The Solar Wind at 1 AU

Observational evidence for a continuous stream of plasma filling interplanetary space was deduced from the properties of cometary tails by Biermann (1951). Parker (1958) demonstrated that solutions of the fluid equations describing the solar atmosphere necessitated the existence of a continuous supersonic wind. The first in situ measurements of this wind were made by Gringauz et al. (1960), and Snyder and Neugebauer (1966).

At 1 Astronomical Unit (AU) the solar wind is a tenuous ionised gas that carries with it magnetic fields reaching back into the solar atmosphere. The density of this gas at 1 AU is typically about 5 particles cm~3. In composition it is about 95% protons, 5% He, with a small fraction of heavy ions. (Although we will not discuss the heavy ions further here, they are of profound importance to studies of the solar atmosphere and composition of the Sun.) The embedded magnetic field has a typical value (at 1 AU) of 5 nT. The wind flows at speeds ranging from a couple of hundred km s^1 to 1000 km s-1, or more. The speed of sound in this plasma is about 40 km s^1. In addition, the speed of the most characteristic plasma wave, i.e., Alfven waves (discussed below), is also about 40kms_1 at 1 AU. Consequently, the flow is both supersonic and super-Alfvenic with a plasma ft ~ 1 where ft is the ratio of thermal to magnetic pressure 2^0nkBT /B2 and kB is Boltzmann's constant.

1NASA Goddard Space Flight Center, Greenbelt, MD, USA

2Max-Planck-Institut für extraterrestrische Physik, Garching, Germany

3Space and Atmospheric Physics, The Blackett Laboratory, Imperial College London, London, UK

4 Department of Physics and Astronomy, The University of Iowa, Iowa City, IA, USA

5LPCE/CNRS and Universite d' Orleans, France

Space Science Reviews 118: 7-39, 2005. DOI: 10.1007/s11214-005-3823-4

© Springer 2005

The proton temperature (at 1 AU) is of order 1.2 x 105 K, while the electrons tend to be somewhat hotter (w 1.4 x 105 K).

Matthaeus et al. (1986) showed that magnetic fluctuations in the solar wind obtained from ISEE3 constituted a stationary ensemble. They used the ensemble to determine a variety of average solar wind properties. For example, they found that the ensemble-average correlation length of the magnetic fluctuations was 4. 9 x 109 m and that the ratios of the average value of the variances of the magnetic field components were 8:9:10, where the third component is the local mean field direction. Solar wind speeds for the intervals included in the ensemble ranged from 295 km s—1 to 700 km s—1 with the modal value lying near 360 km s—1 (no attempt was made to separate the data into fast and slow flow regimes).

Although the solar wind flows radially from the Sun, the rotation of the Sun causes the magnetic field line to form an Archimedean (or 'Parker') spiral in space (Parker, 1958). Given the equatorial rotation rate of the Sun (25.4 days), the magnetic field is makes an angle of w 45° to the flow at 1 AU. Because the polarity of solar magnetic fields tends to be of one sign or the other over large polar regions of the Sun, especially during the minimum of solar activity, the interplanetary magnetic field may point sunward or anti-sunward for extended periods of time as measured by single spacecraft. During each solar rotation near solar minimum, 2 or 4 'sector boundaries', where the field orientation rapidly reversed, are observed in the magnetic field time series (Wilcox and Ness, 1965). The three-dimensional structure of this boundary is referred to as the Heliospheric Current Sheet (HCS).

The fairly simple picture described above applies primarily to the minimum activity levels during the 22-year solar activity cycle. That is the time period during which one observes fast solar wind coming from coronal holes at relatively high speed (w 750 km s^1) and from high latitudes. Slow solar wind, which is significantly more variable (300 — 450 km s^1) is observed at low latitudes. The origin of slow solar wind is less clear. It may arise from the boundary between open and closed magnetic field, or the source of slow wind may be plasma leaking from the helmet streamers that arise from plasma transiently leaking from open magnetic field lines not associated with coronal holes (e.g., Axford and McKenzie, 1996). Models of the global structure of the solar wind have become increasingly detailed and sophisticated. Recent models have incorporated physical sources of heat to the corona and thus relax the (unphysical) isothermal assumption that was used in the earliest treatments (see, e.g., Israelevich et al., 2001; Gombosi et al., 2004; Riley et al., 2002; Usmanov et al., 2000; Usmanov and Goldstein, 2003, and references therein).

One of the curiosities of solar wind observations is the apparent success (as implied in the discussion above) of the fluid or magnetofluid equations in describing many of the macroscopic properties of the wind. This despite the fact that the proton-proton collision time is w 4 x 106 sec, which implies that the solar wind is essentially collisionless (the electrons in the core of the distribution function are not as collisionless, but have proton-electron collision times that correspond to a few collisions between the solar corona and 1 AU). Cluster, with its ability to determine three-dimensional structure and with its full complement of wave and particle instruments, is capable of investigating the relationship between kinetic and fluid properties, especially at boundaries of structures whose scale is of order the spacecraft separation. These structures include the bow shock and interplanetary shock waves, the HCS, interplanetary shocks, flux tubes in magnetic clouds and interplanetary coronal mass ejections (ICMEs), magnetic holes, discontinuities, and weak double layers (bipolar and tripolar electrostatic structures). Investigations of these structures has begun and some results are described below. In 2005, when the spacecraft separation is increased to w 10,000 km, the range of phenomena that can be studied with Cluster will expand considerably. In particular, the three-dimensional symmetries of solar wind turbulence in the inertial and dissipation ranges will be amenable to intensive investigation.

