# Are coronal hole magnetic field lines open?

It is often said that the plasma exiting the coronal hole (of the Sun, obviously) follows the open magnetic field line. E.g. a direct quote:

"Coronal holes are regions of low-density plasma on the Sun that have magnetic fields that open freely into interplanetary space".

So my question is: since the magnetic field is in its essence a solenoidal vector field, could its lines be truly open? That would make the coronal hole a certain magnetic monopole, wouldn't it? Or do they actually close somewhere at the heliospheric boundary, for example?

It's either that or maybe my understanding of electromagnetism doesn't quite fit into plasma behaviour (I've heard this story of "frozen in magnetic field lines", but fail to see how it answers my question), in which case I also ask for some correction/explanation.

Thanks.

• As @Floris says, magnetic fields cannot be be completely "open," basically because of $\nabla \cdot \mathbf{B} = 0$. Eventually they will all close but you should note that field lines are just a visualization tool we use to look at the geometry of fields. They are not physical and are limited by the resolution of the software used to construct them. – honeste_vivere Jan 4 '17 at 13:51

Field lines are always closed. The following diagram shows what your book appears to be talking about (from http://soi.stanford.edu/results/SolPhys200/Poletto/uvcs_spiral.jpg):

Some field lines look obviously "closed" while others "go off into space". But then they turn around and come back again... something like this:

I found the caption that goes along with this image at

From there I quote (emphasis added by me):

The white rays are lines of magnetic force from a theoretical model of the magnetic field of the Sun at the minimum of solar activity (see Banaszkiewicz et al. 1998, Astron. Astrophys., 337, 940). The polar coronal holes (dark regions on the solar disk and in the extended corona) have primarily open magnetic field lines along which the high-speed component of the solar wind accelerates away from the Sun. In the extended corona viewed by UVCS, the density of particles is so low that individual ions very rarely collide with other particles, and thus they execute spiraling motions around the magnetic field lines (see green curve for an illustration of an example particle's motion).

• My understanding of the following blog post is that "open" magnetic field lines don't necessarily come back within a defined distance: dealingwithcreationisminastronomy.blogspot.com/2009/10/… if the sun were the only charged body in the universe, something like your illustration would have to be accurate, but in the actual universe which has charged bodies other than the sun, isn't it possible that particles travelling along the sun's "open" magnetic field lines will never return to the sun? – sumelic Oct 13 '17 at 17:02
• @sumelic it is possible that a field line "ends on" another surface (although that is only superficially true as the lines would presumably continue inside the body). But it cannot "end in space". Yes it is quite possible that particles don't return to the sun - their energy may be such that as the field grows weaker, their radius of curvature become enormous. And they can hit other things. – Floris Oct 13 '17 at 17:06
• Saying that magnetic field lines "end on" or "end in" space certainly seems to be bad/incorrect wording, but I'm confused about why you brought that up and put it in quote marks as I can't see an example of that wording in the OP's question, my comment, or the linked blog post. Magnetic field lines do not "end", but I don't see why we should take that to mean that they are all "closed"; referring to some magetic field lines as "open" seems to be conventional and to have a fairly reasonable meaning – sumelic Oct 13 '17 at 17:18
• In my mind the line is either closed or it has to stop somewhere. But since a field line is a mathematical construct this is all a bit arbitrary and I am not sure I am adding any insights. – Floris Oct 13 '17 at 17:21