Acceleration of the solar wind by whistler waves from coronal holes

We investigate the possibility of an additional acceleration of the high speed solar wind by whistler waves propagating outward from a coronal hole. We consider a stationary, spherically symmetric model and assume a radial wind flow as well as a radial magnetic field. The energy equation consists of (a) energy transfer of the electron beam which excites the whistler waves, and (b) energy transfer of the whistler waves described by conservation of wave action density. The momentum conservation equation includes the momentum transfer of two gases (a thermal gas and an electron beam). The variation of the temperature is described by a polytropic law. The variation of solar wind velocity with the radial distance is calculated for different values of energy density of the whistler waves. It is shown that the acceleration of high speed solar wind in the coronal hole due to the whistler waves is very important. We have calculated that the solar wind velocity at the earth's orbit is about equal to 670 km/sec (for wave energy density about 10^?4 erg cm^?3 at 1.1R⊙). It is in approximate agreement with the observed values.     

On neutral sheets in the solar wind

The structure and dynamics of neutral sheets in the solar wind is examined. The internal magnetic topology of the sheet is argued to be that of thin magnetic tongues greatly distended outward by the expansion inside the sheet. Due to finite conductivity effects, outward flow takes place across field lines but is retarded relative to the ambient solar wind by the reverse J×B force. The sheet thickness as well as the internal transverse magnetic field are found to be proportional to the electrical conductivity to the inverse one third power. Estimating a conductivity appropriate for a current carried largely by the ions perpendicular to the magnetic field, we find sheet dimensions of the order of 500km representative for the inner solar corona. For a radial field of strength 1/2G at 2R , the transverse field there is about 2 × 10^–3G and decreases outward rapidly.The energy release in the form of Joulean dissipation inside the sheet is estimated. It is concluded that ohmic heating in current sheets is not a significant source of energy for the overall solar wind expansion, mainly because these structures occupy only a small percentage of the total coronal volume. However, the local energy release through this mechanism is found to be large - in fact, over 7 times that expected to be supplied by thermal conduction. Therefore, ohmic heating is probably a dominant energy source for the dynamical conditions within the sheet itself.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A model of the magnetized solar wind

A steady state, inviscid, single fluid model of the solar win d in the equatorial plane is developed using magneto-hydrodynamics and including the heat equation wit h thermal conduction but no non-thermal heating (i.e. a conduction model). The effects of solar rotation and magnetic field are included enabling both radial and azimuthal components of the velocity and magnetic fields to be found in a conduction model for the first time.The magnetic field cuts off the thermal conduction far from the sun and leads to an increased temperature at 1 AU and relatively small changes to the radial velocity and density. Models have been found which fit the experimental electron densities in 2 R < r < 16 R . These models predict at 1 AU a radial velocity of 300–380 km·sec^-1 and a density of 8 protons·cm^-3. The latter velocity corresponds to a density profile obtained by Blackwell and Petford (1966) during the last sunspot minimum, and is about 100 km·sec^-1 above that found in previous conduction models which fit the coronal electron densities. The radial velocities are now consistent with the mean quiet solar wind, as are the densities when the experimental values are averaged over a magnetic sector. However, the azimuthal velocity at 1 AU is only 1–2 km·sec^-1 which is low compared to the experimental values, as found by previous authors.     

The proton temperature and the total hourly variance of the magnetic field components in different solar wind speed regions

A comparison has been made between the predictions of the theory for radial variations of both Alfvénic fluctuations and solar wind proton temperatures proposed by Tu (1987, 1988) and the statistical results of hourly averaged plasma and magnetic field data observed by Helios 1 and 2 from launch through 1980 for different solar wind speed regimes. The comparison shows that for speed ranges between 500–800 km s^-1, the radial variation of the proton temperature between 0.3 and 1 AU can be explained by heating from the cascade energy determined by the radial variation of the total variance of magnetic field vector. The explanation of the radial variations of both temperature and the total variance of magnetic fields for speed ranges less than 400 km s ^-1 is less clear.This project was supported by National Natural Science Foundation of China for Tu's part of the work.     

