1. Reinisch_85.511_ch_61 Acknowledgement A number of slides are courtesy of Jeff Forbes

2. Reinisch_85.511_ch_62 The solar wind is the extension of the solar corona to very large heliocentric distances. The solar wind is ionized gas emitted from the Sun flowing radially outward through the solar system and into interstellar space. The Solar Wind

3. Reinisch_85.511_ch_63 Electron density 7.1 cm -3 Proton density6.6 cm -3 He 2+ density0.25 cm -3 Flow speed 425 kms -1 Magnetic field 6.0 nTProton temperature 1.2 x10 5 K Electron temperature1.4 x10 5 K Observed Properties of the Solar Wind at 1 AU The pressure in an ionized gas with equal proton and electron densities is P gas = nk B (T p + T e ) where k B is the Boltzmann constant and T p and T e are proton and electron temperatures. Thus, P gas = 25 pico pascals (pPa) Similarly, a number of other solar wind properties can be derived (see following table) Derived Properties of the Solar Wind

4. Reinisch_85.511_ch_64 Solar wind properties are often expressed in terms of flux densities at 1 AU; by multiplying by the area of a sphere at 1 AU (2.82 x 10 27 cm 2 ), these can be converted to total fluxes: Solar wind flux densities and fluxes at 1 AU Flux through sphereFlux density at 1 AU Protons3.0 x 10 8 cm -2 s -1 8.4 x 10 35 s -1 Mass5.8 x 10 -16 gcm -2 s -1 1.6 x 10 12 g s -1 Radial Momentum Flux* 2.6 x 10 -9 Pa7.3 x 10 14 N Kinetic Energy0.6 erg cm -2 s -1 1.7 x 10 27 erg s -1 (1 erg/s = 10 -7 W) Thermal Energy0.02 erg cm -2 s -1 0.05 x 10 27 erg s -1 _____________ *sometimes called dynamic pressure, because of its role in confining the magnetospheric magnetic field

5. Reinisch_85.511_ch_65 The Solar Wind is Highly Variable – V[m/s] Historical Note: The solar wind was first sporadically detected by the Soviet space probes Lunik 2 and 3. Recent observations fast streams shock

6. Reinisch_85.511_ch_66 Solar Wind Statistics “fast” “slow”

7. Reinisch_85.511_ch_67 The Solar Wind The solar wind exists due to the huge pressure difference between the hot plasma at the base of the corona and the interstellar medium. This pressure difference drives the plasma outward despite the restraining influence of solar gravity. Historical Note: The existence of a continuous solar wind was first suggested by Lugwig Biermann based on his studies of the acceleration of plasma structures in comet tails.

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9. 9 How Does the Solar Wind Escape the Sun’s Gravity ? We will now quantify the basic ideas behind coronal heating and the solar wind through a simplified analytic model. More sophisticated treatments retain the fundamental ideas below. First, we will invoke several simplyfying assumptions: The solar wind is an ideal isothermal gas; The solar wind flows radially away from the sun; Magnetic field effects are neglected; Steady-state solution Let us now outline the basic equations.

10. Reinisch_85.511_ch_610 Ch 6 The Solar Wind

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12. Reinisch_85.511_ch_612 6.1.2 Heat conduction in the solar corona

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14. Reinisch_85.511_ch_614 How does the corona acquire the necessary energy for the mean thermal energy of the coronal gas to increase outward from the sun and overcome the sun's gravity ? A source of coronal heating is required. Four possibilities have been suggested: Acoustic wave dissipation Alfven wave dissipation MHD wave dissipation Microflares - “magnetic carpet” The currently favored mechanism, evolved from multi-instrument observations from SOHO, is that “short-circuit” electric currents flowing in the loops of the “magnetic carpet”, and extending into the corona, provide the energy necessary to raise the coronal temperatures to millions of degrees K. Microflares are thought to accompany these intense currents.

15. Reinisch_85.511_ch_615 Small magnetic loops permeate the surface of the Sun, much like a magnetic carpet Each loop carries as much energy as a large hydroelectric plant (i.e., Hoover Dam) generates in about a million years ! More sensitive instruments are needed to actually observe the microflares thought to exist. Energy flows from the loops when they interact, producing electrical and magnetic “short-circuits”. The very strong currents in these short circuits are what heats the corona to high temperatures.

