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### [astro-ph/0701752] 21 cm radiation - a new probe of variatio

Posted: February 02 2007
This paper looks at the effect of varying \alpha on the 21cm power spectrum at high redshift. Because the Einstein coefficient varies strongly with \alpha, they claim the 21cm is potentially a very good probe.

What confuses me about the plots is the use of redshift. As usual they use that the CMB temperature goes as 1+z. However what you can observe directly from the 21cm absorption is the frequency of the radiation, and hence observationally one defines a redshift $$z_{obs} = \nu_0/\nu_{obs}-1$$, where \nu_0 is the 21cm frequency today. Since \nu scales as \alpha^4, a 2% change in alpha corresponds to about an 8% change in z_{obs}. So isn't the most obvious observable really T_b as a function of z_{obs} rather than z? (i.e. the comparison plot in Fig 2 should shift the varying-\alpha result sideways by ~ 8%).

### [astro-ph/0701752] 21 cm radiation - a new probe of variatio

Posted: February 14 2007
Antony -

Thank you for this suggestion.

Observers will use the current value of the fine structure constant to connect redshift with frequency. So I agree that for observers it may be more useful to have the results plotted in terms of $$z_{obs}$$ since that shows the effect in terms of what would be observed.

On the other hand, from a theoretical perspective $$z_{CMB}$$ is the natural quantity to use in the calculations, and the effects of varying \alpha are physically more transparent when we plot as a function of $$z_{CMB}$$.

Rishi and I are weighing these advantages and disadvantages, but whatever version of the plot ends up in the printed version of the paper, we will provide access to the other version online.

Ben