### [astro-ph/0611080] Revisiting VLT/UVES constraints on a vary

Posted:

**November 14 2006**Hello!

As a theorist who occasionally thinks about 'varying constants' I am interested in the latest observational position. This short paper is not about new observations, but it does highlight a significant aspect : how the observational errors are estimated.

Relevant previous works are astro-ph/0310318, astro-ph/0401094, astro-ph/0511765.

The method for the astrophysical observations is simply to compare the redshifts of many different lines in a given absorber system, where the ratios between line wavelengths depend theoretically on alpha or some other 'constant'. For each system a fit is made for the redshift and the value of the 'constant' under consideration.

The tricky part for error estimation is getting from the measured spectra to a set of line velocities (aka redshifts or wavelengths) with errors. I quote:

'Most metal-line QSO absorption profiles display a complicated velocity structure and oneusually focuses on the propeties of individual velocity components, each of which is typically modelled by a Voigt profile. However, it is important to realize that Delta alpha / alpha and its uncertainty are integrated quantities determined by the entire absorption profile.'

What is actually measured is a set of pixels, each of which has an flux and an associated 1-sigma error, and a wavelength. The velocity uncertainty for a given component can be found from a formula taken from Bouchy, Pepe, Queloz, Astron. Astrophys. 374, 733 (2001), which depends on the individual pixel errors and the derivative of flux wrt wavelength.

Here the authors simply calculate this velocity uncertainty for the lines used in previous results for alpha, and derive a minimum possible uncertainty for the derived value of alpha in each absorber. (Other contributions to uncertainty come from different lines having different optical depths, for example.)

The last page has a plot of this minimum possible error versus the quoted error. Many points lie well *below* the line of minimum possible error - meaning that the quoted error was too small.

Funny thing is that all the Webb group points (which suggest a nonzero variation) lie above the line - while the more recent results which claim no variation are the ones with underestimated errors. The authors make a strong conclusion that the analysis of the recent negative results was not well understood.

Any reaction to this method of estimating the minimum possible error?

As a theorist who occasionally thinks about 'varying constants' I am interested in the latest observational position. This short paper is not about new observations, but it does highlight a significant aspect : how the observational errors are estimated.

Relevant previous works are astro-ph/0310318, astro-ph/0401094, astro-ph/0511765.

The method for the astrophysical observations is simply to compare the redshifts of many different lines in a given absorber system, where the ratios between line wavelengths depend theoretically on alpha or some other 'constant'. For each system a fit is made for the redshift and the value of the 'constant' under consideration.

The tricky part for error estimation is getting from the measured spectra to a set of line velocities (aka redshifts or wavelengths) with errors. I quote:

'Most metal-line QSO absorption profiles display a complicated velocity structure and oneusually focuses on the propeties of individual velocity components, each of which is typically modelled by a Voigt profile. However, it is important to realize that Delta alpha / alpha and its uncertainty are integrated quantities determined by the entire absorption profile.'

What is actually measured is a set of pixels, each of which has an flux and an associated 1-sigma error, and a wavelength. The velocity uncertainty for a given component can be found from a formula taken from Bouchy, Pepe, Queloz, Astron. Astrophys. 374, 733 (2001), which depends on the individual pixel errors and the derivative of flux wrt wavelength.

Here the authors simply calculate this velocity uncertainty for the lines used in previous results for alpha, and derive a minimum possible uncertainty for the derived value of alpha in each absorber. (Other contributions to uncertainty come from different lines having different optical depths, for example.)

The last page has a plot of this minimum possible error versus the quoted error. Many points lie well *below* the line of minimum possible error - meaning that the quoted error was too small.

Funny thing is that all the Webb group points (which suggest a nonzero variation) lie above the line - while the more recent results which claim no variation are the ones with underestimated errors. The authors make a strong conclusion that the analysis of the recent negative results was not well understood.

Any reaction to this method of estimating the minimum possible error?