A cometary ionosphere model for Io

The ionosphere of Jupiter's satellite Io, discovered by the Pioneer 10 radio-occultation experiment, cannot easily be understood in terms of a model of a gravitationally bound, Earth-like ionosphere. Io's gravitational field is so weak that a gravitationally bound ionosphere would probably be blown away by the ram force of the Jovian magnetospheric wind — i.e., the plasma corotating in the Jovian magnetosphere. We propose here a model in which the material for Io's atmosphere and ionosphere is drawn from the ionosphere of Jupiter through a Birkeland current system that is driven by the potential induced across Io by the Jovian corotation electric field. We argue that the ionization near Io is caused by a comet-like interaction between the corotating plasma and Io's atmosphere. The initial interaction employs the critical velocity phenomenon proposed many years ago by Alfvén. Further ionization is produced by the impact of Jovian trapped energetic electrons, and the ionization thus created is swept out ahead of Io in its orbit. Thus, we suggest that what has been reported as a day-night ionospheric asymmetry is in fact an upstream-downstream asymmetry caused by the Jovian magnetospheric wind.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30th May, 1978.     

Non-radial flow near the cometary surface

It is shown that, as a consequence of the non-uniform temperature distribution of the cometary nucleus, large lateral pressure gradients are set up, which in turn drive strong lateral flows. However, at small heliocentric distances the onset of turbulence within a thin boundary layer destroys these steady lateal flows and the eventual outflow of gas from within the outer boundary of this layer is expected to be more or less radial. On the other hand, at large heliocentric distances, turbulence is unlikely to set in, and the lateral flows that are set up, may persist. Consequently, it is expected that the gas flow out of the cometary nucleus at these large distances to be highly non-radial.     

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.     

A kinetic model of gas flow in a porous cometary mantle

A numerical study of gas flow through a porous cometary mantle is presented. A kinetic model based on the well-known Test Particle Monte Carlo Method for the solution of rarefied gas dynamics problems is proposed. The physical model consists of two spatial plane regions: the condensed ice phase and a porous dust mantle. The structure of the porous dust layer is described as a bundle of cylindrical inclined channels not crossing each other. A vertical temperature gradient may exist across the dust mantle. The aim is to investigate how the characteristics of molecular flow depend on the capillary length, inclination angle, and temperature gradient. Examples illustrating a significant deviation of some results from equilibrium values are shown. In particular, the gas velocity distribution at both ends of the pore is strongly non-Maxwellian if there is an important temperature contrast across the pore. The emergent gas flow rate is found to vary with the pore length/radius ratio in excellent agreement with Clausing's empirical formula. The degree of collimation of the flow is quantitatively studied as a function of the length/radius ratio, and consequences for the jet force of outgassing through a dust mantle or, indeed, a rough surface are estimated.     

Induced proton flow in a collapsing post-sunset ionosphere and protonosphere

The effect of the onset of post-sunset conditions on thermal proton flow is examined for mid-latitudes by numerical solution of the equations of continuity, momentum and energy balance for H⁺ and O⁺. Results are calculated for a dipole magnetic field tube situated at L = 4 and acceleration terms are included in the momentum equations. Proton flow into the ionosphere results from decay of the F2-layer. Changes in temperatures and temperature gradients following sunset may not enhance the H⁺ flow. Under extreme conditions the H⁺ flow remains subsonic. It seems unlikely that an interhemispheric flux of protons can directly maintain the nighttime F2-layer.     

Modeling a cometary nucleus

Considerations are summarized concerning the physical properties of and plasma phenomena around a cometary nucleus aiming at a new model of the nucleus and its interaction with the solar wind.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Ionospheric plasma flow past a semi-infinite cylinder

The ionospheric flow regime in which the flow velocity is well above the ambient ion thermal velocity, but far below the ambient electron thermal velocity, is considered. The flow is parallel to the axis of a conducting semi-infinite cylinder and is directed toward the end disk. Taylor's heuristic method is employed to obtain the approximate spatial dependence of the electric potential and the ion density and velocity. An expression is obtained from these parameters for the net current to the end disk.     

