1. Aerospace Environment -- ASEN53351 Aerospace Environment ASEN-5335 Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) Contact info: e-mail: lix@lasp.colorado.edu (preferred)lix@lasp.colorado.edu phone: 2-3514, or 5-0523, fax: 2-6444, website: http://lasp.colorado.edu/~lix Instructor’s hours: 9:00-11:00 pm Wed at ECOT 534; Tue & Thu, after class. TA’s office hours: 3:15-5:15 pm Wed at ECAE 166 Read Chapter 1 & 3, class notes, and handout 2 nd quiz, today, close book HW2 due 2/13

2. Aerospace Environment -- ASEN53352 The Bastille-day flare was an ‘X-class’ and accompanied by one of the largest solar energetic proton events ever recorded c3714 Classification X-Ray Flux (ergs/cm 2 -sec) C10 -3 M10 -2 X10 -1

3. Aerospace Environment -- ASEN53353 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

4. Aerospace Environment -- ASEN53354 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 (1951) based on his studies of the acceleration of plasma structures in comet tails.

5. Aerospace Environment -- ASEN53355

6. 6 The Solar Wind is Highly Variable - V Historical Note: The solar wind was first sporadically detected by the Soviet space probes Lunik 2 and 3 (1960) Recent observations fast streams shock

7. Aerospace Environment -- ASEN53357 The Solar Wind is Highly Variable - n Recent observations Historical Note: The first continuous solar wind observations were made by Mariner 2 on its 1962 voyage to Venus. Nearly 3 months of data unequivocally confirmed the existence of the solar wind.

8. Aerospace Environment -- ASEN53358 Solar Wind Statistics “fast” “slow”

9. Aerospace Environment -- ASEN53359 Aerospace Environment ASEN-5335 Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) Contact info: e-mail: lix@lasp.colorado.edu (preferred)lix@lasp.colorado.edu phone: 2-3514, or 5-0523, fax: 2-6444, website: http://lasp.colorado.edu/~lix Instructor’s hours: 2:15-2:55 pm TA’s office hours: 9:00-11:00 am and 3:15-5:15 pm Wed at ECAE 166 Read Chapter 1 & 3, class notes, and handout HW2 due 2/13, Thursday

10. Aerospace Environment -- ASEN533510 The wavelengths most significant for the space environment are X-rays, EUV and radio waves. Although these wavelengths contribute only about 1% of the total energy radiated, energy at these wavelengths is most variable

11. Aerospace Environment -- ASEN533511 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 (T p + T e ) where k is the Boltzmann constant, 1.3807x10 -23 JK -1, and T p and T e are proton and electron temperatures. Thus, P gas = 2.5 x 10 -10 dyn cm -2 = 25 pico pascals (pPa) Similarly, a number of other solar wind properties can be derived (see following table) Derived Properties of the Solar Wind

12. Aerospace Environment -- ASEN533512 Solar Panel Instrument BenchInstrument

13. Aerospace Environment -- ASEN533513 DERIVED SOLAR WIND PROPERTIES AT 1 AU Gas Pressure30 pPa Dynamic Pressure P d =  u 2 = 2 nPa Magnetic pressure P B = B 2 /8  = 14 pPa Acoustic speed Cs = [  p/  ] 1/2 = [(c p /c v )p/  ] 1/2 = 60 km s -1 c p /c v = 5/3 for ideal gas Alfven speed V A =B/(4   ) 1/2 50 km s -1 Proton gyrating speed 45 km/s Proton gyroradius80 km Proton-Proton collision time4 x 10 6 s Electron-Electron collision time3 x 10 5 s time for wind to travel to 1 AU3.5 x 10 5 s (4 days)

14. Aerospace Environment -- ASEN533514 Supersonic Solar Wind: How to Understand it ?  For a high density gas, the mean free path is a critically important parameter. It determines how fast information can travel through gas by kinetic processes and this limiting speed is call the sonic speed.  Any process exceeding this limit is no longer continuous and at the sonic/supersonic boundary there is a jump in gas characteristics-such as density, temperature, etc.-across the boundary.  However, the mean free path for the solar wind near the Earth is about 1 AU, so how can the fluid methodology apply?  In the early 1960s, aerodynamic models were applied to the magnetosphere and reasonably reproduced the shape of the Earth’s bow shock for an upstream mach number of 8 or more.  The mean free path is just the interaction distance for individual fluid particles; the distance the particle can move before it changes direction.  The individual charged particles in solar wind are limited in range, not by collisions, but by the gyroradius, which acts as an effective interaction length.  In a plasma, a charged particle can make its presence felt without colliding with another charged particle.

