Generalised-Lorentzian Thermodynamics

We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All thermodynamic functions, including the definition of the temperature, are shown to be meaningful. The thermodynamic potential from which all relevant physical information in equilibrium can be extracted, is defined consistently. The most important findings are the following two: (1) The temperature is defined exactly in the same way as in classical statistical mechanics as the derivative of the energy with respect to the entropy at constant volume. (2) Observables are defined in the same way as in Boltzmannian statistics as the linear averages of the new equilibrium distribution function. This lets us conclude that the new state is a real thermodynamic equilibrium in systems capable of strong turbulence with the new distribution function replacing the Boltzmann distribution in such systems. We discuss the ideal gas, find the equation of state, and derive the specific heat and adiabatic exponent for such a gas. We also derive the new Gibbsian distribution of states. Finally we discuss the physical reasons for the development of such states and the observable properties of the new distribution function.Comment: 13 pages, 1 figur

Collisional damping rates for plasma waves

The distinction between the plasma dynamics dominated by collisional transport versus collective processes has never been rigorously addressed until recently. A recent paper [Yoon et al., Phys. Rev. E 93, 033203 (2016)] formulates for the first time, a unified kinetic theory in which collective processes and collisional dynamics are systematically incorporated from first principles. One of the outcomes of such a formalism is the rigorous derivation of collisional damping rates for Langmuir and ion-acoustic waves, which can be contrasted to the heuristic customary approach. However, the results are given only in formal mathematical expressions. The present Brief Communication numerically evaluates the rigorous collisional damping rates by considering the case of plasma particles with Maxwellian velocity distribution function so as to assess the consequence of the rigorous formalism in a quantitative manner. Comparison with the heuristic ("Spitzer") formula shows that the accurate damping rates are much lower in magnitude than the conventional expression, which implies that the traditional approach over-estimates the importance of attenuation of plasma waves by collisional relaxation process. Such a finding may have a wide applicability ranging from laboratory to space and astrophysical plasmas.Comment: 5 pages, 2 figures; Published in Physics of Plasmas, volume/Issue 23/6. Publisher: AIP Publishing LLC. Date: Jun 1, 2016. URL: http://aip.scitation.org/doi/10.1063/1.4953802 Rights managed by AIP Publishing LL

Cluster Multi-spacecraft Determination of AKR Angular Beaming

Simultaneous observations of AKR emission using the four-spacecraft Cluster array were used to make the first direct measurements of the angular beaming patterns of individual bursts. By comparing the spacecraft locations and AKR burst locations, the angular beaming pattern was found to be narrowly confined to a plane containing the magnetic field vector at the source and tangent to a circle of constant latitude. Most rays paths are confined within 15 deg of this tangent plane, consistent with numerical simulations of AKR k-vector orientation at maximum growth rate. The emission is also strongly directed upward in the tangent plane, which we interpret as refraction of the rays as they leave the auroral cavity. The narrow beaming pattern implies that an observer located above the polar cap can detect AKR emission only from a small fraction of the auroral oval at a given location. This has important consequences for interpreting AKR visibility at a given location. It also helps re-interpret previously published Cluster VLBI studies of AKR source locations, which are now seen to be only a subset of all possible source locations. These observations are inconsistent with either filled or hollow cone beaming models.Comment: 5 pages, 4 figures. Geophys. Res. Letters (accepted

A Note on the Statistical Mechanics of Violent Relaxation of Phase Space Elements of Different Densities

The statistical mechanical investigation of Violent Relaxation of phase space elements of different densities first derived by Lynden-Bell (1967) is re-examined. It is found that the mass independence of the equations of motion of Violent Relaxation calls for a constraint on the volume of the phase space elements used to formulate the statistical mechanical description of Violent Relaxation. In agreement with observations of astrophysical objects believed to have been subject to Violent Relaxation (e.g. clusters of galaxies), the coarse grained phase space distribution $\bar{f}$ of the final state in the non-degenerate limit turns into a superposition of Maxwellians of a common velocity dispersion. Thus, the velocity dispersion problem present in the investigation of Lynden-Bell (1967) is removed.Comment: AASTeX, 9 pages, uses aas2pp4.sty. Accepted for publication in Ap

Radio relics in cosmological simulations

Radio relics have been discovered in many galaxy clusters. They are believed to trace shock fronts induced by cluster mergers. Cosmological simulations allow us to study merger shocks in detail since the intra-cluster medium is heated by shock dissipation. Using high resolution cosmological simulations, identifying shock fronts and applying a parametric model for the radio emission allows us to simulate the formation of radio relics. We analyze a simulated shock front in detail. We find a rather broad Mach number distribution. The Mach number affects strongly the number density of relativistic electrons in the downstream area, hence, the radio luminosity varies significantly across the shock surface. The abundance of radio relics can be modeled with the help of the radio power probability distribution which aims at predicting radio relic number counts. Since the actual electron acceleration efficiency is not known, predictions for the number counts need to be normalized by the observed number of radio relics. For the characteristics of upcoming low frequency surveys we find that about thousand relics are awaiting discovery.Comment: 10 pages, 4 figures, Invited talk at the conference "Diffuse Relativistic Plasmas", Bangalore, 1-4 March 2011; in press in special issue of Journal of Astrophysics and Astronom

