A proposed method for the determination of the bivariate luminosity function utilizing an incomplete sample with an application to Seyfert galaxies

Astronomy and Astrophysics – Astrophysics

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Bivariate Analysis, Luminosity, Radio Galaxies, Seyfert Galaxies, Magnitude, Radiant Flux Density, X Ray Sources

Scientific paper

The radio and X-ray surveys of cataloged objects are made with fixed limiting flux densities; however, the distribution of optical magnitudes in these listings is often arbitrary. Thus the subsamples with detected radio or X-ray energy are not complete because the original optically surveyed samples are incomplete. The present paper shows that the results of such surveys can be used for the determination of the bivariate luminosity functions, provided that both the distribution of luminosities of objects in the detected subsample, as well as the distribution of apparent magnitudes in the surveyed sample are taken into account. The proposed method is illustrated in the determination of the bivariate optical and radio luminosity function of Seyfert galaxies.

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