15 Million Degrees

by Lucie Green

  ORIGIN OF THE MAGNETIC STRENGTH

  It’s always a good approach when trying to find an answer to a tricky question to start with a simple scenario and gradually build in the complexity. So let’s ignore the complex magnetic fields of the sunspots for now, and just think of the Sun as having a simple global magnetic field, much like we have here on Earth. The Earth has magnetic north and south poles that are close to the geographic poles about which the Earth is spinning. And the Sun has a magnetic north and a magnetic south pole that are both very close to the axis about which the Sun rotates. The only difference is that the polar magnetic field of the Sun (at the photosphere) is about twenty times as strong as the Earth’s polar magnetic field at the surface. So far so good.

  7.1 A schematic showing the configuration of the Earth’s magnetic field and the Sun’s magnetic field (at the start of cycle 24). Not to scale!

  In both cases we can imagine the field lines coming out of the north pole, curling out through space and then re-entering at the south pole. The magnetic fields of the Sun and the Earth are not that dissimilar to giant bar magnets. All we have to do is close the field lines; as we know, they always form closed loops. For a bar magnet they run straight back up the middle. Within the Earth the magnetic field goes up through the liquid metallic (mainly iron and nickel) outer core and over to the opposite pole. But because the Sun spins at different speeds at different places inside, things get much more complicated.

  Our starting magnetic field has field lines that run parallel to lines of longitude and this configuration is known as a ‘poloidal field’. If the Sun had no interior plasma flows and the Sun rotated as a rigid body, the field lines inside the Sun would always run parallel to lines of longitude, like they do in our very simplified description of the Earth. And this is the case for any magnetic field in the core or the radiation zone, where everything rotates in unison. But in the convection zone, where helioseismology has shown that the plasma flows vary with latitude, known as ‘differential rotation’, there is a very important consequence for the magnetic field. In the convection zone the plasma exerts enough pressure on the magnetic field to drag it with the flow. The internal magnetic field can be distorted by the plasma flows.

  It’s this ability of magnetic fields to be distorted that I find so fascinating. It’s as if they are elastic and flexible – in the Sun, magnetic fields can evolve in ways I never imagined possible. Before I studied the Sun, magnetic fields to me were fairly straightforward. Pass a current through a wire, and you create a magnetic field in the region around it. I could wave my hand around the wire and move the air but this would have no effect on the magnetic field. Turn off the current and the magnetic field disappears. Shortly after starting in solar physics I had to give up all my intuitions.

  Now I have an office full of pipe cleaners and elastic bands that I use with my colleagues to visualize the shapes in the magnetic fields that can come about when the field is threaded through an electrically conducting gas, and how the shapes can change when this electrically conducting gas is moving. I became interested in understanding how this shifting plasma environment might be responsible for evolving a seed magnetic field in ways that lead to sunspots and the sunspot cycle.

  Inside the Sun the plasma flows act as fingers that grasp the magnetic field lines. The rotating plasma at the base of the convection zone (in the tachocline) pulls more on the magnetic field at the equator because that’s where the plasma is rotating faster. Day by day, the plasma fingers stretch the magnetic field and the field lines slowly get drawn out like an archer pulling on the string of a bow. Eventually, after about eight months, the field lines have all been dragged along so much that they wrap all the way around the Sun!

  At this point, the field lines catch up on themselves at the point where they started. And they then overtake the point where they began. Instead of one magnetic field line in this location, there are now two. Rotation after rotation, the magnetic field lines are wrapped around and around the Sun and very tightly wound bundles of magnetic field form in both hemispheres, which connect over the equator. This magnetic field configuration is known as ‘toroidal’ as the shape of the magnetic field looks like two toruses, or doughnuts – one in the northern hemisphere and one in the south.

  7.2 The rotation of the plasma inside the Sun draws out the magnetic field in the tachocline region and starts to wrap it around. This turns the magnetic field from being ‘poloidal’ to ‘toroidal’ in its configuration.

  In this simple scenario the rotation of the plasma has two important effects on the magnetic field. First, the orientation of the field lines inside the Sun has changed. They started off being parallel to lines of longitude and ended up being closely aligned to lines of latitude. And, second, each time a field line wraps more than once around the Sun it has the effect of amplifying the magnetic field strength. Presumably the Sun has been doing this ever since the convection zone developed these sheared flows. Magnetic field lines do not weaken as they are lengthened by the moving plasma. The small seed magnetic field has been stretched, folded and grown into one that can explain the strength of the Sun’s electromagnetic influence we see today.

  ORIGIN OF THE MAGNETIC COMPLEXITY

  We now have an amplified magnetic field at the base of the convection zone, but that does not explain how the magnetic field responsible for sunspots appears at the photosphere. It seems that the magnetic field which causes sunspots to be dotted over the Sun’s surface has its birth down at the tachocline: the region between the radiation zone and the convection zone where the differential rotation can keep amplifying the magnetic field for the longest time. So how, then, does the magnetic field formed at the base of the convection zone form sunspots at the photosphere?

