PHYSICS OF THE SPACE ENVIRONMENT

PHYS/EATS 3280

Notes Set 8

Part 2 - From the Sun to the Top of the Atmosphere

The Solar Wind and its Interactions

The Solar Wind

It is well known that comet tails point away from the sun. Biermann's (1951) observation of comet tails led to a prediction that this was caused by the interaction of plasma flow outward from the sun, because he showed that the photon radiation pressure was insufficient to cause this effect. Sidney Chapman carried out hydrostatic equilibrium model calculations of the corona and found solar wind densities that supported Bierman’s hypothesis; but the problem was that his densities at the edge of the solar system were ten million times higher than what was thought to exist in interstellar space. Parker (1958) abandoned the idea of hydrostatic equilibrium and wrote out equations that yielded several possible solutions; his 'Class 2' solution yields an increasing plasma speed with radial distance and this agrees with observations. The term "solar wind'' was subsequently introduced by Parker.

Essentially, the solar wind is the expansion of a gas/plasma driven by some, as yet unidentified, energy source; at about 150 km s-1 it becomes supersonic. With the advent of space vehicles the detailed characteristics of the solar wind have been measured and the hour-by-hour variations are now sufficiently important that it is considered necessary to have spacecraft monitor continually its properties. Typical characteristics of the quiet Sun solar wind are presented in Table 1. Figure 1 shows how the solar wind speeds varied during the period 1962 – 1970 and Figure 2 shows how the speeds and proton densities varied over one solar rotation during 1962.

Figure 1. Solar wind speeds as observed during 1962-1970

Figure 2. Density and speed of the solar wind over one solar rotation in 1962 as measured by Mariner-2.

In Figure 3 the characteristics of the solar wind, monitored for November 1973, are shown. The region of solar wind influence is called the heliosphere - theoretical estimates of its size have steadily increased as the spacecraft Pioneer and Voyager have travelled further and further from the Sun. The observations show that the heliosphere, the Sun's outermost atmosphere, extends to at least 40 AU and perhaps well beyond.

Figure 3. Solar wind values of plasma temperature (upper panel) from 0 to 250,000 K, ion density in cm-3 (middle panel) from 0 to 40 and bulk speed (lower panel) in km/sec, from 0 to 600. Table 1. Characteristics of the Quiet Solar Wind

Characteristic Value Proton density 5 cm-3 Plasma velocity 400 km sec-1 Proton flux 2 x 108 cm-2 sec-1 Energy flux 2 x 10-4 W m-2 Proton temperature 4 x 104 K Electron temperature 105 K Magnetic flux density 5 nT (nanoTesla)

There are various models for the solar wind and how the velocity of the wind, and its particle densities, may vary with distance from the Sun. Before spacecraft started to probe the wind little was known about these parameters. In lectures we discuss one model known as the "gravitational nozzle" model. We find that the acceleration of the wind at any radial distance, r, given by the rate of change of the radial velocity v with distance r, must satisfy the relation:

2 2 2 dv/dr = (v/r)[2cs - GM/r]/[v -cs ] Eq. 1

where cs is the speed of sound in the plasma.

In the absence of any other ancillary information about the wind, or boundary conditions, there are a number of possible scenarios or solutions to Eq. 1 decribing how the solar wind velocity v might vary with distance from the Sun. These are known as Parker's solutions:

Case 'a':

If the solar wind plasma is ejected from the base of the corona (where r is small and GM/r 2 is likely to be greater than 2cs ) at subsonic speeds then dv/dr in Eq. 1 will be positive. The plasma will therefore accelerate outwards. If it is still subsonic when it reaches the 2 distance where GM/r becomes equals to 2cs , i.e., the critical radius given by:

2 r = rc = GM/2cs

then dv/dr switches negative and the plasma will decelerate and eventually come to rest at some larger r. This is known as Parker's Class 1 solution.

Case 'b':

If the solar wind plasma is ejected from the base of the corona at supersonic speeds then dv/dr in Eq. 1 will be negative at the base. The plasma will therefore decelerate as it moves outwards. If it is still supersonic when it reaches the critical radius then dv/dr switches positive and the plasma will then start to accelerate outwards. This is known as Parker's Class 4 solution.

Case 'c':

If in case 'b' the wind becomes subsonic before reaching the critical radius then we would have a singularity and no viable solution !! - unless it just becomes subsonic at the critical radius. Then we have a physically realistic continuous solution and the plasma will jump the singularity and continue to decelerate and eventually come to rest. This is known as Parker's Class 3 solution.

Case 'd':

Finally, if as in case 'a' the plasma started out subsonic but became supersonic before reaching the critical radius then once again we would have a singularity and no viable solution ! - unless it just becomes supersonic at the critical radius. Then, in analogy with case 'c', the plasma can jump the singularity but this time continue to accelerate outwards. This is known as Parker's Class 2 solution.

These various possible cases and their solutions are illustrated in Figure 4. below.

Figure 4. Parker’s solar wind solutions. Note the critical speed on the y-axis means cs.

The current observational evidence now suggests that Parker's original Class 2 solution (case 'd' above) is correct, i.e., the solar wind first accelerates out to the 'critical radius' at subsonic speed then switches to supersonic at the critical radius and then continues to accelerate but at ever decreasing rates. The critical radius is at about 4 Rs.