For a recent compendium of all aspects of solar wind research, the reader is referred to Velli et al. (2002); a detailed discussion of global solar wind properties can be found in Hundhausen (1995).

1.1.1 Waves and turbulence

One of the most striking features of the solar wind is the presence of large fluctuations in both the magnetic field and plasma velocity. These fluctuations were conjectured by Coleman (1966) to be evidence of magnetofluid turbulence. In making that conjecture, Coleman was primarily motivated by two properties of the wind: The first was that the power spectrum of the magnetic and velocity fluctuations was a power law with an index of approximately —5/3, the value characterising the inertial range of three-dimensional incompressible fluid turbulence (Kolmogorov, 1941). The second was the existence of large velocity shears at the boundaries between fast and slow solar wind, being significant sources of free energy that would stir the medium and generate turbulence.

The correlation between the fluctuating magnetic, 5b, and velocity, 5v, fields suggested that the fluctuations were nearly pure Alfven waves (Belcher and Davis, 1971; Unti and Neugebauer, 1968) propagating outward from the solar corona, defined by the relation 5v = ±5b/^/¡i0p. Here p is the mass density of the plasma, and the + and - signs indicate propagation parallel or anti-parallel to the background magnetic field, respectively. Pure Alfven waves are exact solutions of the incompressible equations of magnetohydrodynamics (MHD). This led to questioning whether or not the solar wind was a dynamically turbulent medium, or merely reflected remnants of coronal processes of no dynamical importance.

The resolution that emerged from analyses of data from the Helios, Voyager, ISEE, and IMP 8 spacecraft, among others, combined with numerical solutions of the MHD equations, was that the fluctuations represented both a source of 'waves' emanating from the solar corona as well as a consequence of turbulent evolution



Figure 1.1. Two examples of turbulence. Left: A one-dimensional spectrum from a tidal channel collected on March 10, 1959. The straight line has a slope of 5/3 (Grant et al., 1962). Right: Solar wind magnetic field fluctuations from Voyager 1 at 1 AU (Matthaeus and Goldstein, 1982a). In the inertial range, the spectral index is almost exactly -5/3. The time resolution of these data was 28.8 s. In general, at 1 AU, the -5/3-spectrum continues almost another decade before steepening as dissipation sets in near 0.1 Hz.

Figure 1.1. Two examples of turbulence. Left: A one-dimensional spectrum from a tidal channel collected on March 10, 1959. The straight line has a slope of 5/3 (Grant et al., 1962). Right: Solar wind magnetic field fluctuations from Voyager 1 at 1 AU (Matthaeus and Goldstein, 1982a). In the inertial range, the spectral index is almost exactly -5/3. The time resolution of these data was 28.8 s. In general, at 1 AU, the -5/3-spectrum continues almost another decade before steepening as dissipation sets in near 0.1 Hz.

driven by the free energy contained in velocity shears that bound fast and slow solar wind (Matthaeus and Goldstein, 1982a; Roberts et al., 1987a,b). For a review, see Tu and Marsch (1995).

Understanding the nature of magnetohydrodynamic turbulence is even more challenging than is the problem of understanding fluid turbulence. On one level there are many similarities between magnetic and velocity fluctuations observed in the solar wind and fluctuations observed in fluids. For example, a classic example of fluid turbulence is the nearly perfect power-law power spectrum of velocity fluctuations obtained from flow in a tidal channel. That spectrum spans more than two-decades in frequency (see Figure 1.1, left panel) with a power law index of -5/3 (Grant et al., 1962). A similar spectrum of magnetic fluctuations derived from Voyager observations of solar wind magnetic field fluctuations also spans more than two decades (Figure 1.1, right panel) and also has a power law index of -5/3 (Matthaeus and Goldstein, 1982a; Tu and Marsch, 1995). However, fluid turbulence is generally isotropic and homogeneous. The presence of the large-scale solar wind magnetic field implies that the solar wind is not isotropic. The Voyager spectra shown above are one-dimensional spectra - the three-dimensional properties of those fluctuations are not well understood and Cluster, at large spacecraft

Figure 1.2. Comparison of observations (heavy lines) determined from 621 days of IMP data with predictions of the ergodic theorem modified to include the effects of solar rotation (for the x- and y-components). From Matthaeus and Goldstein (1982b).

separations, should have the capability to elucidate the nature of the turbulence in an anisotropic magnetofluid.

As a first step in the investigation of solar wind fluctuations as an example of a turbulent magnetofluid, one must justify the use of Fourier transforms and other techniques in the construction of power spectra of solar wind magnetic and velocity fluctuations. For such power spectra to be meaningful, it is necessary that the fluctuations represent a stationary random process. The assumption of stationarity is implicit in theoretical derivations of spatial mean-free-paths for 180° scattering of energetic solar and galactic particles in the solar wind in resonance with the Fourier components of the magnetic field. Energetic protons 'resonate' with wave numbers k\\rci = cos Q, where rci is the Larmor radius of the energetic particles and cos Q = ^ is the pitch-angle. Matthaeus and Goldstein (1982b) analysed two years of magnetic field data and constructed a zero parameter fit to the predictions of the ergodic theorem (Panchev, 1971; Monin and Yaglom, 1975) for stationary random data. When the effects of solar rotation were included, the solar wind was shown to satisfy the conditions of 'weak' stationarity (cf. Figure 1.2).

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