  The short answer is simple: the magnetic field floats to the surface. In reality, the process is much more complicated. As the toroidal magnetic field grows, where the magnetic field wraps around itself the most, it weaves together to form ‘flux ropes’, complete with plasma now trapped inside these ropes. A flux rope is actually somewhere between a rope and a hose. It is rope-like in that there is magnetic field distributed right through it; it’s not hollow. But it is hose-like in that plasma is trapped in it, only allowed to flow along the flux rope and not leak out of the sides.

  The magnetic field in a flux rope really does start to act like it is made of elastic bands. A flux rope has an aspect of springiness to it. This means that if the plasma outside the magnetic flux rope pushes on it, the flux rope can deform inwards, responding to the plasma pressure outside. But if the flux rope is squashed inwards, it means that the flux rope becomes more densely packed with magnetic field lines, and this has an important effect because it increases the magnetic pressure in the rope. The magnetic field presses on the plasma within the rope and it starts to move along it and thins out. With the aid of the magnetic field, the plasma inside can be less dense and yet the flux rope can still have the same pressure as the ambient plasma around it.

  This means that within the flux ropes there can be patches of plasma that become less dense than the plasma outside the rope. We are not sure why certain sections develop this low density before others, but once the plasma starts to thin out in one part of the rope it can become buoyant. And like anything that is less dense than the fluid around it, it will start to float to the surface. But instead of dragging the whole flux rope up, one part of it will bow out and start to stretch up towards the surface of the Sun. As the buoyant plasma rises, it carries the magnetic field with it and forces the magnetic field to start to resemble the shape of the Greek letter omega, Ω, as part of it stretch
es away, making a bid for the photosphere. Eventually the top of the omega loop penetrates the photosphere and, as it crosses, a pair of sunspots form.

  7.3 Sunspots form when a loop of magnetic field rises from the tachocline and bursts through the photosphere.

  The ongoing weaving and release of flux ropes at the tachocline explains why we see pairs of sunspots in the Sun’s photosphere. Each pair represents the two locations where the loop of magnetic field crosses the photosphere. Instead of a relatively contained magnetic field like that of the Earth, the Sun’s magnetic field is constantly building up and spilling out of the sides. It is these highly strung flux ropes that caused the catastrophic event witnessed by Carrington. But there are still a few other sunspot mysteries to clear up before we come back to that.

  MAGNETIC MYSTERIES

  As soon as it was possible to measure the magnetic field within sunspots, something interesting was noticed about the pairs. In each pair, one sunspot seemed to be ‘leading the way’ around the Sun. On average, a line drawn between leaders and followers shows a very slight tilt of about 4 degrees away from the east–west line. This tilt doesn’t depend on which hemisphere the spots are in. This tilt of the sunspots is known as ‘Joy’s law’, after Alfred Harrison Joy, who worked at the Mount Wilson Observatory.

  Hale wrote in 1919: ‘The following spot of the pair tends to appear farther from the equator than the preceding spot, and the higher the latitude, the greater is the inclination of the axis to the equator.’ The preceding spot refers to the spot which is at the front in relation to the rotation of the Sun. It’s the one on the right-hand side of the pair. And, more than that, the leading sunspot of the pair always has the same magnetic polarity as other leading spots in the same hemisphere: either always a positive magnetic polarity or a negative. But if the leading spot of the pair in the northern hemisphere was positive, then the leading spot in the southern hemisphere would be negative. Across 1735 sunspot pair observations, Hale only found forty-one that did not have the same leading magnetic field direction.

  Even more interesting was that each time a new cycle started, the magnetic polarity of the leading and following sunspots switched. Two sunspot cycles needed to play out before the Sun returned to its original magnetic configuration. The Sun may have an eleven-year sunspot cycle, but its magnetic cycle is twenty-two years in length. In solar cycle 23 the leading sunspots in the northern hemisphere were of a positive magnetic polarity (negative magnetic field led in the south); in cycle 24 the leading spots have a negative magnetic field (positive magnetic field leads in the south). The Mount Wilson data were throwing up lots of observations that needed an explanation.

  We’ll start by explaining the tilt in sunspot pairs named after Joy. On the way floating up from the tachocline there are several competing effects that can influence the ascending flux tube. The effect responsible for misaligning the eventual sunspot pairs is actually one we are familiar with here on Earth: the Coriolis force. This is the force imparted on anything moving within a larger spinning system. Because both the Earth and the Sun are constantly rotating, everything that moves within them experiences a Coriolis force.

