Spectral index has been traditionally used to separate extragalactic radio sources into compact and extended populations, with the spectral transition placed variably between −0.4 and −0.6. We use high angular resolution data, measured from visibility of sources at the longest baseline of 4500 m of the Australia Telescope Compact Array (ATCA), for the Australia Telescope 20 GHz (AT20G) survey to obtain angular size information for over 94 per cent of AT20G sources. We confirm the previous AT20G result that due to the high survey frequency of 20 GHz, the source population is strongly dominated by compact sources (79 per cent). At 0.15-arcsec angular resolution limit, we show a very strong correlation between the compact and extended sources with flat and steep-spectrum sources respectively for spectral indices obtained between 1 and 5 GHz. Thus, we provide a firm physical basis for the traditional spectral classification into flat and steep-spectrum sources to select compact and extended sources. We find that for spectral indices between 1 and 5 GHz, the cut-offs at −0.4 and −0.5 are quite similar to the optimum cut-off of −0.46 and, hence, recommend the continued use of −0.5 for future studies.
We use the recently published redshift data to study the effect of spectral curvature on the redshift cut-off of compact active galactic nuclei (AGNs). Using spectral indices at different frequencies, we correct for the redshift effect and also produce rest-frame frequency spectra for compact sources for redshifts up to z∼ 5. We show that the spectra of most compact sources are flat to ∼30 GHz and then start to steepen. At higher frequencies, the spectra of both compact and extended sources are steep, so the use of spectral index does not separate the compact and extended source populations as well as in lower frequencies. We also find that due to spectral steepening at high frequencies, surveys of compact sources at higher frequencies (ν > 5 GHz) will have redshift cut-off due to spectral curvature but at frequencies below a few gigahertz, the surveys are not significantly affected by spectral curvature and, thus, the evidence for a strong redshift cut-off in AGNs found in lower frequency surveys is a real cut-off and not a result of K-correction.