2. The Earth’s atmosphere is stationary
The Earth’s atmosphere is stationary. The Sun’s atmosphere is not stable but is blown out into space as the solar wind filling the solar system and then some.
The first direct measurements of the solar wind were in the 1960’s but it had already been suggested in the early 1900s.
To explain a correlation between auroras and sunspots Birkeland [1908] suggested continuous particle emission from these spots.
Others suggested that particles were emitted from the Sun only during flares and that otherwise space was empty [Chapman and Ferraro, 1931].
Observations of comet tails lead to the suggestion of a continuous solar wind.
The question of a continuous solar wind was resolved in 1962 when the Mariner 2 spacecraft returned 3 months of continuous solar wind data while traveling to Venus.

3. Bierman, 1951: Cometary tails point directly away from Sun regardless of comet’s velocity => must be ionized gas pushed away by solar ionized gas, the solar wind
To Sun
Solar Wind forms the ion tail. Solar wind must have very high speed relative to comet, to align tail with sun direction.
Radiation pressure on micro-size dust grains forms the diffuse dust tail.
Grains have less sunward force, move further away from Sun, but fall behind the radial direction because their angular speed is lower than closer in. Dust tails curve around (lag from radial direction).
Image of Hale Bopp (Courtesy: John Gleason and NASA)

4. Measured solar wind speeds (heavy lines) and densities (light lines) with Mariner 2 in 1962 [Hundhausen, 1995].

5. The most detailed observations of the solar wind have been made from spacecraft near the Earth.
Observed Properties of the Solar Wind near the Orbit of the Earth (after Hundhausen, [1995])
Proton density
6.6 cm-3
Electron density
7.1 cm-3
He2+ density
0.25 cm-3
Flow speed (nearly radial)
450 km s-1
Proton temperature
1.2x105K
Electron temperature
1.4x105K
Magnetic field
7x10-9T

6. Flux Through a Sphere at 1AU
It is useful to describe the solar wind in terms of quantities that are conserved in the plasma flow.
Flux Through a Sphere at 1AU
(after Hundhausen, [1995])
Protons
8.4x1035 s-1
Mass
1.6x1012 g s-1
Radial momentum
7.3x1014 N (Newton)
Kinetic energy
1.7x1027 erg s-1
Thermal energy
0.05x1027 erg s-1
Magnetic energy
0.025x1027 erg s-1
Radial magnetic flux
1.4x1015 Wb (Weber)

8. The solar wind exists because the Sun maintains a 2x106K corona as its outer most atmosphere.
The Sun’s atmosphere “boils off” into space and is accelerated to high velocities (> 400 km s-1).
Parker [1958] proposed that the solar wind was the result of the high temperature corona and developed a hydrodynamic model to support his idea. Based on this Dessler developed a simple gravitational nozzle which demonstrates the basic physics.
Simplifying assumptions:
The solar wind can be treated as an ideal gas.
The solar wind flows radially from the Sun.
Acceleration due to electromagnetic fields is negligible.
The solution is time stationary (i.e. the time scale for solar wind changes is long compared to the time scale for solar wind generation).

10. Assume hydrostatic equilibrium:
- no flow (u=0)
- no forces (true for radial fields)

11. Not possible !

12. Solar Wind Acceleration 4
Conservation of mass -
Conservation of momentum -
Speed of sound -
Combining (1), (2), (3) gives
If and then

13. In order for a real continuous solution to exist at rc
The transition from subsonic to supersonic occurs at a critical radius rc where
In order for a real continuous solution to exist at rc
The form of solutions for the expansion of the solar wind
Solution A is the “observed” solar wind. It starts as a subsonic flow in the lower corona and accelerates with increasing radius. At the critical point the solar wind becomes supersonic.
For solution F the speed increases only weakly with height and the critical velocity is not reached. For this case the solar wind is a “solar breeze”.
For solution C the flow accelerates too fast, becomes supersonic before reaching the critical radius and turns around and flows into the Sun.

