The APEX case as of 2019-07-06

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The APEX case as of 2019-07-06

At APEX, the velocity convention used to stop the periodic shift due to Earth rotation (see Sect. ) is the special relativity one. In order to try to fit into the CLASS format, it was decided to deliver the frequency axis in the source frame at the systemic velocity defined using the special relativity convention and to set the doppler factor to 0. In other words, the interpretation of spectroscopy section of the CLASS header as explained in Table has been tweaked as follows.

fres
  is the channel spacing in the rest frame.
vres
  is the velocity spacing in the frame where the systemic velocity is defined, e.g., LSR.
voff
  is the systemic velocity in the same frame, e.g., LSR.
doppler
  is set to zero.

All other spectroscopic parameters keep their standard definition.

The advantage of this method is that it gives 1) the correct frequency axis in the rest frame, and 2) the correct velocity axis in the velocity frame, as long as the systemic velocity is correct (see Sect. and ). The inconvenient of this method is that the change the systemic velocity as coded in CLASS can not work. Indeed, this change uses the doppler parameter (see Sect. and Sect. ), which has been set to zero. While the MODIFY FREQUENCY command works as expected, the MODIFY VELOCITY command gives unexpected results. Note that the MODIFY DOPPLER command will not fix the situation either because it just recomputes the Doppler factor (assuming the radio velocity convention) but it will not change the other parameters of the spectroscopy section accordingly. This command should only be used when the Doppler factor is wrong. This is not the case here as a zero valued Doppler factor is consistent with the definition of the frequency axis.

The only correct solution is to undo the Doppler correction applied at observing time and apply the new Doppler correction associated to the new velocity, all this using the same velocity convention (i.e., the special relativity one) to avoid having CLASS files containing APEX data with different interpretation of the spectroscopy section. We need to update the signal frequency, the image frequency, and the frequency and velocity channel spacing as follows

(80)
(81)

One difficulty is the fact that filling the spectroscopic section as described above implies that the Doppler correction to go from the observatory to the LSR frame has been lost. Fortunately, the velocity composition rule in special relativity implies that

(82)
We can thus replace the previous set of equations by
(83)
(84)
And finally to update the value of to the new one.

This situation should not happen often because galactic targets often have well defined systemic velocity and the general advice is to observe extra-galactic target at the red-shifted frequency to avoid trouble (, ).