15. Aerospace Environment -- ASEN533515 Alfven waves  One effective way of exchanging information between particles in the plasma is via Alfven waves.  We all know that waves can travel on a 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.  Charged particles gyrate around a magnetic field line, “beads on a string.” The gyroradius r c =mv  /qB. So r c is proportional to m and v  and inversely proportional to q and B  From classic physics the velocity of the wave depends on the tension of the string and the inverse mass density. V T =(T/  ) 1/2, where the T is the tension and  is the mass density per unit length.  The magnetic field tension is given by B 2 /  0 (Chapter 1) so that velocity of waves traveling along a uniform B field should be of the form V A =(B 2 /  0  ) 1/2 [in MKS. In Gaussian: V A =(B 2 /4   ) 1/2 ]  The Alfven velocity is the limit at which information can be carried in collisionless plasma.  For normal solar wind at 1 AU: V/ V A ~10

16. Aerospace Environment -- ASEN533516 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

17. Aerospace Environment -- ASEN533517 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

18. Aerospace Environment -- ASEN533518 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). Later we will consider deviations from these assumptions.

19. Aerospace Environment -- ASEN533519 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

20. Aerospace Environment -- ASEN533520 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. ( s -1 = rad s -1 /rad ) In a plasma, a charged particle can make its presence felt with out colliding with another charged particle.

21. Aerospace Environment -- ASEN533521 By analogy with the ideal thermalized gas, we can calculate an ”interaction speed" as follows: Therefore the effective mach number is (see HMWK # 3) So, in the above crude sense the solar wind can be described as "supersonic".

22. Aerospace Environment -- ASEN533522 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.”

23. Aerospace Environment -- ASEN533523 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".

24. Aerospace Environment -- ASEN533524 How to Describe Solar Wind: Fluid and MHD Theory  In its most general form the Boltzmann equation is a seven-dimensional nonlinear integra-differential equation. The solutions of the Boltzmann equation provides a full description of the phase-space distribution function at all times.  In most cases, however, it is next to impossible to solve the full Boltzman equation and one has to resort to various approximate methods to describe the spatial and temporal evolution of macroscopic quantities of the environment  Transport equations for macroscopic averages are obtained by taking velocity moments of the Boltzmann equation.  The macroscopic transport equations for the whole gas as a single conducting fluid together with Maxwell’s equations constitute the equations of magnethydrodynamics (MHD).  These equations together form a complete set of partial differential equations which fully determine the fluid and field quantities.  In practice, usually a simplified set of MHD equations is used. These equations are obtained with the following simplifying assumptions:

25. Aerospace Environment -- ASEN533525 Ideal MHD  The gas components are not far from local thermodynamic equilibrium. Therefore, the scalar pressure can be used (instead of the full pressure tensor).  Heat flow is neglected in the fluid.  Charge quasi- neutrality is assumed.  The high-frequency component of the electric field is neglected (this means that the time derivative in Ampere’s law is neglected.

26. Aerospace Environment -- ASEN533526 Further Simplified Ideal MHD Equations  By eliminating the electric field and the electric current density, and assuming the plasma is perfectly conducting (  0  infinity), the previous equations reduced to:

27. Aerospace Environment -- ASEN533527 Description of the Solar Corona  The simplest theoretical description of the solar corona is based on the assumption of a spherically symmetric, steady-state hydrostatic corona. Ideal MHD equations can be applied. Further, the effects of magnetic field are neglected. Under these approximation, the governing equation become the following:  4  r 2  u=constant In a planetary atmosphere, the variation in gravitational force is usually negligible over the depth of the atmosphere, and we can write -dp/dr -  g=0

28. Aerospace Environment -- ASEN533528 Early simple models of the solar corona  In the early simple models of the solar corona an isothermal corona was assumed. In this case the pressure can be expressed as In a planetary atmosphere, p=nkT and  =nm, we have dp/dr=-p/H, H=kT/mg (scale hight), p=p 0 exp(-z/H), z=r-r 0 where r 0 is the planetary radius.

