1,721,387 research outputs found
The supermodel of the intracluster plasma
No full textThe equilibria of the intracluster plasma (ICP) and of the gravitationally dominant dark matter (DM) are governed by the hydrostatic and the Jeans equation, respectively. Jeans, with the DM “entropy” set to K∝rα and α~1.25–1.3 applying from groups to rich clusters, yields our radial α-profiles for DM density and gravitational potential. In the ICP the entropy run k(r) is mainly shaped by shocks, as steadily set by supersonic accretion of gas at the cluster boundary, and intermittently driven from the center by merging events or by AGNs; the resulting equilibrium is described by the exact yet simple formalism constituting the ICP “Supermodel”. With a few parameters, this accurately represents the runs of density n(r) and temperature T(r) as required by recent X-ray data on surface brightness and spectroscopy for both cool core (CC) and non cool core (NCC) clusters; the former are marked by a middle temperature peak, whose location is predicted from rich clusters to groups. The Supermodel inversely links the inner runs of n(r) and T(r), and highlights their central scaling with entropy nc∝kc−1 and Tc∝kc0.35, to yield radiative cooling times tc≈0.3 (kc/15keV cm2)1.2Gy. We discuss the stability of the central values so focused both in CC and NCC clusters. From the Supermodel we derive as limiting cases the classic polytropic β-models, and the “mirror” model with T(r)∝σ2(r) suitable for NCC and CC clusters, respectively; these highlight how the ICP temperature T(r) tends to mirror the DM velocity dispersion σ2(r) away from entropy injections. Finally, we discuss how the Supermodel connects information derived from X-ray and gravitational lensing observations
Probing Structure and History of Dark Matter Halos with Gravitational Lensing Observations
No full textWe discuss the structure and history of dark matter halos in galaxies and galaxy systems, in terms of the halo two-stage development and of the related ‘α-profiles’. We probe both with the recent extensive dataset from weak and strong lensing observations in and around the cluster A1689
Searching for AGN-driven Shocks in Galaxy Clusters
No full textShocks and blast waves are conceivably driven into the intracluster medium filling galaxy groups and clusters by powerful outbursts of active galactic nuclei or quasars in the member galaxies; the first footprints of shock fronts have been tentatively traced out with X-ray imaging. We show how overpressures in the blasts behind the shock can prove the case and also provide specific marks of the nuclear activity: its strength, its current stage, and the nature of its prevailing output. We propose to detect these marks with the aimed pressure probe constituted by the resolved Sunyaev-Zel'dovich effect. We compute and discuss the outcomes to be expected in nearby and distant sources at different stages of their activity
Structure and history of dark matter halos probed with gravitational lensing
No full textWe test with gravitational lensing (GL) data the dark matter (DM) halos embedding the luminous baryonic component of galaxy clusters; our benchmark is provided by their two-stage cosmogonical development that we compute with its variance, and by the related "α-profiles" we derive. The latter solve the Jeans equation for the self-gravitating, anisotropic DM equilibria, and yield the radial runs of the density ρ(r) and the velocity dispersion σ2 r (r) in terms of the DM "entropy" K ≡ σ2 r /ρ2/3 r α highlighted by recent N-body simulations; the former constrains the slope to the narrow range α 1.25-1.3. These physically based α-profiles meet the overall requirements from GL observations, being intrinsically flatter at the center and steeper in the outskirts relative to the empirical Navarro, Frenk, & White formula. Specifically, we project them along the line of sight and compare with a recent extensive data set from strong and weak lensing observations in and around the cluster A1689. We find an optimal fit at both small and large scales in terms of a halo constituted by an early body with α 1.25 and by recent extensive outskirts, that make up an overall mass 1015 M ☉ with a concentration parameter c 10 consistent with the variance we compute in the ΛCDM cosmogony. The resulting structure corresponds to a potential well shallow in the outskirts as that inferred from the X rays radiated from the hot electrons and baryons constituting the intracluster plasma
The astrophysics of the intracluster plasma
No full textSince 1971 observations in X rays of several thousands of galaxy clusters have uncovered huge amounts of hot baryons filling up the deep gravitational potential wells provided by dark matter (DM) halos with masses of some 1015 M&sun; and sizes of millions of light-years. At temperatures T~108 K and with average densities of n~1 particle per liter, such baryons add up to some 1014 M&sun;. With the neutralizing electrons, they constitute the best proton-electron plasma in the Universe (whence the apt name Intra Cluster Plasma, ICP), one where the thermal energy per particle overwhelms the electron-proton Coulomb interaction by extralarge factors of order 1012. The ICP shines in X rays by thermal bremsstrahlung radiation, with powers up to several 1045erg s-1 equivalent to some 1011 solar luminosities. The first observations were soon confirmed in X rays by the detection of high excitation emission lines, and in the radio band by studies of streamlined radiogalaxies moving through the ICP. Later on they were nailed down by the first measurements in microwaves of the Sunyaev-Zel'dovich effect, i.e., the inverse Compton upscattering of cold cosmic background photons at T≈2.73 K off the hot ICP electrons at kBT~5 keV. A key physical feature of the ICP is constituted by its good local thermal equilibrium, and by its overall hydrostatic condition in the DM wells, modulated by entropy. The latter is set up in the cluster center by the initial halo collapse, and is progressively added at the outgrowing cluster boundary by standing shocks in the supersonic flow of intergalactic