Unravelling magnetic knots in sunspots

Jun 2, 2023


Aimee Norton. (Photo courtesy the author.)

by Aimee Norton, Stanford Solar Group

As our closest star, the Sun gives us much of the information we know about stars in general, since it’s the only one close enough to study in detail.  One intriguing feature of the Sun is sunspots, dark spots on the surface that increase and decrease in number with the Sun’s solar cycle. Sunspots hold clues to solar flares and coronal mass ejections (CMEs), two energetic types of solar activity that can disrupt local “space weather”—the term given to conditions in the outermost layers of the Earth’s atmosphere such as the magnetosphere and the ionosphere, which help protect us from solar radiation and charged particles. Such disruptions can damage everything from satellites in Earth orbit to transmission lines on the surface, and even expose astronauts to dangerous radiation. A solar storm comparable to the Carrington Event of 1859 occurring in today’s more technologically advanced world could cause trillions of dollars worth of damage.  

Sunspots have been observed for thousands of years, but it was only in the early 1900’s that their magnetic nature was established. Sunspots usually come in pairs—one with positive polarity and one with negative polarity, like the poles of a bar magnet. A magnetic flux tube, an isolated region of magnetized plasma that buoyantly rises from inside the Sun, emerges from one sunspot and re-enters at the other, like a thread stitching through solar fabric. 

Sunspots appear dark because pressure from the magnetic field inside the sunspot suppresses convective motions that bring hotter gas to the surface, rendering the spot cooler than the surrounding area. The sunspots that form a pair are usually separated by some distance (see Figure 1, below). 

A pair of sunspots are shown as observed by the Helioseismic Magnetic Imager (HMI) on board the NASA Solar Dynamics Observatory (SDO). The sunspot on the right has a positive polarity, (i.e., the field points out of the Sun), while the one on the left has a negative polarity. (Source: A.A. Norton, not published.)
Figure 1.  A pair of sunspots are shown as observed by the Helioseismic Magnetic Imager (HMI) on board the NASA Solar Dynamics Observatory (SDO). The sunspot on the right has a positive polarity, (i.e., the field points out of the Sun), while the one on the left has a negative polarity. The distance between the two sunspots is roughly 75 million meters. The diameter of the sunspot with positive polarity is roughly the size of the Earth. An arched magnetic field is sketched on top of the image.  (Source: A.A. Norton, not published.)


Delta (δ)-spots: Uncommon and Eruptive 

Sometimes, two sunspots of opposite magnetic polarity are scrunched together, as if a knot has formed (see Figure 2A, below). These complicated regions are called delta (δ)-spots. 

δ-spots not only are of interest to solar astrophysicists but they also impact our lives on Earth. They are a source of the strong flares and violent CMEs that fling energetic radiation and material into space, sometimes causing geomagnetic storms on Earth, damaging power grids, and interfering with communication and navigation (see Figure 2B). In fact, 80% of the most energetic solar flares originate in δ-spots, even though only 8% of all sunspot groups are δ-spots, making δ-spots important objects of study.

Forecasting solar flares and eruptions has gained importance as society becomes increasingly reliant on vulnerable infrastructure such as satellites. A recent example of very costly damage due to a solar eruption is the forty SpaceX Starlink satellites that were lost in 2022 (Figure 2C).


(A) A group of sunspots with a δ-spot in the center (A.A. Norton); (B) A CME from 27 February 2000 (SOHO, ESA and NASA);  (C) Starlink sattelite dragged back to Earth by a solar storm (Sociedad de Astronomia del Caribe).
Figure 2.  (A) A group of sunspots with a δ-spot in the center with sketched magnetic fields laid atop the image showing the geometry of a twisted flux rope.  (B) A CME from 27 February 2000 is shown as it blasts a billion tons of material into space. The white circle in the center of the image is the radius of the Sun, whose light is blocked to better capture the structure of the CME as observed by SOHO/LASCO. An image of SpaceX Starlink satellites is shown re-entering Earth’s atmosphere (C) after a solar storm kept it from achieving its planned orbit. (Source:  (A) A.A. Norton, unpublished,  (B) Courtesy of SOHO, ESA and NASA, and (C) Sociedad de Astronomia del Caribe.)


δ-spot Formation Mechanisms—Which, if any, present the greatest risk?

The formation mechanisms of δ-spots are still not fully understood. One possibility is an instability acting on a highly twisted flux tube (Tanaka, 1991). If you’ve ever looked closely at a rope, or even sewing thread, you will notice that it’s often made of strands that are twisted together. Twist is a property that adds coherence to a rope because it keeps it from unraveling easily. 

However, a high twist can lead to a deformation of the flux rope’s shape through something called a ‘kink instability’ (Figure 2A, above). A ‘kink’ can form quite easily if the ropes are highly twisted.  When a kink instability occurs, twist (the winding of lines around an axis) is converted into writhe (the winding or deformation of the axis itself).

Two competing δ-spot formation mechanisms are strong convective turbulence and flux-tube collisions. 

It may be that δ-spots formed by the kink instability are more of a threat for flares or CMEs than those formed by either of the other methods. But even before that question can be asked, a way to identify an individual δ-spot’s formation method must be found.

Flux tube collisions are somewhat simpler to identify than either δ-spots or convective buffeting.  In order to determine the frequency with which magnetic knots are formed by the kink instability, we have pioneered a method by measuring the twist and writhe which was able to confirm three δ-spots formed by the kink instability.

Isolating the Magnetic Knots from the Entire Sunspot Region

We used data from the Helioseismic Magnetic Imager on board the NASA Solar Dynamics Observatory (HMI/SDO) to study the magnetic knots in sunspot groups and compare the characteristics of δ-spots to simpler sunspots, studying more than 120 regions. 

The research posed several challenges. For example, we discovered we needed to isolate a magnetic knot for study because the dynamics of the knot were lost in the activity of the larger sunspot group (Figure 3). This implies that δ-spot formation mechanisms act on a smaller spatial scale than the size of the average sunspot group (Figure 3)—information that will help us in future efforts to identify and characterize δ-spots.

Figure 3. A δ-spot from 2011 is shown forming in SDO/HMI continuum intensity (left) and magnetic field (right). The red-yellow and blue-green colors show if the magnetic field is negative or positive and the yellow contours in the intensity show the location of the magnetic knot. The dynamics of the smaller magnetic knot are distinctly different from the average behavior of the larger sunspots. (Credit: P. Levin.)

We will continue to build toward a statistically significant sample to determine the relative frequencies at which the different mechanisms are forming these regions, and find out if a particular formation mechanism is more associated with flares than the others.

Mitigating the harmful effects of space weather is an area of research that concerns not only solar astrophysicists, but many others, including geomagnetic researchers, satellite communications specialists, astronauts and more. Ultimately, our study of magnetic knots of δ-spots will improve the ability of the solar physics community to forecast solar storms so that we can minimize their detrimental effects through preventative actions, such as delaying launches, canceling spacewalks for astronauts, changing airplane navigation routes, and safeguarding satellites by shielding sensitive electronics.  


Observations of Twist, Current Helicity and Writhe in the Magnetic Knots of δ-Sunspots Consistent with the Kink Instability of a Highly Twisted Flux Rope

Characterizing the Umbral Magnetic Knots of δ-Sunspots 

Nonlinear Evolution of Kink-unstable Magnetic Flux Tubes and Solar δ-Spot Active Regions

Studies on a very flare-active δ-group: Peculiar δ-spot evolution and inferred subsurface magnetic rope structure