29. Aerospace Environment -- ASEN533529 Hydrostatic Equilibrium– not working  It is easy to confirm that for a ~10 6 K coronal temperature p infi /p corona ~3x10 -4. However, the pressure at the base of corona is a few tenths of a Pascal, whereas the estimated pressure of the interstellar medium is at least 10 orders of magnitude smaller. It is immediately realized that the hydrostatic solution cannot represent an equilibrium solution for the hot solar corona.  The recognition that a hot, static corona cannot exist motivated the young Eugene Parker in the late 1950s to turn his attention to coronal solutions with nonzero radial velocities.  The physics behind the idea of an expanding solar corona is that the very low pressure of the interstellar medium acts as a “vacuum cleaner,” which “suck out” the gas from the solar corona  Consider the simplest scenario and assume a steady-state spherically symmetric corona and neglect electromagnetic effects. In this case the fully ionized plasma is described by Eqs. (12.1).

30. Aerospace Environment -- ASEN533530 Corona Expansion I where C is an integration constant. Next figure shows the mathematically admissible classes of isothermal solution (depending on the constant C).

31. Aerospace Environment -- ASEN533531 Possible solutions  Because we are interested in physically meaningful single valued solutions that describe plasma continuous expansion from the Sun, some of the solution classes can be eliminated right away. Class I and II describe double-valued solutions, which are unphysical. Class III solutions are supersonic at the base of the corona and therefore cannot meet the physical requirements.  Solutions of type V are physically admissible. They are subsonic everywhere and predict speeds of about 10km/s at Earth orbit. This solar breeze solution was a competing solution with the wind solution. The main problem with the solar breeze solution is that it gives finite pressure at infinity and this pressure far exceeds the pressure of the interstellar medium.  The solution favored by Parker was the type IV solution, starting subsonically at the base of the corona and accelerating to supersonic speeds.

32. Aerospace Environment -- ASEN533532 Corona Expansion II  when one opens a gas reservoir filled with stationary gas to vacuum the gas outflow will be sonic at the surface of the reservoir and it accelerates outward: This outflow is driven by ……  The addition of solar gravity introduces a retarding (backward) force, which rapidly reduces with distance.  The outflow starts subsonically and undergoes a sonic transition and the goes supersonically; from (12.10):

33. Aerospace Environment -- ASEN533533 Corona Expansion III  The type IV solution given by (12.13) is the isothermal solar wind, see figure. This is naturally a greatly simplified situation, because the coronal temperature does not remain constant.  The energetics of the solar wind are quite poorly understood (especially near the Sun). A source of coronal heating is required (will be discussed later)  It is well established that the solar wind temperature decreases with radial distance as r -  with  <1 (0.3— 0.4 on average).  The solar wind solution (type IV) gives zero pressure as r  infinity. (r 2  u=const.)

34. Aerospace Environment -- ASEN533534 The Class IV solution, corresponding to low velocity at the sun, is one where everywhere; that is, the velocity increases monotonically away from the sun. Borrowing from this result, then 1. (subsonic) 2. (supersonic) 3.When, then for a mathematically valid solution.

35. Aerospace Environment -- ASEN533535 The following condition is therefore required for transition to supersonic flow: gravitational mean potential  thermal energy ( m = mass of a solar wind particle). Therefore, for at the mean thermal energy of the expanding solar wind must exceed the gravitational potential energy of the gas.

