Egil Leer

Acceleration of the Solar Wind

In this review, we discuss critically recent research on the acceleration of the solar wind, giving emphasis to high-speed solar wind streams emanating from solar coronal holes. We first explain why thermally driven wind models constrained by solar and interplanetary observations encounter substantial difficulties in explaining high speed streams. Then, through a general discussion of energy addition to the solar wind above the coronal base, we indicate a possible resolution of these difficulties. Finally, we consider the question of what role MHD waves might play in transporting energy through the solar atmosphere and depositing it in the solar wind, and we conclude by examining, in a simple way, the specific mechanism of solar wind acceleration by Alfven waves and the related problem of accelerating massive stellar winds with Alfven waves.

Coronal heating, densities, and temperatures and solar wind acceleration

The outflow of coronal plasma into interplanetary space is a consequence of the coronal heating process. Therefore the formation of the corona and the acceleration of the solar wind should be treated as a single problem. The deposition of energy into the corona through some “mechanical” energy flux is balanced by the various energy sinks available to the corona, and the sum of these processes determines the coronal structure, i.e., its temperature and density. The corona loses energy through heat conduction into the transition region and through the gravitational potential energy and kinetic energy put into the solar wind. We show from a series of models of the chromosphere-transition region-corona-solar wind system that most of the energy deposited in a magnetically open region goes into the solar wind. The transition region pressures and the coronal density and temperature structure may vary considerably with the mode and location of energy deposition, but the solar wind mass flux is relatively insensitive to these variations; it is determined by the amplitude of the energy flux. In these models the transition region pressure decreases in accordance with the increasing coronal density scale height such that the solar wind mass loss is consistent with the energy flux deposited in the corona. On the basis of the present study we can conclude that the exponential increase of solar wind mass flux with coronal temperature, found in most thermally driven solar wind models, is a consequence of fixing the transition region pressure.

The Role of Helium in the Outer Solar Atmosphere

We construct models of the outer solar atmosphere comprising the region from the mid-chromosphere and into the solar wind in order to study the force and energy balance in models with a significant helium abundance. The corona is created by dissipation of an energy flux from the Sun. The energy flux is lost as radiation from the top of the chromosphere and as gravitational and kinetic solar wind energy flux. We find that in models with significant ion heating of the extended corona most of the energy flux is lost in the solar wind. The ion temperatures are higher than the electron temperature in these models, and the α-particle temperature is much higher than the proton temperature, so there is energy transfer from the α-particle fluid to the protons and electrons, but this energy exchange between the different species is relatively small. To a fairly good approximation we can say that the energy flux deposited in the protons and α-particles is lost as kinetic and gravitational energy flux in the proton and α-particle flow. How this energy flux is divided between gravitational and kinetic energy flux (i.e., how large the particle fluxes and flow speeds are) depends upon details of the heating process. We also find that mixing processes in the chromosphere play an important role in determining the coronal helium abundance and the relative solar wind proton and α-particle fluxes. Roughly speaking, we find that the relative α-particle and proton fluxes are set by the degree of chromospheric mixing, while the speeds are set by the details of the coronal heating process.

Kinetic electrons in high‐speed solar wind streams: Formation of high‐energy tails

We study the evolution of the electron velocity distribution function in high-speed solar wind streams from the collision-dominated corona and into the collisionless interplanetary space. The model we employ solves the kinetic transport equation with the Fokker-Planck collision operator to describe Coulomb collisions between electrons. We use a test particle approach, where test electrons are injected into a prescribed solar wind background. The density, temperature, and electric field associated with the background are computed from fluid models. The test electrons are in thermal equilibrium with the background at the base of the corona, and we study the evolution of the velocity distribution of the test electrons as a function of altitude. We find that velocity filtration, due to the energy dependence of the Coulomb cross section, is a small effect and is not capable of producing significant beams in the distribution or a temperature moment that increases with altitude. The distribution function is mainly determined by the electric field and the expanding geometry and consists of a population with an almost isotropic core which is bound in the electrostatic potential and a beam-like high-energy tail which escapes. The trapped electrons contribute significantly to the even moments of the distribution function but almost nothing to the odd moments; the drift speed and energy flux moments are carried solely by the tail. In order to describe the high-speed solar wind observed near 0.3 AU by the Helios spacecraft, we use a multifluid model where ions are heated preferentially. The resulting test electron distribution at 0.3 AU, in this background, is in very good agreement with the velocity distributions observed by the Helios spacecraft.

A 16‐moment solar wind model: From the chromosphere to 1 AU

We present a solar wind fluid model extending from the chromosphere to Earth. The model is based on the gyrotropic approximation to the 16-moment set of transport equations, in which we solve for the density, drift speed, temperature parallel and perpendicular to the magnetic field, and transport of parallel and perpendicular thermal energy along the magnetic field (heat flux). The solar wind plasma is created dynamically through (photo) ionization in the chromosphere, and the plasma density in the transition region and corona is computed dynamically, dependent on the type of coronal heating applied, rather than being set arbitrarily. The model improves the description of proton energy transport in the transition region, where classical heat conduction is only retrieved in the collision-dominated limit. This model can serve as a “test bed” for any coronal heating mechanism. We consider heating of protons by a turbulent cascade of Alfven waves in rapidly expanding coronal holes. The resulting high coronal proton temperatures lead to a downward proton energy flux from the corona which is much smaller than what classical transport theory predicts, causing a very low coronal density and an extremely fast solar wind with a small mass flux. Only when some of the wave energy is forcibly deposited in the lower transition region can a realistic solar wind be obtained. Because of the poor proton heat transport, in order to produce a realistic solar wind any viable heating mechanism must deposit some energy in the transition region, either directly or via explicit heating of coronal electrons.