16. Reinisch_85.511_ch_616 WHAT ABOUT THE EFFECTS OF THE SOLAR MAGNETIC FIELD ? To understand the importance of a magnetic field to the behavior of a plasma, it is convenient to define a "magnetic pressure” P mag = where B is the magnetic field strength and is the magnetic permeability. Another way of thinking of the magnetic pressure is as the energy density stored at any point where the magnetic field strength is B. A relevant comparison then is between the plasma gas pressure P and P mag. This ratio is defined as "beta”

17. Reinisch_85.511_ch_617 Return to Cravens: 4.5.1 Magnetic pressure

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19. Reinisch_85.511_ch_619 A "high beta plasma" (  >> 1) is one which is controlled principally by the plasma gas dynamics. A "low beta plasma" (  << 1) is one which is dominated by the intrinsic magnetic field. IN THE CORONA If the magnetic field is small, we would expect the expanding corona to drag the magnetic field with it --- this is called a "frozen- in" magnetic field, characteristic of a high-beta plasma. If the magnetic field is large, we expect the magnetic field to "contain" the plasma, or at least to inhibit its expansion. For the real corona, where the magnetic pressure is a few times the gas pressure, a mixture of these extreme behaviors is expected.

20. Reinisch_85.511_ch_620 Magnetic-field lines deduced from the isothermal MHD coronal expansion model of Pneuman and Kopp (1971) for a dipole field at the base of the corona. The dashed lines are field lines for the pure dipole field. MHD modeling shows that the inner magnetic field lines (R < 2) near the equator are closed, and that at higher latitudes the field lines are drawn outward and do not close. These field lines that do not close nearly meet at low latitudes, but do not reconnect; this abrupt change in the magnetic field polarity is maintained by a thin region of high current density called the interplanetary current sheet. This current sheet separates the plasma flows and fields that originate from opposite ends of the dipole-like field.

21. Reinisch_85.511_ch_621 Coronal Holes and Solar Wind Speed and Density The interplay between the inward pointing gravity and outward pointing pressure gradient force results in a rapid outward expansion of the coronal plasma along the open magnetic field lines. At low latitudes the direction of the coronal magnetic field is far from radial. Therefore the plasma cannot leave the vicinity of the Sun along magnetic field lines. At the base of low-latitude coronal holes, however, the magnetic field direction is not far from radial, and the expansion of the hot plasma can take place along open magnetic field lines without much resistance  fast solar wind.

22. Reinisch_85.511_ch_622 THE INTERPLANETARY MEDIUM AND IMF Intermixed with the streaming solar wind is a weak magnetic field, the IMF. The solar wind is a “high-  ” plasma, so the IMF is "frozen in”; the IMF goes where the plasma goes. Consequently, the "spiral" pattern formed by particles spewing from a rotating sun is also manifested in the IMF. The field winds up because of the rotation of the sun. Fields in a low speed wind will be more wound up than those in high speed wind.

23. Reinisch_85.511_ch_623 Loci of a succession of fluid particles emitted at constant speed from a source fixed on the rotating Sun. Loci of a succession of fluid parcels (eight of them in this sketch) emitted at a constant speed from a source fixed on the rotating Sun.

24. Reinisch_85.511_ch_624 Plasma leaves the sun predominantly at high latitudes and flows out and towards the the equator where a current sheet is formed corresponding to the change in magnetic field polarity. The Sun’s magnetic field is dragged out by the high-beta solar wind. The current sheet prevents the oppositely-directed fields from reconnecting. The current sheet is tilted with respect to the ecliptic (about 7°), ensuring that earth will intersect the current sheet at least twice during each solar rotation. This gives the appearance of "magnetic sectors". 2 3 1 j 1976 (max 1979) 1986 1998 (max 2001) 2008

25. Reinisch_85.511_ch_625 At Earth, the IMF can be directed either inward or outward with respect to the Sun, forming a pattern of “magnetic sectors” that appear to rotate with the Sun.

26. Reinisch_85.511_ch_626 Wavy Structure of the Interplanetary Current Sheet Where Earth’s orbit intersects this current sheet determines whether Earth “sees” a positive or negative magnetic sector.

