next up previous contents
Next: Interpretation 2: At fixed Up: Interpreting the spectral axis Previous: Splitting the change of   Contents


Interpretation 1: At fixed \ensuremath{z_{\ensuremath{\mathrm{}}}} and fixed \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}

Combining Eq. 22 to 24, we yield

\begin{displaymath}
\ensuremath{\Delta \ensuremath{v_{\ensuremath{\mathrm{}}}...
...{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}},
\end{displaymath} (25)

i.e., the local velocity difference in the source/rest frame is proportional to the observed frequency difference in the observatory frame. We can define a linear velocity axis associated to the set of brightnesses, $T(\ensuremath{i_{\ensuremath{\mathrm{}}}})$ as
\begin{displaymath}
\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\math...
...{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}}.
\end{displaymath} (26)

This can be interpreted as follows. Let's assume that the measured spectrum is made of a line centered around \ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{obs}}}} in the observatory frame. The associated rest frame frequency, i.e., the frequency of the line at rest, will be \ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}. If the tuned frequency at channel \ensuremath{i_{\ensuremath{\mathrm{}}}} in the observatory frame is set to the redshifted frequency
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mat...
...hrm{rest}}}}}{1+\ensuremath{z_{\ensuremath{\mathrm{tuned}}}}},
\end{displaymath} (27)

the velocity axis defined in Eq. 26 can be interpreted as the local variation of the gas velocity in the rest/source frame for the line whose rest frequency is \ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}.


next up previous contents
Next: Interpretation 2: At fixed Up: Interpreting the spectral axis Previous: Splitting the change of   Contents
Gildas manager 2015-03-01