14. Solution B starts as a supersonic flow in the lower corona and becomes subsonic at the critical point.
If the flow decelerates less as in D it would still be supersonic at the critical point and be accelerated again.
Solution E is an inward blowing wind that is subsonic. The flow accelerates as it approaches the Sun, turns back and leaves the Sun supersonically.
Quantitative solutions (after Parker [1958])

15. For the solar wind to continue to accelerate then the mean thermal energy must exceed the gravitational energy.
To have a solar wind a star must have a cool lower atmosphere and a hot outer atmosphere.
Following derivation in Ch.3 but using  =5/3 you can show that there is no solution that reaches supersonic speed, i.e., the solar wind does not accelerate unless there is heating. Actually only for  <=3/2 can reach supersonic speeds.
The solar wind heating is provided by electrons:
At 10^6 degrees, electrons have thermal speeds >1000km/s
At 10^6 degrees, ions have thermal speeds < 100km/s
Electrons move along field lines fast, create an electric field, pull ions
Heating of the base in the solar corona provides energy for acceleration
Using equation of energy conservation you can prove that
The initial energy in the enthalpy minus potential energy in the solar gravity
Final energy is in the kinetic energy of solar wind
Energy transformation depletes enthalpy and increases solar wind speed to supersonic speeds.

16. Impulsive energy release?
Waves and turbulence?
One possibility is that the corona is heated by compressional waves at or just below the surface. Oscillatory motion of the Sun’s surface could drive pressure waves. In theory fast mode waves could propagate up to 20RSun. Experiments designed to detect sound waves propagating into the corona have not detected them.
Impulsive energy release?
The Sun has a magnetic field that contains magnetic energy. Magnetic energy can be converted into thermal energy. This is done by reconnection. The granularity of the photosphere as the top of the convection zone is caused by bubbles rising and falling. These might reconnect. X-ray bursts may be evidence of this happening.
We still don’t know how the corona is heated!

17. Motion of granules and magnetic structures – Hinode observations

18. As the feet of the field lines move they are twisted and since they can’t cross current sheets develop. Reconnection across these current sheets is thought to heat the corona.

19. In summary the outer layer of the solar atmosphere will accelerate outward provided a suitable heating source adds enough energy to overcome the Sun’s gravitational energy.
There is a limit to how hot the atmosphere can be and still produce a supersonic solar wind!
For an ideal gas and where m is the mass of the gas particles, =1 for isothermal plasma.
Using this the equation for the solar wind expansion becomes
For very hot stars the numerator is always positive and the denominator is initially negative so that as the atmosphere expands the velocity decreases and never becomes supersonic.
For cool stars both numerator and denominator start negative and flow accelerates outward. At some time v approaches the sonic velocity. Past this point the acceleration will only continue if the thermal energy exceeds the gravitational energy.

20. Intermixed with the outflowing solar wind is a weak magnetic field – the interplanetary magnetic field (IMF).
On the average the IMF is in the ecliptic plane at the orbit of the Earth although at times it can have substantial components perpendicular to the ecliptic.
The hot coronal plasma has extremely high electrical conductivity and the IMF becomes “frozen in” to the flow.
If the Sun did not rotate the resulting magnetic configuration would be very simple: magnetic field lines stretching radially from the Sun.
As the Sun rotates (sidereal period 27 days) the base of the field line frozen into the plasma rotates westward creating an Archimedean spiral.

21. Assume a plasma parcel on the Sun at a source longitude of and a source radius of r0.
At time t the parcel will be found at the position and
Eliminating the time gives
In order to determine the radial falloff of the magnetic field and the shape of the field lines, we can use flux conservation and the frozen in condition either in a rotating frame (book) or a fixed frame

22. Let us express the magnetic field in the equatorial plane in polar coordinates as
Gauss’s Law in spherical coordinates is since the field depends only on r so that
The magnetic flux through radial shells is conserved and the radial component of the field decreases as
The frozen-in field condition gives
or If we assume that is radial at r0 we get

23. At large distances and
The radial component falls off as r-2 while the azimuthal component falls off as r-1.
The angle between the magnetic field direction and the radius vector from the Sun is For typical solar wind parameters at the Earth it is about 450 with respect to the radial direction.
The stretched out heliospheric configuration is maintained by an equatorial current sheet. The magnetic field lines and current lines are sketched below.

24. At the edges of the heliosphere the radial field drops off as r2 and the azimuthal component as r, both approach zero as r -> 
The mach number u/cs goes to infinity either because the flow increases or because the temperature decreases
The only way to stop the supersonic wind is for a shock to form at the interface with the interstellar medium.
At the “termination” shock the dynamic pressure of the flow balances the interstellar gas pressure.

