Gas flow and dust acceleration in a cometary Knudsen layer

An analytical model of the innermost gas–dust coma region is proposed. The kinetic Knudsen layer adjacent to the surface of the cometary nucleus, where the initially non-equilibrium velocity distribution function of gas molecules relaxes to Maxwell equilibrium distribution function and, as a result, the macro-characteristics of gas and dust flows vary several-fold, is considered. The gas phase model is based on the equations for mass, momentum and energy flux conservation, and is a natural development of the Anisimov, 1968 and Cercignani, 1981 approaches. The analytical relations between the characteristics of the gas flow on the boundaries of the non-equilibrium layer and the characteristics of the returning gas flow adsorbed by the surface are determined. These values form a consistent basis both for hydrodynamic models of the inner coma and for jet force models. Three particular models are presented: (1) sublimation of a polyatomic one-component gas; (2) sublimation of a two-component polyatomic gas mixture, in both cases from a plane surface; and (3) sublimation of water ice through a porous dust mantle. We conclude that the characteristics of the gas flow emerging from the Knudsen layer over a porous dust mantle is not very sensitive to the structure of the mantle.We also treat the expansion of dust into the coma, concentrating on the interaction between a non-equilibrium gas flow and a test particle. The dynamics of a grain of idealized shape is explored by using several simplifying assumptions for the variation of the drag force. The velocity of a particle at the exterior boundary of the Knudsen layer is thus estimated. Examining various model behaviours of the drag force inside the Knudsen layer, we show that the dust velocity is not sensitive to these variations.     

Nonequilibrium Processes in the Solar Corona,Transition Region,Flares, and Solar Wind <Emphasis Type="Italic">(Invited Review)</Emphasis>

We review the presence and signatures of the non-equilibrium processes, both non-Maxwellian distributions and non-equilibrium ionization, in the solar transition region, corona, solar wind, and flares. Basic properties of the non-Maxwellian distributions are described together with their influence on the heat flux as well as on the rates of individual collisional processes and the resulting optically thin synthetic spectra. Constraints on the presence of high-energy electrons from observations are reviewed, including positive detection of non-Maxwellian distributions in the solar corona, transition region, flares, and wind. Occurrence of non-equilibrium ionization is reviewed as well, especially in connection to hydrodynamic and generalized collisional-radiative modeling. Predicted spectroscopic signatures of non-equilibrium ionization depending on the assumed plasma conditions are summarized. Finally, we discuss the future remote-sensing instrumentation that can be used for the detection of these non-equilibrium phenomena in various spectral ranges.     

On the equilibrium of an exact charge neutral magnetopause

The way is discussed by which microinstabilities of an exact charge neutral magnetopause could lead to a trapped particle flow, the absence of which causes the non-existence of an equilibrium magnetospheric boundary layer in the Parker-Lerche model. Furthermore, it is argued that instead of the non-equilibrium effect of Parker and Lerche, microinstabilities of an exact charge neutral magnetopause might be the underlying physical process of an Axford and Hines' type viscous interaction.     

Effects on UV lines observations of stationary plasma flows confined in coronal loops

We describe a method which uses a rather detailed model of coronal loop hosting a siphon flow as a diagnostic tool to interpret solar UV and X-ray observations in selected bands and lines. We apply the method to investigate the deviations from ionization equilibrium induced by stationary plasma flows confined in coronal loops and their effects on the UV and EUV emission lines observed by the instruments on board SOHO. We present results on the detailed synthesis of loop emission in a set of selected emission lines observed by CDS and SUMER, taking into account the non-equilibrium of ionization effects.     

The flare process in a topologically non-equilibrium magnetohydrodynamical system

The existing models for solar flares fail to treat in an appropriate manner the energy release mechanisms based on a step-like transformation of the magnetic field energy from magnetic field to energy of the hydrodynamical motion of the medium and dissipation of these motions through shock waves into heat.In considering an example of the relaxation process in a topologically non-equilibrium magnetohydrodynamical system resulting from the merging of two magnetic loops that possess balanced longitudinal currents, this paper suggests one such energy release mechanism. Due to a certain degree of universality for different topologically non-equilibrium systems, a variety of characteristics of the relaxation process obtained may form the basis for constructing a model of solar flares based on a step-like transformation of the magnetic field energy in topologically non-equilibrium magnetohydrodynamical systems.     

