Mechanical Feedback from Active Galactic Nuclei in Galaxies, Groups, and Clusters

The radiative cooling timescales at the centers of hot atmospheres surrounding elliptical galaxies, groups, and clusters are much shorter than their ages. Therefore, hot atmospheres are expected to cool and to form stars. Cold gas and star formation are observed in central cluster galaxies but at levels below those expected from an unimpeded cooling flow. X-ray observations have shown that wholesale cooling is being offset by mechanical heating from radio active galactic nuclei. Feedback is widely considered to be an important and perhaps unavoidable consequence of the evolution of galaxies and supermassive black holes. We show that cooling X-ray atmospheres and the ensuing star formation and nuclear activity are probably coupled to a self-regulated feedback loop. While the energetics are now reasonably well understood, other aspects of feedback are not. We highlight the problems of atmospheric heating and transport processes, accretion, and nuclear activity, and we discuss the potential role of black hole spin. We discuss X-ray imagery showing that the chemical elements produced by central galaxies are being dispersed on large scales by outflows launched from the vicinity of supermassive black holes. Finally, we comment on the growing evidence for mechanical heating of distant cluster atmospheres by radio jets and its potential consequences for the excess entropy in hot halos and a possible decline in the number of distant cooling flows.Comment: Accepted for publication in New Journal of Physics Focus Issue on Clusters of Galaxie

Inelastic Collapse of Three Particles

A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time. Analytic and simulation results show that for a sufficiently small restitution coefficient, $0\leq r<7-4\sqrt{3}\approx 0.072$, collapse can occur. In one dimension, such a collapse is stable against small perturbations within this entire range. In higher dimensions, the collapse can be stable against small variations of initial conditions, within a smaller $r$ range, $0\leq r<9-4\sqrt{5}\approx 0.056$.Comment: 6 pages, figures on request, accepted by PR

X-ray Supercavities in the Hydra A Cluster and the Outburst History of the Central Galaxy's Active Nucleus

A 227 ksec Chandra Observatory X-ray image of the hot plasma in the Hydra A cluster has revealed an extensive cavity system. The system was created by a continuous outflow or a series of bursts from the nucleus of the central galaxy over the past 200-500 Myr. The cavities have displaced 10% of the plasma within a 300 kpc radius of the central galaxy, creating a swiss-cheese-like topology in the hot gas. The surface brightness decrements are consistent with empty cavities oriented within 40 degrees of the plane of the sky. The outflow has deposited upward of 10^61 erg into the cluster gas, most of which was propelled beyond the inner ~100 kpc cooling region. The supermassive black hole has accreted at a rate of approximately 0.1-0.25 solar masses per year over this time frame, which is a small fraction of the Eddington rate of a ~10^9 solar mass black hole, but is dramatically larger than the Bondi rate. Given the previous evidence for a circumnuclear disk of cold gas in Hydra A, these results are consistent with the AGN being powered primarily by infalling cold gas. The cavity system is shadowed perfectly by 330 MHz radio emission. Such low frequency synchrotron emission may be an excellent proxy for X-ray cavities and thus the total energy liberated by the supermassive black hole.Comment: 8 pages, 3 figures; Submitted to ApJ, revised per referee's suggestion

Quasi-rigidity: some uniqueness issues

Quasi-rigidity means that one builds a theory for assemblies of grains under a slowly changing external load by using the deformation of those grains as a small parameter. Is quasi-rigidity a complete theory for these granular assemblies? Does it provide unique predictions of the assembly's behavior, or must some other process be invoked to decide between several possibilities? We provide evidence that quasi-rigidity is a complete theory by showing that two possible sources of indeterminacy do not exist for the case of disk shaped grains. One possible source of indeterminacy arises from zero-frequency modes present in the packing. This problem can be solved by considering the conditions required to obtain force equilibrium. A second possible source of indeterminacy is the necessity to choose the status (sliding or non-sliding) at each contact. We show that only one choice is permitted, if contacts slide only when required by Coulomb friction.Comment: 14 pages, 3 figures, submitted to Phys Rev E (introduction and conclusion revised

The Detectability of AGN Cavities in Cooling-Flow Clusters

Chandra X-ray Observatory has revealed X-ray cavities in many nearby cooling flow clusters. The cavities trace feedback from the central active galactic nulceus (AGN) on the intracluster medium (ICM), an important ingredient in stabilizing cooling flows and in the process of galaxy formation and evolution. But, the prevalence and duty cycle of such AGN outbursts is not well understood. To this end, we study how the cooling is balanced by the cavity heating for a complete sample of clusters (the Brightest 55 clusters of galaxies, hereafter B55). In the B55, we found 33 cooling flow clusters, 20 of which have detected X-ray bubbles in their ICM. Among the remaining 13, all except Ophiuchus could have significant cavity power yet remain undetected in existing images. This implies that the duty cycle of AGN outbursts with significant heating potential in cooling flow clusters is at least 60 % and could approach 100 %, but deeper data is required to constrain this further.Comment: 4 pages, 2 figures; to appear in the proceedings of "The Monsters' Fiery Breath", Madison, Wisconsin 1-5 June 2009, Eds. Sebastian Heinz & Eric Wilcots; added annotation to the figur

Phase transition in inelastic disks

This letter investigates the molecular dynamics of inelastic disks without external forcing. By introducing a new observation frame with a rescaled time, we observe the virtual steady states converted from asymptotic energy dissipation processes. System behavior in the thermodynamic limit is carefully investigated. It is found that a phase transition with symmetry breaking occurs when the magnitude of dissipation is greater than a critical value.Comment: 9 pages, 6 figure