Number Counts and Spectral Distribution of Radio Sources at Centimeter Wavelengths

Abstract

Abstract. The results of a survey of selected regions of sky made at a frequency of 5 GHz, and of measurements of the spectral index distributions for sources selected from low frequency surveys are presented. The source counts and spectral distribution at 5 GHz are in excellent agreement with those expected from surveys made at lower frequencies. There is no significant dependence of the spectral distribution on flux density in any of the surveys we have investigated, implying either a low redshift for the sources, or a systematic change in their properties with redshift.In 1968, a survey of selected regions of sky at a frequency of 5 GHz (A = 6 cm) was begun at the National Radio Astronomy Observatory. A preliminary report (Keller mann et al, 1968, hereinafter referred to as Paper I) showed that the source counts and spectral distribution of this and other surveys at centimeter and decimeter wave lengths were consistent with the data from surveys at meter wavelengths, in contra diction to the conclusions of Shimmins et al (1968).The present paper reports on an extension of the 5 GHz survey and of the spectral measurements. It is hoped that this survey will ultimately cover most of the northern sky to a moderate flux level and that measurements of accurate positions, optical identifications and observations of source structure will lead to a picture of the sky at centimeter wavelengths similar to that now available at meter wavelengths.A particular aim is to look for a distance indicator in the radio data alone. This may be provided by the dependence of the radio 'A-correction' on the spectral index, a of the source. This correction is given by S = S'(1 +z) 1+a where S' is the flux density in the rest-frame of the source, S is the observed flux density and a is defined by Soc (frequency)*. This correction is small for sources with a~-l, that is, for almost all sources detected in surveys at meter wavelengths, but can be large for sources with a~0, which form a large fraction of sources found by surveys made at centimeter wavelengths. The effect of this term is that the proportion of sources with flat spectra in any survey is expected to increase with increasing redshift. If, for example, for sources with a~ -1, a number-flux relation N(S) = KS X is ob served, then the proportion of sources with a~0, for a typical redshift z = 2 and for x= -1.5, is expected to increase by a factor of about 5 over its value at low redshifts. A further effect is that the redshifts of sources with a~0 should become progressively higher, compared to those of sources with a~ -1 as the flux density decreases.In practice, the magnitude of the effect is difficult to assess for several reasons. First, because of the wide range in the absolute radio luminosities, there is a large * Present address: