# Coronal hole and magnetic field

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1. Sep 4, 2015

### ATY

Hey guys,
I have a question. I am doing some homework for university and got super confused (probably just messing up things). So in school you learn that magnetic monopols do not exist. But my question is now: On the sun there are coronal holes, region where the magnetic field is not able to connect to a field of opposite polarity, so that the magnetic field lines reach out into space.
But this confuses me: When the magnetic field lines can not connect to something else, wouldn't this be a magnetic monopol ?
Also another question: the "polarity inversion line" is the line, where both magnetic fields are equally strong ?

Sorry for this stupid question, but we never really learned much about magnetic stuff and all these lines and fields really confuse me.

Have a nice day.
ATY

2. Sep 4, 2015

### davenn

no, cuz the magnetic poles still exist on the Sun's surface and within the outer layers of the sun and there are still field lines closer in that are still connected. It's just that some of the outer lines, where the magnetic field is much weaker, become disconnected.

3. Sep 4, 2015

### Staff: Mentor

https://en.m.wikipedia.org/wiki/Coronal_hole

That wikipedia article certainly suggests that the lines do not connect in coronal holes. I suspect that there is more to the story. I'll leave it to others more expert than I to explain.

If you were my student, I would give you an A for your question.

4. Sep 4, 2015

### jasonRF

good question.
It has been many years (~ 20) since I took a class on solar-terrestrial physics but here is my recollection:

The "open" field lines on the sun occur in hemisphere. that is, one hemisphere has outgoing magnetic field liines, and the other has inward going field lines. The solar wind, which is the flow of plasma (charged particles) leaving the sun is highly conducting, so the magnetic field lines are effectively "frozen in" to the plasma. That is, as the plasma flows out, the magnetic field lines stick to the plasma and are convected outwards, getting stretched.

If you look a long way away from the sun, you will see a thin, azimuthal current sheet separating the outward field lines in one hemisphere from the inward field lines in the other hemisphere. Think about what the magnetic field of an infinite current sheet looks like - that is approximately what you will see locally deep in the heliosphere. This current sheet is not typically in the ecliptic plane, so as the sun rotates (every ~27 days I think?) at the Earth we see different polarities for a couple weeks at a time.

EDIT: Note that many (most?) of the field lines of the sun are closed. When you see the cool pictures of the sun you can often see the magnetic field loops in the corona.

Keep reading if you are interested in how we typically model this:

For these large scale, low frequency phenomenon we typically use a single fluid (magnetohydrodynamic, or MHD for short) model of the plasma coupled with Maxwell's equations in order to understand what is going on. In this case, "low frequency" implies that the displacement current is much smaller than the conduction current, so we have (in MKS units)
$$\nabla \times \mathbf{B} = \mu_0 \mathbf{J}$$
For a highly conductive fluid like the solar wind, a reasonable "Ohm's law" is,
$$\mathbf{J} = \sigma \left( \mathbf{E + v \times B} \right)$$
where $\mathbf{v}$ is the plasma fluid velocity and $\sigma$ is the conductivity. Combining these equations with Faraday's law yields an equation the describes the magnetic field evolution:
$$\frac{\partial \mathbf{B}}{\partial t} = \nabla \times \left( \mathbf{v \times B} \right) + \frac{1}{\sigma \mu_0} \nabla^2 \mathbf{B}$$
The conductivity of the plasma is HUGE, and in most locations the scale sizes over which things change are very large, so the first term on the right-hand-side usually dominates. This provides the "frozen in" magnetic flux.

However, when the current sheets get thin enough, the second term on the right dominates and we basically have a diffusion equation. So when you get these field lines in opposite directions they diffuse together and a processes known as reconnection occurs:
http://mrx.pppl.gov/Physics/physics.html
This reconnection effectively changes the topology of the magnetic field, and can have the effect of accelerating particles and heating up the plasma.

jason

Last edited: Sep 4, 2015