A river model of space

Within the theory of general relativity gravitational phenomena are usually attributed to the curvature of four-dimensional spacetime. In this context we are often confronted with the question of how the concept of ordinary physical three-dimensional space fits into this picture. In this work we present a simple and intuitive model of space for both the Schwarzschild spacetime and the de Sitter spacetime in which physical space is defined as a specified set of freely moving reference particles. Using a combination of orthonormal basis fields and the usual formalism in a coordinate basis we calculate the physical velocity field of these reference particles. Thus we obtain a vivid description of space in which space behaves like a river flowing radially toward the singularity in the Schwarzschild spacetime and radially toward infinity in the de Sitter spacetime. We also consider the effect of the river of space upon light rays and material particles and show that the river model of space provides an intuitive explanation for the behavior of light and particles at and beyond the event horizons associated with these spacetimes.Comment: 22 pages, 5 figure

A Mini-survey of Ultracool Dwarfs at 4.9 GHz

A selection of ultracool dwarfs are known to be radio active, with both gyrosynchrotron emission and the electron cyclotron maser instability being given as likely emission mechanisms. To explore whether ultracool dwarfs previously undetected at 8.5 GHz may be detectable at a lower frequency. We select a sample of fast rotating ultracool dwarfs with no detectable radio activity at 8.5 GHz, observing each of them at 4.9 GHz. From the 8 dwarfs in our sample, we detect emission from 2MASS J07464256+2000321, with a mean flux level of 286 $\pm$ 24 $\mu Jy$. The light-curve of 2MASS J07464256+2000321, is dominated towards the end of the observation by a very bright, $\approx$100 % left circularly polarized burst during which the flux reached 2.4 mJy. The burst was preceded by a raise in the level of activity, with the average flux being $\approx$ 160 $\mu Jy$ in the first hour of observation rising to $\approx$ 400 $\mu Jy$ in the 40 minutes before the burst. During both periods, there is significant variability. The detection of 100% circular polarization in the emission at 4.9 GHz points towards the electron cyclotron maser as the emission mechanism. However, the observations at 4.9 GHz and 8.5 GHz were not simultaneous, thus the actual fraction of dwarfs capable of producing radio emission, as well as the fraction of those that show periodic pulsations is still unclear, as indeed are the relative roles played by the electron cyclotron maser instability versus gyrosynchrotron emission, therefore we cannot assert if the previous non-detection at 8.5 GHz was due to a cut-off in emission between 4.9 and 8.4 GHz, or due to long term variability

Fast Reconnection in a Two-Stage Process

Magnetic reconnection plays an essential role in the generation and evolution of astrophysical magnetic fields. The best tested and most robust reconnection theory is that of Parker and Sweet. According to this theory, the reconnection rate scales with magnetic diffusivity lambda as lambda^0.5. In the interstellar medium, the Parker-Sweet reconnection rate is far too slow to be of interest. Thus, a mechanism for fast reconnection seems to be required. We have studied the magnetic merging of two oppositely directed flux systems in weakly ionized, but highly conducting, compressible gas. In such systems, ambipolar diffusion steepens the magnetic profile, leading to a thin current sheet. If the ion pressure is small enough, and the recombination of ions is fast enough, the resulting rate of magnetic merging is fast, and independent of lambda. Slow recombination or sufficiently large ion pressure leads to slower merging which scales with lambda as lambda^0.5. We derive a criterion for distinguishing these two regimes, and discuss applications to the weakly ionized ISM and to protoplanetary accretion disks.Comment: 21 pages, 13 figures, submitted to Ap

Plasmoid-Induced-Reconnection and Fractal Reconnection

As a key to undertanding the basic mechanism for fast reconnection in solar flares, plasmoid-induced-reconnection and fractal reconnection are proposed and examined. We first briefly summarize recent solar observations that give us hints on the role of plasmoid (flux rope) ejections in flare energy release. We then discuss the plasmoid-induced-reconnection model, which is an extention of the classical two-ribbon-flare model which we refer to as the CSHKP model. An essential ingredient of the new model is the formation and ejection of a plasmoid which play an essential role in the storage of magnetic energy (by inhibiting reconnection) and the induction of a strong inflow into reconnection region. Using a simple analytical model, we show that the plasmoid ejection and acceleration are closely coupled with the reconnection process, leading to a nonlinear instability for the whole dynamics that determines the macroscopic reconnection rate uniquely. Next we show that the current sheet tends to have a fractal structure via the following process path: tearing, sheet thinning, Sweet- Parker sheet, secondary tearing, further sheet thinning... These processes occur repeatedly at smaller scales until a microscopic plasma scale (either the ion Larmor radius or the ion inertial length) is reached where anomalous resistivity or collisionless reconnection can occur. The current sheet eventually has a fractal structure with many plasmoids (magnetic islands) of different sizes. When these plasmoids are ejected out of the current sheets, fast reconnection occurs at various different scales in a highly time dependent manner. Finally, a scenario is presented for fast reconnection in the solar corona on the basis of above plasmoid-induced-reconnection in a fractal current sheet.Comment: 9 pages, 11 figures, with using eps.sty; Earth, Planets and Space in press; ps-file is also available at http://stesun8.stelab.nagoya-u.ac.jp/~tanuma/study/shibata2001