From Global to Local Dynamics: Effects of the Expansion on Astrophysical Structures

We explore the effects of background cosmology on large scale structures with non-spherical symmetry by using the concept of quasi-equilibrium which allows certain internal properties (e.g. angular velocity) of the bodies to change with time. In accordance with the discovery of the accelerated phase of the universe we model the cosmological background by two representative models: the $\Lambda$CDM Model and the Chaplygin Gas Model. We compare the effects of the two models on various properties of large astrophysical objects. Different equations of state are also invoked in the investigation.Comment: References added To be published in CQ

The REFLEX II galaxy cluster catalogue

In this work I present the characterization of the spatial distribution of X-ray galaxy clusters, based on the the measurements of the cluster power spectrum. The analysis is developed on the new ROSAT-ESO Flux-Limited X-Ray (REFLEX II) galaxy cluster catalogue. This new sample extends the flux limit of the original REFLEX to 1.8×10−12 erg s−1 cm−2, yielding a total of 911 clusters with 94% completeness in redshift followup. The X-ray luminosity function was measured and parameterized in order to be used as cosmological probe. The statistical analysis is complemented by creating a set of 100 REFLEX II-like mock catalogues, built from a suite of large volume LCDM Nbody simulations (L-BASICC II). We have characterized the main properties of this set of simulations, such as the halo abundance, the halo bias, the halo clustering and the mass-X-ray luminosity relations, all these required to properly understand the observed clustering signal of X-ray galaxy clusters. The mock catalogues have been designed to reproduce the observed X-ray luminosity function by calibrating the a mass-X ray luminosity relation. Our measurements of the X-ray cluster power spectrum are in agreement with predictions from the LCDM cosmological model and show the expected increase in the amplitude of the power spectrum with increasing X-ray luminosity. The better statistics of the REFLEX II sample allowed us to explore the issue of luminosity bias in some detail. On large scales it was observed a scale-independent relative luminosity bias, which implies that the clustering of galaxy clusters, on those scales, is a scaled version of the clustering of dark matter. Moreover, this suggests that within the precision given by the surveyed volume of the REFLEX II catalogue, the shape of the measured galaxy cluster power spectrum is not affected by distortions induced due to the presence of clusters with different X-ray luminosities. We confirmed this result by implementing a luminosity dependent power spectrum estimator. The measured power spectrum is statistically compatible with a featureless power spectrum on scales k > 0.01 h/Mpc and hence no statistically significant signal of baryonic acoustic oscillations has been detected. Similar conclusions are drawn from the analysis of the clustering in configurations space by means of the cluster correlation function. For the first time, a signature of non-linear evolution in the galaxy cluster power spectrum has been detected on scales k~0.15 h/Mpc. We model the shape of the measured power spectrum by means of phenomenological parameterizations, which are useful for our measurements due the moderate volume probed by the survey. The measurements of cluster power spectrum described in this work are suitable to be used as probes for cosmological parameters.In dieser Arbeit wird die großskalige Struktur von Galaxienhaufen aus dem ROSATESO Flux-Limited X-Ray (REFLEX II) Katalog untersucht. Aufgrund der im Vergleich zum urspr¨unglichen REFLEX Katalog schw¨acheren Grenzhelligkeit von 1.8 × 10−12 er/s/cm−2 konnte eine Gesamtanzahl von 911 Haufen gefunden werden; f¨ur mehr als 84% von diesen existieren spektroskopische Rotverschiebungen. Die R¨ontgenleuchtkraftfuntkion wurde gemessen und parametrisiert, um sie zur Bestimmung kosmologischer Parameter verwenden zu k¨onnen. Zur weitergehenden statistischen Analyse dieses neuen Samples wurden 100 REFLEX II Mock-Kataloge aus großen LCDM N-body Simulationen (L-BASICC II) hergestellt, und Messgr¨oßen wie die Massenfunktion, den Bias, die großskalige Struktur und die Masse-R¨ontgenleuchtkraft-Beziehung der Dunklen Halos charakterisiert, die ben¨otigt werden, um die beobachtete großskalige Struktur der Galaxienhaufen zu verstehen. Unter Verwendung der Masse-R¨ontgenleuchtkraftbeziehung wurden die Mock-Kataloge so konstruiert, dass die beobachtete R¨ontgenleuchtkraftfunktion reproduziert wird. Die gemessenen Leistungsspektren der R¨ontgenhaufen stimmen mit Vorhersagen der LCDM-Kosmologie ¨uberein und zeigen das erwartete Anwachsen der Amplitude des Leistungsspektrums mit wachsender R¨ontgenhelligkeit, was eine Folge der direkten Beziehung zwischen der beobachteten Leuchtkraft und der Gesamtmasse des Haufens ist. Die bessere Statistik des REFLEX II Samples erlaubt es, den Leuchtkraft bias mit hoher Genauigkeit zu untersuchen. Der beobachtete relative Leuchtkraft bias entspricht einem skalenunabh¨angigen Halomassenbias, in ¨ Ubereinstimmung mit Befunden aus N-body Simulationen. Dies l¨asst darauf schließen, dass die Form des Leistungsspektrums der REFLEX II Galaxienhaufen innerhalb der durch das Beobachtungsvolumen gegebenen Genauigkeit nicht durch den Einfluss des beobachteten Populationsmixes verzerrt wird. Dies wird durch die Verwendung eines leuchtkraftunabh ¨angigen Sch¨atzers f¨ur das Leistungsspektrums best¨atigt. Im Rahmen der Messgenauigkeit ist das gemessene Leistungsspektrum auf Skalen von k > 0.01hMpc−1 vereinbar mit einem glatten Leistungsspektrum, weshalb kein statistisch signifikantes Signal der Baryonischen Akustischen Oszillationen detektiert werden kann. ¨ Ahnliche Schlussfolgerungen lassen sich aus der Analyse der großskaligen Struktur im Konfigurationsraum mithilfe der Korrelationsfunktion ziehen. Es kann jedoch gezeigt werden, dass das REFLEX II Leistungsspektrum auf Skalen von k > 0.15hMpc−1 Signaturen von nichtlinearer Entwicklung aufweist. Die Form des gemessenen Leistungsspektrums wurde mithilfe ph¨anomenologischer Parametrisierungen modelliert, welche aufgrund des ¨uberschaubaren Volumens der Himmelsdurchmusterung benutzbar sind

