Extragalactic radio source evolution under the dual-population unification scheme

We show that a dual-population unification scheme provides a successful paradigm with which to describe the evolution and beaming of all bright extragalactic radio sources. The paradigm consists of two intrinsic radio-source populations, based on the two distinct radio-galaxy morphologies of Fanaroff-Riley classes I and II. These represent the `unbeamed' or `side-on' parent populations of steep radio spectra; the `beamed' source types including flat-spectrum quasars and BL Lac objects, arise through the random alignment of their radio-axis to our line-of-sight where Doppler-beaming of the relativistic radio jets produces highly anisotropic radio emission.Comment: 18 pages & 18 postscript figures, accepted for publication in MNRA

The Parkes quarter-Jansky flat-spectrum sample 3. Space density and evolution of QSOs

We analyze the Parkes quarter-Jansky flat-spectrum sample of QSOs in terms of space density, including the redshift distribution, the radio luminosity function, and the evidence for a redshift cutoff. With regard to the luminosity function, we note the strong evolution in space density from the present day to epochs corresponding to redshifts ~ 1. We draw attention to a selection effect due to spread in spectral shape that may have misled other investigators to consider the apparent similarities in shape of luminosity functions in different redshift shells as evidence for luminosity evolution. To examine the evolution at redshifts beyond 3, we develop a model-independent method based on the V_max test using each object to predict expectation densities beyond z=3. With this we show that a diminution in space density at z > 3 is present at a significance level >4 sigma. We identify a severe bias in such determinations from using flux-density measurements at epochs significantly later than that of the finding survey. The form of the diminution is estimated, and is shown to be very similar to that found for QSOs selected in X-ray and optical wavebands. The diminution is also compared with the current estimates of star-formation evolution, with less conclusive results. In summary we suggest that the reionization epoch is little influenced by powerful flat-spectrum QSOs, and that dust obscuration does not play a major role in our view of the QSO population selected at radio, optical or X-ray wavelengths.Comment: 18 pages, 11 figures, accepted 18 Dec 2004, Astron. & Astrophys. The accepted version is expanded to include an analysis of the form of the decline in radio-QSO space density at high redshifts. This is compared with the forms of epoch dependence derived for optically-selected QSOs, for X-ray-selected QSOs, and for star formation rat

Equivariant Poincar\'e series of filtrations and topology

Earlier, for an action of a finite group $G$ on a germ of an analytic variety, an equivariant $G$-Poincar\'e series of a multi-index filtration in the ring of germs of functions on the variety was defined as an element of the Grothendieck ring of $G$-sets with an additional structure. We discuss to which extend the $G$-Poincar\'e series of a filtration defined by a set of curve or divisorial valuations on the ring of germs of analytic functions in two variables determines the (equivariant) topology of the curve or of the set of divisors