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.
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) |
![]() |
(83) |
![]() |
(84) |
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 (, ).