Can self-organized critical accretion disks generate a log-normal emission variability in AGN?

Active Galactic Nuclei (AGN), such as Seyfert galaxies, quasars, etc., show light variations in all wavelength bands, with various amplitude and in many time scales. The variations usually look erratic, not periodic nor purely random. Many of these objects also show lognormal flux distribution and RMS–flux relation and power law frequency distribution. So far, the lognormal flux distribution of black hole objects is only observational facts without satisfactory explanation about the physical mechanism producing such distribution in the accretion disk. One of the most promising models based on cellular automaton mechanism has been successful in reproducing PSD (Power Spectral Density) of the observed objects but could not reproduce lognormal flux distribution. Such distribution requires the existence of underlying multiplicative process while the existing SOC models are based on additive processes. A modified SOC model based on cellular automaton mechanism for producing lognormal flux distribution is presented in this paper. The idea is that the energy released in the avalanche and diffusion in the accretion disk is not entirely emitted instantaneously as in the original cellular automaton model. Some part of the energy is kept in the disk and thus increase its energy content so that the next avalanche will be in higher energy condition and will release more energy. The later an avalanche occurs, the more amount of energy is emitted to the observers. This can provide multiplicative effects to the flux and produces lognormal flux distribution.     

The Effect of Helicity Dissipation on the Critical State of an Avalanche Model for Solar Flares

We perform numerical simulations using an avalanche model for solar flares, in which the effect of avalanche event duration is included and the lateral boundary condition can be either open or periodic. The results from the simulations show that self-organized criticality (SOC) exists under a variety of conditions of helicity dissipation, and they are similar in the sense that the indices of power-law distributions of avalanche sizes are the same, while the duration and waiting time distributions differ little. Of interest are: (1) if there exists helicity dissipation in the course of avalanches, SOC exists only when the amount of helicity dissipation per avalanche is small; (2) sudden reductions in the total helicity of the system do not severely disturb SOC, if the amount reduced is moderate; (3) the distribution of waiting times is shown to be exponential, in consistent with the Poisson statistics other avalanche models have predicted, and the exponent increases as the effect of event duration becomes larger. The self-similar structure of the avalanche time series is also examined. These results imply that, although helicity is dissipated in resistive diffusion of flares, the amount of dissipation should be small and the conservation law of helicity thus holds in an approximate sense. Also, the coronal mass ejections (CMEs), observed to take helicity out of the solar corona in an eruptive way, may disrupt the statistical equilibrium of the corona only temporarily.     

Global versus local flare energy distributions

The avalanche model of Lu and coworkers successfully reproduces important qualitative features of the flare-energy distribution. We test the prediction of the avalanche model that all active regions share a common power-law exponent by using it to derive a local flare-energy distribution from SXR GOES data, then using the convolution proposed by Wheatland and Sturrock to compare it with the global distribution. The local distribution we derive is not consistent with the global distribution, so it appears that active regions do not share a common power-law distribution.     

Test Particle Simulations of Interaction Between Monochromatic Chorus Waves and Radiation Belt Relativistic Electrons

Chorus waves have been suggested to be effective in acceleration of radiation belt electrons. Here we perform gyro-averaged test-particle simulations to calculate the bounce-averaged pitch angle and energy diffusion coefficients for parallel-propagating monochromatic chorus waves, and perform a comparison of test-particle (TP) model with quasi-linear (QL) theory to evaluate the influence of nonlinear processes. For small amplitude chorus waves, the diffusion coefficients of TP and QL models are in good agreement. As the wave amplitude reaches a threshold value, two nonlinear processes (phase trapping and phase bunching) start to occur, especially at large equatorial pitch angles. Phase trapping yields rapid increases in pitch angle and kinetic energy. In contrast, phase bunching causes overall decreases in pitch angle and kinetic energy. For the waves with amplitudes slightly above the threshold value, the average behavior is dominated by the phase trapping, and TP diffusion coefficients are larger than QL ones. As wave amplitude increases, TP diffusion coefficients become smaller than QL ones, indicating that phase trapping gradually reduces the dominance over phase bunching.     