Spatial structure of transverse oscillations in the interplanetary magnetic field

The spatial structure of the transverse oscillations in the interplanetary magnetic field at 1 AU is studied by comparing the simultaneous observations by Explorer 33 and 35 satellites at the maximum separation of about 200R _E. The anisotropy characteristics of these oscillations suggest that the oscillations sampled are Alfvén waves. It is found that the size of the region of the wave coherence is related to the solar wind velocity; the size is 80R _E when the wind velocity is lower than 500 km s^–1 but becomes less than this when the wind velocity is higher. An inference is made that the solar atmospheric turbulence contributing to the faster solar wind is finer in scale than that associated with the slower wind.A postgraduate student at the Tokai University     

Interaction of interstellar pick-up ions with the solar wind

The interaction of interstellar pick-up ions with the solar wind is studied by comparing a model for the velocity distribution function of pick-up ions with actual measurements of He⁺ ions in the solar wind. The model includes the effects of pitch-ang'e diffusion due to interplanetary Alfvén waves, adiabatic deceleration in the expanding solar wind and the radial variation of the source function. It is demonstrated that the scattering mean free path is in the range 0.1 AU and that energy diffusion can be neglected as compared with adiabatic deceleration. The effects of adiabatic focusing, of the radial variation of the neutral density and of a variation of the solar wind velocity with distance from the Sun are investigated. With the correct choice of these parameters we can model the measured energy spectra of the pick-up ions reasonably well. It is shown that the measured differential energy density of the pick-up ions does not vary with the solar wind velocity and the direction of the interplanetary magnetic field for a given local neutral gas density and ionization rate. Therefore, the comparison of the model distributions with the measurements leads to a quantitative determination of the local interstellar gas density.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Gamma-ray lines and neutrons from solar flares

An analysis, with a representative (canonical) example of solar-flare-generated equatorial disturbances, is presented for the temporal and spatial changes in the solar wind plasma and magnetic field environment between the Sun and one astronomical unit (AU). Our objective is to search for first order global consequences rather than to make a parametric study. The analysis - an extension of earlier planar studies - considers all three plasma velocity and magnetic field components (V _r, V_φ, V₀, and B _r, B₀, B_φ) in any convenient heliospheric plane of symmetry such as the ecliptic plane, the solar equatorial plane, or the heliospheric equatorial plane chosen for its ability (in a tilted coordinate system) to order northern and southern hemispheric magnetic topology and latitudinal solar wind flows. Latitudinal velocity and magnetic field gradients in and near the plane of symmetry are considered to provide higher-order corrections of a specialized nature and, accordingly, are neglected, as is dissipation, except at shock waves. The representative disturbance is examined for the canonical case in which one describes the temporal and spatial changes in a homogeneous solar wind caused by a solar-flare-generated shock wave. The ‘canonical’ solar flare is assumed to produce a shock wave that has a velocity of 1000 km s^#X2212;1 at 0.08 AU. We have examined all plasma and field parameters at three radial locations: central meridian and 33° W and 90° W of the flare's central meridian. A higher shock velocity (3000 km s^#X2212;1) was also used to demonstrate the model's ability to simulate a strongly-kinked interplanetary field. Among the global (first-order) results are the following: (i) incorporation of a small meridional magnetic field in the ambient magnetic spiral field has negligible effect on the results; (ii) the magnetic field demonstrates strong kinking within the interplanetary shocked flow, even reversed polarity that - coupled with low temperature and low density - suggests a viable explanation for observed ‘magnetic clouds’ with accompanying double-streaming of electrons at directions ～ 90° to the heliocentric radius.     

Measurement of the solar wind velocity with cometary tail rays

Cometary tail rays are traces of the magnetic fields caught in the cometary magnetosphere. Time variations of these rays give us a way to measure the local solar wind velocity at the location of a comet. We introduce a simple method for determining the radial velocity of the solar wind by observing the ray folding motion, and show an example of its application to comet P/Brorsen-Metcalf 1989o, which resulted in 340 ± 35 km s^–1.     

