Linear and Circular Polarization Properties of Jets

I discuss the transfer of polarized synchrotron radiation in relativistic jets. I argue that the main mechanism responsible for the circular polarization properties of compact synchrotron sources is likely to be Faraday conversion and that, contrary to common expectation, a significant rate of Faraday rotation does not necessarily imply strong depolarization. The long-term persistence of the sign of circular polarization, observed in some sources, is most likely due to a small net magnetic flux generated in the central engine, carried along the jet axis and superimposed on a highly turbulent magnetic field. I show that the mean levels of circular and linear polarizations depend on the number of field reversals along the line of sight and that the gradient in Faraday rotation across turbulent regions can lead to "correlation depolarization''. The model is potentially applicable to a wide range of synchrotron sources. In particular, I demonstrate how the model can naturally explain the excess of circular over linear polarization in the Galactic Center (Sgr A*) and the low-luminosity AGN M81*.Comment: Invited Talk, to appear in "Circular Polarisation in Relativistic Jet Sources", Astrophysics and Space Science, Fender R.P. and Macquart J.-P. (Eds

Are black holes big enough to quench cooling in cluster cool cores?

Total energy arguments (e.g., Fabian et al. 2002) suggest that black holes need to have masses significantly in excess of the prediction from the classic black hole mass - velocity dispersion relation (M-sigma) in order to offset the cooling losses in massive cool core clusters. This suggests that the black holes may be too small to power such clusters. However, Lauer et al. (2007) argue that the black hole mass - bulge luminosity relationship is a better predictor of black hole masses in high luminosity galaxies and that this relationship predicts significantly higher masses in BCGs. They find slow increase in the velocity dispersion with luminosity and a more rapid increase in effective radii with luminosity seen in BCGs as opposed to less luminous galaxies. Motivated by these results and the theoretical work of Boylan-Kolchin et al. (2006) on isolated mergers, we perform high-resolution cosmological simulations of dry mergers in a massive galaxy cluster identified in the Millennium Run including both the dark matter halos and stellar bulges of merging galaxies. We demonstrate that the BCG clearly evolves away from the size-luminosity relation as defined by the smaller galaxies (i.e., the relation bends) and we also see a bending in the luminosity-sigma relation. As black hole mass is expected to be proportional to the mass and luminosity of the stellar bulge of the BCGs (if they were formed in predominantly dissipationless mergers), our findings are consistent with those of Lauer et al. (2007) on a qualitative level and suggest that the black holes in BCGs may indeed be more massive than predicted from the standard M-sigma relation.Comment: submitted to the conference proceedings of "The Monster's Fiery Breath

Structure of the solution set to differential inclusions with impulses at variable times

A topological structure of the solution set to differential inclusions with impulses at variable times is investigated. In order to do that an appropriate Banach space is defined. It is shown that the solution set is an $R_{\delta}$-set. Results are new also in the case of~differential equations with impulses at variable times