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,
(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,
. This yields
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
, 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
as