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HyperLEDA documentation: compilation of cz measurements (a110)

Compilation of cz (radial velocity) measurements

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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 redshift from Wikipedia.

Radial Velocity

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

V_optic = 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

V_radio = c (ν₀-ν) / ν₀

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 = V_radio / (1 - V_radio/c).

Hubble law

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, D_P, as

cz = D_PH₀

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, D_L, uses the standard candle and the angular diameter distance, D_A, uses the standard ruler as distance indicators. The distance catalog in HyperLEDA compiles the distance measurements, most of them are luminosity distances.

Short statistics on catalog (March 2006)

The five main references for this compilation are

Ref. number	Reference	Number of cz
27127	SDSS - DR2	254507
24401	2DF	236202
27139	SDSS - DR4	136637
27128	SDSS - DR3	114701
27124	SDSS (Stoughton 2002)	85221

The three main references from radio measurements are

23289 Theureau et al. 1998 2143

4008 de Vaucouleurs et al. RC3 1487

24372 Haynes et al. 1999 1201

Description of the fields

Below is a description of the fields of the table that can be accessed through the interfaces.

Field: vel

Heliocentric radial velocity (CZ) in km/s with its uncertainty and quality flag in parentheses (in html displays). The quality flag has the following meaning:

description of quality flag

value signification

0 regular measurement

1 uncertain measurement, its weight is decreased by a factor 2 when computing the average value

3 preliminary measurement, probably superseeded in a more recent publication, it is ignored unless no other measurement is available

4 compilation, it is ignored unless no other measurement is available

9 rejected measurement

description of quality flag
value	signification
0	regular measurement
1	uncertain measurement, its weight is decreased by a factor 2 when computing the average value
3	preliminary measurement, probably superseeded in a more recent publication, it is ignored unless no other measurement is available
4	compilation, it is ignored unless no other measurement is available
9	rejected measurement

Field: method

Method of Measurement

code	definition
0	unspecified method
1	optical measurement
2	radio measurement
3	optical measurement from a particular region (knot. region HII)
4	radio CO
5	radio OH
6	average of measurements of members
7	RVSAO (cross correlation)
8	EMSAO (emission lines)

Field: res

Resolution in km/s when the velocity comes from radio measurement

Field: line

Line Code: code of the spectral line used for making a measurement

code	definition
0	unspecified
1	emission line (like 21-cm line or H_alpha line)
2	absorption line

HyperLeda

Questions: leda@univ-lyon1.fr

23289	Theureau et al. 1998	2143
4008	de Vaucouleurs et al. RC3	1487
24372	Haynes et al. 1999	1201