November 2001

M.T. Murphy, J.K. Webb, V.V. Flambaum, V.A. Dzuba, C.W. Churchill, J.X. Prochaska, J.D. Barrow, A.M. Wolfe (2001) Possible evidence for a variable fine-structure constant from QSO absorption lines: motivations, analysis and results
Monthly Notices of the Royal Astronomical Society 327 (4) , 1208–1222


An experimental search for variation in the fundamental coupling constants is strongly motivated by modern high-energy physics theories. Comparison of quasar (QSO) absorption-line spectra with laboratory spectra provides a sensitive probe for variability of the fine-structure constant, α, over cosmological time-scales. We have previously developed and applied a new method providing an order-of-magnitude gain in precision over previous optical astrophysical constraints. Here we extend that work by including new quasar spectra of damped Lyman-α absorption systems. We also reanalyze our previous lower-redshift data and confirm our initial results. The constraints on α come from simultaneous fitting of absorption lines of subsets of the following species: Mg i, Mg ii, Al ii, Al iii, Si ii, Cr ii, Fe ii, Ni ii and Zn ii. We present a detailed description of our methods and results based on an analysis of 49 quasar absorption systems (towards 28 QSOs) covering the redshift range $0.5 < z < 3.5$ . There is statistical evidence for a smaller α at earlier epochs:$\Delta \alpha/\alpha = (-0.72 \pm 0.18) x 10^{-5}$ . The new and original samples are independent but separately yield consistent and significant non-zero values of $\Delta \alpha/\alpha$. We summarize the results of a thorough investigation of systematic effects published in a companion paper. The value we quote above is the raw value, not corrected for any of these systematic effects. The only significant systematic effects so far identified, if removed from our data, would lead to a more significant deviation of $\Delta \alpha/\alpha$ from zero.

Abundantly relevant information on p 7 of the PDF or 1214 of the journal (right hand side):

"We also noted a small but important difference between the IRAF and MAKEE wavelength calibration software. IRAF makes use of an internal list of vacuum ThAr wavelengths and so spectra calibrated with IRAF have ‘correct’ wavelength scales. However, the MAKEE package calibrates spectra with a list of air ThAr wavelengths and converts the final QSO wavelength scale to vacuum using the Cauchy formula for the refractive index (Weast 1979). However, this formula does not reproduce the experimental dispersion: it shows deviations from experiment at the level of 10-6 in the optical range. We therefore converted the wavelength scales of the spectra reduced with MAKEE back to air wavelengths using the Cauchy formula and then reconverted to vacuum wavelengths with the preferred Edlen (1966) formula. A detailed discussion of air – vacuum conversion with caveats of the above statements is given in M01a."

November 2001

M.T. Murphy, J.K. Webb, V.V. Flambaum, C.W. Churchill, J.X. Prochaska (2001) Possible evidence for a variable fine-structure constant from QSO absorption lines: systematic errors
Monthly Notices of the Royal Astronomical Society 327 (4) , 1223–1236


Comparison of quasar (QSO) absorption spectra with laboratory spectra allows us to probe possible variations in the fundamental constants over cosmological time-scales. In a companion paper we present an analysis of Keck/HIRES spectra and report possible evidence suggesting that the fine-structure constant, α, may have been smaller in the past: $\Delta \alpha/\alpha = (-0.72 \pm 0.18) x 10^{-5}$ over the redshift range $0.5 < z < 3.5$. In this paper we describe a comprehensive investigation into possible systematic effects. Most of these do not significantly influence our results. When we correct for those which do produce a significant systematic effect in the data, the deviation of $\Delta \alpha/\alpha$ from zero becomes more significant. We are led increasingly to the interpretation that α was slightly smaller in the past.

The above mentioned Air-Vacuum Wavelength Conversion is discussed in section 2.9 of this paper.

June 2003

M. T. Murphy, J. K. Webb and V. V. Flambaum Further evidence for a variable fine-structure constant from Keck/HIRES QSO absorption spectra
Mon. Not. R. Astron. Soc. 345, 609–638 (2003)


We have previously presented evidence for a varying fine-structure constant, α, in two independent samples of Keck/HIRES quasi-stellar object (QSO) absorption spectra. Here we present a detailed many-multiplet analysis of a third Keck/HIRES sample containing 78 absorption systems. We also re-analyse the previous samples, providing a total of 128 absorption systems over the redshift range 0.2 < zabs < 3.7 . The results, with raw statistical errors, indicate a smaller weighted mean α in the absorption clouds: Δα/α= (−0.574 ± 0.102) × 10−5 . All three samples separately yield consistent and significant values of Δα/α . The analyses of low-z (i.e. zabs < 1.8 ) and high-z systems rely on different ions and transitions with very different dependences on α, yet they also give consistent results. We identify an additional source of random error in 22 high-z systems characterized by transitions with a large dynamic range in apparent optical depth. Increasing the statistical errors on Δα/α for these systems gives our fiducial result, a weighted mean Δα/α= (−0.543 ± 0.116) × 10−5 , representing 4.7σ evidence for a varying α. Assuming that Δα/α= 0 at zabs= 0 , the data marginally prefer a linear increase in α with time rather than a constant offset from the laboratory value: . The two-point correlation function for α is consistent with zero over 0.2–13 Gpc comoving scales and the angular distribution of Δα/α shows no significant dipolar anisotropy. We therefore have no evidence for spatial variations in Δα/α .

We extend our previous searches for possible systematic errors, giving detailed analyses of potential kinematic effects, line blending, wavelength miscalibration, spectrograph temperature variations, atmospheric dispersion and isotopic/hyperfine structure effects. The latter two are potentially the most significant. However, overall, known systematic errors do not explain the results. Future many-multiplet analyses of independent QSO spectra from different telescopes and spectrographs will provide a now crucial check on our Keck/HIRES results.

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