The

**source counts** distribution of radio-sources from a

radio-astronomicalRadio astronomy is a subfield of astronomy that studies celestial objects at radio frequencies. The initial detection of radio waves from an astronomical object was made in the 1930s, when Karl Jansky observed radiation coming from the Milky Way. Subsequent observations have identified a number of...

survey is the

cumulative distributionIn probability theory and statistics, the cumulative distribution function , or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x. Intuitively, it is the "area so far"...

of the number of sources (

*N*) brighter than a given flux density (

*S*). It is one out of a half-dozen cosmological tests that was conceived in the 1930s to check the viability of and compare new cosmological models.

Early work on cataloguing radio sources had as an aim the determination of the source counts distribution to help ia decide between cosmological models. For a uniform distribution of radio sources at not too large redshift (ie in a 'steady-state, Euclidean universe') the slope of the cumulative distribution of log(

*N*) versus log(

*S*) would be −1.5.

Data from the early Cambridge

2C survey (published 1955) apparently implied a (log(

*N*), log(

*S*)) slope of nearly −3.0. This appeared to invalidate the

steady stateA system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:...

theory of

Fred HoyleSir Fred Hoyle FRS was an English astronomer and mathematician noted primarily for his contribution to the theory of stellar nucleosynthesis and his often controversial stance on other cosmological and scientific matters—in particular his rejection of the "Big Bang" theory, a term originally...

,

Hermann BondiSir Hermann Bondi, KCB, FRS was an Anglo-Austrian mathematician and cosmologist. He is best known for developing the steady-state theory of the universe with Fred Hoyle and Thomas Gold as an alternative to the Big Bang theory, but his most lasting legacy will probably be his important...

and

Thomas GoldThomas Gold was an Austrian-born astrophysicist, a professor of astronomy at Cornell University, a member of the U.S. National Academy of Sciences, and a Fellow of the Royal Society . Gold was one of three young Cambridge scientists who in the 1950s proposed the now mostly abandoned 'steady...

. Unfortunately many of these weaker sources were subsequently found to be due to 'confusion' (the blending of several weak sources in the side-lobes of the interferometer, to give a response like one stronger one).

By contrast, analysis from the contemporaneous Mills Cross data (by Slee and Mills) were consistent with an index of −1.5.

Later and more accurate surveys from Cambridge,

3C, 3CRThe Third Cambridge Catalogue of Radio Sources is an astronomical catalogue of celestial radio sources detected originally at 159 MHz, and subsequently at 178 MHz. It was published in 1959 by members of the Radio Astronomy Group of the University of Cambridge...

, and 4C, also showed source count slopes steeper than −1.5, though by a smaller margin than 2C. This convinced some cosmologists that the steady state theory was wrong, although residual problems with confusion provided some defense for Hoyle and his colleagues.

The immediate interest in testing the steady-state theory through source-counts was reduced by the discovery of the 3K microwave background radiation in the mid 1960s, which essentially confirmed the

Big-BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

model.

Later radio survey data have shown a complex picture — the 3C and 4C claims appear to hold up, while at fainter levels the source counts flatten substantially

*below* a slope of −1.5. This is now understood to reflect the effects of both density and luminosity evolution of the principal radio sources over cosmic timescales.