Magnetic clouds: Voyager observations between 2 and 4 AU

Magnetic clouds were observed in the solar wind between 2–4 AU by Voyagers 1 and 2, indicating that they are stable enough to persist without major changes out to such distances. The average size in radial extent of the clouds observed at these distances was 0.47 AU, compared to 0.25 for clouds observed at 1 AU. Assuming that these numbers are representative, we estimate that the clouds were expanding at a speed of the order of 45 km s^-1. This is consistent with the expansion speed derived from the difference of the speeds of the front and rear boundaries of the clouds, 33 km s^-1. The average Alfvén speed at the front and rear boundaries was 104 km s^-1, so our estimated expansion speed is nearly half of the Alfvén speed, consistent with an earlier estimate of the expansion speed of clouds between the Sun and 1 AU. The magnetic field configuration cannot be determined uniquely, but it is highly ordered and consistent with the passage of some kind of loop. The simple model of a magnetic tongue with magnetic field lines in planes, e.g., meridian planes, is not consistent with the data.     

First order latitude effects in the solar wind

The Weber-Davis model of the solar wind is generalized to include the effects of latitude. The principal assumptions of perfect electrical conductivity, rotational symmetry, a polytropic relation between pressure and density, and a flow aligned magnetic field in a system rotating with the Sun, are retained. A flow aligned magnetic field in the rotating system may be expressed in terms of the flow velocity and density. Rotational symmetry fixes the longitudinal flow velocity V_φ in terms of the flow in the r?θ plane. Thus, the original three dimensional magnetohydrodynamic flow problem is reduced to a two dimensional hydrodynamic flow problem in the r?θ plane.There are three critical surfaces associated with the equations which supply conditions to determine three of six required boundary conditions. The specified boundary conditions at the base of the corona are the temperature, density, and magnitude of the magnetic field. The equations are then expanded about the radial, nonrotating Parker solution and an analytic solution is obtained for the resulting first order equations. The results show that for constant coronal boundary conditions there is a latitudinal flow toward the solar poles, as a result of magnetic stresses, which persists out to large distances for the Sun. Associated with this flow is a latitudinal component of the magnetic field. The radial flow parameters are, to within small first order differences, in agreement with those of the Parker and the Weber-Davis models of the solar wind.The equations are further generalized to permit first order latitudinal variations in the specified coronal boundary conditions. Results at 1 a.u. are presented for 5 per cent latitudinal differences between the equatorial and polar values. These results show that the solution at 1 a.u. is most sensitive to a latitudinal dependence in the boundary temperature and least sensitive to a latitudinal dependence in the magnetic field magnitude.A solution is then obtained for an approximate dipolar variation in the coronal magnetic field magnitude. This solution predicts that the latitudinal flow is initially toward the Equator due to magnetic channeling; however, this effect is rapidly overcome and the latitudinal flow at 1 a.u. is toward the pole and not significantly different from the solution for constant boundary conditions.     

Unipolar induction in the moon and a lunar limb shock mechanism

The unipolar induction mechanism is employed to calculate electric field profiles in the interior of a chemically homogeneous Moon possessing a steep radial thermal gradient characteristic of long-term radioactive heating. The thermal models used are those of Fricker, Reynolds, and Summers. From the magnetic field, the magnetic back pressure upon the solar wind is found. The electric field profile is shown to depend only upon the activation energy,E _o, of the geological material and the radial gradient of the reciprocal temperature. The current is additionally dependent upon the coefficient of the electrical conductivity function but only by a scale factor. Since the Moon is experimentally known to correspond to the case of weak interaction with the solar wind, the magnetic back pressure is calculated without the need for an iterative procedure. The results indicate that a hot Moon can yield sufficient current flow so that the magnetic back pressure is observable as a vestigial limb shock wave using an activation energy of about 2/3 eV together with a conductivity coefficient of about 10³ mhos/m. Such matter is approximated by diabase-like composition, although the result that both the activation energy and coefficient enter into the current determination does not rule out the possibility of a match with other similar substances. The calculations are entirely consistent with earlier results which indicated a model where the unipolar current density is dominated by a high impedance surface layer and a strong shock wave is inhibited. In addition to the magnetic back pressure, the integration of the current continuity equation permits current densities and joule heating rates to be calculated, though the magnitude of the latter for present solar wind conditions is not thermally important.On leave from NASA Ames Research Center     

