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

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**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 [tex]z_{obs} = \nu_0/\nu_{obs}-1[/tex], 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%).

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 [tex]z_{obs} = \nu_0/\nu_{obs}-1[/tex], 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%).