The end of the dark ages in modified Newtonian dynamics

We study the evolution of a spherically symmetric density perturbation in the Modified Newtonian Dynamics model applied to the net acceleration over Hubble flow. The background cosmological model is a Λ-dominated, low-Ω_b Friedmann model with no cold dark matter. We include thermal processes and non-equilibrium chemical evolution of the collapsing gas. We find that under these assumptions the first low-mass objects  ( M ≤ 3 × 10⁴ M_⊙)  may collapse already for   z ∼ 30  , which is in quite good agreement with the recent Wilkinson Microwave Anisotropy Probe results. A lower value of a ₀ would lead to much slower collapse of such objects.     

Non-equilibrium of Magnetic Flux Tubes emerging into the Solar Corona

A lack of equilibrium of twisted magnetic flux tubes emerging from the photosphere into the corona is considered. Assuming mass and flux conservation in the tube and an isothermal tube that is in thermal equilibrium with the surrounding plasma, it is shown that a sufficently rapid temperature increase through the transition zone may lead to the loss of magnetohydrostatic equilibrium of the emerging flux tube due to the enhancement of the plasma pressure inside the tube. The non-equilibrium leads to a rapid expansion of the tube to reach a new equilibrium state. The rise and expansion of the tube before and after the non-equilibrium are accompanied by an increase in the twist of the magnetic field. This may lead to the field exceeding the threshold for the onset of the kink instability and a subsequent explosive release of magnetic energy.     

Non-equilibrium ionization in coronal loops

The ionization conditions in coronal loops are investigated in the temperature range 2 × 10⁵–2 × 10⁶K, assuming velocity, density and temperature distributions computed for a siphon model of a pure hydrogen plasma. Use is made of the set of the carbon ions as an example of the general behaviour of the ions characteristic of that temperature range. It is found that the deviation from equilibrium ionization is large for subsonic-supersonic flow if the density is less than 5 × 10⁹cm^–-3, with the exception of the lower part of the first leg of very cool loops (T 2 × 10 K). With this exception cooler loops, given their larger density drop along the axis, show deviations from ionization equilibrium more easily than hotter ones, in spite of their lower flow velocity. We conclude that the possibility of a non-equilibrium state must be taken into account when deducing from measurements of line intensities the temperature of loops in which a flow may occur.Now at Institute for Plasma Research, Stanford University, as an E.S.A. Fellow.     

The magnetic non-equilibrium of buoyant flux tubes in the solar corona

The equilibrium shape of a slender flux tube in the stratified solar atmosphere is studied. The path is determined by a balance between the downwards magnetic tension, which depends on the curvature of the loop, and the upwards buoyancy force. Previous results for untwisted slender tubes are extended to include twisted tubes embedded in an external magnetic field.The path of an untwisted tube in an atmosphere with an ambient magnetic field is calculated. For a given footpoint separation, the height of the tube is lowered by increasing the strength of the external magnetic field. If the footpoints are slowly moved apart, the tube rises, until a threshold separation is reached beyond which there is no possible equilibrium height. This threshold width does not depend on the strength of the external field.The effects of twisting up a curved loop are studied, using an extension of results obtained for slender curved tubes with a straight axis. It is shown that for a twisted tube of given width, there can be two possible values of the equilibrium height. If, however, the tube is twisted more than a certain amount or if the footpoints are too widely separated there is no equilibrium. The critical footpoint separation for non-equilibrium is smaller for a twisted tube that an untwisted one.Twisting a tube or moving its feet apart is thus likely to result in non-equilibrium, causing the tube to rise indefinitely under the influence of the unbalanced buoyant force. It is suggested that this phenomenon could be important in the preflare stage of a large two-ribbon solar flare, by causing the initial slow rise of an active region filament. As well as being involved in the onset of an erupting prominence, this non-equilibrium may also be relevant to the formation of coronal loop transients.     

Colliding stellar wind models with non-equilibrium ionization: X-rays from WR 147

The effects of non-equilibrium ionization are explicitly taken into account in a numerical model which describes colliding stellar winds (CSW) in massive binary systems. This new model is used to analyse the most recent X-ray spectra of the WR+OB binary system WR 147. The basic result is that it can adequately reproduce the observed X-ray emission (spectral shape, observed flux) but some adjustment in the stellar wind parameters is required. Namely (i) the stellar wind velocities must be higher by a factor of 1.4–1.6 and (ii) the mass loss must be reduced by a factor of ∼2. The reduction factor for the mass loss is well within the uncertainties for this parameter in massive stars, but given the fact that the orbital parameters (e.g. inclination angle and eccentricity) are not well constrained for WR 147, even smaller corrections to the mass loss might be sufficient. Only CSW models with non-equilibrium ionization and equal (or nearly equal) electron and ion post-shock temperature are successful. Therefore, the analysis of the X-ray spectra of WR 147 provides evidence that the CSW shocks in this object must be collisionless .     