Quantitative model of the release of sodium from meteoroids in the vicinity of the Sun: Application to Geminids

A considerable depletion of sodium was observed in Geminid meteoroids. To explain this phenomenon, we developed a quantitative model of sodium loss from meteoroids due to solar heating. We found that sodium can be lost completely from Geminid meteoroids after several thousands of years when they are composed of grains with sizes up to ∼100 μm. The observed variations of sodium abundances in Geminid meteor spectra can be explained by differences in the grain sizes among these meteoroids. Sodium depletions are also to be expected for other meteoroid streams with perihelion distances smaller than ∼0.2 AU. In our model, the meteoroids were represented by spherical dust-balls of spherical grains with an interconnected pore space system. The grains have no porosity and contain usual minerals known from meteorites and IDP's, including small amount of Na-bearing minerals. We modeled the sequence of three consecutive processes for sodium loss in Geminid meteoroids: (i) solid-state diffusion of Na atoms from Na-bearing minerals to the surface of grains, (ii) thermal desorption from grain surfaces and (iii) diffusion through the pore system to the space. The unknown material parameters were approximated by terrestrial analogs; the solid-state diffusion of Na in the grains was approximated by the diffusion rates for albite and orthoclase.     

Diffusion in helium white dwarf stars

This paper is aimed at exploring the effects of diffusion on the structure and evolution of low-mass helium white dwarfs. To this end, we solve the multicomponent flow equations describing gravitational settling and chemical and thermal diffusion. The diffusion calculations are coupled to an evolutionary code in order to follow the cooling of low-mass, helium core white dwarf models having envelopes made up of a mixture of hydrogen and helium, as recently suggested by detailed evolutionary calculations for white dwarf progenitors in binary systems. We find that diffusion causes hydrogen to float and the other elements to sink over time-scales shorter than evolutionary time-scales. This produces a noticeable change in the structure of the outer layers, making the star inflate. Thus, in order to compute accurately the mass–radius relation for low-mass helium white dwarfs we need to account for the diffusion processes during (at least) the white dwarf stages of the evolution of these objects. This should be particularly important when studying the general characteristics of binary systems containing a helium white dwarf and a pulsar.
In addition, we present an analytic, approximate model for the outer layers of the white dwarf aimed at interpreting the physical reasons for the change in the surface gravity for low-mass white dwarfs induced by diffusion.     

Nanoflare mechanisms: Twisting and braiding

In this paper we will show that the twisting mechanism of Sturrock and Uchida is as viable a heating source for the active corona as Parker's braiding. This conclusion contradicts that of Berger (1990). Moreover, we shall show that if we adopt Berger's criterion for reconnection, braiding produces far more flare energy than is observed. A modified criterion, consistent with twisting, produces insufficient heating but, coupled to an avalanche process, could account for active region flares.Operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation.     

Clues to the origin of jupiter’s trojans: the libration amplitude distribution

We model with numerical algorithms the dynamical processes that possibly lead to the trapping of Jupiter’s Trojans from a primordial population of planetesimals orbiting nearby a proto-Jupiter. The predictions of models based on mutual planetesimal collisions and on the mass growth of Jupiter are compared with observations. In particular, we concentrate on the distribution of the libration amplitude. The two mechanisms for trapping reproduce closely the libration amplitude distribution of the real Trojans only when the long-term dynamical diffusion described by Levison et al. (1997, Nature 385, 42-44) is taken into account.     

On the treatment of entropy mixing in numerical cosmology

For simulations of fluid dynamics in astrophysics, physical viscosity and diffusion are typically neglected. However, in this high Reynolds number regime, real fluids become highly turbulent and turbulent processes mediate substantial transport of momentum and heat that is diffusive in nature. In the absence of models for these processes, code-dependent numerical effects dominate how diffusion operates and may lead to physically incorrect simulation results. We highlight the qualitative difference in these numerical effects for smooth particle hydrodynamics (SPH) and grid-based Eulerian codes using two test problems: a buoyant gas bubble and gas in a galaxy cluster. Grid codes suffer from numerical diffusion in the absence of explicit terms, and small-scale diffusion of heat is completely absent in the Lagrangian SPH method. We find that SPH with heat diffusion added at a level similar to that expected from turbulence diffusion generates more physically appealing results. These results suggest, but do not confirm, that a flat entropy core is to be expected for gas in an idealized galaxy cluster (i.e. one without physics beyond that of a non-radiating gas). A goal of this work is thus to draw attention to the as yet unfulfilled need for models of turbulent diffusive processes in compressible gases in astrophysics.     