  The Coriolis force works in different directions, depending on your hemisphere, and is often thought to determine the way in which your water spins down the plughole, but in reality the water can spin either way because the Coriolis force is too weak compared to any movement the water may already have from when the bath or sink was filled. But, even so, scientific research has been done on whether the Coriolis effect is seen when emptying a sink. A paper was published in the prestigious journal Nature in 1962 that set out to test this hypothesis. A special circular tank was designed and built by the engineer Ascher Shapiro at MIT that was 1.8 metres across and 15 centimetres deep. The tank was filled with water and left to settle for twenty-four hours. The plug was then pulled and in the first fifteen minutes of draining no rotation was seen in the way the water left the tank. But in the last few minutes a counter-clockwise rotation was seen, the direction expected for the northern hemisphere. A flurry of similar experiments followed, including a test in the southern hemisphere, which showed the water rotating clockwise as it drained.

  Were these results concrete proof? The answer isn’t clear. The Coriolis force only really comes into play when things are moving over vast distances. On the Earth this explains why hurricanes and cyclones spin in opposite directions in different hemispheres. Within the Sun it explains why flux ropes, or more accurately the plasma trapped inside, rotate in slightly different directions in different hemispheres as they float to the surface. But even with structures as massive as flux ropes, they only spin by around 4 degrees across their entire journey. And in forty-one of the cases Hale observed, the buffeting from the convection currents or other flows swamped the Coriolis force completely.

  More interesting, though, is trying to explain why the activity on the Sun is not constant. This is perhaps the most exciting part – the flows within the convection zone do not simply keep amplifying the magnetic field so that it grows and grows and grows. This isn’t what we see at the photosphere. Instead there is an ebb and flow – the magnetic field pulses in strength as it changes from sunspot minimum to sunspot maximum. Somehow it is being regenerated and reconfigured from one cycle to the next. And these changes aren’t restricted to the sunspots – they reach throughout the Sun.

  The magnetic field in the polar regions reverses in magnetic polarity and it does this at the same point in each and every solar cycle – around the maximum of the solar cycle, when sunspots are most abundant and when the spots are forming at roughly 15 degrees from the equator in the northern and southern hemispheres. Could the peak in the sunspot number and the polar reversal somehow be connected? Given that the internal changes that come from the different rates of plasma rotation aren’t able to affect changes at the poles, it’s not straightforward to see how sunspots at such low latitudes could have consequences so far away. To probe this question needs a more detailed look at the photosphere and exactly what is happening to the magnetic fields that emerge there and, once again, at how the plasma is flowing.

  All spots are transient features only blighting the photosphere for days or weeks. Only the largest, rare, spots will survive for several months. But with 400 years of observations, we have very detailed images of what happens to sunspots in the lead-up to their disappearance from the photosphere, when they start to fade away, and they all show the same evolution. The initially coherent dark annulus splits apart and hot plasma from the surrounding photosphere breaches the spot. Bridges of light start to form that connect from one side of the spot to the other. The spot keeps on splitting and smaller and smaller fragments form.

  So, over time, the once coherent tube of magnetic field that formed the sunspots is slowly broken up and subdivided into smaller and smaller magnetic tubes which separate from each other and start to spread over a larger and larger area. The sunspot disappears from our view as the magnetic field breaks into pieces and is no longer able to trap enough plasma to cause it to cool. But, even though there are no sunspots, the magnetic field is still there.

  The ongoing presence of the magnetic field at the photosphere is a crucial point. The sunspot does not decay in the sense that the magnetic field ceases to exist – we’ve already seen that the Sun is such a good conductor of electricity that the currents which are maintaining the magnetic field still flow. What’s happening is a redistribution of the magnetic flux over the photosphere, and the important mechanism that moves the magnetic field around is the convection which we see as supergranulation. These flows sweep
the small bundles of weak magnetic field around the photosphere. And since there is no constant pattern to the convection flows – the cells constantly appear and disappear all over the photosphere in a random way – the magnetic fields are randomly dispersed over a larger and larger area.

  Is this gradual dispersal enough to produce changes at the poles? If the very small magnetic fragments of the dispersed sunspots are tracked, another subtle but important flow is revealed that means the fragments might be able to reach this far.

  Following the movement of the magnetic fragments and the plasma reveals that there is a flow from the equator towards the poles and this acts as a giant conveyor belt for the remnant sunspot magnetic field. Such a poleward conveyor belt was first considered in 1925 by Eddington when he was thinking about how a star might redistribute its plasma to maintain shells of constant temperature within the star. He realized that circulation currents would flow in meridian planes (along lines of longitude) – called ‘meridional flows’ – that make giant conveyor belts in the outer layers.

  But it was not until the development of helioseismology that we could properly probe these flows. This technique was used in the rise phase of cycle 23 to show that the photospheric poleward flow extended into the Sun for about 26 million metres, 4 per cent of the solar radius. And they extend to more than 75 degrees in latitude in each hemisphere. In this zone the plasma was flowing towards the poles at around 10–20 metres per second – a difficult flow to detect against the random surface motions that move the plasma at speeds of 1000 metres per second and the rotation of the Sun which carries the plasma at 2000 metres per second. But how do these flows reverse the magnetic field at the poles?