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Splitting the change of frame

Gordon et al. (1992) proposed to split the problem of high redshift sources by combining a double change of frame with a change of interpretation of the spectral axis for each change of frame.

In the first change of frame, we consider a ``local'' observer in the source frame (i.e., having the same systemic velocity viewed from Earth). This observer will interpret the change of velocities as changes in frequency for a fixed rest frequency chosen as reference, \ensuremath{f_\ensuremath{\mathrm{ref}}^{\ensuremath{\mathrm{rest}}}} (see Section 1.3.2). Assuming that the velocity of the gas in the source frame are non-relativistic, he can use Eq. 18 to convert from velocities to frequencies in the source frame, i.e., the rest frame. The only differences in this case are 1) that the observation frame is the source or rest frame, and 2) the notion of tuned frequency is replaced by the notion of reference frequency. There is no tuned frequency in this thought experiment. However, just as a convenience, we will note this reference frequency, \ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}. This yields

\begin{displaymath}
\quad \ensuremath{\Delta \ensuremath{v_{\ensuremath{\math...
...{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}}.
\end{displaymath} (22)

The second change of frame goes from the rest/source frame to the observatory frame. The key point here is that we are at fixed redshift. It could be said that we are at fixed \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}}, as in section 1.3.1, except that for high redshift source, the observational quantity is the redshift and not the source systemic velocity. We thus define the tuned redshift \ensuremath{z_{\ensuremath{\mathrm{tuned}}}} as

\begin{displaymath}
\ensuremath{z_{\ensuremath{\mathrm{tuned}}}} \ensuremath{...
...\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{obs}}}}} - 1.
\end{displaymath} (23)

With this definition, we write
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm...
...ensuremath{z_{\ensuremath{\mathrm{tuned}}}} = \mbox{constant}.
\end{displaymath} (24)


next up previous contents
Next: Interpretation 1: At fixed Up: Interpreting the spectral axis Previous: The redshift: An observational   Contents
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