Scales Set by the Cosmological Constant

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 adde

Dark Energy in an Astrophysical Context

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 adde

Astrophysical Configurations with Background Cosmology: Probing Dark Energy at Astrophysical Scales

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 prin

Physics of dark energy particles

We consider the astrophysical and cosmological implications of the existence of a minimum density and mass due to the presence of the cosmological constant. If there is a minimum length in nature, then there is an absolute minimum mass corresponding to a hypothetical particle with radius of the order of the Planck length. On the other hand, quantum mechanical considerations suggest a different minimum mass. These particles associated with the dark energy can be interpreted as the ``quanta'' of the cosmological constant. We study the possibility that these particles can form stable stellar-type configurations through gravitational condensation, and their Jeans and Chandrasekhar masses are estimated. From the requirement of the energetic stability of the minimum density configuration on a macroscopic scale one obtains a mass of the order of 10^55 g, of the same order of magnitude as the mass of the universe. This mass can also be interpreted as the Jeans mass of the dark energy fluid. Furthermore we present a representation of the cosmological constant and of the total mass of the universe in terms of `classical' fundamental constants.Comment: 10 pages, no figures; typos corrected, 4 references added; 1 reference added; reference added; entirely revised version, contains new parts, now 14 page

Quasi-spherical collapse with cosmological constant

The junction conditions between static and non-static space-times are studied for analyzing gravitational collapse in the presence of a cosmological constant. We have discussed about the apparent horizon and their physical significance. We also show the effect of cosmological constant in the collapse and it has been shown that cosmological constant slows down the collapse of matter.Comment: 7 pages, No figures, RevTeX styl

Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter black holes

We study two different ways to analyze the Hawking evaporation of a Schwarzschild-de Sitter black hole. The first one uses the standard approach of surface gravity evaluated at the possible horizons. The second method derives its results via the Generalized Uncertainty Principle (GUP) which offers a yet different method to look at the problem. In the case of a Schwarzschild black hole it is known that this methods affirms the existence of a black hole remnant (minimal mass $M_{\rm min}$) of the order of Planck mass $m_{\rm pl}$ and a corresponding maximal temperature $T_{\rm max}$ also of the order of $m_{\rm pl}$. The standard $T(M)$ dispersion relation is, in the GUP formulation, deformed in the vicinity of Planck length $l_{\rm pl}$ which is the smallest value the horizon can take. We generalize the uncertainty principle to Schwarzschild-de Sitter spacetime with the cosmological constant $\varLambda=1/m_\varLambda^2$ and find a dual relation which, compared to $M_{\rm min}$ and $T_{\rm max}$, affirms the existence of a maximal mass $M_{\rm max}$ of the order $(m_{\rm pl}/m_\varLambda)m_{\rm pl}$, minimum temperature $T_{\rm min} \sim m_\varLambda$. As compared to the standard approach we find a deformed dispersion relation $T(M)$ close to $l_{\rm pl}$ and in addition at the maximally possible horizon approximately at $r_\varLambda=1/m_\varLambda$. $T(M)$ agrees with the standard results at $l_{\rm pl} \ll r \ll r_\varLambda$ (or equivalently at $M_{\rm min} \ll M \ll M_{\rm max}$).Comment: new references adde