Non-Equilibrium Distribution Functions in the Heliospheric Interface and Their Relaxation by Local Wave–Particle Interactions

The partially ionized local interstellar medium, before interacting with the heliospheric plasma on the upwind side, most probably undergoes an outer bow shock. After conversion into a sub-magnetosonic plasma flow, it then passes around the heliopause. While the ionized component at the bow shock undergoes abrupt changes of its dynamical properties, the neutral component first continues to flow downstream of the shock with its unperturbed properties. Consequently, the two fluids immediately after the bow shock passage are out of dynamical and thermodynamical equilibrium. Neutral atoms move with a higher bulk velocity and are cooler than the ions. Due to intensive local charge-exchange couplings between neutral atoms and protons these different properties tend to mix each other via momentum and energy exchanges. It turns out that the charge exchange period is shorter than the relaxation period. Hence the distribution functions cannot relax rapidly enough to their highest-entropy forms, i.e. shifted Maxwellians. Here we study the transport processes of newly injected ions in velocity space considering their quasi-linear and non-linear interactions with the ambient MHD turbulence in the plasma interface region. For that purpose we study the turbulence levels in the helio-sheath plasma region. We calculate the expected deviations from equilibrium distributions of ionic and atomic species in the outer heliospheric interface. It clearly turns out from these studies that non-relaxated non-equilibrium distribution functions have to be expected both for O-/H-ions and atoms in this region. This has inherent implications for the diagnostics of interstellar parameters, deduced from observations made further inwards from the interface region.     

Stability of the complete cycle in hydrogen combustion inside the stars

In this paper, the stability of the complete cycle in hydrogen combustion inside the stars is investigated with generating-function and linear stability analysis methods based on the Prigogine's non-equilibrium thermodynamic theory (Nicolis and Prigogine, 1977).     

Multiscale Magnetic Underdense Regions on the Solar Surface: Granular and Mesogranular Scales

The Sun is a non-equilibrium, dissipative system subject to an energy flow that originates in its core. Convective overshooting motions create temperature and velocity structures that show a temporal and spatial multiscale evolution. As a result, photospheric structures are generally considered to be a direct manifestation of convective plasma motions. The plasma flows in the photosphere govern the motion of single magnetic elements. These elements are arranged in typical patterns, which are observed as a variety of multiscale magnetic patterns. High-resolution magnetograms of the quiet solar surface revealed the presence of multiscale magnetic underdense regions in the solar photosphere, commonly called voids, which may be considered to be a signature of the underlying convective structure. The analysis of such patterns paves the way for the investigation of all turbulent convective scales, from granular to global. In order to address the question of magnetic structures driven by turbulent convection at granular and mesogranular scales, we used a voids-detection method. The computed distribution of void length scales shows an exponential behavior at scales between 2 and 10 Mm and the absence of features at mesogranular scales. The absence of preferred scales of organization in the 2?–?10 Mm range supports the multiscale nature of flows on the solar surface and the absence of a mesogranular convective scale.     

X-ray Line and Recombination Emission in the Afterglow of Grb

We calculate the time-dependent line and recombination spectrum of nonequilibrium plasma heated by the strong radiation as the test model of X-ray line emission of GRB afterglows. Our calculation shows that the non-equilibrium effect of plasma is complex and important to the time evolution of the spectrum. The origin of these lines puzzles us, but is essential to understand the nature of GRBs and their circumstellar matter.     

Space Flows and Disturbances Due to Bodies in Motion Through the Magnetoplasma

In this paper a method is concerned which makes it possible to describe numerically and analytically the most famous structures in the non-equilibrium ionosphere, such as stratified and yacht sail like structures, flute jets, wakes and clouds. These problems are of practical interest in space sciences, astrophysics and in turbulence theory, and also of fundamental interest since they enable one to concentrate on the effects of the ambient electric and magnetic fields. Disturbances of charged particle flows due to the ambient flow interactions with bodies are simulated with taking into account the ambient magnetic field effect. The effects of interactions between solid surfaces and the flows was simulated by making use of an original image method. The flow disturbances were described by the Boltzmann equation. In the case of the ambient homogeneous magnetic field the Boltzmann equation is solved analytically. The case of diffuse reflection of particles by surface is considered in detail. The disturbances of charged particle concentration are calculated in 3D space. The contours of constant particle concentration obtained from numerical simulations illustrate the dynamics of developing stratifications and flute structures in charged particle jets and feffect. The wakes under the ambient magnetic field effect. The basic goal of this paper is to present the method and to demonstate its possibility for simulations of turbulence, plasma jets, wakes and clouds inthe ionosphere and Space when effects of electric and magnetic fields are taken into account. This revised version was published online in July 2006 with corrections to the Cover Date.     

