class-spectral-axis-v12

IRAM Memo 2011-4
Description of the spectral axis handling in CLASS
J. Pety & S. Bardeau
1. IRAM (Grenoble)
2. LERMA, Observatoire de Paris
July 6 , 2019
Version 1.2
(Version 1.1 released on October 10 , 2014)
(Version 1.0 released on October 20 , 2011)

### Abstract:

An observer is interested by the physical properties (line frequencies, velocity of the gas) of a source in its own reference frame. However, the observations happen in a different frame, namely the topocentric frame for ground-based observations. This implies a change of frame to infer the physical properties in the source frame from the measured frequencies in the measurement frame. This memo tries to explain the different interpretation of the spectral axis, the additional subtleties related to heterodyne receivers in radio-astronomy, the current description of the spectral axis handling in CLASS, and the impact of various short-comings that happen for historical reasons.

- Contents
- Introduction
  - Spectrometers in radio-astronomy
  - The Doppler effect
  - Interpretation 1: At fixed
  - Interpretation 2: At fixed
- Heterodyne receivers and signal/image frequency axes
  - USB and LSB frequency axes in the observatory frame
  - Signal and image frequency axes in the observatory frame
  - Signal and image frequency axes in the rest frame
- Earth movements
  - Periodic shift and dilatation of the rest frequency axis
  - Stopping the periodic shift
  - Stopping the periodic dilatation
- CLASS implementation
  - The header parameters
  - The IRAM-30m case as of 2019-07-06: Systemic velocity in (slightly) different frames
  - The MODIFY FREQUENCY command
    - Signal frequency axis
    - Image frequency axis
    - Velocity axis
  - The MODIFY VELOCITY command
    - Principle
    - The signal frequency axis
    - The image frequency axis
    - The doppler factor
- Velocity conventions
  - The generic Doppler formula
  - The radio velocity convention
  - The optical velocity convention
  - Mixing conventions between observation and analysis
    - General case
    - The IRAM-30m case as of 2019-07-06
    - The APEX case as of 2019-07-06
- Acknowledgement
- References
- About this document ...