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Velocity conventions

For historical reasons, the velocity convention used to stop the periodic shift due to Earth rotation (see Sect. 3.2) is the optical convention at the IRAM-30m. Let's assume that the systemic velocity of the source is given in the radio convention as it is the natural convention for radio-observatories (see Sect. 1.2.3). The tuned frequency in the observatory frame is thus

\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{tuned,opt}}^{\ensuremath{...
...\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}}},
\end{displaymath} (101)

while it should be
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{tuned,rad}}^{\ensuremath{...
...ys}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}} \right) }.
\end{displaymath} (102)

The output spectrum will appear shifted in the observatory frame by
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{tuned,rad}}^{\ensuremath{...
...\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}}}.
\end{displaymath} (103)

And the signal frequency in the rest frame is shifted by
\begin{displaymath}
\ensuremath{f_\ensuremath{\mathrm{sig,tuned,rad}}^{\ensurem...
..._{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}}^2}.
\end{displaymath} (104)

At 115 GHz, this gives a shift of 3.2 kHz for a velocity of 50 \ensuremath{\, \ensuremath{\mathrm{km\,s^{-1}}}} and 1.3 MHz for a velocity of 1000 \ensuremath{\, \ensuremath{\mathrm{km\,s^{-1}}}}. Hence both Galactic and extra-Galactic measurements are affected in a measurable way. Nevertheless, this can be measured only by comparison of the lines measured at the IRAM-30m with other radio-observatories.

We recommend that the 30m changes the formula it uses to stop the periodic shift due to Earth rotation and now use the radio convention.


next up previous contents
Next: Systemic velocity in different Up: The situation at the Previous: The situation at the   Contents
Gildas manager 2015-03-01