Parker Solar Probe Provides Hitherto Unknown Insights Into The Corona

Artist's conception of the Parker Solar Probe

The Parker Solar Probe  is in the news again- a welcome break from Trump -  with further discoveries providing novel insights into the physics of our Sun.   Important,  because the Sun is the only star we can study up close, using actual sacecraft and instruments..  To many of us who've invested  significant segments of our lives in solar research it is fitting the probe is named after Eugene Parker, seen as the father of solar physics. It was while Dr. Parker was still a budding young astrophysicist at the University of Chicago that he wrote a seminal paper in 1958 about the solar wind and its association with the interplanetary magnetic field. (Parker, E.N. : Dynamics of the interplanetary gas and magnetic fields,” 128, 664, Astrophys. J., 1958.) The paper can be accessed at the link below for those interested:

http://adsabs.harvard.edu/full/1958ApJ...128..664P

Fast forward some 21 years, to ca. 1979. Measurements over decades 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. 

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  e.g.

v  _A   = B_o  / [m ₀  r _o]  ^{1/ 2}

for this region, where   B_o  is the equilibrium magnetic field,  m ₀  is the magnetic permeability of free space,  and r _o   is the plasma density. This leads to v  _A   =  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.

The full paper can be accessed here:

http://articles.adsabs.harvard.edu//full/1979ApJ...230..905P/0000905.000.html

We now know that NASA's  probe  has flown closer to the Sun than any spacecraft before. In so doing it has beamed back its first observations from the edge of the Sun’s atmosphere, called the corona.   The first tranche of data offers clues to its long-standing mysteries, including why the the corona, is hundreds of times hotter than its surface, as well as the precise origins of the solar wind.  According to Prof Stuart Bale, a physicist at the University of California, in Berkeley, who led the analysis from one of the craft’s instruments:

“The first three encounters of the solar probe that we have had so far have been spectacular.  We can see the magnetic structure of the corona, which tells us that the solar wind is emerging from small coronal holes; we see impulsive activity, large jets or switchbacks, which we think are related to the origin of the solar wind. And we are also surprised by the ferocity of the dust environment.”

Here is the paradox we face  in solar physics: the corona is at an estimated  2 million degrees Kelvin, but the actual solar surface (photosphere) is only in the "thousands” of degrees.   This pointed out by  Prof Tim Horbury, a co-investigator on the Parker Solar Probe Fields instrument (based at Imperial College London.)   According to Prof. Horbury:

 “It’s as if the Earth’s surface temperature were the same, but its atmosphere was many thousands of degrees. How can that work? You’d expect to get colder as you moved away.”

The critical clue for this disparity  is that there is a rapid release of energy from the solar interior into its corona and this could help explain why the latter is so staggeringly hot compared to the solar surface.   The Parker Fields instrument  observations have indeed  revealed that the particles in the solar wind appear to be released in explosive jets called switchbacks, rather than being radiated out in a steady stream.   

“It’s bang, bang, bang,” said Horbury, in a recent interview with the UK Guardian. Fine, but what about the "bang"? Exactly what are these 'switchbacks'?

They appear to be, as the name implies, rapid "flips" in the direction of the magnetic field which flows out from the Sun, embedded in the solar wind. 

These switchbacks into the corona could help explain the temperature anomaly by way of their rapid reversals of  the localized magnetic fields and the rapid release  of stored magnetic energy into the ambient plasma..  This then affecting the "Strahl" electrons of the solar wind stream.  (See e.g. the linked paper at the end :'A Step Closer To The Sun's Secrets')   Thus, localized field reversals - which can last anywhere from a few seconds to several minutes -  are the drivers for the localized enhancements in the radial component of the plasma velocity .(The component directed away from the Sun's center)  The energy released into the plasma can  be enormous given the stored magnetic energy:

E _m   =      B² / 2 m

Where B is the magnetic induction (B =  m H )  and  m is the magnetic permeability. Given a magnitude of field intensity (H)  of 0.1 T (Tesla) and an order of magnitude for  m  of  10^-7  H/m  it can easily be seen the magnetic energy would be sufficient to trigger explosive release, say if the energy change occurred in seconds.  According to one solar physicist (Justin Kasper)  from the Univ. of Michigan:

"We are detecting remnants of structures from the Sun being hurled into space and violently changing the organization of the flows and magnetic field. This will dramatically change our theories for how the corona and solar wind are being heated."

Yet another  Parker probe surprise was the dustiness of the region close to the Sun. During the nearest approach of its orbit, the probe was peppered with a fine dust, chipping tiny pieces off its heat shield.  These detached pieces showed up as white streaks in images captured by the high-resolution camera. The dust is thought to be the remains of asteroids and comets that came close to the sun, causing them to evaporate, leaving behind just a dusty haze.

The new observations were made when Parker was about 15m miles (24m km) from the Sun. But this is just a tease for what will follow, given 21 more progressively closer passes.  The final one will  fly to about 6m km of the solar surface — more than seven times closer than the previous closest mission, the Helios 2 spacecraft in 1976.

The extreme conditions faced by Parker have required the use of unconventional materials and spacecraft design. The craft’s white ceramic heat shields will reach a temperature of nearly 1,400C (2,552F) during the mission’s closest approach. As it passes close to the sun, its solar panels are retracted into the shadow of the heat shield, with just a tiny area remaining exposed to generate power. The craft has also broken the record for the fastest moving spacecraft, relative to the sun. It will reach speeds of nearly 435,000 mph (700,000 km/h) in 2024.