Solar Wind and Chromospheric Network

A physical model of the transition region, including upflow of the plasma in magnetic field funnels that are open to the overlying corona, is presented. A numerical study of the effects of Alfvén waves on the heating and acceleration of the nascent solar wind originating in the chromospheric network is carried out within the framework of a two-fluid model for the plasma. It is shown that waves with reasonable amplitudes can, through their pressure gradient together with the thermal pressure gradient, cause a substantial initial acceleration of the wind (on scales of a few Mm) to locally supersonic flows in the rapidly expanding magnetic field trunks of the transition region network. The concurrent proton heating is due to the energy supplied by cyclotron damping of the high-frequency Alfvén waves, which are assumed to be created through small-scale magnetic activity. The wave energy flux of the model is given as a condition at the upper chromosphere boundary, located above the thin layer where the first ionization of hydrogen takes place.Among the new numerical results are the following: Alfvén waves with an assumed f ^-1 power spectrum in the frequency range from 1 to ⁴ Hz, and with an integrated mean amplitude ranging between 25 and 75 km s⁴, can produce very fast acceleration and also heating through wave dissipation. This can heat the lower corona to a temperature of 5× 10⁵ K at a height of h=12,000 km, starting from 5× 10⁴ K at h=3000 km. The resulting thermal and wave pressure gradients can accelerate the wind to speeds of up to 150 km s^-1 at h=12,000 km, starting from 20 km s^-1 at h=3000 km in a rapidly diverging flux tube. Thus the nascent solar wind becomes supersonic at heights well below the classical Parker-Type sonic point. This is a consequence of the fact that any large wave-energy flux, if it is to be conducted through the expanding funnel to the corona, implies the building-up of an associated wave-pressure gradient. Because of the diverging field geometry, this might lead to a strong initial acceleration of the flow. There is a multiplicity of solutions, depending mainly on the coronal pressure. Here we discuss two new (as compared with a static transition region model) possibilities, namely that either the flow remains supersonic or slows down abruptly by shock formation, which then yields substantial coronal heating up to the canonical 10⁶ K for the proton temperature.     

A dynamical model of the corona

The hydrodynamic equations for an ideal, inviscid, fully ionized hydrogen gas in a gravitational, but not magnetic, field are solved by an explicit Lax-Wendroff two-step technique using a one-dimensional slab symmetry. Radiation and thermal conductivity are included. The model spans 100000 km starting from the chromosphere-corona transition region. An initially isothermal gas is seen to evolve coronal properties in 4000 s, by which time it settles into dynamic equilibrium characterized by a 2000 km transition region, a temperature maximum of 1.6 × 10⁶ K at a height of 60000 km, and a solar wind mass flux of 10^-9 g cm^-2 s^-1.     

Signatures of the Interplanetary Helium Cone Reflected by Pick-up Ions

As known for a long time, interstellar wind neutral helium atoms deeply penetrate into the inner heliosphere and, when passing through the solar gravity field, form a strongly pronounced helium density cone in the downwind direction. Helium atoms are photoionized and picked-up by the solar wind magnetic field, but as pick-up ions they are not simply convected outwards with the solar wind in radial directions as assumed in earlier publications. Rather they undergo a complicated diffusion-convection process described here by an appropriate kinetic transport equation taking into account adiabatic cooling and focusing, pitch angle scattering and energy diffusion. In this paper, we solve this equation for He⁺pick-up ions which are injected into the solar wind mainly in the region of the helium cone. We show the resulting He⁺pick-up ion density profile along the orbit of the Earth in many respects differs from the density profile of the neutral helium cone: depending on solar-wind-entrained Alfvénic turbulence levels, the density maximum when looking from the Earth to the Sun is shifted towards the right side of the cone, the ratio of peak-densities to wing-densities varies and a left-to-right asymmetry of the He⁺-density profile is pronounced. Derivation of interstellar helium parameters from these He⁺-structures, such as the local interstellar medium (LISM) wind direction, LISM velocity and LISM temperature, are very much impeded. In addition, the pitch-angle spectrum of He⁺pick-up ions systematically becomes more anisotropic when passing from the left to the right wing of the cone structure. All effects mentioned are more strongly pronounced in high velocity solar wind compared to the low velocity solar wind.     