36. Aerospace Environment -- ASEN533536 Aerospace Environment ASEN-5335 Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) Contact info: e-mail: lix@lasp.colorado.edu (preferred)lix@lasp.colorado.edu phone: 2-3514, or 5-0523, fax: 2-6444, website: http://lasp.colorado.edu/~lix TA’s office hours: 9:00-11:00 am and 3:15-5:15 pm Wed at ECAE 166 Read 3 and class notes HW2 due today Quiz-3 next Tuesday (2/18), close book.

37. Aerospace Environment -- ASEN533537 Interplanetary Magnetic Field (IMF)  The importance of a magnetic field to the behavior of a plasma is determined by the ratio of the plasma pressure, P th to the magnetic pressure P B,  = P th /P B.  A “high beta plasma” (  >>1) is controlled principally by the plasma gas dynamics. A “low beta plasma” (  <<1) is dominated by the magnetic field.  If the magnetic field is weak, 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 strong, we expect the magnetic field to “contain” the plasma, or at least to inhibit its expansion.  Near the Sun, the magnetic pressure can be a few times the gas pressure at some regions for sometimes and can also be much smaller than the gas pressure. A mixture of these extreme behaviors is expected (spherical symmetry is a poor approximation).  There are two fundamentally different types of coronal magnetic field structures that results in quite different solar wind properties: regions of open magnetic field lines and regions of closed magnetic field lines.

38. Aerospace Environment -- ASEN533538 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.

39. Aerospace Environment -- ASEN533539 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.

40. Aerospace Environment -- ASEN533540 Coronal Structure and Magnetic Field  Let us consider the corona containing hot plasma and an axisymmetric magnetic field. From the ideal MHD equation, assuming the plasma temperature is uniform and the situation is steady state, we have The above equations can be solved iteratively. One starts with a dipole B  j; B and j   m and u; u  B. These steps are successfully repeated until the solution converges.

41. Aerospace Environment -- ASEN533541 Coronal magnetic field line configuration  Closed field line near the equator and open field line at higher latitudes.  Open field lines spread in latitude and cover the entire 4  solid angle beyond about three solar radii.  The first open field lines originating from opposite hemispheres come quite close together and extend radially outward.  IMF must change sign rather suddenly within this narrow region.  A thin sheet of high current density pointing in the azimuthal direction has to be there.  This current circulates around the dipole axis in the same direction as the original current generating the dipole field.  It is this heliospheric current sheet that separates fields and plasma flows originating from different hemispheres.  The predicted coronal structures are clearly visible in the photographs of the solar corona.

42. Aerospace Environment -- ASEN533542 Closed magnetic structures should form over those locations where the vertical component of the field at the base of the corona changes sign (i.e., above so-called "neutral lines" in the solar magnetic field).

43. Aerospace Environment -- ASEN533543 Extension/generalization of the features indicated in the above model to more complicated solar fields at the lower boundary of the corona suggest the following: Closed magnetic structures should form over those locations where the vertical component of the field at the base of the corona changes sign (i.e., above so-called "neutral lines" in the solar magnetic field). These closed structures should be limited in extent to about 2 solar radii. Open magnetic structures should form over regions where the vertical component of the field at the base of the corona is of the same sense or sign over a large area (i.e., above so-called "unipolar regions" in the solar magnetic field. The open structures should spread laterally with increasing height to fill all space above closed regions with outward-flowing solar wind. Current sheets should form where these flows meet.

44. Aerospace Environment -- ASEN533544 Ulysses Measurements The unipolar regions occur at higher latitudes and are the origin of the so-called high-speed streams in the solar wind

45. Aerospace Environment -- ASEN533545 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.

46. Aerospace Environment -- ASEN533546 Solar wind speed and IMF 1995-1999 Descending phase Solar Minimum Ascending phase

47. Aerospace Environment -- ASEN533547 Near the ecliptic plane the solar wind tends to be organized into alternating slow and fast streams, often forming a pattern of recurring high-speed streams from solar rotation to solar rotation. Vn Mariner 2 measurements The high-speed streams originate in coronal holes, the unipolar regions in the solar atmosphere. The recurring high-speed streams are also referred to as co-rotating interaction regions (see following slide).

