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

  $\displaystyle \frac{\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm...
...{obs}}}}}{\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},
$ (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
  $\displaystyle \frac{\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{o...
...math{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}}.
$ (3)