Solar-interplanetary modeling: 3-D solar wind solutions in prescribed non-radial magnetic field geometries

A model is presented which describes the 3-dimensional non-radial solar wind expansion between the Sun and the Earth in a specified magnetic field configuration subject to synoptically observed plasma properties at the coronal base. In this paper, the field is taken to be potential in the inner corona based upon the Mt. Wilson magnetograph observations and radial beyond a certain chosen surface. For plasma boundary conditions at the Sun, we use deconvoluted density profiles obtained from synopticK-coronameter brightness observations. The temperature is taken to be 2 × 10⁶ K at the base of closed field lines and 1.6 x 10⁶K at the base of open field lines. For a sample calculation, we employ data taken during the period of the 12 November 1966 eclipse. Although qualitative agreement with observations at 1 AU is obtained, important discrepancies emerge which are not apparent from spherically symmetric models or those models which do not incorporate actual observations in the lower corona. These discrepancies appear to be due to two primary difficulties - the rapid geometric divergence of the open field lines in the inner corona as well as the breakdown in the validity of the Spitzer heat conduction formula even closer to the Sun than predicted by radial flow models. These two effects combine to produce conductively dominated solutions and lower velocities, densities, and field strengths at the Earth than those observed. The traditional difficulty in solar wind theory in that unrealistically small densities must be assumed at the coronal base in order to obtain observed densities at 1 AU is more than compensated for here by the rapid divergence of field lines in the inner corona. For these base conditions, the value ofβ(ratio of gas pressure to magnetic pressure) is shown to be significantly greater than one over most of the lower corona - suggesting that, for the coronal boundary conditions used here, the use of a potential or force-free magnetic field configuration may not be justified. The calculations of this paper point to the directions where future research on solar-interplanetary modelling should receive priority:

1. better models for the coronal magnetic field structure
2. improved understanding of the thermal conductivity relevant for the solar wind plasma.

     

An explanation of the observed differences between coronal holes and quiet coronal regions

The main differences between a coronal hole and quiet coronal regions are explained by a reduction of the thermal conduction coefficient by transverse components of the magnetic field in the transition region of quiet coronal regions.Calculations of minimum flux coronae show that if the flux of energy heating the corona is maintained constant while the thermal conductivity in the transition region is reduced, the coronal temperature, the pressure in the transition region and the corona, and the temperature gradient in the transition region all increase. At the same time the intensities of lines emitted from the transition region are almost unchanged. Thus all the main spectroscopically observed differences between coronal holes and quiet coronal regions are explained.The flux of energy heating the corona in both coronal holes and quiet coronal regions is 3.0 × 10⁵ erg cm^-2 s^-1.The energy lost from coronal holes by the high speed streams in the solar wind is not sufficient to explain the difference in the coronal temperature in coronal holes and quiet coronal regions. The most likely explanation of the high velocity streams in the solar wind associated with coronal holes is that of Durney and Hundhausen.     

Synoptic Maps of Solar Wind: Comparison of IPS Data and the NOAA/SEC Version of the Wang and Sheeley Model

Since the 1970s, the Solar-Terrestrial Environment Laboratory, Japan, has been publishing synoptic maps of solar wind velocity prepared using the technique of interplanetary scintillation. These maps, known as V-maps, are useful to study the global distribution of solar wind in the heliosphere. As the Earth-orbiting satellites are unable to probe regions outside the ecliptic, it is important to exploit the scope of interplanetary scintillation to study the solar wind properties at these regions and their relation with coronal features. It has been shown by Wang and Sheeley that there exists an inverse correlation between rate of magnetic flux expansion and the solar wind velocity. The NOAA/Space Environment Center daily updated version of the Wang and Sheeley model has been used to produce synoptic maps of solar wind velocity and magnetic field polarity for individual Carrington rotations. The predictions of the model at 1 AU have been found to be in good agreement with the observed values of the same. The present work is a comparison of the synoptic maps on the source surface using the interplanetary scintillation measurements from Japan and the NOAA/SEC version of the Wang and Sheeley model. The two results agree near the equatorial regions and the slow solar wind locations are consistent most of the times. However, at higher latitudes within ±60°, the wind velocities differ considerably. In the Wang and Sheeley model the highest speed obtained is 600 km s^–1 whereas in the IPS results velocities as high as 800 km s^–1 have been detected. The paper discusses the possible causes for this discrepancy and suggestion to improve the agreement between the two results.     