Evolution of a 3-M⊙ star from the main sequence to the ZZ Ceti stage: the role played by element diffusion

The purpose of this paper is to present new full evolutionary calculations for DA white dwarf stars with the major aim of providing a physically sound reference frame for exploring the pulsation properties of the resulting models in future communications. Here, white dwarf evolution is followed in a self-consistent way with the predictions of time-dependent element diffusion and nuclear burning. In addition, full account is taken of the evolutionary stages prior to white dwarf formation. In particular, we follow the evolution of a 3-M_⊙ model from the zero-age main sequence (the adopted metallicity is   Z =0.02)  , all the way from the stages of hydrogen and helium burning in the core up to the thermally pulsing phase. After experiencing 11 thermal pulses, the model is forced to evolve towards its white dwarf configuration by invoking strong mass loss episodes. Further evolution is followed down to the domain of the ZZ Ceti stars on the white dwarf cooling branch.
Emphasis is placed on the evolution of the chemical abundance distribution caused by diffusion processes and the role played by hydrogen burning during the white dwarf evolution. We find that discontinuities in the abundance distribution at the start of the cooling branch are considerably smoothed out by diffusion processes by the time the ZZ Ceti domain is reached. Nuclear burning during the white dwarf stage does not represent a major source of energy, as expected for a progenitor star of initially high metallicity. We also find that thermal diffusion lessens even further the importance of nuclear burning.
Furthermore, the implications of our evolutionary models for the main quantities relevant for adiabatic pulsation analysis are discussed. Interestingly, the shape of the Ledoux term is markedly smoother compared with previous detailed studies of white dwarfs. This is translated into a different behaviour of the Brunt–Väisälä frequency.     

Avalanche models of active region heating and flaring

In a previous paper, we suggested that the twisting of coronal magnetic fiels by photospheric motions produces the steady heating of an active region, while braiding of these fields stores energy which is eventually released in an avalanche process, as sporadic large flares. We explore these ideas with numerical simulations. Our results indicate that the combined effect of twisting and braiding can account for the observed power input and the flare frequency spectrum of typical active regions.Operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under coooperative agreement with the National Science Foundation.     

A distinct class of avalanche scars on Mars

We report observations of a set of surface features on Mars that form a distinct class of avalanche scars. These features have a horizontal scale of hundreds of meters, but a depth scale of meters distinguishes them from the shallower features known as slope streaks. The meters-thick avalanche scars have escaped previous attention because of weak contrast between the interiors of the scarred regions and their surroundings. Often the most visible feature is a shadow cast by the trough wall, a band 1-3 pixels wide in Mars Orbiter Camera narrow angle images, indicating maximum depths of 4-10 m. We investigate the morphology of more than 500 such features. Slopes upon which the avalanches occur average about 27°. Impact craters are seen at the heads of some avalanche scars; this subset exhibits statistically wider opening angles. The scars span an estimated several Ma in age. Those found so far occurred mainly in the Olympus Mons lower aureole. We compare shapes of slope streaks to shapes of meters-thick avalanches, and the results support the notion that the two classes are distinct. The newly-discovered avalanches resemble some terrestrial flows of loose, dry material such as dry snow and glass beads. On the basis of these analogs, we suggest a physical model.     

Predicting Solar Flares by Data Assimilation in Avalanche Models

Data assimilation techniques, developed in the past two decades mainly for weather prediction, produce better forecasts by taking advantage of both theoretical/numerical models and real-time observations. In this paper, we explore the possibility of applying the four-dimensional variational data assimilation (4D-VAR) technique to the prediction of solar flares. We do so in the context of a continuous version of the classical cellular-automaton-based self-organized critical avalanche models of solar flares introduced by Lu and Hamilton (Astrophys. J. 380, L89, 1991). Such models, although a priori far removed from the physics of magnetic reconnection and magnetohydrodynamical evolution of coronal structures, nonetheless reproduce quite well the observed statistical distribution of flare characteristics. We report here on a large set of data assimilation runs on synthetic energy release time series. Our results indicate that, despite the unpredictable (and unobservable) stochastic nature of the driving/triggering mechanism within the avalanche model, 4D-VAR succeeds in producing optimal initial conditions that reproduce adequately the time series of energy released by avalanches and flares. This is an essential first step toward forecasting real flares.     

