We solve the equation of the equilibrium of the gravitating body, with a polytropic equation of state of the matter P = K rho^gamma, in the frame of the newtonian gravity, with non-zero cosmological constant Lambda. We consider here the cases with n = 1; 3, gamma = 1 + 1/n. For each n, the non-dimensional equation of the static equilibrium has a family of solutions, instead of only one solution of the Emden equation at Lambda = 0. The equilibrium state exists only for the central density rho_0 greater or equal than rho_c. There are no static solutions at rho_0 < rho_c. We show, that the presence of dark energy decrease a dynamic stability of the configuration. We apply our results for the analysis of a possibility of existence of equilibrium states of cluster of galaxies in the present universe with non-zero Lambda.

Galaxy clusters in presence of dark energy / Bisnovatyi Kogan, G. S.; Merafina, Marco. - STAMPA. - (2010). (Intervento presentato al convegno Frontier Objects in Astrophysics and Particle Physics tenutosi a Vulcano, Italy nel 24-29 Maggio 2010).

Galaxy clusters in presence of dark energy

MERAFINA, Marco
2010

Abstract

We solve the equation of the equilibrium of the gravitating body, with a polytropic equation of state of the matter P = K rho^gamma, in the frame of the newtonian gravity, with non-zero cosmological constant Lambda. We consider here the cases with n = 1; 3, gamma = 1 + 1/n. For each n, the non-dimensional equation of the static equilibrium has a family of solutions, instead of only one solution of the Emden equation at Lambda = 0. The equilibrium state exists only for the central density rho_0 greater or equal than rho_c. There are no static solutions at rho_0 < rho_c. We show, that the presence of dark energy decrease a dynamic stability of the configuration. We apply our results for the analysis of a possibility of existence of equilibrium states of cluster of galaxies in the present universe with non-zero Lambda.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/478521
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