Long-period observations of the solar wind plasma between 0.3 and 1.0 AU — Solar activity

Hourly interplanetary plasma data measured by Helios-1 satellite over the period 10 December 1974–31 December 1977 are analysed. This analysis showed that the slow solar wind first increases its speed with heliocentric distance and then becomes more or less constant; the mean speed in the range 0.3 to 1.0 AU is 350 km s^–1 for the slow solar plasma, while for the fast the mean value is between 650 and 700 km s^–1.It seems, particularly in the neighbourhood of the earth, that except for the two dominated types of solar wind (fast and slow) an additional (intermediate) appears at 450 km s^–1.During the phase of enhanced solar activity (11-yr solar cycle) the slow solar wind only is present, while at solar minimum all three types of the solar wind are equally represented.The dependence of the proton temperature on the solar wind speed, in the general solar wind, is the same irrespectively of the phase of solar activity. But, the same dependence is stronger during the compression at the leading edge than during the expansion at the trailing edge of a solar wind stream.     

Evidence for a coronal magnetic bottle at 10 solar radii

The Faraday rotation of a radio source (Pioneer 6) occulted by the solar corona has been measured by Levy et al. (1969). During the course of these measurements, three large-scale transient phenomena were observed. These events were preceded by subflares and class 1 flares. These transient events are interpreted as evidence for a coronal magnetic bottle at 10 R _⊙. The velocity of propagation for the disturbance is set at 200 km/sec; the dimension of the region, 10 R _⊙; field strength at 10 R _⊙, 0.02 G; particle density, 2.0 × 10⁴/cm³; Alfvén speed, 320 km/sec. From the nature of the observations and the lack of related effects from similar flares on the interplanetary sector pattern observed at 1 AU, it is suggested that such coronal magnetic bottles expand to perhaps 10–30 R _⊙ and then contract to a few solar radii. Such a phenomena is evidence for an expansion of the corona with a sub-Alfvénic velocity. It is further suggested that such magnetic bottles may be important in the storage and diffusion of solar generated cosmic ray particles. NAS-NRC Postdoctoral Resident Research Associate.     

The Bastille day Shocks and Merged Interaction Region

Near 1 AU the solar wind structure associated with the solar flare of 14 July 2000 (Bastille Day) consisted of a large high-speed stream of 15 July and five nearby small streams during a 10-day period. At the leading edge of the large high-speed stream, in less than 6 hours, the flow speed increased from 600 km s⁻¹ to 1100 km s⁻¹, the magnetic field intensity increased from 10 nT to 60 nT, and an interaction region was identified. The interaction region was bounded between the pair of a forward shock F and a reverse shock R. Additional forward shocks were also identified at the leading edge of each of the five smaller streams. This paper presents a magnetohydrodynamics (MHD) simulation using ACE plasma and magnetic field data near 1 AU as input to study the radial evolution of the Bastille Day solar wind event. The two shocks, F and R, propagated in opposite directions away from each other in the solar wind frame and interacted with neighboring shocks and streams; the spatial and temporal extent of the interaction region continued to increase with the heliocentric distance. The solar wind was restructured from a series of streams at 1 AU to a huge merged interaction region (MIR) extending over a period of 12 days at 5.5 AU. Throughout the interior of the MIR bounded by the shock pair F and R the magnetic field intensity was a few times stronger than that outside the MIR. The simulation shows how merging of shocks, collision of shocks, and formation of new shocks contributed to the evolution process.