Transterminator ion flow in the Martian ionosphere

The upper ionospheres of Mars and Venus are permeated by the magnetic fields induced by the solar wind. It is a long-standing question whether these fields can put the dense ionospheric plasma into motion. If so, the transterminator flow of the upper ionosphere could explain a significant part of the ion escape from the planets atmospheres. But it has been technically very challenging to measure the ion flow at energies below 20 eV. The only such measurements have been made by the ORPA instrument of the Pioneer Venus Orbiter reporting speeds of 1-5 km/s for O⁺ ions at Venus above 300 km altitude at the terminator ( [Knudsen et al., 1980] and [Knudsen et al., 1982]). At Venus the transterminator flow is sufficient to sustain a permanent nightside ionosphere, at Mars a nightside ionosphere is observed only sporadically. We here report on new measurements of the transterminator ion flow at Mars by the ASPERA-3 experiment on board Mars Express with support from the MARSIS radar experiment for some orbits with fortunate observation geometry. We observe a transterminator flow of O⁺ and O₂⁺ ions with a super-sonic velocity of around 5 km/s and fluxes of 0.8×10⁹/cm² s. If we assume a symmetric flux around the terminator this corresponds to an ion flow of 3.1±0.5×10²⁵/s half of which is expected to escape from the planet. This escape flux is significantly higher than previously observed on the tailside of Mars. A possible mechanism to generate this flux can be the ionospheric pressure gradient between dayside and nightside or momentum transfer from the solar wind via the induced magnetic field since the flow velocity is in the Alfvénic regime. We discuss the implication of these new observations for ion escape and possible extensions of the analysis to dayside observations which may allow us to infer the flow structure imposed by the induced magnetic field.     

A note on the mass-loaded MHD flow of the solar wind towards a cometary nucleus

Dependence of the central velocity gradients on Hubble's type is presented for 78 spiral galaxies with existing rotation curves. Also the dependence of the maximum rotational velocities of 27 galaxies on both Hubble's type and the luminosity is studied. The central velocity gradient is shown to be related with Hubble's type. Maximum rotational velocities of 27 galaxies of our sample depend on Hubble's type such that the mean values of maximum rotational velocity decrease from Sa through Sc. It is also determined that there is a dependence of the maximum rotational velocity on the absolute blue magnitude for each intrinsic Hubble type. For each Hubble type, maximum rotational velocity increases with increasing absolute blue magnitudes.     

Magnetohydrodynamic boundary-layer flow for a non-Newtonian fluid past a wedge

The flow of a power law fluid past a symmetrical wedge is studied in the neighbourhood of the stagnation point when an external magnetic field is applied. The nonlinear equation of motion is transformed to a similarity differential equation which is solved using the method of successive approximations. The analytical solutions found by this method yield numerical values in good agreement with tabulated calculations obtained before via numerical methods for electrically nonconducting fluids. Analytical expressions are derived for both the velocity profile and the local non-dimensional skin friction coefficient. Also the three thicknesses of displacement, momentum and kinetic energy are given in closed forms.     

Magnetohydrodynamic flow of a non-Newtonian fluid past a porous plate

This article studies the laminar flow of an electrically conducting non-Newtonian fluid (Rivlin-Encksen type) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The Laplace transform technique has been employed to solve the basic differential equations. The solutions of the velocity profile and skin-friction are obtained and the effects of the visco-elastic parameter, the magnetic field and the time parameter on the fluid flow have been studied in several tables.     

Physical-mechanical properties of a cometary nucleus

Physical-mechanical properties of cometary nuclei matter are described in detail. As compared to other Solar System bodies, cometary nuclei are characterized by low strength properties. The ultimate tensile strength of cometary matter and cometary nuclei on the whole is about 2 kPa. An analysis performed based on a rheological model of a self-gravitating triaxial solid body showed that cometary nuclei less than 50–60 km (this actually being all known comets) are characterized by a constant ultimate tensile strength which is determined only by the matter composition and structure. The effective ultimate tensile strength for bodies larger than 50–60 km is determined by the body mass and figure parameters and increases according to the quadratic law depending on the body dimensions and mass. Such an increase of the effective strength can explain the absence or deficit of cometary nuclei more than 60 km in size, since it can significantly affect the parameters of the parent body destruction and the formation of a secondary population. The dependence of the mechanism and character of destruction on the parameters of the figure for Kuiper objects more than 50–60 km is size can yield a deficit of the population of the bodies whose figure parameters are a/c > 1.75 with respect to the bodies with a/c < 1.75 figure parameters.     

Transient flow of a relativistic radiating gas past a horizontal plate

The problem of unsteady flow of a relativistic radiating neutrino gas is studied by imposing a time-dependent perturbation on a basic flow. When the perturbation is small, the problem, which is ill-posed, is reduced to a well-posed spatial value problem for the transverse velocity and the temperature. Subsequently the axial velocity and number density may be obtained by straightforward integration with respect to time and imposition of the initial condition. The solution for the initial value problem is tackled by the Laplace transform technique and the results are discussed quantitatively.     

Unsteady hydromagnetic flow past a porous spherical or cylindrical surface

The problem of unsteady hydromagnetic axial flow near the porous surface of a sphere or a cylinder is studied numerically. The fluid is considered to be electrically conducting, viscous and incompressible subjected to a magnetic field. Results are presented for the case of injected or sucked fluid with a constant velocity through the porous surfaces. The magnetic Prandtl number is set equal to one, while the magnetic Reynolds number is taken to be small enough so that the inducted magnetic field is negligible.     

A cometary aurora

It is proposed that the cometary analog of a terrestrial aurora was responsible for the enhanced fluxes of suprathermal (keV) electrons and associated plasma waves observed in the cometosheath of Comet Halley during its VEGA 2 encounter. The non-detection of such suprathermal electron fluxes during the GIOTTO encounter is ascribed to the much quieter solar wind conditions at that time.     

Diffusion and heat flow equations for the mid-latitude topside ionosphere

For application to the mid-latitude topside ionosphere, we have derived diffusion and heat flow equations for a gas mixture composed of two major ions, electrons and a number of minor ions. These equations were derived by expanding the velocity distribution of each constituent about its 13 lower order velocity moments. As a consequence, each constituent was allowed to have its own temperature and drift velocity. The restriction to mid-latitudes results because we have assumed that the species temperature and drift velocity differences were small. In deriving the diffusion and thermal conduction equations, we have discovered some new transport effects. For the major ions, we have found that: (1) a temperature gradient in either gas causes thermal diffusion in both gases; (2) a temperature gradient in either gas causes heat to flow in both gases; and (3) a relative drift between the major ion gases induces a heat flow in both gases. Similar transport effects have also been found for the minor ions.     

Solar Activity Cycle in Solar-wind Sources and Flows

Experiments based on multi-source radio occultation measurements of the circumsolar plasma at R∼4.0−70R _S were carried out during 1997 – 2008 to locate the inner boundary of the solar-wind transonic transition region, R _in. The data obtained were used to correlate the solar-wind stream structure and magnetic fields on the source surface (R=2.5R _S) in the solar corona. The method of the investigation is based on the analysis of the dependence R _in=F(|B _R|) in the correlation diagrams, where R _in is the inner boundary of the solar-wind transition region and |B _R| is the intensity of the magnetic field at the source surface. On such diagrams, the solar wind is resolved into discrete branches, streams of different types. The analysis of the stream types using a continuous series of data from 1997 to 2008 allowed us to propose a physical criterion for delimiting the epochs in the current activity cycle.     

MHD flow of an elasto-viscous fluid past a porous flat plate

An analytical study is performed to examine the laminar flow of an electrically-conducting elasto-viscous fluid (Walters's liquidB) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The influence of the various parameters, entering in the problem, on the velocity field and shearing stress is extensively discussed.     

Hydromagnetic flow past a continuously moving semi-infinite plate for large suction

The similarity solution for hydromagnetic flow of an incompressible viscous electrically conducting fluid past a continuously moving semi-infinite porous plate in the presence of a magnetic field has been obtained for the case of small magnetic Reynolds number. The perturbation method has been used to solve the similarity equations at large suction. The resulting equations have been solved by analytical method. The effect of the magnetic parameter is to increase the skin-friction coefficient while it has no significant effect on the Nusselt number.