Sunspots

I have had a number of questions about sun spots, so instead of putting them in comments, I thought I'd give a brief overview in a post. Feel free to ask any questions you may still have in comments.

*********************************

The life of a sunspot begins deep in the solar convection zone. Here tubes of strong magnetic field are generated by the dynamo processes. Examples of such magnetic structures appear in our simulations (although not yet our simulations of the sun - this one comes from a solar mass star spinning 3 times faster - but we're getting there), as seen here in a 3-D visualization that I made for the San Diego Supercomputing Center's 2008 calender. The blue and yellow-red bands are two loops of magnetic field in the middle of the convection zone. The fact that they even exist in the middle of violently turbulent convection is amazing - but that is another post. For right now, they are remarkable because they are regions of strong (as much as ~2 Tesla) magnetic field.
Magnetic fields produce pressure in the fluid proportional to the square of the magnetic field. This causes the regions of extremely strong field to expand - thereby becoming less dense than the surrounding fluid. This results in the regions of strong field becoming buoyant and rising. Occasionally, one of these tubes of magnetic field lines makes it all the way through the convection zone and manages to rise out of the photosphere - the solar surface.

In plasmas, the fluid and the magnetic field are stuck together. In most of the sun, fluid forces are much greater than magnetic forces, so the fluid ends up dragging the magnetic field around. In areas of strong magnetic field, however, the magnetic forces dominate and so the fluid can no longer push the magnetic fields around. This means that in a sunspot, the fluid in the spot can no longer mix effectively with the fluid outside of the sunspot. This causes the fluid to cool (and become darker) as it is radiating all of its heat out into space without getting much from the hot plasma around or below it. Thus the sunspot is an indirect effect of the magnetic field looping in and out of the photosphere.

A great picture of a sunspot can be found below. This was taken by the Swedish Solar Telescope, which uses adaptive optics to get really amazing pictures. As you can see, the story I'm telling is a very simplified one, but it is essentially true. With convection turned off by the strong magnetic fields, the only way to get heat into a sunspot is via conduction - a much less efficient process near the solar surface than convection. Conduction , in part, causes the smearing that appears near the edge of sunspots. Solar flares and coronal mass ejections occur when the magnetic field sticks too far out of the solar surface in a upside-down U shape. At some point, the bottom ends of the U get too close together and "reconnect". This reconnection leaves a smaller U shape and a closed loop of magnetic field floating above the solar surface. This closed loop quickly decays, pumping all of the energy stored in the magnetic field into heat which essentially causes a massive explosion releasing magnetic energy as kinetic energy. This explosion can shoot huge amounts of x-rays and 10 million degree plasma into space. Occasionally, we happen to be unlucky enough to get in the way.

Sunspots always obey a few rules:
1) They can never appear alone. In the image above, there is an entire group of spots, which is quite common. But for every field line that exits the solar surface there must be a field line entering the solar surface. This means that sunspots dissapear together - even when there are explosive events like reconnection.
2)For reasons we still don't understand, for each 11 year solar cycle, all of the sunspots in northern hemisphere appear with the same leading polarity and all sunspots in the southern hemisphere will have the opposite polarity in the leading spot. For example, in the current solar cycle, all of the leading spots have the magnetic field pointing out of the surface and the trailing spots have the field pointing into the surface. Every 11 years, that polarity switches.
3)Most sunspots do not causes flares or coronal mass ejections - they simply fade away as the magnetic field slowly diffuses outward.

I hope that answers some questions. Please feel free to ask any more in the comments.

"Public" Science

Last week I got an e-mail from the San Diego Supercomputing Center asking if I would be willing to provide one of the images for their 2008 calendar. Every year SDSC puts out a calendar that they give to people that donate money, funding agencies, people that SDSC wishes would give them money, etc. Since July, I have been working with Steve Cutchin, director of visualization services at SDSC, on adapting our data and his 3-D volume rendering program, Vista, to work with each other. It's been a productive collaboration and I've enjoyed working with Steve, so when SDSC came calling, I was happy to provide one of the images and a short caption.

