World's Largest Solar Telescope Helps To Reveal New Insights Into Sunspots

Note the extremely dark umbra in this delta class sunspot - photo taken by me in November, 1980 using the instrument shown in the side profile  graphic.


Sunspot structure has long been of interest to astronomers from the time these dynamical astrophysical entities could be seen via optical telescope filters. (Such as visible in the image shown taken by me using a catadioptric telescope equipped with Solar Skreen (R)).  In my own research, the focus has been on complex magnetic fields (such as in 'quadripolar'  sunspots) used to classify the morphology of spots and forecast those most likely to yield solar flares.

Of particular interest to me at the time my first research paper was published was the nature of "umbral dots". These "dots" were actually tiny bright points with scales 300-400km across, scattered around the umbra and roughly the same temperature as the photosphere.(Which is about 1500K hotter than the dark umbral regions of sunspots)

How to account for the umbral dots, say using magnetic flux tube models? The only way to explain the dots using a single flux tube model would be propose that each dot is a sign of convection still going on inside the tube. If this is so each dot represents a column of rising plasma that must have done a tremendous amount of work against the magnetic field.

At the time solar astronomers were left with a quandary. If the dots represented the upper area of a rising convective column then where was the 'return' or downward column? What route would it take? Logically, it was initially believed that the penumbra of spots answered this question. However, measurements of the so -called Evershed effect showed the plasma motions to be radial and inwards. There did not appear to be any 'escape hatch' for the rising gas columns represented by the umbral dots. This being the case sunspots ought to heat up and reach equilibrium with the surrounding photosphere after a few days, and yet spots with umbral dots were observed to last weeks.

And so the "multiple flux tube" model of Eugene Parker was born (cf. Astrophys. J., 230, 905-13). In the diagram shown below note the geometry of the field lines extending from beneath the photosphere (in the convective zone) to far above it. The 'flaring field' on top is buoyant for reasons that have to do with the stratification of the solar atmosphere. The Wilson depression is shown as the indentations at the umbral surface on either side.



Note carefully that we have, in effect, a single flux unit up to a distance 'x'  below the umbral surface. After that, the multiple flux tube structure becomes quite evident. Observe further that regions of field-free gas occur between the separate flux elements. Lastly, the arrows labeled v _d indicate the direction of the convective downdraft. This downdraft has a twofold purpose in Parker's model:

I) To 'herd' separate flux tubes together and keep them together, and
2) To remove heat from beneath the sunspot

Parker in his paper (ibid.) showed that the downdraft velocity needed to remove heat from beneath a sunspot  (at a depth of 2500- 5000 km) is on the order of the Alfven velocity for this region or about 2 kilometers per second. This then is adequate to provide the observed umbral energy flux of 0.2 F _o  where F _o  denotes the normal photospheric flux.

A key fact relevant here is that heat flux and magnetic field strength is independent of sunspot area. The parameter that best helps to explain this is the vertical distance 'x'  which the model predicts is characteristic of all sunspots whether they be 4,000 km or 40,000 km across. Calculations by Parker show x = 1150 km approximately. It is the limiting distance below which an instability would occur in a single flux tube.

All Parker's earlier work has now been amplified and built upon thanks to  groundbreaking images of the Sun captured by scientists at Big Bear Solar Observatory (BBSO) which have provided us the first-ever detailed view of the interior structure of umbrae.  Their research was presented last week at the first Triennial Earth-Sun Summit meeting between the American Astronomical Society's Solar Physics Division and the American Geophysical Union’s Space Physics and Aeronomy section in Indianapolis. The high-resolution images, taken through the observatory’s New Solar Telescope (NST), show the atmosphere above the umbrae to be finely structured, consisting of hot plasma intermixed with cool plasma jets as wide as 100 kilometers.   Thus, we are now at a scale four times less than that observed for the umbral dots.

According to Vasyl Yurchyshyn, a research professor of physics at NJIT and the lead author of two recent journal articles based on the NST observations:

“We would describe these plasma flows as oscillating cool jets piercing the hot atmosphere. Until now, we didn’t know they existed.  While we have known for a long time that sunspots oscillate – moderate resolution telescopes show us dark shadows, or penumbral waves, moving across the umbra toward the edge of a sunspot – we can now begin to understand the underlying dynamics,”


The oscillating jets, called spikes,  result from the penetration of magnetic and plasma waves from the Sun’s photosphere  into the adjacent chromosphere, which they reach by traveling outward along magnetic flux tubes that serve as energy conduits. 

Sunspots are formed when strong magnetic fields rise up from the convection zone, a region beneath the photosphere that transfers energy from the interior of the Sun to its surface. At the surface, the magnetic fields concentrate into bundles of flux elements or tubes, which prevent the hot rising plasma from reaching the surface. This energy deficit causes the magnetic bundles to cool down to temperatures about 1,000 degrees lower than their surroundings. They therefore appear darker against the hotter, brighter background.