A study of solar wind acceleration based on gyrotropic transport equations

The gyrotropic transport equations are used to describe an electron-proton solar wind from the 500,000 K level in the upper transition region and out to 30 solar radii. These equations allow for different temperatures parallel and perpendicular to the magnetic field, as well as transport of parallel and perpendicular thermal energy along the field. We find that in models with significant coronal proton heating, the electron temperature is much lower than the proton temperature. The electron gas is collision dominated, the thermal anisotropy is small, and the heat flux is close to a “classical” heat flux. The proton gas is collision dominated in the upper transition region, but the temperature increases rapidly in the inner corona, and the protons become collisionless close to the Sun. The proton heat flux is proportional to the temperature gradient very close to the Sun, but in the extended corona it deviates substantially from a classical heat flux. In models where the proton heating is in the direction perpendicular to the magnetic field, a large perpendicular temperature is produced locally, but the perpendicular thermal motion couples into parallel thermal motion, and the parallel temperature increases outward from the Sun. We obtain a maximum parallel temperature that is comparable to the maximum perpendicular temperature. This result seems to hold for all models where the energy flux necessary to drive high-speed wind is deposited in the corona as heat. The result is not in agreement with UVCS/SOHO observations of the 1216 A Ly-α line in large coronal holes. These observations are consistent with a much larger random proton motion perpendicular to the magnetic field than parallel to the field. Such anisotropies can be obtained in models of high-speed solar wind if we allow for a significant fraction of the energy flux from the Sun to be in the form of low-frequency, transverse waves. These waves accelerate the solar wind without heating the corona, and they contribute to the line broadening in the direction perpendicular to the magnetic field.

Helmet Streamers Gone Unstable: Two-Fluid Magnetohydrodynamic Models of the Solar Corona

The equations of magnetohydrodynamics (MHD) are used to study heating of electrons and protons in an axially symmetric model of the solar corona, extending from the coronal base to 15 solar radii. To study heating of electrons and protons separately, as well as the collisional coupling between the particle species, we use a two-fluid description of the electron-proton plasma. A steady coronal heat input, uniform base pressure, and dipole field boundary conditions produce a magnetic field configuration similar to that seen with white-light coronagraphs during quiet-Sun conditions: a helmet streamer is formed in the inner corona around the equator, surrounded by coronal holes at higher latitudes. The plasma inside the helmet streamer is in hydrostatic equilibrium, while in the coronal holes a transonic solar wind is accelerated along the field. The collisional coupling between electrons and protons becomes weak close to the coronal base. In the case of proton heating, the thermal structure along open and closed field lines is very different, and there is a large pressure jump across the streamer-coronal hole boundary. When the equations are integrated on a long timescale, the helmet streamer becomes unstable, and massive plasmoids are periodically released into the solar wind. These plasmoids contribute significantly to the total mass and energy flux in the solar wind. The mass of the plasmoids is reduced when electrons are heated.

Constraints on the solar coronal temperature in regions of open magnetic field

It is shown that the simultaneous consideration of observed values of the solar wind proton flux density at 1 AU and of the electron pressure at the base of the solar corona leads to relatively strong constraints on the coronal temperature in the region of subsonic solar wind flow. The extreme upper limit on the mean coronal temperature in the subsonic region is found to be about 2.6 × 106 K, but this upper limit is reduced to about 2.0 × 106 K if reasonable, rather than extreme, assumptions are made; the limit on the maximum temperature is about 0.5 × 106 K greater than the limit on the mean. It is also found that the same two observations limit the rate of momentum addition possible in the region of subsonic solar wind flow.

Solar wind from a corona with a large helium abundance

Observations of quasi-steady high-speed solar wind streams show that the proton mass flux density at 1 AU is remarkably constant, varying by less than 10% over long time periods. These observations are problematic, for simple theoretical models predict that the proton mass flux density is a sensitive function of the coronal base temperature, which is not expected to be unvarying to the degree required by the observations. In this paper we investigate the possibility that the presence of alpha particles in the coronal base region can reduce the sensitivity of the proton mass flux to the base temperature. The equations of mass and momentum conservation are solved for electrons, protons, and alpha particles using a variety of assumed temperature profiles for each species. A wide range of base conditions are considered. We find that for an alpha particle to proton density ratio at the base as small as 10%, alpha particles can reduce the sensitivity of the proton mass flux density to variations in the base temperature. We also study the effects of enhanced collisional coupling and of Alfven waves on the flux of protons and alpha particles. As an aid to future observational determination of the alpha particle density in the corona, we present calculations of the intensities of the resonantly scattered lines He II λ304 and H I λ1216 for selected models.

Solar wind heating beyond 1 AU

The effect of an interplanetary atomic hydrogen gas on solar wind proton, electron and α-particle temperatures beyond 1 AU is considered. It is shown that the proton temperature (and probably also the α-particle temperature) reaches a minimum between 2 AU and 4 AU, depending on values chosen for solar wind and interstellar gas parameters. Heating of the electron gas depends primarily on the thermal coupling of the protons and electrons. For strong coupling (whenTp≳Te), the electron temperature reaches a minimum between 4 AU and 8 AU, but for weak coupling (Coulomb collisions only), the electron temperature continues to decrease throughout the inner solar system. A spacecraft travelling to Jupiter should be able to observe the heating effect of the solar wind-interplanetary hydrogen interaction, and from such observations it may be possible of infer some properties of the interstellar neutral gas.