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The Doppler effect

The Doppler effect is used to interpret the frequency axis of the measured spectrum. Using the radio convention, the non-relativistic Doppler effect in the observatory frame can be written as

\begin{displaymath}
\frac{\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\...
...emath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},
\end{displaymath} (2)

where \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}} is the velocity of the source in the observatory frame, \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}} and \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}} are the frequency of the measured photon in the observatory and rest frame respectively. \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}} is positive if the source recesses and the rest frame is defined as the frame where the velocity of the emitting gas cell is zero. Introducing the doppler parameter \ensuremath{d_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}}, we obtain
\begin{displaymath}
\frac{\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\ma...
...ath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}}.
\end{displaymath} (3)



Gildas manager 2023-06-01