Frequency → velocity and reference frames

The spectrum is recorded in frequency; the astronomy is in velocity. The reference frame is part of the answer.

The idea

A spectrum measured in frequency can be read as a velocity

The historical spectra were recorded as frequency. Astronomers usually interpret the 21-cm line as a velocity, because the Doppler shift of the line tells how fast the gas moves along the line of sight. The conversion depends on whose velocity is meant, which is why the reference frame must always be stated.

Using the radio convention with the H I rest frequency, the velocity relative to the telescope is:

v_topo = c (f0 - f_obs) / f0, f0 = 1420.40575 MHz

Reference frames

Topocentric → heliocentric / barycentric → LSR

Topocentric
Relative to the telescope itself. This is what the measured frequency gives directly, and it includes the Earth's rotation and orbital motion.
Heliocentric / barycentric
Relative to the Sun, or to the centre of mass of the Solar System. The Earth's motion is removed.
LSR / LSRK
Relative to the Local Standard of Rest. The kinematic definition (LSRK) adds the Sun's standard motion: 20 km/s towards RA 18h03m50s, Dec +30°00′17″, the value used for the project's 26 Aug products. Galactic-structure work normally uses this frame.

Original and derived

Keep the two apart

Original Recorded

The frequency axis as recorded at the telescope. Nothing about it depends on a velocity convention or frame.

Derived Computed

Every velocity: topocentric, heliocentric, barycentric and LSR. Each depends on the convention, the rest frequency, the date, the time and the pointing direction.

Explorer

Velocity-frame explorer

Velocity-frame explorer Processing Under validation

An interactive view of one spectrum in each reference frame is intended here. The historical fixed-telescope processing pipeline is not complete, so no transformation is applied and no values are shown.

For a worked example on real data, see the DISH222 chain (step 7) and the lecture on LSR correction.