Homogeneous cooling of rough, dissipative particles: Theory and simulations

We investigate freely cooling systems of rough spheres in two and three dimensions. Simulations using an event driven algorithm are compared with results of an approximate kinetic theory, based on the assumption of a generalized homogeneous cooling state. For short times $t$, translational and rotational energy are found to change linearly with $t$. For large times both energies decay like $t^{-2}$ with a ratio independent of time, but not corresponding to equipartition. Good agreement is found between theory and simulations, as long as no clustering instability is observed. System parameters, i.e. density, particle size, and particle mass can be absorbed in a rescaled time, so that the decay of translational and rotational energy is solely determined by normal restitution and surface roughness.Comment: 10 pages, 10 eps-figure

Energy flows in vibrated granular media

We study vibrated granular media, investigating each of the three components of the energy flow: particle-particle dissipation, energy input at the vibrating wall, and particle-wall dissipation. Energy dissipated by interparticle collisions is well estimated by existing theories when the granular material is dilute, and these theories are extended to include rotational kinetic energy. When the granular material is dense, the observed particle-particle dissipation rate decreases to as little as 2/5 of the theoretical prediction. We observe that the rate of energy input is the weight of the granular material times an average vibration velocity times a function of the ratio of particle to vibration velocity. `Particle-wall' dissipation has been neglected in all theories up to now, but can play an important role when the granular material is dilute. The ratio between gravitational potential energy and kinetic energy can vary by as much as a factor of 3. Previous simulations and experiments have shown that E ~ V^delta, with delta=2 for dilute granular material, and delta ~ 1.5 for dense granular material. We relate this change in exponent to the departure of particle-particle dissipation from its theoretical value.Comment: 19 pages revtex, 10 embedded eps figures, accepted by PR

Chandra Observation of the Radio Source / X-ray Gas Interaction in the Cooling Flow Cluster Abell 2052

We present a Chandra observation of Abell 2052, a cooling flow cluster with a central cD that hosts the complex radio source 3C 317. The data reveal ``holes'' in the X-ray emission that are coincident with the radio lobes. The holes are surrounded by bright ``shells'' of X-ray emission. The data are consistent with the radio source displacing and compressing, and at the same time being confined by, the X-ray gas. The compression of the X-ray shells appears to have been relatively gentle and, at most, slightly transonic. The pressure in the X-ray gas (the shells and surrounding cooler gas) is approximately an order of magnitude higher than the minimum pressure derived for the radio source, suggesting that an additional source of pressure is needed to support the radio plasma. The compression of the X-ray shells has speeded up the cooling of the shells, and optical emission line filaments are found coincident with the brightest regions of the shells.Comment: accepted for publication in ApJ Letters; for high-resolution color figures, see http://www.astro.virginia.edu/~elb6n/abell2052.htm

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

Jet Interactions with the Hot Halos of Clusters and Galaxies

X-ray observations of cavities and shock fronts produced by jets streaming through hot halos have significantly advanced our understanding of the energetics and dynamics of extragalactic radio sources. Radio sources at the centers of clusters have dynamical ages between ten and several hundred million years. They liberate between 1E58-1E62 erg per outburst, which is enough energy to regulate cooling of hot halos from galaxies to the richest clusters. Jet power scales approximately with the radio synchrotron luminosity to the one half power. However, the synchrotron efficiency varies widely from nearly unity to one part in 10,000, such that relatively feeble radio source can have quasar-like mechanical power. The synchrotron ages of cluster radio sources are decoupled from their dynamical ages, which tend to be factors of several to orders of magnitude older. Magnetic fields and particles in the lobes tend to be out of equipartition. The lobes may be maintained by heavy particles (e.g., protons), low energy electrons, a hot, diffuse thermal gas, or possibly magnetic (Poynting) stresses. Sensitive X-ray images of shock fronts and cavities can be used to study the dynamics of extragalactic radio sources.Comment: 10 pages, 3 figures, invited review, "Extragalactic Jets: Theory and Observation from Radio to Gamma Ray, held in Girdwood, Alaska, U.S.A. 21-24 May, 2007, minor text changes; one added referenc

Temperature-dependent Kelvin probe measurements of band bending in p-type GaN

The band bending in a Mg-doped, p-type GaN film grown by hydride vapor phase epitaxy was studied at various temperatures. At 295 K, the band bending in dark was calculated to be approximately −1.5 eV. However, when the sample was heated to 600 K for 1 h in dark before performing a measurement at 295 K, the calculated value of band bending in dark became about −2.0 eV. These results are explained by the fact that increasing the sample temperature exponentially increases the rate at which the band bending restores and allows for a more accurate value of band bending to be measured

A Deep Chandra Observation of the AGN Outburst and Merger in Hickson Compact Group 62

We report on an analysis of new Chandra data of the galaxy group HCG 62, well known for possessing cavities in its intragroup medium (IGM) that were inflated by the radio lobes of its central active galactic nucleus (AGN). With the new data, a factor of three deeper than previous Chandra data, we re-examine the energetics of the cavities and determine new constraints on their contents. We confirm that the ratio of radiative to mechanical power of the AGN outburst that created the cavities is less than 10^-4, among the lowest of any known cavity system, implying that the relativistic electrons in the lobes can supply only a tiny fraction of the pressure required to support the cavities. This finding implies additional pressure support in the lobes from heavy particles (e.g., protons) or thermal gas. Using spectral fits to emission in the cavities, we constrain any such volume-filling thermal gas to have a temperature kT > 4.3 keV. For the first time, we detect X-ray emission from the central AGN, with a luminosity of L(2-10 keV) = (1.1 +/- 0.4) x 10^39 erg s^-1 and properties typical of a low-luminosity AGN. Lastly, we report evidence for a recent merger from the surface brightness, temperature, and metallicity structure of the IGM.Comment: Accepted to MNRAS, 14 pages, 9 figure

Metaplectic Ice

Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation