The asymptotic behavior of the supersonic solutions of the two-fluid solar wind equations

Three different asymptotic branches of the two-fluid equations are found with _e ^m , _p ⁿ , where, is the inverse distance from the Sun, with (m, n) = (2/7, 2/7), (2/7, 6/7), (4/3, 4/3); other special solutions are also found but they correspond to special choices of density and temperature at the corona. In all the (4/3, 4/3) solutions, the electron and proton temperatures tend to equality at large distances.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Restrictions on radial magnetic field and flow solutions for the solar wind

In Parker's original model, the solar wind is represented as a spherically symmetric hydrodynamic flow. The velocity is radially directed and decoupled from the magnetic field. The simple extension of this model to include a dependence on the polar angle, , is shown to be invalid for radial flow and radial magnetic field. This work demonstrates how ad hoc symmetry conditions imposed to simplify a non-linear problem can be incompatible with the basic hydromagnetic equations.     

Meridional flow in the solar wind in the presence of latitudinally dependent boundary conditions

The influence of latitudinally dependent boundary conditions on the large radius values of meridional flow in the distant solar wind is examined through a double perturbation expansion of the magnetohydrodynamic equations. A general result is derived for the meridional velocity which allows arbitrary specification of radial velocity, radial magnetic field, and mass flux, as a function of colatitude at some coronal reference surface. Three specific examples are treated, including the model of Pneuman and Kopp (1971). The latter example indicates that there may be flow toward the equator at large radii, as opposed to the pure equatorial divergence of internally generated motion due to a flow which is latitudinally uniform at the reference radius. A solar cycle effect most probably averages the boundary conditions so that only the equatorial divergence from an average spherically symmetric corona is seen in comet-tail observations. This may also explain the off-and-on-again nature of the meridional gradient in the radial velocity of the solar wind as seen in radio scintillation observations.     

Transient response of the solar wind to changes in flow geometry

The transient response of the solar wind to changes in geometry is examined. An initial stationary flow in a configuration that diverges as r ² is assumed. This state corresponds to the usual solar wind solution. The effect on the flow through a tube whose area A(r, t) diverges faster than r ², with the degree of divergence increasing in time, is considered. The asymptotic form of A(r, t) is chosen to mimic the form inferred in coronal holes. A detailed parameter study relating the form of A(r, t) to the pattern of flow in the tube is presented. It is observed that in the limit of large time (large compared to , the time constant for change in geometry of a flow tube) the solutions obtained from a time-dependent analysis can depend upon . For sufficiently large , the asymptotic solution is the same as the steady state solution obeying the correct boundary conditions and possessing a smooth sonic transition. However, if the geometry changes rapidly enough, solutions exhibiting shock-like discontinuities can also exist. This is essentially a new feature that emerges from the present investigation. Finally, it is suggested that this study may be useful in describing flows in evolving coronal holes.     

Viscous flow properties in the transport of solar wind momentum to the Venus upper ionosphere

A comparative study of the viscous transport of solar wind momentum to the upper layers of the Venus ionosphere with that occurring within the trans-terminator flow leads to estimates of the ratio of the viscosity coefficients that are applicable to both cases. Support for viscous forces between the solar wind and the ionospheric plasma in the trans-terminator flow derives from the momentum flux balance between the momentum flux in the latter flow and the deficiency of solar wind momentum along the flanks of the ionosheath. By comparing the relative width of the viscous boundary layer in the Venus ionosheath and the width of the trans-terminator flow we find that the transport of momentum within the upper ionosphere proceeds at a rate similar to that at which momentum is delivered to the upper ionosphere from the solar wind. Comparable values are obtained for the viscosity coefficient of the solar wind that streams over the ionosphere and that implied from momentum transport within the ionospheric trans-terminator flow. It is further suggested that despite the different nature of the processes that give place to the viscous transport of the solar wind momentum to the upper ionosphere (wave-particle interactions) and those responsible for its distribution within the ionosphere (through coulombian collisions) there is a similar response in the behavior of both plasmas to momentum transport. Calculations show that with comparable values of the viscosity coefficient in the ionosheath and in the upper ionospheric plasma the mean free path suitable to wave-particle interactions in the ionosheath is of the same order of magnitude as the mean free path of the planetary O⁺ ions that interact through coulombian collisions in the upper ionosphere. The effects of this similarity are considered in the discussion.     

Solutions of the two-fluid solar wind equations: Adiabatic and conduction dominated solutions

The equations governing the two-fluid spherically symmetric models of the solar wind have been solved numerically for a wide range of base conditions. As predicted from an asymptotic analysis we find a whole domain of solutions which are asymptotically adiabatic with the proton and electron temperatures tending to equality and varying like r ^{- 4/3}. In these 4/3 solutions the electron and proton heat conduction is asymptotically negligible and if it is neglected the resulting equations can be integrated analytically and shown to have the 4/3, 4/3 behaviour.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Heavy ion escape from Mars, influence from solar wind conditions and crustal magnetic fields

We have used more than 4 years of Mars Express ion data to estimate the escape of heavy ions ( and ) from Mars. To take the limited field of view of the instrument into account, the data has been binned into spatial bins and angular bins to create average distribution functions for different positions in the near Mars space. The net escape flux for the studied low solar activity period, between May 2007 and May 2011, is 2.0 ± 0.2 × 10²⁴ s⁻¹. The escape has been calculated independently for four different quadrants in the Y_MSO − Z_MSO plane, south, dusk, north and dawn. Escape is highest from the northern and dusk quadrants, 0.6 ± 0.1 × 10²⁴ s⁻¹, and smallest from the south and dawn quadrants, 0.4 ± 0.1 × 10²⁴ s⁻¹. The flux ratio of molecular ( and ) to O⁺ ions is 0.9 ± 0.1, averaged over all quadrants. The flux difference between the north and south quadrants is statistically significant, and is presumed to be due to the presence of significant crustal magnetic fields in the southern hemisphere, reducing the outflow. The difference between the dawn and dusk quadrants is likely due to the magnetic tension associated with the nominal Parker angle spiral, which should lead to higher average magnetic tension on the dusk side. The escape increases during periods of high solar wind flux and during times when co-rotating interaction regions (CIR) affect Mars. In the latter case the increase is a factor 2.4-2.9 as compared to average conditions.     

The green corona,the solar wind and geoactivity

The long-term distribution of the Green Corona Low Brightness Regions (GCLBR) on the solar surface is investigated. The frequency curves of the GCLBR follow the solar cycle, but are displaced considerably relative to the curve of the sunspot number cycle. The observed displacement increases with the size of the GCLBR and reaches up to 4–5 years for the largest regions. It is, however, interesting that the displacement in the equatorial zone is opposite to that in the higher-latitude zones.An older idea on the physical affinity between GCLBR and coronal holes led us to study the frequency of GCLBR and the properties of High-Speed Plasma Streams (HSPS) in the solar wind. Maximum velocity and duration of the coronal-hole-related HSPS seem to be well correlated with the number and size of GCLBR located in the N 60-N 20 and S 20-S 60 latitudinal zones. This is particularly evident at the end of the solar cycle.Geophysical Kp and aa indices are used to demonstrate a possible genetic dependence of geoactivity on the size, position on the Sun's surface and frequency of the GCLBR. In this sense, the most pronounced period is 1973–1976.

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Numerical solutions to the problem of charged particel flow around an ionospheric spacecraft

The interaction of a conducting body moving through the ionosphere with the surrounding plasma is treated numerically. The Poisson and Vlasov equations are solved using computer techniques to give information about the redistribution of charged particles in the wake behind the body and the perturbation of the electric potential sheaths around the body. Three cases of interest are studied: body size less than, equal to, and greater than the Debye length in the surrounding plasma. A range of body potentials and ion Mach numbers are considered which are typical of conditions found in the ionosphere. Wake features, such as ion-free wake lengths and angles of propagation of disturbances in the wakes, are investigated for these conditions. Physical pictures of the mechanisms of wake formation behind a plate and a disc are built up for the three classes of body size, and differences due to geometry or size are explained. The smaller bodies are comparable in size to instrument booms, diagnostic probes, antennae, etc. and the larger bodies approach the dimensions of ionospheric satellites and space probes.     

Calculating the plasma deformation tensor and kinetic vorticity from magnetic field time series: Applications to the solar wind

It is shown that the magnetic induction equation reduces to an autoregressive model equation. Assuming weakly ergodic field variations in steady mean plasma flow, this model permits the estimation of the mean flow deformation tensor, velocity divergence and kinetic vorticity from magnetic field time series. Applications, made to hourly-averaged, in-ecliptic interplanetary magnetic field (IMF) measurements from Ulysses spacecraft, showed that the direction of maximum deformation rate was, for most of the time, aligned to the mean field, while the vorticity tended to become perpendicular to the mean radial direction at large heliodistances.     

Equilibrium points and zero velocity surfaces in the restricted four-body problem with solar wind drag

We have analyzed the motion of an infinitesimal mass in the restricted four-body problem with solar wind drag. It is assumed that the forces which govern the motion are mutual gravitational attractions of the primaries, radiation pressure force and solar wind drag. We have derived the equations of motion and found the Jacobi integral, zero velocity surfaces, and particular solutions of the system. It is found that three collinear points are real when the radiation factor 0<β<0.1 whereas only one real point is obtained when 0.125<β<0.2. The stability property of the system is examined with the help of Poincaré surface of section (PSS) and Lyapunov characteristic exponents (LCEs). It is found that in presence of drag forces LCE is negative for a specific initial condition, hence the corresponding trajectory is regular whereas regular islands in the PSS are expanded.     

