A new method for detecting velocity shifts and distortions between
  optical spectra
  Recent quasar spectroscopy from the VLT and Keck telescopes suggests that
fundamental constants may not actually be constant. To better confirm or refute
this result, systematic errors between telescopes must be minimized. We present
a new method to directly compare spectra of the same object and measure any
velocity shifts between them. This method allows for the discovery of
wavelength-dependent velocity shifts between spectra, i.e. velocity
distortions, that could produce spurious detections of cosmological variations
in fundamental constants. This "direct comparison" method has several
advantages over alternative techniques: it is model-independent (cf.
line-fitting approaches), blind, in that spectral features do not need to be
identified beforehand, and it produces meaningful uncertainty estimates for the
velocity shift measurements. In particular, we demonstrate that, when comparing
echelle-resolution spectra with unresolved absorption features, the uncertainty
estimates are reliable for signal-to-noise ratios >7 per pixel. We apply this
method to spectra of quasar J2123-0050 observed with Keck and the VLT and find
no significant distortions over long wavelength ranges (~1050 Angstroms)
greater than ~180 m/s. We also find no evidence for systematic velocity
distortions within echelle orders greater than 500 m/s. Moreover, previous
constraints on cosmological variations in the proton--electron mass ratio
should not have been affected by velocity distortions in these spectra by more
than 4.0 +/- 4.2 parts per million. This technique may also find application in
measuring stellar radial velocities in search of extra-solar planets and
attempts to directly observe the expansion history of the Universe using quasar
absorption spectra.
