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Interpretation 2: At fixed \ensuremath{z_{\ensuremath{\mathrm{}}}} and fixed \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{sou}}}}

Let's assume that the same gas cell in the source emits two lines at different frequencies. We are at fixed \ensuremath{z_{\ensuremath{\mathrm{tuned}}}} because we consider the same gas cell. The frequency axes in the rest and observatory frames are thus given by

\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{r...
...hrm{obs}}}}\,(1+\ensuremath{z_{\ensuremath{\mathrm{tuned}}}}).
\end{displaymath} (28)

This means that the frequency separation between the two lines is different in the rest and observatory frames. The modeller has easily access to the rest frame frequencies of the line. It is thus important to display the spectrum frequency axis in the rest frequency axis. This can be achieved only for one redshift (The reasoning is here done at fixed \ensuremath{z_{\ensuremath{\mathrm{tuned}}}}), which is by default assumed to be the systemic redshift of the source in the observatory frame, i.e., the mean redshift of the source gas in the observatory frame.

As a convention, we can in addition assume that the tuned rest frequency and its corresponding observatory frequency at the source systemic velocity are associated to the common reference channel \ensuremath{i_{\ensuremath{\mathrm{0}}}}. The frequency axis in the rest frame is then defined as

\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{r...
...{obs}}}}}\,(1+\ensuremath{z_{\ensuremath{\mathrm{tuned}}}}).
\end{displaymath} (29)

The plotted spectrum thus correctly displays the line at rest frequency positions, i.e., the brightnesses of the gas at rest in the source frame.


next up previous contents
Next: Interpretation 3: At fixed Up: Interpreting the spectral axis Previous: Interpretation 1: At fixed   Contents
Gildas manager 2015-03-01