25. The solar wind forms a bubble, called the heliosphere, in the partially ionized local interstellar medium (LISM).
We do not know if the LISM is subsonic – the LISM flow will be diverted around the heliospheric obstacle either adiabatically or by forming a bow shock.
The boundary separating the heliosphere from the LISM is the heliopause (HP).
The solar wind is supersonic and a shock (the termination shock-TS) forms within the heliosphere as it approaches the heliopause.
The region of shocked plasma between the TS and the heliopause is called the inner heliosheath.
In the simulation below the LISM flow was assumed to be supersonic and no interstellar neutral hydrogen was assumed.
Contours of temperature and flow streamlines- from Zank et al., 2001

26. Observations from Voyager 1 as it crossed the termination shock.
(left) Energetic particle measurements show increase in particle fluxes at shock (A, B, D) and change in first order anisotropies (C) and radial velocity (F). (Decker et al., 2005)
(right) The magnetic field magnitude increased (A) and the galactic cosmic ray intensity increased. (Burlaga et al., 2005)

27. The Voyager passage through the termination shock
Voyager moving at a speed of 3.6 AU/year was 94AU from the Sun when it encountered the shock.
The shock was moving toward the Sun possibly because decreasing solar wind dynamic pressure.
As of December, 2005 Voyager 1 was still in the heliosheath.

28. The IMF can be directed either inward or outward with respect to the Sun.
One of the most remarkable observations from early space exploration was that the magnetic field polarity was uniform over large angular regions and then abruptly changed polarity.
This polarity pattern repeated over succeeding solar rotations. The regions of one polarity are called magnetic sectors.
In a stationary frame of reference the sectors rotate with the Sun.
Typically there are about four sectors.
The sector structure gets very complicated during solar maximum.

29. The sector structure inferred from IMP satellite observations
The sector structure inferred from IMP satellite observations. Plus signs are away from the Sun and minus signs are toward the Sun.

30. A meridian view of the IMF
The rotation and dipole axes are along the left edge of the figure and the solar equator is horizontal
The dipole component of the solar magnetic field (dashed lines) is distorted by the solar wind flow
The expected IMF is shown by solid lines.
Beyond a distance of about 2 solar radii the solar wind is stronger than the tension in the field lines and the field lines are pulled outward
The IMF that reaches the Earth has its foot-points rooted at middle latitudes
The antiparallel field lines in the equatorial plane require a current sheet between them.

31. That the IMF has sector structure suggests that plasma in a given sector comes from a region on the Sun with similar magnetic polarity.
The sector boundaries are an extension of the “neutral line” associated with the heliospheric current sheet (HCS).
The dipolar nature of the solar magnetic field adds latitudinal structure to the IMF.
The radial magnetic field has one sign north of the HCS and one sign south of the HCS.
The current sheet is inclined by about 70 to the rotational equator.
As the Sun rotates the equator moves up and down with respect to the solar equator so that the Earth crosses the equator twice a rotation. [From Kallenrode, 1998].

32. As the Sun rotates the three dimensional current sheet becomes wavy
As the Sun rotates the three dimensional current sheet becomes wavy. This is sometimes called the Ballerina skirt model of the heliosphere.

33. The solar wind speed and density have large variations on time scales of days. Of special interest are high speed streams.
The flow speed varies from pre-stream levels (400 km/s) reaching a maximum value (600 km/s – 700 km/s) in about one day.
The density rises to high values (>50 cm-3) near the leading edges of the streams and these high densities generally persist for about a day. The peaks are followed by low densities lasting several days.
The proton temperature varies like the flow speed.
The high speed streams tend to have a dominant magnetic polarity.
The dominant source of high speed streams is thought to be field lines that are open to interplanetary space. These regions are known as coronal holes.

34. Observations of high speed streams
Velocity, density and proton temperature of two high speed streams
Speed and temperature have similar variations with time
Note that low speed corresponds to high density and vice versa
750
Flow Speed (km/s)
250
100
Density (cm-3) 10 1
Temp. (K)
105
104

35. The shock pair propagate away from the interface.
The Archimedean spiral associated with slow streams is curved more strongly than for a fast stream.
Because field lines are not allowed to intersect at some point an interaction region develops between fast and slow streams. Since both rotate with the Sun these are called corotating interaction regions (CIR).
On the Sun there is an abrupt change in the solar wind speeds but in space the streams are spread out.
At the interface between fast and slow streams the plasma is compressed.
The characteristic propagation speeds (the Alfven speed and the sound speed) decrease.
At some distance between 2AU and 3AU the density gradient on both sides of the CIR becomes large and a pair of shocks develop.
The shock pair propagate away from the interface.
The shock propagating into the slow speed stream is called a forward shock.
The shock propagating into the fast wind is called a reverse shock.