27. Reinisch_85.511_ch_627 Acceleration of High-Energy Particles: Near the Sun & in Interplanetary Shocks The measured spectra of energetic particles near Earth indicate 2 spectral regimes. The time history indicates the high-energy component was accelerated near the Sun, and the low-energy component in interplanetary space, probably in association with shocks.

28. Reinisch_85.511_ch_628 Two Classes of Solar Particle Events

29. Reinisch_85.511_ch_629 WHAT IS MEANT BY SUPERSONIC ? Let us now examine more quantitatively the behavior of a charged particle in a constant, uniform B-field. This will allow us to comment on the notion previously introduced of a "supersonic" solar wind. Particle Motion in a Magnetic Field The force on a charged particle in a magnetic field is called the Lorenz force q = charge intensity = charged particle velocity = magnetic field strength

30. Reinisch_85.511_ch_630 In a plane to, the force on a particle is always to, similar to a ball on a string; the particle executes a circular motion where the centrifugal force is balanced by : For circular motion: Therefore

31. Reinisch_85.511_ch_631 And we may now define the "gyroradius" or "cyclotron radius": Since, the "gyrofrequency" or "cyclotron frequency" may be defined: The above results assume that the B-field is uniform, and that there are no external forces applied (i.e., an electric field).

32. Reinisch_85.511_ch_632 The Notion of "Supersonic" The transmission of sound as we know it depends on collisions, the average distance between collisions and the average frequency of collisions being important parameters. For an ideal (thermalized) gas, the speed of sound is given by: average kinetic speed of particles collisionmean frequencyfree path

33. Reinisch_85.511_ch_633 Now, the mean free path calculated for the solar wind near the earth is nearly 1 AU (!), implying an essentially collisionless fluid. How can the idea of a "supersonic" solar wind be at all credible under these circumstances ? The mean free path is the "interaction distance" for individual particles, i.e., the average distance a particle moves before changing direction. For particles in a magnetic field, the "effective interaction distance" is the gyroradius, and the "effective collision frequency" is the gyrofrequency. In a plasma, a charged particle can make its presence felt with out colliding with another charged particle.

34. Reinisch_85.511_ch_634 By analogy with the ideal thermalized gas, we can calculate an ”interaction speed" as follows: Therefore the effective mach number is So, in the above crude sense the solar wind can be described as "supersonic".

35. Reinisch_85.511_ch_635 An alternative analogy is found by asking what is the physical mechanism in plasmas that "transmits information" in a manner similar to sound waves in a gas with collisions? We all know that waves can travel on a string, and that a standing wave pattern is set up when you pluck the string. Think of beads on a string. If some mechanism makes the string shake, then all the beads are affected even though they do not actually collide with each other. From classical physics, the velocity with which waves travel along the string is Where T = tension and  is the mass per unit length. Charged particles similarly gyrate around a magnetic field line, like “beads on a string.”

36. Reinisch_85.511_ch_636 Alfven waves are solutions to the hydromagnetic equations, and are analagous to the classical physics waves traveling along a string in the sense that waves replace collisions as a means of transmitting information Alven waves have a velocity = magnetic field tension  = mass density of particles Alfven waves are "magnetic" waves traveling along the field lines, and represent the limiting speed at which information can be carried in a collisionless plasma. Near earth, so the solar wind is "superalfvenic".

37. Reinisch_85.511_ch_637 The Heliosphere and its Interaction with the Interstellar Medium Interstellar Medium Heliospheric Bow Shock ? Heliopause Heliosphere Termination Shock The heliosphere and heliopause represent the region of space influenced by the Sun and its expanding corona, and in some respects encompass the true extent of the solar system.

38. Reinisch_85.511_ch_638 The radially-expanding supersonic solar wind must be somehow diverted to the downstream direction to merge with the flow of the interstellar medium. This diversion can only take place in subsonic flow, and therefore the supersonic expansion of the solar wind must be terminated by an “inner shock” or “termination shock”. Flow lines of the interstellar plasma do not penetrate into the region dominated by the solar wind flow but flow around a “contact surface” called the heliopause, which is considered to be the outer boundary of the heliosphere. The interstellar medium (ISM) will form a heliospheric bow shock if it is supersonic with respect to the heliopause 26 km/sec

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