Compilation of cz (radial velocity) measurements
The catalog (table a110 in the database) presents the compilation of redshift of galaxies, z,
z = (λ-λ0) / λ0 = (ν0-ν) / ν
where λ and λ0 refer the observed and emitted wavelength,
ν and ν0 are the observed and emitted frequency.
The data are stored in units of km/s as cz,
where c is the speed of light (299792.458 km/s).
The redshift should be reduced to heliocentric restframe, where the rotation of Earth and orbital motions
have been removed from the measured velocity.
The observed shift in wavelength or frequency of light emitted by an object consists of relativistic Doppler effect,
gravitational and cosmological redshifts.
We can neglect the gravitational redshift in most of cases of extragalactic astronomy
because the effect is very small.
The cosmological redshift arises due to Hubble expansion of the Universe.
The relativistic Doppler effect appears because of physical motion of the object and observer with respect to each other.
See also the article on
Statistics of the compilation of cz measurements
The ten main references for this compilation are:
The first ten sources of redshifts
The relativistic Doppler effect is appeared due to relative motion of the observer and the source.
The redial velocity can be expressed from the observable shift in the frequency or in the wavelength as
V = c (ν02-ν2) / (ν02+ν2)
= c (λ2-λ02) / (λ2+λ02)
= c [(1+z)2-1] / [(1+z)2+1]
There are two frequently used approximations of this equation for small z, the "optical" and "radio" conventions.
So called "optical" convention is
Voptic = c (λ-λ0) / λ0 = cz
Thus, for small z, z << 1, the value, cz, can be treated as radial velocity of the object.
Because of it, the therminology "radial velocity" is often used as synonym of the redshift, cz.
Many catalogs, databases and surveys use the "radial velocity" to refer the redshift.
Of course, this interpretation can not be applied to object on high z.
The "radio" convention is
Both conventions have the "equal rights",
but because of the cosmological reason the "radio" convention was suppressed by "optical" one,
but this does not stop it being commonly used.
For homogeneity of the HyperLEDA,
the radial velocity from "radio" convention has to be transferred to redshift using formula
cz = Vradio / (1 - Vradio/c).
The cosmological redshift is caused by Hubble expansion.
The increase of distance between objects in the universe with time in General relativity is
described by the metric expansion of space.
The cosmological redshift is directly corresponds to the Proper Distance, DP, as
where H0 is the Hubble constant. This equation represents the famous Hubble's law.
There are several types of the distance measures.
The luminosity distance, DL, uses the standard candle and
the angular diameter distance, DA, uses the standard ruler as distance indicators.
The distance catalog in HyperLEDA compiles the distance measurements,
most of them are luminosity distances.