The radio velocity convention

If the radial velocity is negligeable compared to the light velocity, we obtain to first order

  $\displaystyle \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}...
...{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}} \right) }.
$ (68)
In this case, we can establish a linear velocity scale (see Sect. [*])
  $\displaystyle \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}...
...}}}}{\ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}}.
$ (69)
This linear velocity scale is only a first order approximation, which is called the radio velocity convention. Indeed, it is well adapted to the radio spectrometer because 1) their natural output is a spectral axis regularly spaced in frequency and 2) the radio velocity convention gives a linear relation between the velocity and the frequency scale. This is why this convention is the default in CLASS.