Extreme Ultraviolet Emission from Clusters of Galaxies: Inverse Compton Radiation from a Relic Population of Cosmic Ray Electrons?

We suggest that the luminous extreme ultraviolet (EUV) emission which has been detected recently from clusters of galaxies is Inverse Compton (IC) scattering of Cosmic Microwave Background (CMB) radiation by low energy cosmic ray electrons in the intracluster medium. The cosmic ray electrons would have Lorentz factors of gamma ~ 300, and would lose energy primarily by emitting EUV radiation. These particles have lifetimes comparable to the Hubble time; thus, the electrons might represent a relic population of cosmic rays produced by nonthermal activity over the history of the cluster. The IC model naturally explains the observed increase in the ratio of EUV to X-ray emission with radius in clusters. The required energy in cosmic ray electrons is typically 1--10% of the thermal energy content of the intracluster gas. We suggest that the cosmic ray electrons might have been produced by supernovae in galaxies, by radio galaxies, or by particle acceleration in intracluster shocks.Comment: ApJ Letters, in press, 4 pages with 1 embedded figure, Latex in emulateapj styl

A massive warm baryonic halo in the Coma cluster

Several deep PSPC observations of the Coma cluster reveal a very large-scale halo of soft X-ray emission, substantially in excess of the well known radiation from the hot intra-cluster medium. The excess emission, previously reported in the central region of the cluster using lower-sensitivity EUVE and ROSAT data, is now evident out to a radius of 2.6 Mpc, demonstrating that the soft excess radiation from clusters is a phenomenon of cosmological significance. The X-ray spectrum at these large radii cannot be modeled non-thermally, but is consistent with the original scenario of thermal emission from warm gas at ~ 10^6 K. The mass of the warm gas is on par with that of the hot X-ray emitting plasma, and significantly more massive if the warm gas resides in low-density filamentary structures. Thus the data lend vital support to current theories of cosmic evolution, which predict that at low redshift \~30-40 % of the baryons reside in warm filaments converging at clusters of galaxies.Comment: Astrophysical Journal, in pres

Non-thermal Origin of the EUV and Soft X-rays from the Coma Cluster - Cosmic Rays in Equipartition with the Thermal Medium

The role of cosmic rays (CR) in the formation and evolution of clusters of galaxies has been much debated. It may well be related to other fundamental questions, such as the mechanism which heats and virializes the intracluster medium (ICM), and the frequency at which the ICM is shocked. There is now compelling evidence both from the cluster soft excess (CSE) and the `hard-tail' emissions at energies above 10 keV, that many clusters are luminous sources of inverse-Compton (IC) emission. This is the first direct measurement of cluster CR: the technique is free from our uncertainties in the ICM magnetic field, and is not limited to the small subset of clusters which exhibit radio halos. The CSE emitting electrons fall within a crucial decade of energy where they have the least spectral evolution, and where most of the CR pressure resides. However their survival times do not date them back to the relic CR population. By using the CSE data of the Coma cluster, we demonstrate that the CR are energetically as important as the thermal ICM: the two components are in pressure equiparition. Thus, contrary to previous expectations, CR are a dominant component of the ICM, and their origin and effects should be explored. The best-fit CR spectral index is in agreement with the Galactic value.Comment: ApJ accepted; 10 pages LaTeX; 2 figures and 1 table in PostScrip

Time Uncertainty in Quantum Gravitational Systems

It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We consider a simple family of gravitational models, including the Einstein-Rosen waves, in which the (non-linearized) inclusion of gravity changes the normalization of time translations by a monotonic energy-dependent factor. In these circumstances, it is shown that a maximum time resolution emerges non-perturbatively only if the total energy is bounded. Perturbatively, however, there always exists a minimum uncertainty in the physical time.Comment: (4 pages, no figures) Accepted for publication in Physical Review

