The Heliosphere in the Kitchen Sink

Co-starring: A Planetary Bow Shock

Anders Eriksson
Swedish Institute of Space Physics
Uppsala, Sweden

The solar wind blows out from the sun in all directions, sweeping through the solar system and out in interstellar space. This plasma flow is supersonic, meaning that the flow velocity relative to its source (the sun) is higher than the local speed of sound in the solar wind itself. Through most of the solar system, the solar wind flows quite unperturbed, only being influenced by the few and, on a relative scale, small objects it passes: planets, comets, asteroids. However, somewhere outside the planetary system, the solar wind meets the interstellar medium. Here, the supersonic flow of the solar wind is terminated at a boundary called the heliopause. The region within the heliopause, which may be pictured as a gigantic cave or cell in space, is known as the heliosphere.

To understand what happens at the heliopause, we have to look at the properties of a supersonic wind. What is so special with a flow being supersonic? Well, if we only have an unperturbed flow, not interacting with any other matter, nothing is special at all. Velocity is a relative concept: by itself, the fact that the flow has high speed in some frame of reference does not imply anything. The concept of supersonic motion is interesting only when interpreted as the relative motion of the flow with respect to some other material object with which it interacts. Thus, nothing very special goes on in the solar wind as it flows through the vast empty regions of the solar system, but when it passes the obstacle created by for example a planet and its magnetosphere, the supersonic flow forms a shock front. The same thing happens when the solar wind hits the interstellar medium at the heliopause.

What is a shock front? To understand this, we may perform a simple two-dimensional experiment. The material needed for the experiment is a kitchen sink, bathtub, or the like, with a tap providing a reasonably smooth flow of water, (no dripping) giving a setup something like this:

Figure 1. Experimental setup. Arrows denote flow direction.

Where the water jet from the tap hits the almost horizontal bottom surface of the sink, an almost radial horizontal flow results (A). At some distance from the impact point of the water jet, the water depth suddenly increases (B). Outside of this distance (C), the water depth stays deep.

If we make some waves in the water in the region C, for instance by the use of a finger, we find that waves propagate on the surface of the water in all directions. If looking carefully, we find that downstream moving waves travel faster than waves propagating against the flow direction, which is quite natural.

Now try to generate waves in the region A! What happens is that waves propagates only downstream from the point where you create them: no upward propagation is found. The reason for this is simply that the speed of the water is higher than the speed of the waves. Thus it is reasonable to call the flow "supersonic"! This designation may seem strange, as the water surface waves has nothing to do with sound waves, but the physics of the situation is basically the same in both cases.

In region A, we thus have a supersonic flow, while in region C, the flow is subsonic. The transition occurs in a fairly narrow shock front, B. Upstream of B, the flow is supersonic, downstream it is subsonic.

This is a two-dimensional analogy of what happens when the solar wind hits the interstellar flow. The sun is the point where the water jet hits the sink, the solar wind is the region A, the heliopause is the shock front at B, and the interstellar flow is the region C. If you wanted to make the analogy more perfect, you would have to pull in some water from one of the boundarys of the sink in order to simulate an interstellar medium with a source separate from the solar wind. In this way, you would be able to study the different distance to and characteristics of the heliopause in the directions up- and downstream with respect to the moving interstellar medium.

The flow in the kitchen sink is essentially two-dimensional, and the important wave mode for transporting information on flow patterns here is the surface waves. In three dimensions, information on flow changes are transported as pressure waves, i.e. sound waves. If we let the term "sonic" in the words subsonic and supersonic refer to the important wave speed in the situation at hand and not necessarily to the speed of sound, the designation of the flows A and C as super- and subsonic, respectively, is clearly reasonable.

Another shock phenomenon found in space is the bow shock found in front of planetary magnetospheres, shown below:

Figure 2. A planetary magnetosphere. Arrows denote flow direction (outside the magnetosphere) or magnetic field direction (inside the magnetosphere). The circle in the centre is the planet.

Here, the solar wind flow is again supersonic with respect to a rest frame of the magnetosphere. A shock front known as the bow shock is therefore formed in front of the magnetopause. Before the shock front, the solar wind is supersonic, afterwards, in the region known as the magnetosheath, the flow is subsonic and rather turbulent.

Our kitchen sink may again help us to depict this phenomenon, albeit in two dimensions instead of three, just as before. Put some object, your fingertip for instance, in the flow A of Figure 1. A bow shock, where the water depth increases, will show in front of your finger, and extend in some approximate V shape behind the finger. The shock front which forms is actually more similar to the shock where the solar wind hits some unmagnetized object, like an asteroid or the planet Venus, as such objects are point-like, as is your fingertip, while a magnetosphere is elongated in the downstream direction. So, to more accurately simulate a magnetospheric bow shock, put not just your fingertip in the water, but the full length of a finger, pointing in toward the "sun", i.e. toward the jet from the tap.
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