Deterministically Driven Avalanche Models of Solar Flares

We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They share similarities with other avalanche models, such as the classical stick–slip self-organized critical model of earthquakes, in that they are driven globally by a fully deterministic energy-loading process. The model design leads to a systematic deficit of small-scale avalanches. In some portions of model space, mid-size and large avalanching behavior is scale-free, being characterized by event size distributions that have the form of power-laws with index values, which, in some parameter regimes, compare favorably to those inferred from solar EUV and X-ray flare data. For models using conservative or near-conservative redistribution rules, a population of large, quasiperiodic avalanches can also appear. Although without direct counterparts in the observational global statistics of flare energy release, this latter behavior may be relevant to recurrent flaring in individual coronal loops. This class of models could provide a basis for the prediction of large solar flares.     

Radiatively driven mass accretion on to galactic nuclei by circumnuclear starbursts

We examine the physical processes of radiatively driven mass accretion on to galactic nuclei, owing to intensive radiation from circumnuclear starbursts. The radiation from a starburst not only causes the inner gas disc to contract via radition flux force, but also extracts angular momentum owing to relativistic radiation drag, thereby inducing an avalanche of the surface layer of the disc. To analyse such a mechanism, the radiation–hydrodynamical equations are solved, including the effects of the radiation drag force as well as the radiation flux force. As a result, it is found that the mass accretion rate owing to the radiative avalanche is given by M ˙ ( r )= η ( L _*/ c ²)( r / R )² (Δ R / R )(1 −  e ^−τ) at radius r , where the efficiency η ranges from 0.2 up to 1, L _* and R are respectively the bolometric luminosity and the radius of the starburst ring, Δ R is the extent of the emission regions, and τ is the face-on optical depth of the disc. In an optically thick regime, the rate depends upon neither the optical depth nor the surface mass density distribution of the disc. The present radiatively driven mass accretion may provide a physical mechanism which enables mass accretion from 100-pc scales down to ∼ parsec scales, and it may eventually be linked to advection-dominated viscous accretion on to a massive black hole. The radiation–hydrodynamical and self-gravitational instabilities of the disc are briefly discussed. In particular, the radiative acceleration possibly builds up a dusty wall, which 'shades' the nucleus in edge-on views. This provides another version of the model for the formation of an obscuring torus.     

On the 'coarse-grained' evolution of collisionless stellar systems

We have suggested in a previous article that the coarse-grained evolution of a collisionless stellar system could be viewed as a diffusion process in velocity space compensated by an appropriate friction. Using a quasi-linear theory, we calculate the diffusion coefficient associated with this evolution. This provides a new self-consistent relaxation equation for f , the locally averaged distribution function. This equation bears some resemblance to the conventional Fokker–Planck equation of collisional systems but the friction term is non-linear in f (accounting for degeneracy effects) and the relaxation time is much smaller (in agreement with the concept of 'violent relaxation'). Under the condition that the diffusion current vanishes identically at equilibrium, we recover Lynden-Bell's distribution function; but if we allow stars to escape from the system at a constant rate, we can derive a truncated model which coincides with Lynden-Bell's solution in the core but provides a depletion of high-energy stars in the halo. This distribution function has a finite mass and is the generalization of the Michie–King model to the case of (possibly degenerate) collisionless stellar systems.     

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker–Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.     

A symplectic mapping approach to the study of the stochasticity in asteroidal resonances

In the case of the 2:1 and 3:2 resonances with Jupiter, it has not been yet possible to have a complete identification of all chaotic diffusion processes at work, mainly because the time scale of some of them are of an order still out of the reach of precise integrations. A planar Hadjidemetriou's mapping, using expansions valid for high eccentricities and scaled in order to accelerate the diffusion processes, was derived. The solutions obtained with the mapping show huge eccentricity variations in all orbits starting in the middle of the 2:I resonance, when the main short-period perturbations of Jupiter's orbit are considered. The solutions starting in the middle of the 3:2 resonance do not show any important diffusion.