The relative concentration of visible and dark matter in clusters of galaxies

[Abridged] We consider two clusters (A496 and Coma) that are representative of the two classes of cool-core and non-cool-core clusters. We first refer to a two-component dynamical model that ignores the contribution from the galaxy density distribution and study the condition of hydrostatic equilibrium for the hot intracluster medium (ICM) under the assumption of spherical symmetry, in the presence of dark matter. We model the ICM density distribution in terms of a standard $\beta$-model with $\beta=2/3$, i.e. with a distribution similar to that of a regular isothermal sphere (RIS), and fit the observed X-ray brightness profiles. With the explicit purpose of ignoring cosmological arguments, we na\"ively assume that dark matter, if present, has an analogous density distribution, with the freedom of two different density and length scales. The relative distribution of visible and dark matter is then derived by fitting the temperature data for the ICM under conditions of hydrostatic equilibrium. For both clusters, we find that dark matter is more concentrated with respect to visible matter. We then test whether the conclusion changes significantly when dark matter is taken to be distributed according to cosmologically favored density profiles and when the contribution of the mass contained in galaxies is taken into account. Although the qualitative conclusions remain unchanged, we find that the contribution of galaxies to the mass budget is more important than generally assumed. We also show that, without resorting to additional information on the small scale, it is not possible to tell whether a density cusp is present or absent in these systems. [Abridged]Comment: 13 pages, 3 figures, accepted for publication in Il Nuovo Cimento

Involutive constrained systems and Hamilton-Jacobi formalism

In this paper, we study singular systems with complete sets of involutive constraints. The aim is to establish, within the Hamilton-Jacobi theory, the relationship between the Frobenius' theorem, the infinitesimal canonical transformations generated by constraints in involution with the Poisson brackets, and the lagrangian point (gauge) transformations of physical systems

An experimental investigation of the flow field for double-wedge configurations in a Mach 4.97 stream

The viscous-inviscid interactions which perturb the flow around the wing leading edge are discussed. The flow field perturbation results when the fuselage-generated shock wave interacts with the wing-generated shock wave. Three types of shock interference patterns are possible for the wing leading edge of the orbiter

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit

The Kovacs effect in model glasses

We discuss the `memory effect' discovered in the 60's by Kovacs in temperature shift experiments on glassy polymers, where the volume (or energy) displays a non monotonous time behaviour. This effect is generic and is observed on a variety of different glassy systems (including granular materials). The aim of this paper is to discuss whether some microscopic information can be extracted from a quantitative analysis of the `Kovacs hump'. We study analytically two families of theoretical models: domain growth and traps, for which detailed predictions of the shape of the hump can be obtained. Qualitatively, the Kovacs effect reflects the heterogeneity of the system: its description requires to deal not only with averages but with a full probability distribution (of domain sizes or of relaxation times). We end by some suggestions for a quantitative analysis of experimental results.Comment: 17 pages, 6 figures; revised versio

Trap models with slowly decorrelating observables

We study the correlation and response dynamics of trap models of glassy dynamics, considering observables that only partially decorrelate with every jump. This is inspired by recent work on a microscopic realization of such models, which found strikingly simple linear out-of-equilibrium fluctuation-dissipation relations in the limit of slow decorrelation. For the Barrat-Mezard model with its entropic barriers we obtain exact results at zero temperature $T$ for arbitrary decorrelation factor $\kappa$. These are then extended to nonzero $T$, where the qualitative scaling behaviour and all scaling exponents can still be found analytically. Unexpectedly, the choice of transition rates (Glauber versus Metropolis) affects not just prefactors but also some exponents. In the limit of slow decorrelation even complete scaling functions are accessible in closed form. The results show that slowly decorrelating observables detect persistently slow out-of-equilibrium dynamics, as opposed to intermittent behaviour punctuated by excursions into fast, effectively equilibrated states.Comment: 29 pages, IOP styl

Evidence for unidimensional low-energy excitations as the origin of persistent spin dynamics in geometrically frustrated magnets

We report specific heat, magnetic, and muon spin relaxation measurements performed on a polycrystalline sample of the normal spinel CdHo2S4. The rare-earth ions sit on a lattice of corner-sharing regular tetrahedra as in pyrochlore compounds. Magnetic ordering is detected at Tc ~ 0.87 K. From spin-lattice relaxation rate measurements on both sides of Tc we uncover similar magnetic excitation modes driving the so-called persistent spin dynamics at T < Tc. Unidimensional excitations are argued to be at its origin. Often observed spin loop structures are suggested to support these excitations. The possibility of a generic mechanism for their existence is discussed.Comment: 7 pages, 8 figure

Self-consistent nonspherical isothermal halos embedding zero-thickness disks

Disk-halo decompositions of galaxy rotation curves are generally performed in a parametric way. We construct self-consistent models of nonspherical isothermal halos embedding a zero-thickness disk, by assuming that the halo distribution function is a Maxwellian. The method developed here can be used to study other physically-based choices for the halo distribution function and the case of a disk accompanied by a bulge. In a preliminary investigation we note the existence of a fine tuning between the scalelengths R_{\Omega} and h, respectively characterizing the rise of the rotation curve and the luminosity profile of the disk, which surprisingly applies to both high surface brightness and low surface brightness galaxies. This empirical correlation identifies a much stronger conspiracy than the one required by the smoothness and flatness of the rotation curve (disk-halo conspiracy). The self-consistent models are characterized by smooth and flat rotation curves for very different disk-to-halo mass ratios, hence suggesting that conspiracy is not as dramatic as often imagined. For a typical rotation curve, with asymptotically flat rotation curve at V_{\infty} (the precise value of which can also be treated as a free parameter), and a typical density profile of the disk, self-consistent models are characterized by two dimensionless parameters, which correspond to the dimensional scales (the disk mass-to-light ratio M/L and the halo central density) of standard disk-halo decompositions. We show that if the rotation curve is decomposed by means of our self-consistent models, the disk-halo degeneracy is removed and typical rotation curves are fitted by models that are below the maximum-disk prescription. Similar results are obtained from a study of NGC 3198. Finally, we quantify the flattening of the spheroidal halo, which is significant, especially on the scale of the visible disk.Comment: accepted for publication in A&

Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit

We study the dynamics of the one dimensional disordered trap model presenting a broad distribution of trapping times $p(\tau) \sim 1/\tau^{1+\mu}$, when an external force is applied from the very beginning at $t=0$, or only after a waiting time $t_w$, in the linear as well as in the non-linear response regime. Using a real-space renormalization procedure that becomes exact in the limit of strong disorder $\mu \to 0$, we obtain explicit results for many observables, such as the diffusion front, the mean position, the thermal width, the localization parameters and the two-particle correlation function. In particular, the scaling functions for these observables give access to the complete interpolation between the unbiased case and the directed case. Finally, we discuss in details the various regimes that exist for the averaged position in terms of the two times and the external field.Comment: 27 pages, 1 eps figur