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We explore the effects of a positive cosmological constant on astrophysical and cosmological configurations described by a polytropic equation of state. We derive the conditions for equilibrium and stability of such configurations and consider some astrophysical examples where our analysis may be relevant. We show that in the presence of the cosmological constant the isothermal sphere is not a viable astrophysical model since the density in this model does not go asymptotically to zero. The cosmological constant implies that, for polytropic index smaller than five, the central density has to exceed a certain minimal value in terms of the vacuum density in order to guarantee the existence of a finite size object. We examine such configurations together with effects of $\Lambda$ in other exotic possibilities, such as neutrino and boson stars, and we compare our results to N-body simulations. The astrophysical properties and configurations found in this article are specific features resulting from the existence of a dark energy component. Hence, if found in nature would be an independent probe of a cosmological constant, complementary to other observations., Comment: 23 pages, 11 figures, 2 tables. Reference added. Mon. Not. Roy. Astro. Soc in print

We explore local consequences of a non-zero cosmological constant on astrophysical structures. We find that the effects are not only sensitive to the density of the configurations but also to the geometry. For non-homogeneous configurations, we calculate the effects for a polytropic configurations and the isothermal sphere. Special emphasis is put on the fact that the cosmological constant sets certain scales of length, time, mass and density. Sizable effects are established for non spherical systems such as elliptical galaxy clusters where the effects of $\Lambda$ are growing with the flatness of the system. The equilibrium of rotating ellipsoids is modified and the cosmological constant allows new configurations of equilibrium., Comment: talk given at Albert Einstein International Conference in Palais de l'Unesco, Paris, France, 18-23 July 2005; references added

The cosmological constant sets certain scales important in cosmology. We show that Lambda in conjunction with other parameters like the Schwarzschild radius leads to scales relevant not only for cosmological but also for astrophysical applications. Of special interest is the extension of orbits and velocity of test particles traveling over Mpc distances. We will show that there exists a lower and an upper cut-off on the possible velocities of test particles. For a test body moving in a central gravitational field Lambda enforces a maximal value of the angular momentum if we insist on bound orbits of the test body which move at a distance larger than the Schwarzschild radius., Comment: 15 pages, 2 figures, 1 table; one reference added

Astrophysical bounds on the cosmological constant are examined for spherically symmetric bodies. Similar limits emerge from hydrostatical and gravitational equilibrium and the validity of the Newtonian limit. It is argued that the bound coming from the analysis of exact solutions is not a feature of the relativistic theory since it also emerges from the Newtonian theory. The methods in use seem to be disjoint from the basic principles, however they have the same implication regarding the upper bounds. Therefore we will compare different inequalities and comment on the possible relationship between them., Comment: 19 pages, LaTeX; revised version with new section 8, improved introduction and summary; one reference added