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Shock Waves

The solar wind is highly supersonic, so obstacles in the flow, large variations in stream speeds, or fast ejecta produce shock waves, just as shock waves are produced by a supersonic jet. With a jet, sound waves develop ahead of the jet nose because the aircraft is traveling faster than the waves can escape. A shock wave forms, due to pressure buildup, to keep the air flowing around the jet. The shock wave communicates information very abruptly about the obstacle, enabling the surrounding medium to "see" it (a).

a. Image
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Two figures showing the formation of shock waves at the nose of a supersonic jet.

There are several ways to produce shocks in the solar wind, such as blast waves (b) emitted from the Sun, CME-driven shocks, and interactions between the fast and slow streams (c) that cause forward-reverse pairs of shocks to form eventually.

b. Image
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c. Image
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Left: A blast wave associated with a flare and CME on April 7, 1997. These images are based on ultraviolet images from the SOHO telescope EIT. Since the shock is relatively difficult to see in the original images, displayed here are running difference images, i.e. each image shows the difference from the previous image. This emphasizes the changes in the images and makes the blast wave more apparent. Here we see four different times as it moves across the Sun's surface, which can be seen as the mottled circle that fills most of each frame. The speed at which the shock wave runs across the solar disk was estimated at 1.5 million km/h-supersonic even for the Sun!

Right: Low-speed winds come from the regions above helmet streamers while high-speed winds come from coronal holes. As the Sun rotates these various streams rotate as well (co-rotation) and produce a pattern in the solar wind much like that of a rotating lawn sprinkler. However, if a slow moving stream is followed by a fast moving stream, the faster moving material will catch-up to the slower material and plow into it. This interaction produces shock waves that can accelerate particles to very high speeds.

Examples of interplanetary shocks include bow shocks at planets and comets (d). The largest shocks in the heliosphere are the termination shock and the heliospheric bow shock (e).

d. Image
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e. Image
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The left-hand image was produced using a 1.0 second exposure. More of the dominant jets can be seen streaming away from the comet. The bow shock (a shock wave created in front of the comet during its interaction with the solar wind) can readily be seen on the sunward facing side of the comet. The right-hand image is a temperature contour plot illustrating the termination shock and the heliospheric bow shock.

How do we describe shocks theoretically? At one end, we have the cruder macroscopic MHD description and, at the kinetic, microscopic end, we have particle simulations. The MHD description is limited in that it doesn't provide details of the shock structure; the shock is a pure discontinuity. Within the MHD framework, we assume that the particles have a Maxwellian, or normal, distribution, whereas in the kinetic description we consider particle distributions directly.

How do shocks evolve in the inhomogeneous solar wind? The MHD description is ideally suited to describing the evolution, with radial distance, of shocks in the expanding inhomogeneous solar wind. A blast wave or a driven interplanetary shock will weaken with increasing distance from the Sun, often forming an N-like profile in velocity, bounded by a forward or reverse shock pair.

f. Image
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The characteristic N-shaped velocity profile for a forward-reverse shock pair.

Within some 6-8 AU, that is, in the inner heliosphere, the forward-reverse shock pair weakens, broadens, and expands in an approximately self-similar fashion. Beyond this, the influence of the pick-up ions changes the character of the propagating shock because the effective sound speed increases.

This simulation shows the evolution of an initially complex structure of a series of shocks and rarefactions. The series of shocks merges, forward shocks merging with forward shocks and reverse with reverse, to form eventually a single forward-reverse shock pair with the characteristic N-profile (g).

g. Image
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The multi-dimensional expansion of a driven shock into the spiral interstellar magnetic field means that parts of the shock can be quasi-parallel, while other parts are quasi-perpendicular, which affects the shock strength, expansion characteristics, and even particle acceleration at different parts of the shock, as we can see from this 2D CME-driven shock simulation (h).

h. Image
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The collision of fast streams with slow streams leads initially to a pressure enhancement between the streams. By about 2 AU the pressure increase has evolved into a forward-reverse shock pair with a tangential discontinuity separating the fast and slow streams, which we call a Co-rotating Interaction Region (i) or CIR.

i. Image
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A numerical simulation of a CIR. A fast stream catches up and collides with a slow stream, forming initially a pressure pulse, which then steepens to form a forward-reverse shock pair.

Multiple fast and slow streams lead to multiple CIRs that can eventually catch up to one another to form Merged Interaction Regions (j) or MIRs. Voyager has been instrumental in discovering and elucidating the nature of CIRs and MIRs, which form some of the largest coherent structures in the heliosphere.

j. Image
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Five streams merged to form one compound stream. Figure courtesy of Burlaga et al., JGR 91, p13331, 1986

Occasionally, especially during solar maximum, numerous shock waves can be driven off all parts of the Sun over a short time. These shocks, propagating in all directions away from the Sun, can eventually merge to form a gigantic structure of enhanced magnetic field and compressed plasma that almost encircles the Sun completely. Such Global Merged Interaction Regions (k), or GMIRs, were observed simultaneously by Voyager and Pioneer at opposite sides of the Sun.

k. Image
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Example of a GMIR. This is the first GMIR of this solar cycle. The density enhancement at 2000.4 lasts about 30 days (black line). The enhanced magnetic fields form a barrier to inward diffusing cosmic rays, so the cosmic ray intensities (red + symbols) decrease dramatically with the arrival of the GMIR.

As the simulation illustrates, the massive extent of GMIRs can have an enormous influence on the heliosphere. Once the GMIR has formed, it propagates out to the asymmetric termination shock, colliding first with the nose portion and last with the tailward part. The collision of the GMIR with the termination shock sets the entire heliosphere "ringing" as it shakes back and forth, driving pressure waves, and eventually shocks, into the interstellar medium (l).

l. Image
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A simulation of a GMIR propagating through the heliosphere and eventually colliding with the boundaries separating the solar wind and the interstellar medium.

Let us now consider the microstructure of shocks. When examined at the microscopic level, a feature of both quasi-perpendicular and quasi-parallel shocks is reflected ions and electrons. At a perpendicular shock, the reflected ions gyrate no more than a few times ahead of the shock, before being swept through and downstream. The reflected ions decelerate the incident solar wind, creating a "foot" just ahead of the steep ramp. In perpendicular shocks, the reflected ions provide the primary dissipation mechanism. Because the reflected ions sweep through the perpendicular shock rapidly, the shock is narrow overall (only several ion gyroradii thick) with a very narrow ramp. The ramp can be even more finely structured and highly temporal (m).

Quasi-perpendicular:
In a quasi-perpendicular shock the angle between the magnetic field direction and a normal to the shock front is greater than 45 degrees, i.e. the magnetic field is almost perpendicular to the shock normal.

m. Image
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A schematic showing the structure of a quasi-perpendicular shock. Principal features are the foot, produced by gyrating reflected ions, the ramp, where the primary jump occurs, and an oscillatory downstream structure.

By contrast, reflected ions at a parallel shock stream away along the magnetic field and can only diffuse back to the shock by scattering on magnetic fluctuations upstream. The presence of extended ion beams renders the physics of quasi-parallel shocks very different from that of quasi-perpendicular shocks. Since the particle scattering process is slow, parallel shocks are much wider than perpendicular shocks, are often highly turbulent, and reform constantly.

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