The Physics of Cluster Mergers

Clusters of galaxies generally form by the gravitational merger of smaller clusters and groups. Major cluster mergers are the most energetic events in the Universe since the Big Bang. Some of the basic physical properties of mergers will be discussed, with an emphasis on simple analytic arguments rather than numerical simulations. Semi-analytic estimates of merger rates are reviewed, and a simple treatment of the kinematics of binary mergers is given. Mergers drive shocks into the intracluster medium, and these shocks heat the gas and should also accelerate nonthermal relativistic particles. X-ray observations of shocks can be used to determine the geometry and kinematics of the merger. Many clusters contain cooling flow cores; the hydrodynamical interactions of these cores with the hotter, less dense gas during mergers are discussed. As a result of particle acceleration in shocks, clusters of galaxies should contain very large populations of relativistic electrons and ions. Electrons with Lorentz factors gamma~300 (energies E = gamma m_e c^2 ~ 150 MeV) are expected to be particularly common. Observations and models for the radio, extreme ultraviolet, hard X-ray, and gamma-ray emission from nonthermal particles accelerated in these mergers are described.Comment: 38 pages with 9 embedded Postscript figures. To appear in Merging Processes in Clusters of Galaxies, edited by L. Feretti, I. M. Gioia, and G. Giovannini (Dordrecht: Kluwer), in press (2001

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

Fluid phonons and inflaton quanta at the protoinflationary transition

Quantum and thermal fluctuations of an irrotational fluid are studied across the transition regime connecting a protoinflationary phase of decelerated expansion to an accelerated epoch driven by a single inflaton field. The protoinflationary inhomogeneities are suppressed when the transition to the slow roll phase occurs sharply over space-like hypersurfaces of constant energy density. If the transition is delayed, the interaction of the quasi-normal modes related, asymptotically, to fluid phonons and inflaton quanta leads to an enhancement of curvature perturbations. It is shown that the dynamics of the fluctuations across the protoinflationary boundaries is determined by the monotonicity properties of the pump fields controlling the energy transfer between the background geometry and the quasi-normal modes of the fluctuations. After corroborating the analytical arguments with explicit numerical examples, general lessons are drawn on the classification of the protoinflationary transition.Comment: 30 pages, 3 figure

Neutralinos and the Origin of Radio Halos in Clusters of Galaxies

We assume that the supersymmetric lightest neutralino is a good candidate for the CDM and explore the possibility to produce diffuse radio emission from high-energy electrons arising from the neutralino annihilation in galaxy clusters whose intracluster medium is filled with a large-scale magnetic field. We show that these electrons fit the population of seed relativistic electrons postulated in many models for the origin of cluster radio halos. For magnetic fields with central values $3 \div 30$ $\mu$G (depending on the DM profile), the population of seed relativistic electrons from neutralino annihilation can fit the radio halo spectra of Coma and 1E0657-56. The shape and the frequency extension of the radio halo spectra are connected with the mass and physical composition of the neutralino. A pure-gaugino neutralino with mass $M_{\chi} \geq 80$ GeV can reasonably fit the spectra of both Coma and 1E0657-56. This model provides a number of extra predictions that make it definitely testable. On the one hand, it agrees with the observations that {\it (i)} the radio halo is centered on the cluster dynamical center, usually coincident with the X-ray center, {\it (ii)} the radio halo surface brightness is similar to the X-ray one, and {\it (iii)} the monochromatic radio luminosity at 1.4 GHz correlates strongly with the IC gas temperature. On the other hand, the model predicts that radio halos should be present in every cluster, which is not actually observed, although the predicted radio halo luminosities can change by a large amount ($\sim 10^2 \div 10^6$), depending on the amplitude and the structure of the IC magnetic field. Also, neutral pions arising from neutralino annihilation should give rise to substantial gamma-ray emission that could be tested by the next generation gamma-ray experiments.Comment: 49 pages, 11 Figures, Latex (using epsfig), submitted to The Astrophysical Journal. submitted to The Astrophysical Journa