Little did I know what I was getting myself into. I have made publication quality figures before and I know that a good figure is a bit of trick, but "public" quality figures are a different story. The image I submitted is shown on the right, and let me tell you, it's hard to try and make a scientific image both visually appealing and, in some small degree, understandable to someone who does work in astrophysical fluid dynamics.

The image shows the large (greater than 5 Tesla in magnitude) components of the toroidal magnetic field (red positive, blue negative) in one of our simulations of a sun-like star spinning at three times the solar rate. As you can see, the star's rotation has organized the random, chaotic small magnetic fields generated by the turbulent convection below the star's surface into strong, organized magnetic fields that last for thousands of days (as long as we've run the simulations).

In the sun, the global magnetic fields are believed to be generated in random, small segments in the turbulence of the sun's convection zone and then pulled by down-flows into a region where the sun switches differential rotation (near the Sun's surface, the equator rotates faster than the poles) to solid body rotation rather abruptly. This region of strong shear known as the tachocline organizes the magnetic field into large, coherent structures.

The reason that the image above is remarkable is that in this simulation, there was no tachocline. The simulated region only covered the convection zone, so in some way, this star was able to organize its magnetic field without a layer of strong shear. As far as we know, this is the first time this has ever been demonstrated and there is no known theoretical method for creating this type of field - yet there it is.

The problem is how on earth do I convey the importance of this image to non-physicists in a three sentence caption?

Sadly, the answer is that I can't. It is simply not possible to explain the importance of this image if it is displayed opposite the month of March or June. So the question then becomes, what is my objective? Do I even try to explain what the image means or do I just go for the "Wow, that's very important science" effect?

I'm not sure that there is a good answer to this question, and it certainly isn't going away anytime soon. So how do we make our physics relevant to the public?

The Sun and I

As most of you know, I have ventured into the realm of solar modeling in my research here at Colorado. Specifically, I work of global-scale models of the sun's convection zone, which extends from about 75% of the sun's radius to about 98% of the sun's radius. In this area, energy is being transported mainly by convection - hot fluid rises and cold fluid sinks. When you add a magnetic field, this creates a self-sustaining dynamo that turns convective energy into magnetic energy, which creates a sustained magnetic field in the sun's convection zone.

Magnetic fields play an important role in solar activity. When magnetic field lines poke up out of the solar surface, you get sun spots, flares, and coronal mass ejections - the fireworks. In order to better understand what is driving these explosive events, we need to better understand what is driving the sun's magnetic field and how it changes in time.

Below is a movie created from data from our numerical models of the sun's convection zone. This particular model has been "spun-up" to three times the solar rotation rate in order to exaggerate the effects and speed up the solar cycles. A normal solar magnetic cycle takes 22 years - in this simulation, we see strong magnetic variability in cycles that take about 2 years of simulation time. The movie specifically shows some 3-D visualizations of the toroidal magnetic field (i.e. the magnetic field with the dipole part removed). The positive (in the direction of the sun's rotation) field is displayed in red (strongest) to yellow (weakest). The negative field is displayed in blue (strongest) to purple (weakest). For ease of viewing, only the strong fields are displayed.

As you can see, the magnetic field has organized itself into two bands of magnetic field in the tropics. In this cycle, both bands have been greatly weakened in the second image - particularly the negative (blue/purple) band. Since our model uses constant inner and outer boundary conditions, this clearly shows that the sun's magnetic variability can be caused purely by oscillations in the convection zone.

Aside from the science we are able to do with these types of visualizations, it's also just fun to be able to actually see the 3-D data we work with. In the future, I think that 3-D visualizations are going to become more and more common as more numerical models progress into three dimensions.

These videos were created using Vista, developed at the San Diego Supercomputing Center. Special thanks to Steve Cutchin at SDSC for working with me to get Vista running with our data.