Massive black holes interactions during the assembly of heavy sub-structures in the centre of galaxy clusters

We performed a series of direct N-body simulations with the aim to follow the dynamical evolution of a galaxy cluster (GC) ($M_{clus}\simeq 10^{14} M_{\odot}$) in different environment. The results show the formation of heavy sub-structures in the cluster centre in consequence of multiple merging among the innermost galaxies. Moreover we investigate the dynamics of super-massive black holes (SMBHs) residing in the centre of galaxies that form the most massive sub-structure.Comment: 2 pages, 3 figures. To be published in the proceedings of the conference Cosmic-Lab, Modest 201

Galactic cluster winds in presence of a dark energy

We obtain a solution for the hydrodynamic outflow of the polytropic gas from the gravitating center, in presence of the uniform Dark Energy (DE). The antigravity of DE is enlightening the outflow and make the outflow possible at smaller initial temperature, at the same density. The main property of the wind in presence of DE is its unlimited acceleration after passing the critical point. In application of this solution to the winds from galaxy clusters we suggest that collision of the strongly accelerated wind with another galaxy cluster, or with another galactic cluster wind could lead to the formation of a highest energy cosmic rays.Comment: 13 pages, 7 figure

Selfgravitating Gas Spheres in a Box and Relativistic Clusters: Relation between Dynamical and Thermodynamical Stability

We derive a variational principle for the dynamical stability of a cluster as a gas sphere in a box. Newtonian clusters are always dynamically stable and, for relativistic clusters, the relation between dynamical and thermodynamical instabilities is analyzed. The boundaries between dynamically and thermodynamically stable and unstable models are found numerically for relativistic stellar systems with different cut off parameters. A criterion based on binding energy curve is used for determination of the boundary of dynamical stability.Comment: 10 figure

Polytropic configurations with non-zero cosmological constant

We solve the equation of the equilibrium of the gravitating body, with a polytropic equation of state of the matter $P=K\rho^{\gamma}$, with $\gamma=1+1/n$, in the frame of the Newtonian gravity, with non-zero cosmological constant $\Lambda$. We consider the cases with $n=1,\,\,1.5,\,\,3$ and construct series of solutions with a fixed value of $\Lambda$. For each value of $n$, the non-dimensional equation of the static equilibrium has a family of solutions, instead of the unique solution of the Lane-Emden equation at $\Lambda=0$. The equilibrium state exists only for central densities $\rho_0$ larger than the critical value $\rho_c$. There are no static solutions at $\rho_0 < \rho_c$. We find the values of $\rho_c$ for each value of $n$ and show that the presence of dark energy decrease the dynamic stability of the configuration. We apply our results for analyzing the possibility of existence of equilibrium states for cluster of galaxies in the present universe with non-zero $\Lambda$.Comment: submitted to Astron. A

A Polytropic Approach to Semi-relativistic Isothermal Gas Spheres at Arbitrary Temperature

We use standard polynomial expansion technique to show the existence of a relation between polytropic model and the description of gas spheres at finite temperature. A numerical analysis is made concerning the obtained perturbative parameters. It is shown that there is a correspondence between polytropic and gas sphere thermal models for fermions and bosons. For instance, the polytropic index $n$ displays evident correlation with temperature and chemical potential.Comment: Latex, 7 pages, 7 figures. New section introduced (Limits and validity