Erratum: Luminosity function, sizes and FR dichotomy of radio-loud AGN

This erratum corrects a number of formulae containing mistakes in the paper 'Luminosity function, sizes and FR dichotomy of radio-loud AGN', 2007, MNRAS, v. 381, p.1548. The corrections do not alter any of the conclusions in the original paper.Comment: single page, no figures, erratum to MNRAS, 2007, v. 381, p. 154

Luminosity function, sizes and FR dichotomy of radio-loud AGN

The radio luminosity function (RLF) of radio galaxies and radio-loud quasars is often modelled as a broken power-law. The break luminosity is close to the dividing line between the two Fanaroff-Riley (FR) morphological classes for the large-scale radio structure of these objects. We use an analytical model for the luminosity and size evolution of FRII-type objects together with a simple prescription for FRI-type sources to construct the RLF. We postulate that all sources start out with an FRII-type morphology. Weaker jets subsequently disrupt within the quasi-constant density cores of their host galaxies and develop turbulent lobes of type FRI. With this model we recover the slopes of the power laws and the break luminosity of the RLF determined from observations. The rate at which AGN with jets of jet power $Q$ appear in the universe is found to be proportional to $Q^{-1.6}$. The model also roughly predicts the distribution of the radio lobe sizes for FRII-type objects, if the radio luminosity of the turbulent jets drops significantly at the point of disruption. We show that our model is consistent with recent ideas of two distinct accretion modes in jet-producing AGN, if radiative efficiency of the accretion process is correlated with jet power.Comment: 13 pages, 1 figure, accepted by MNRA

Entropy Evolution of the Gas in Cooling Flow Clusters

We emphasise the importance of the gas entropy in studying the evolution of cluster gas evolving under the influence of radiative cooling. On this basis, we develop an analytical model for this evolution. We then show that the assumptions needed for such a model are consistent with a numerical solution of the same equations. We postulate that the passive cooling phase ends when the central gas temperature falls to very low values. It follows a phase during which an unspecified mechanism heats the cluster gas. We show that in such a scenario the small number of clusters containing gas with temperatures below about 1 keV is simply a consequence of the radiative cooling.Comment: Contribution to Proceedings of `The Riddle of Cooling Flows in Galaxies and Clusters of Galaxies', Charlottesville, VA, USA. May 31 -- June 4, 2003. Editors: Reiprich, T. H., Kempner, J. C., and Soker, N. Requires included style fil

The stability of buoyant bubbles in the atmospheres of galaxy clusters

The buoyant rise of hot plasma bubbles inflated by active galactic nuclei outflows in galaxy clusters can heat the cluster gas and thereby compensate radiative energy losses of this material. Numerical simulations of this effect often show the complete disruption of the bubbles followed by the mixing of the bubble material with the surrounding cluster gas due to fluid instabilities on the bubble surface. This prediction is inconsistent with the observations of apparently coherent bubble structures in clusters. We derive a general description in the linear regime of the growth of instabilities on the surface between two fluids under the influence of a gravitational field, viscosity, surface tension provided by a magnetic field and relative motion of the two fluids with respect to each other. We demonstrate that Kelvin–Helmholtz instabilities are always suppressed, if the fluids are viscous. They are also suppressed in the inviscid case for fluids of very different mass densities. We show that the effects of shear viscosity as well as a magnetic field in the cluster gas can prevent the growth of Rayleigh–Taylor instabilities on relevant scalelengths. Rayleigh–Taylor instabilities on parsec scales are suppressed even if the kinematic viscosity of the cluster gas is reduced by two orders of magnitude compared to the value given by Spitzer for a fully ionized, unmagnetized gas. Similarly, magnetic fields exceeding a few ?G result in an effective surface tension preventing the disruption of bubbles. For more massive clusters, instabilities on the bubble surface grow faster. This may explain the absence of thermal gas in the north-west bubble observed in the Perseus cluster compared to the apparently more disrupted bubbles in the Virgo cluster