gas into the DM potential wells. Such physical conditions are amenable to detailed modeling. We review here these entropy-based models and discuss their outcomes and predictions concerning the ICP observables in X rays and in microwaves, as well as the underlying DM parameters. These quantitative outcomes highlight the tight relationship between the detailed ICP profiles and the cosmological evolution of the containing DM potential wells. The results also provide the simplest baseline for disentangling a number of additional and intriguing physical processes superposed to the general equilibrium. The present Report is focused on the ICP physics as driven by the two-stage evolution of the containing DM halos. We extensively discuss the basic entropy pattern established by the cluster formation and development, and cover: the central entropy erosion produced by radiative cooling that competes with the intermittent energy inputs due to active galactic nuclei and mergers; outer turbulent support linked with weakening shocks and decreasing inflow through the virial boundary, causing reduced entropy production during the late stage of DM halo evolution; the development from high to low entropy levels throughout a typical cluster; perturbations of the equilibrium up to outright disruption due to deep impacts of infalling galaxy groups or collisions with comparable companion clusters; relativistic energy distributions of electrons accelerated during such events, producing extended radio emission by synchrotron radiation and contributing non thermal pressure support for the ICP. We conclude with discussing selected contributions from cluster astrophysics to cosmology at large, and by addressing how the ICP features and processes will constitute enticing targets for observations with the ongoing Planck mission, for upcoming instrumentation like ALMA and other ground-based radio observatories, and for the next-generation of X-ray satellites from ASTRO-H to eROSITA
Missing baryons, from clusters to groups of galaxies
Full text linkFrom clusters to groups of galaxies, the powerful bremsstrahlung radiation LX emitted in X-rays by the intracluster plasma is observed to decline sharply with lowering virial temperatures T (i.e., at shallower depths of the gravitational wells) after a steep local LX-T correlation; this implies increasing scarcity of diffuse baryons relative to dark matter, well under the cosmic fraction. We show how the widely debated issue concerning these ``missing baryons'' is solved in terms of the thermal and/or dynamical effects of the kinetic (at low redshifts z) and radiative (at high z) energy inputs from central active galactic nuclei, of which independent evidence is being observed. From these inputs we compute shape and z-evolution expected for the LX-T correlation which agree with the existing data, and provide a predictive pattern for future observations
Structure and History of Dark Matter Halos in Galaxies and Galaxy Systems
No full textWe investigate the structure and history of Dark Matter (DM) halos in galaxies and galaxy systems. Our theoretical framework is provided by the two-stage cosmogonical development of DM halos, and by the related “α-profiles”. The latter solve the Jeans equation for the self-gravitating DM equilibria, and yield the radial runs of the density ρ(r) and the velocity dispersion σr2(r) in terms of the DM “entropy” K≡σr2/ρ2/3∝rα highlighted by recent N-body simulations to have a uniform slope α within the halo “body”. The former constrains the entropy slope α to a value within the narrow range 1.25–1.3; such a value applies in the halo body since the transition time that, both in our semianalytic description and in state-of-the-art numerical simulations, is found to separate two stages in the development of a DM halo: an early fast collapse including a few violent major mergers building up the halo body by dynamical relaxation; and a later, quasi-equilibrium stage during which the body is almost unaffected while the outskirts develop from the inside-out by minor mergers and smooth accretion. These physically based α-profiles meet the overall requirements from gravitational lensing observations, being intrinsically flatter at the center and steeper in the outskirts relative to the empirical NFW formula. In quantitative detail, we test them with the recent extensive dataset from weak and strong lensing observations in and around the cluster A1689. We find an optimal fit at both small and large scales in terms of a halo constituted by an early body with α≈1.25 and by recent extended outskirts making up a concentration parameter c≈10; we consistently interpret the latter value in terms of the variance expected in the two-stage halo development under the standard ΛCDM cosmology
Brand premia driven by perceived vertical differentiation in markets with information disparity and optimistic consumers
No full textWe have considered a duopoly with perceived vertical differentiation, information disparity and optimistic consumers. When firms compete for informed and uninformed consumers, the former contribute to raise product quality, while equilibrium prices increase with optimistic misperception of the latter, in our first equilibrium. Brand premium includes a quality premium and a misperception rent. In our second equilibrium, informed consumers buy low-quality goods and minimum product differentiation without Bertrand competition occurs. The brand premium is just a misperception rent, however, an increase of the informed consumers share implies price re-balancing and rent reduction. Consumers externalities arise in both equilibria. Firms compete only for informed consumers within our third and fourth equilibrium, as uninformed ones are passive and represent a captive market. Uninformed consumers in one case are overoptimistic, they buy the high quality good and can be cheated in equilibrium. Uninformed consumers approach the real quality differential in the fourth equilibrium, and the model reduces to standard vertical differentiation with perfect information
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