36. Time series of parameters associated with a CIR
Between the two shock waves, and centered on the interface, the plasma is compressed
This implies a higher density of S’ plasma than unshocked S plasma
Similarly the shocked F’ plasma is higher density than unshocked F plasma, but the density of F’ < density S’ since fast plasma has lower density than slow plasma
The S’ plasma is moving faster than S, but slower than F’ which is slower still than F
The S’ plasma has a positive azimuthal velocity, the interface a zero azimuthal velocity, and the F’ a negative azimuthal velocity
The magnitude of the magnetic field is compressed between the shocks
There is increased magnetic turbulence and temperature in the interaction region
Not shown is a tipping of the IMF out of the ecliptic plane

37. Changes in the solar wind plasma parameters (speed V, density N, proton and electron temperatures TP and TE, magnetic-field intensity B, and plasma pressure P) during the passage of an interplanetary shock pair past the ISEE 3 spacecraft. [Hundhausen, 1995].

38. No latitudinal gradient in Br.
Until the 1990’s our knowledge of the heliosphere was limited to the ecliptic.
The Ulysses spacecraft observed the flow over both the northern and southern poles of the Sun.
No latitudinal gradient in Br.
Magnetic flux is removed from the poles toward the equatorial regions.
Sketch showing equatorial current sheet and magnetic field lines coming from the polar regions toward the equator. [Smith et al., 1978]

39. Plasma measurements show a dramatic change in velocity with latitude in observations taken between 1992 and [McComas et al., 1998].
The velocity increases from about 450 km/s at the equator to about 750 km/s above the poles.
Above 500 only fast solar winds streaming out of coronal holes were observed.
Up to about 300 a recurrent CIR was observed with a period of about 26 days.

40. The heliospheric current sheet shows marked variation during the solar cycle.
The “waviness” of the current sheet increases at solar maximum.
The current sheet is rather flat during solar minimum but extends to high latitudes during solar maximum.
During solar minimum CIRs are confined to the equatorial region but cover a wide range of latitudes during solar maximum.
The average velocity of the solar wind is greater during solar minimum because high-speed streams are observed more frequently and for longer times

41. A coronal mass ejection in space
A time sequence of differences between four images taken with the Solar Maximum Mission coronagraph during a coronal mass ejection on 14 April 1980 and a single "pre-event" image.
Positive differences (brightenings of the corona since the pre-event image) are shown in red and orange, negative differences in blue.
A pair of bright (red) loops moved outward through the corona between 0544 and 0709 UT, leaving a wedge of depleted (blue) corona behind them (as at 0847 UT).
Coronal features to the sides of the loops were progressively pushed away from the ejection during its passage through the coronagraph field of view, and are thus visible on these difference images

42. Observations of a CME in space
CMEs are often referred to as magnetic clouds, bottles, or flux ropes. At 1 AU they take about a day to pass the Earth.
The axis of these may have any orientation. The simplest rope lies in the ecliptic plane orthogonal to the Earth-Sun line
Their identifying characteristic is a region of nearly constant magnetic field strength with slow sinusoidal changes in the two field angles. N is generally low.
If the cloud is traveling fast relative to the solar wind a shock will form ahead of the cloud. The shock is evident from the increase in B, N, T (VT), and V. These are called Interplanetary Shocks (IPS).
In the sheath between the shock and cloud the field and density are compressed and turbulent.

43. The magnetic field configuration of a magnetic cloud can be inferred from the variation in the elevation.
At the beginning of the event the field is perpendicular to the ecliptic plane.
After the cloud has passed the field has almost reversed direction.
This is an indication of a magnetic field wrapped around the structure – sometimes called a flux rope.
Note the increasing helicity of the field from the inside out.
The orientation of the magnetic cloud (i.e. whether is it north then south or vice versa depends on the field at the source).

44. In some CMEs there are both forward and reverse shocks.
The forward shock forms in the slow solar wind speeding it up relative to the Earth, but slowing the flow as seen by the CME.
The reverse shock propagates into the magnetic cloud slowing it down relative to the Earth.
The cloud may be rotated an any angle about the Earth-Sun line.
How long the cloud stays connected to the Sun is not known.
Magnetic clouds are the main cause of geomagnetic disturbances called magnetic storms at Earth.