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Coronal Hole Area and Solar Wind Speed

Drax Spacex

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A small circular shaped transequatorial coronal hole just passed by the center of the solar disk.  I'm curious what sort of solar wind speed we might expect in a few days from this Earth-directed coronal hole.

I wonder if the physical analogies of a nozzle attached to a garden hose, or small hole punctured in a water-filled balloon apply.  For the case of the water flowing through a garden hose through a outlet nozzle, the speed of the water coming out of the nozzle is proportional to the ratio of the hose cross sectional area and the area of the nozzle opening.   A smaller outlet area results in higher outlet water speed.

This fluid dynamics analogy of course may not apply to the physics of the Sun, but this will be an interesting test case to see if at least in part it applies if we should see high solar wind speed from this small coronal hole.

Is there any theory or empirical data relating solar wind speed from a earth directed coronal hole as a function of coronal hole size/shape?

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Well, let's think about that balloon for a moment. The material of a balloon can expand under pressure quite significantly, and that pressure is what creates the POP! of an empty balloon when punctured. This is akin to a sunspot erupting, as a direct analogy: The strong magnetism of a sunspot builds and entraps energy, and then releases it suddenly. What then results from the explosion isn't even the same material which prompted the genesis for this event.

By comparison to an air-filled balloon, a water-filled balloon doesn't exert nearly the same amount of pressure, so when it is punctured, the release isn't nearly as violent. That's your analogy to a coronal hole. In other words, regardless of the size of the hole, or "puncture", the key to getting that POP! lies in the amount of energy stored and released. Without a known value for the stored energy, the magnitude of the release is mostly unpredictable.

Since the driving forces for every coronal hole are not measured in a dynamic and interesting way(only the consequence i.e. solar wind), they don't become classified in regards to their magnitude, shape, or size. We don't know the water pressure of the hose in question, to refer back to your analogy. I do recall reading that there's a correlation between the latitude of the CH and solar wind direction... its speed at arrival to Earth... but nothing empirical describing the nature of the forces acting upon the gasses which are propelled strongly outward into space - not in totality.

Remember though, that there are coronal holes at both poles, so the internal pressure is never varying too violently in either direction. Thus, it's like a water balloon that is constantly emptying(yet never seeming to run out). The larger the hole, the more wind that comes out. Considering the path of least resistance, a large hole would dominate smaller holes in terms of outflow. As for the speed it exits at, for the sake of empirical data? We just won't know without new instruments.

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It's always good to have empirical data to test a hypothesis.  I didn't see much of an increase in solar wind speed from that small transequatorial coronal hole.  So no, it doesn't appear that the nozzle or punctured balloon analogy applies.   There may be other relationships between earth-directed coronal hole area, shape, location and solar wind speed.

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I searched the web for "solar wind nozzle" and did find that the solar wind has been modelled as a nozzle (though not as I suggested here as relating to the area of a coronal hole).

Eugene Parker (yes, that one) submitted a journal paper in 1958 in which he modelled the solar wind in a high-level, macro sense as a de Laval nozzle used in supersonic jets and rockets.

Adolfo F. Viñas (NASA/GSFC Heliosphysics Science Division) in a 2014 presentation summarized it thusly:

"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:
1. The solar wind can be treated as an ideal gas.
2. The solar wind flows radially from the Sun.
3. Acceleration due to electromagnetic fields is negligible.
4. 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).

Parker developed the hydrodynamic theory of the solar wind and proposed that the solar wind escapes from the solar corona with a velocity changing from subsonic to supersonic speeds.

The Sun behaves like a rocket engine blasting its exhaust into space. The expansion of the solar corona is similar to that describing the flow of a gas through a divergent-convergent de Laval nozzle."

Viñas continues, "To have a solar wind, a star must have a cool lower atmosphere and a hot outer atmosphere.  We still don’t know how the corona is heated!"


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