
A second independent sample, of damped Lyman-α absorbers, (Prochaska
and Wolfe, 1999) used different atomic transitions (including Niii, Znii,
Crii, Alii and Alliii) and produced the same statistically significant
non-zero result for ∆α/α over the redshift range 1.8 < z < 3.5. The
paper.tex; 2/02/2008; 1:11; p.2
Figure 1. Illustration of line shifts as a function of α for the multiplets used in our
analysis. Note how Mg and Si act as “anchor” lines, and how Zn and Cr move in
results of these first 2 samples are summarised in Webb et al. (2001)
and full analysis details are given in Murphy et al. (2001a).
The analysis of the third sample (graciously provided by W. Sargent
and collaborators) is now complete and we report the preliminary re-
sults here. Each of the three samples produces the same result and for
the entire dataset, comprising all three samples, the result is ∆α/α ≡
(αz− α0)/α0= (−0.57 ± 0.10) × 10−5for the redshift range 0.2 < z <
3.7. We are unable to explain this result in terms of any systematic
error despite an exhaustive search (Murphy et al., 2001b).
2. A third independent quasar absorption line sample
The new sample, like the previous two, was also obtained using the
HIRES spectrograph on the Keck telescope. The spectral resolution is
FWHM ≈ 6.6kms−1and the signal-to-noise ratio per pixel averages
30, with most of the sample in the range 10 to 50. Individual exposure
times ranged from 1000 to 6000s depending on the quasar’s apparent
magnitude. Several individual exposures were combined to make the
final spectrum. The reader is referred to Murphy et al. (2001b) for
specific details regarding the correction of the wavelength scales to
paper.tex; 2/02/2008; 1:11; p.3
Figure 2. All results from the many-multiplet method to date. ∆α/α for all 3 sam-
ples combined. Hollow circles (Churchill), triangles (Prochaska and Wolfe), squares
(Sargent). Upper panel: unbinned individual values. Middle panel: binned but differ-
ent symbols still reveal results for each sample. Lower panel: binned over the whole
78 absorption systems were identified which contain a sufficiently
large sample of transitions such that the many-multiplet method can
provide meaningful constraints on ∆α/α. The redshift range covered
by this sample is 0.2 < z < 3.7. As with the previous two samples, this
broad redshift coverage means that ∆α/α is derived using different sets
of transitions at different redshifts.
3. Systematic effects and numerical analysis considerations
Here we begin a discussion of systematic effects. The discussion con-
tinues in the companion paper in this volume, Murphy et al. (2003).
paper.tex; 2/02/2008; 1:11; p.4
3.1. Wavelength distortions
The simplest systematic problem one can imagine is a low order distor-
tion in the wavelength scale due to errors in the wavelength calibration
procedure. Quasar exposures at the telescope are bracketed in time by
exposures of a standard calibration source, ThAr. The ThAr laboratory
wavelengths are taken from Palmer and Engleman (1983) and Norl´ en
(1973) and the measurement errors in the individual ThAr wavelengths
are ∼ 5 × 10−5˚ A. Assuming no systematic trends, and taking the
literature-quoted errors, these errors are too small by a factor of ∼ 40
to produce a ∆α/α at the level we observe.
However, any mistakes made during the process of transferring wave-
length information from the ThAr to quasar exposures could in princi-
ple emulate a non-zero ∆α/α. To check this, we repeat a test previously
applied to samples 1 and 2, analysing the ThAr emission line spectra in
the same way as the quasar spectra (Murphy et al., 2001b). For every
transition in every quasar absorption system, we identify individual
ThAr emission lines in the corresponding calibration spectra which
fall close to the observed quasar absorption line wavelengths. These
emission lines are then fitted with Gaussian profiles instead of Voigt
profiles. We parameterize the “observed” ThAr wavelength using the
same relation given in Section 1 in this paper, using the known ThAr
laboratory wavelength for ω0, but still using the q coefficients from
the quasar transition. We then fit the ThAr datasets, which directly
sample the same wavelength regions as do the quasar transitions, for all
absorption systems in all quasars. In this way, the ThAr spectra become
“fake quasar spectra”, and provide a direct test on the reliability of the
wavelength calibration procedure.
The results are illustrated in Figure 3. The “∆α/α” for the ThAr
points are plotted on the same scale as the quasar results. This test
demonstrates conclusively that the calibration process itself introduces
no significant errors.
3.2. Minimising the number of free parameters
Although the analysis methods have been applied extensively in other
contexts, and have also been described elsewhere in detail as applied
to ∆α/α, we re-iterate some of the features of the numerical methods
which are of particular importance here. The absorption systems are
essentially always found to comprise multiple components, spread over
10s to 100s of kms−1. Two assumptions are made in order to reduce
the number of free parameters in the fitting process, and hence to
maximise the potential precision of the measurement: (i) we adopt the
same redshift (as a free parameter) for corresponding components in
paper.tex; 2/02/2008; 1:11; p.5