The influence of spatial dispersion on the coefficient of spontaneous emission of cyclotron radiation in a non-equilibrium plasma

The coefficient of spontaneous emission of cyclotron radiation propagating in the direction of an external magnetic field in non-equilibrium plasma is calculated including the effect of spatial dispersion on the emission process. The resulting part of the emission coefficient may become important in the vicinity of the cyclotron frequency.     

The eruption of a prominence and coronal mass ejection which drive reconnection

Two possible limiting scenarios are proposed for the production of a coronal mass ejection. In the first the magnetic field around a prominence evolves until it loses equilibrium and erupts, which drives reconnection below the prominence and an eruption of the overlying magnetic arcade. In the second a large-scale magnetic arcade evolves until it loses equilibrium and erupts, thereby causing a prominence to erupt. In general it is likely to be the non-equilibrium of the coupled system which creates the eruption. Furthermore, large quiescent prominences are expected to be centred within the magnetic bubble of a coronal mass ejection whereas when active-region prominences erupt they are likely to be located initially to one side of the bubble.A model is set up for the eruption of a magnetically coupled prominence and coronal mass ejection. This represents a development of the Anzer and Pneuman (1982) model by overcoming two limitations of it, namely that: it is not globally stable initially and so one wonders how it can be set up in a stable way before the eruption; it has reconnection driving the CME whereas recent observations suggest that the reverse may be happening. In our model we assume that magnetic reconnection below the prominence is driven by the eruption and the driver is magnetic non-equilibrium in the coupled prominence-mass ejection system. The prominence is modelled as a twisted flux tube and the mass ejection as an overlying void and magnetic bubble. Two different models of the prominence are considered. In one a globally stable equilibrium becomes unstable when a threshold magnetic flux below the prominence is exceeded and, in the other, equilibrium ceases to exist. In both cases, the prominence and mass-ejection accelerate upwards before reaching constant velocities in a manner that is consistent with observations. It is found that the greater the reconnection that is driven by the eruption, the higher is the final speed.     

Steady state charge neutral models of the magnetopause

Plane models of the magnetopause are investigated under the assumption that ionospheric electrons are able to short-circuit electric fields (exact charge neutrality). Using the Vlasov theory a general method is presented for constructing distribution functions that lead to given magnetic field and tangential bulk velocity profiles. As an example we describe the magnetic field transition in terms of error functions and obtain particle distributions in explicit form, including bulk velocities.It is thus shown that bulk velocities in the direction of the magnetic field do not necessarily lead to a non-equilibrium magnetopause which investigations by Parker and Lerche seem to suggest.Of the European Space Research Organisation (ESRO).     

The thermal statics of coronal loops

The thermal statics of constant pressure coronal loops is discussed, with particular emphasis on non-equilibrium and scaling relations. An analytical solution showing explicitly the occurrence of non-equilibrium in radiation dominated loops is presented. In addition, the general scaling law for hot loops is given. However, in view of the uncertainties in the coronal heating function and the observational determined loop parameters, it is suggested that scaling laws are currently of limited value.     

Equilibrium rotational stability and figure of Mars

Studies extending over three decades have concluded that the current orientation of the martian rotation pole is unstable. Specifically, the gravitational figure of the planet, after correction for a hydrostatic form, has been interpreted to indicate that the rotation pole should move easily between the present position and a site on the current equator, 90° from the location of the massive Tharsis volcanic province. We demonstrate, using general physical arguments supported by a fluid Love number analysis, that the so-called non-hydrostatic theory is an inaccurate framework for analyzing the rotational stability of planets, such as Mars, that are characterized by long-term elastic strength within the lithosphere. In this case, the appropriate correction to the gravitational figure is the equilibrium rotating form achieved when the elastic lithospheric shell (of some thickness LT) is accounted for. Moreover, the current rotation vector of Mars is shown to be stable when the correct non-equilibrium theory is adopted using values consistent with recent, independent estimates of LT. Finally, we compare observational constraints on the figure of Mars with non-equilibrium predictions based on a large suite of possible Tharsis-driven true polar wander (TPW) scenarios. We conclude, in contrast to recent comparisons of this type based on a non-hydrostatic theory, that the reorientation of the pole associated with the development of Tharsis was likely less than 15° and that the thickness of the elastic lithosphere at the time of Tharsis formation was at least ∼50 km. Larger Tharsis-driven TPW is possible if the present-day gravitational form of the planet at degree 2 has significant contributions from non-Tharsis loads; in this case, the most plausible source would be internal heterogeneities linked to convection.