48. Aerospace Environment -- ASEN533548 Corotating Interaction Regions (CIRs)  The fast streams “catch up” with slower streams. The leading edge of fast streams compresses the plasma and produces a high- pressure region that prevents actual overlap between fast and slow solar wind regions.  Since these structures usually persist over several solar rotations, a conventionally used name is corotating interaction region or CIR.

49. Aerospace Environment -- ASEN533549 3 CMEs in the Solar Wind during April 2002 Density Temperature Absolute B Bz (B-south) Nonrecurring Disturbances in the Solar wind Outward propagating CMEs generate interplanetary shock waves. The slower, “quiet” solar wind is “snowplowed” by the fast material, forming a traveling shock ahead of the ejecta. shock compressed heated plasma earth

50. Aerospace Environment -- ASEN533550 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.

51. Aerospace Environment -- ASEN533551 Two Classes of Solar Particle Events

52. Aerospace Environment -- ASEN533552 Coronal magnetic field line configuration  Closed field line near the equator and open field line at higher latitudes.  Open field lines spread in latitude and cover the entire 4  solid angle beyond about three solar radii.  The first open field lines originating from opposite hemispheres come quite close together and extend radially outward.  IMF must change sign rather suddenly within this narrow region.  A thin sheet of high current density pointing in the azimuthal direction has to be there.  This current circulates around the dipole axis in the same direction as the original current generating the dipole field.  It is this heliospheric current sheet that separates fields and plasma flows originating from different hemispheres.  The predicted coronal structures are clearly visible in the photographs of the solar corona.

53. Aerospace Environment -- ASEN533553 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

54. Aerospace Environment -- ASEN533554 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.

55. Aerospace Environment -- ASEN533555 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.

56. Aerospace Environment -- ASEN533556 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.

57. Aerospace Environment -- ASEN533557 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.

58. Aerospace Environment -- ASEN533558 IMF as a function of the distance  The following equations shows the IMF as a function of r. The radial and azimuthal component of the IMF behave quite differently.  The radial component decreases with r -2, whereas the azimuthal component decreases only as r -1. Thus as going outward, the magnetic field becomes more and more azimuthal (it “wraps around”) in the equatorial plane.  At the same time the field behaves quite differently over the solar polar regions.

59. Aerospace Environment -- ASEN533559 Heliosphere, a schematic view Note that IMF is dominated by the azimuthal component at large distance, while the solar wind flow is always dominated by the radial component.

60. Aerospace Environment -- ASEN533560 The Heliosphere  The heliosphere is the region of space influenced by the Sun and its expanding corona, the solar wind. In some respects the heliosphere encompasses the true extent of the solar system.  The solar corona is continuously expanding into the interstellar medium. We showed earlier that the pressure of this expanding coronal “bubble” asymptotically approaches zero as the heliospheric distance goes to infinity.  However, if there is a finite pressure in the surrounding interstellar medium, the coronal expansion must eventually stop at a point where the solar wind pressure becomes equal to the interstellar pressure.  The solar system is located in a low-density interstellar cloud. The solar system is moving through this cloud with a velocity of about 26km/s.

61. Aerospace Environment -- ASEN533561 The interstellar medium, heliopause, termination shock  It is generally assumed that the partially ionized interstellar gas is fairly cold (even thought the thermodynamic properties of this region are only poorly known), and consequently the solar system’s motion (26 km/s) is most likely supersonic (not fully settled yet).  An immediate consequence is the formation of an upstream bow shock, which decelerates and deflects the interstellar charged particles.  Flow lines of the interstellar plasma do not penetrate into the region dominated by the solar wind flow but flow around a “contact surface”, also called the heliopause, which is considered to be the outer boundary of the heliosphere.  The third large-scale discontinuity is expected to form inside the heliopause. On the upwind (upstream) side of the heliosphere, the initial radially expanding supersonic solar wind must be somehow diverted to the downstream direction. 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”.

62. Aerospace Environment -- ASEN533562 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.

63. Aerospace Environment -- ASEN533563 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

64. Aerospace Environment -- ASEN533564