The solar wind cycle,the sunspot cycle,and the corona

Recent theories of the solar cycle and of coronal heating strongly suggest that solar cycle variations of different quantities (i.e. sunspots, coronal green line, etc.) ought not to be expected to be in phase with one another. In agreement with this notion we note that the shape of the corona typical of a maximum eclipse occurs 1.5yr before sunspot maximum, compared with 2 yr as might be expected from Leighton's standard model. Further, we argue that the phase of the solar wind cycle can be determined from geomagnetic observations. Using this phase, a solar cycle variation of 100 km s^–1 in the solar wind velocity and 1 in the magnetic field intensity becomes apparent. In general, the solar wind cycle lags the coronal-eclipse-form cycle by 3 yr, compared with the 2 yr that might be expected from model calculations.     

The G‐dwarf problem in the solar neighbourhood: a statistical approach within a inhomogeneous,simple model

Because of a technical problem in the final production step of the paper “The G‐dwarf problem in the solar neighbourhood: a statistical approach within a inhomogeneous, simple model” by R. Caimmi (AN 321 (2000) 5/6, 323) figures 2–8 and 10 were set incorrectly. The Editors sincerely regret this error. The figures with their corresponding captions follow.     

Perturbative effects on a Mercurian orbiter due to the solar radiation pressure,solar wind and the coronal mass ejections

To explore the dynamics of a test particle in the near-Mercury’s environment, the orbital motion of an orbiter around Mercury is considered. Different perturbing forces, namely the Mercurian gravity field, the solar radiation pressure, the solar wind and the coronal mass ejections, are taken into account. The order of magnitude of each perturbing term is assessed. The equations of motion in canonical representation are obtained. The Hamiltonian in terms of Hansen coefficients is expressed. A procedure for solution is presented. The short and long periodic terms are removed from the Hamiltonian and the solution is obtained. Long periodic perturbations on the orbital dynamics of an orbiter around Mercury due to the solar events are found as revealed by Eq. (26) in the text. Resonance cases are discussed and the different resonant inclinations are obtained. A procedure for the computation of the position and velocity is presented.     

Neutral and ion-exospheres in the solar wind with applications to mercury

A model of planetary neutral and ion-exospheres in the solar wind is formulated for weak or lunar like solar-wind interaction with a planet. The neutral exosphere model allows for density and temperature variations and for rotation at the exobase. The ion-exosphere is produced by ionization of the neutral exosphere in the solar wind and its density distribution is obtained by solving the continuity equation in the drift approximation. Applying to Mercury a surface temperature distribution inferred from infra-red data and a vanishing bound neutral flux at the base, He and He⁺ density distributions are found. When the He atmosphere of Mercury is due entirely to the surface bombardment by solar wind He⁺⁺, the resulting He⁺ density is found to vary from 1.5 × 10⁻¹ to 10⁻³ cm⁻³ over the range 1.5–5 planetocentric radii on the dayside. These densities are found to be detectable by typical solar-wind plasma instruments. The possible effects of cyclotron-resonant scattering by interplanetary magnetic field fluctuations are examined and shown to be negligible. An electromagnetic plasma instability, triggered by the birth of ions in the exosphere, is shown to be important for the thermalization of the energy mode transverse to the interplanetary magnetic field, allowing more ions to be detected by solar-wind ion probes.     

Summary of solutions to the spherically symmetric accretion and stellar wind problems

The stellar wind and accretion problems described by the steady, spherically symmetric continuum equations incorporating thermal conduction and viscosity are studied. A summary of solutions, including some new solutions, is presented and the solution properties are briefly examined.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Coronal holes,solar wind streams,and geomagnetic activity during the new sunspot cycle

We have extended our previous study of coronal holes, solar wind streams, and geomagnetic disturbances from the declining phase (1973–1975) of sunspot cycle 20 through sunspot minimum (1976) into the rising phase (1977) of cycle 21. Using daily He I 10830 Å spectroheliograms and photospheric magnetograms, we found the following results:

1. As the magnetic field patterns changed, the solar atmosphere evolved from a structure having a few, large, long-lived, low-latitude coronal holes to one having numerous small, short-lived, high-latitude holes (in addition to the polar holes which persisted throughout this 5-year interval).
2. The high-latitude holes recurred with a synodic rotation period of 28–29 days instead of the 27-day period already known to be characteristic of low-latitude holes.
3. During 1976–1977 many coronal holes were intrinsically ‘weak’ in the sense that their average intensities did not differ greatly from the intensity of their surroundings. Such low-contrast holes were rare during 1973–1975.

An updated Bartels display of the occurrence of holes, wind speed, and geomagnetic activity summarizes the evolution of their characteristics and interrelations as the sunspot cycle has progressed. Long-lived, low-latitude holes have become rare but remain terrestrially effective. The more common high-latitude holes are effective only when the Earth lies at a relatively high heliographic latitude in the same solar hemisphere.     

Abundances of carbon,oxygen, and neon in the solar wind during the period from August 1978 to June 1982

From four years of data provided by the Ion Composition Instrument on ISEE-3, we have derived flux ratios of minor elements in the solar wind and found He/O = 75 ± 20 and Ne/O = 0.17 ± 0.02. These results are compared with recent solar energetic particle composition data and photospheric values, and they are discussed in the light of theoretical models of ionization and acceleration of heavy ions in the solar chromosphere and corona.