Yurchyshyn added:

“But the magnetic field is not a monolith and there are openings in the umbra from which plasma bursts out as lava does from a volcano’s side vents. These plumes create the bright, nearly circular patches we call umbral dots. Sunspots that are very dark have strong magnetic fields and thus fewer openings.”

Thus, the connection is now evident between the strength of the field and the frequency of the umbral dots in sunspots

Yurchyshyn again:

“We had no sense of what happens inside an umbra until we were able to see it in the high-resolution images obtained with the world’s largest solar telescope. These data revealed to us unprecedented details of small-scale dynamics that appear to be similar in nature to what we see in other parts of the Sun. There is growing evidence that these dynamic events are responsible for the heating of coronal loops, seen in ultraviolet images as bright magnetic structures that jet out from the Sun’s surface. This is a solar puzzle we have yet to solve.”

Since it began operating in 2009, Big Bear’s NST has given scientists a closer look at sunspot umbrae, among other solar regions. It has also allowed them to measure the shape of chromospheric spectral lines, enabling scientists to probe solar conditions.

“These measurements tell us about the speed, temperature, and pressure of the plasma elements we are observing, as well as the strength and the direction of the solar magnetic fields,” said Yurchyshyn, who is also a distinguished scholar at the Korea Astronomy and Space Science Institute. “Thus we were able to find that spikes, or oscillating jets, are caused by chromospheric shocks, which are abrupt fluctuations in the magnetic field and plasma that constantly push plasma up along nearly the same magnetic channels.”

The study on umbral spikes was published in the Astrophysical Journal in 2014. In a second paper published in the Astrophysical Journal in 2015,  another set of NST observations is presented, taking a closer look at the sunspot oscillations that occur every three minutes and are thought to produce bright umbral flashes - emissions of plasma heated by shock waves.

The NST takes snapshots of the Sun every 10 seconds, which are then strung together as a video to reveal fast-evolving small explosions, plasma flows and the movement of magnetic fields. “We were able to obtain photographs of these flashes of unique clarity that allowed us to follow their development inside the umbra,” he said. Previously believed to be diffuse patches randomly distributed over the umbra, the researchers found their location is in fact not random. They mainly form along so-called sunspot umbral light bridges, which are very large openings in the sunspot magnetic fields that often split an umbra into two or more parts.

“Even more importantly, we found that umbral flash lanes tend to appear on the side of light bridges that face the center of the sunspot,” Yurchyshyn added. “This finding is significant because it indicates that sunspot oscillations may be driven by one energy source located under the umbra. There are simulations that appear to reproduce what we have observed, which is very encouraging. We, as a community, are finally in the position to be able to directly compare the observations and the state-of-the-art simulation results, which is the key to making further progress in our field.”

This strongly suggests to me more intense research, by way of numerical simulations, into the plasma dynamics that may be at work, sub-umbra. In particular, this might represent an opportunity to get beyond the MHD plasma regime, to investigate say the plasma from two fluid theory. We know MHD (magnetohydrodynamics) actually arises from a progressive degradation in physical detail, starting from two-fluid theory, to one fluid theory to MHD. (See e.g. Chen, Introduction to Plasma Physics, Ch. 7)

The two-fluid regime embodies much more detail and accuracy than the cruder 1-fluid and MHD approaches, though it is or can be more difficult to apply. Basically given an "ion fluid" and an "electron fluid" and  there are three essential equations which apply to describe the properties, one for continuity, the other for force.

1)      ¶r _a / ¶t  +  Ñ ·(r_a v_a) =  0

2)     r_a ¶v / ¶t  +  r v_a·Ñ v_a  = -Ñ p _a +    e_a n_a (E  +  v_a X B )

3)     p _o r_a ^γ  = const     

(Where the alpha subscript denotes e,i  for electrons, ions) .  For completeness these are then combined with Maxwell’s equations. See, e.g.

http://brane-space.blogspot.com/2015/03/solar-electrodynamics-part-3-of-3.html

One relatively straightforward numerical simulation would entail "explicit differencing."

Explicit differencing implies that the update is obtained from preceding quantities known in the vicinity of the particular node i, i.e., this form of model usually requires nodes i-1, i, and i+1.  Assume information is carried in the simulation with a velocity v_{a  typ}  implying that the information is carried a distance L = v_{a  typ}  *(Dt) in a single time step Dt.  The information could be a wave or temperature front and the typical velocity could be a phase velocity like the ion sound speed in the medium.

However, if L is much larger than the grid separation Dx then it travels more than a single grid spacing in one time step.  Of course, explicit finite difference methods are subject to a stability for any given time step such that:

Dt <   O (Dx/ v_{a typ} )

Which is known as the Courant condition.

Since the update of density ( r_a) for example, uses only local information then the arrival of some wave front - say from an umbral oscillation - cannot be predicted correctly at any given grid point or node.  Thus, the maximum velocity that can be resolved by an explicit numerical scheme is given by, e.g.

v _max =  (Dx/ Dt)

yielding the condition:  Dt <   Dx/ v_{a typ}   

As per the Courant condition above. In a future blog I will suggest ways of  numerically simulating two fluid behavior for the sub-umbral plasma regime.