Keywords: class-spectral-axis-v12

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## The IRAM-30m case as of 2019-07-06: Systemic velocity in (slightly) different frames

The previous equations assume that the systemic velocity is given in the same frame as the frequency channel spacing. However, at the 30m the systemic velocity is usually given in the LSR frame (as requested by the user) and the channel spacing and the doppler factor are given in the observatory frame.

On one hand, the rest frequency scale is correctly computed by `CLASS` because the channel spacing and the doppler factor are given in the same frame. On the other hand, the velocity scale is only approximated because the source systemic velocity is given in another frame, most often the LSR frame.

The end-user (astronomer) is interested with the velocity scale in the LSR frame

| (39)

But he actually gets

| (40)

The relative error can be expressed as

| (41)

We yield to first order in

| (42)

If we tolerate an error of 1/10th of a channel on the velocity, this implies that the velocity scale is correct for about 1000 channels around the systemic velocity. This translates into at 1 for a spectral resolution of 195 . This means that the interpretation of the velocity scale of Galactic observations is correct. On the other hand, this could be a problem for extra-galactic observations at extremely high spectral resolution, assuming that the observers do not first downsample their spectra to increase the signal-to-noise ratio per channel...

The easiest way out of the problem would be to write the parameters of the header in the LSR frame in the calibration software that writes the `CLASS` observation with

| (43)

In other words, we trick `CLASS` into thinking that the measurement frame is LSR, while the true measurement frame was the observatory.

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