“It’s a very bold mission, it’s really extreme and it’s an enormously impressive engineering effort,” said Prof.  Horbury.

Interested readers can access the primary findings  in three papers in the journal Nature.  (Each paper opened has links to the others, including pdfs.)

What Aspects Of The Coming Total Solar Eclipse Are Most Critical For Astrophysics?

Image showing totality in a previous  solar eclipse. The Sun is totally blocked out by the Moon - in the line of sight- and the solar corona is seen expanding from the solar limb


Graphic showing the path for Aug. 21 total eclipse - and the partial zones to either side, with the percentages of the Sun to be covered.

As we approach August 21 and the first total eclipse to appear in in the U.S. in38 years, many are trying to stay ahead of the fervid hype. Here are the only two things you need to know: 1) In most of the U.S. the eclipse will be seen as partial only and you need special glasses in order to observe the transition to maximum coverup, and 2) If you want to observe the total eclipse (see top image) you will have to travel to some place within the band of totality (see graphic).  For example, in our location (Colorado Springs) the Sun will be roughly 85 percent covered.

Here's the skinny on stats for this eclipse: Approximately 12 million Americans will be directly in the totality band shown in the graphic. Another 88 million will be within 200 miles of some place inside the totality band. Naturally then, those living in communities right in the band (e.g. Jackson Hole, WY, St. Joseph, MO) are expecting eclipse watchers to pour in and pump up their economies - buying t-shirts, special glasses and other paraphernalia.

While the basic image of totality will be the appeal for casual observers,  and even partial eclipse will occur for (and excite)  many others, this doesn't hold quite the same spell for solar physicists or astrophysicists. They look to good observations made during totality, namely to be able to record and analyze the solar corona.   This is the outermost region of the solar atmosphere, at millions of kelvins temperature and extending sometimes millions of kilometers into space.

The corona up to now has presented a mystery, especially in terms of its "inverse" increasing temperature profile considered in the context the general temperature profile is steadily decreasing from the Sun's interior to outside.   For example, the Sun's "surface" or photosphere has an effective temperature of 5,777 K .   The corona's temperature by contrast is at least 2 million degrees K.

How did we find this out?  The key breakthrough probably arrived in 1939 when astronomer Walter Grotrian found that a previously discovered spectral line (attributed to "coronium") was actually 13 times ionized iron. Since it takes enormous energy to ionize even one iron atom (meaning stripping one of its outer electrons away) this meant the iron had to be subject to enormously high temperatures.  Indeed, such ions can only exist in plasmas with temperatures between 1 million and 5 million K.

The first clue as the cause of the extraordinary hearing came with high altitude rocket flights in the 1970s, bearing x-ray telescopes. These showed  features down to a resolution of 1 arcsec or 730 km.  Careful observations showed a positive correlation between the x-ray brightness of active regions (i.e. containing complex sunspots) and plasma-filled magnetic loops, e.g.



















The above image was taken by the much more recent Atmospheric Imaging Assembly, built for the Solar Dynamics Observatory . But you easily get the idea noting the brightness (representative image taken at  211Å) and the magnetic loop structures.

Another milestone occurred when Eugene Parker predicted the hot corona must expand into space as a solar "wind". It could not remain stationary or in place with no expansion. The proof of this is left at the end for those interested.

The next question, of course, is where the energy comes from not only to heat the corona but accelerate the solar wind which is an extension of it.  We believe now that MHD or "magnetohydrodynamic" waves of some type provide an answer.   Field lines such as shown in the previous image are rooted at both ends in the Sun's convection zone where they are jostled by the churning of convective cells.  If sufficiently rapid these field line motions could generate magnetic waves capable of carrying energy upward into the loop.   It seems that Alfven waves e.g.

http://brane-space.blogspot.com/2011/04/getting-handle-on-alfven-waves-2.html

are the most effective in reaching coronal heights. (Alas, Alfven waves do not compress the ambient plasma so we still need to identify some other mechanism that can effectively transfer the wave energy to the plasma. A clue may lie with Landau damping, say associated with a beam (or 2-stream)  instability in the plasma. We have a dual Maxwellian profile.


In the region where the slope is positive (¶f(v)  / ¶ v > 0) there is a greater number of faster than slower particles so a greater amount of energy is transferred from particles to associated (e.g. Alfven) waves.  Since f _eb contains more fast than slow particles a wave is excited.

But in Landau damping, with the slope negative (¶f(v)  / ¶ v < 0) the number of particles slower than the waves phase velocity exceeds the number of those that are faster. Thus, more particles gain energy from the wave than lose energy to it.

Whatever new data the eclipse generates, and there will be lots of it, we can be confident that the mysteries of the solar corona won't be solved even after it's all analyzed and multiple papers published. But I will keep readers abreast of any new findings say that appear in the next 8-12 months.

Those interested in actual scientific participation are invited to go to the Globe Observer site, where you can collect the app and then be prepared to make temperature measurements.

https://observer.globe.gov/

See also:

https://www2.mps.mpg.de/meetings/ccmag/dokumente/presentations/A.04.06.pdf

----------
Proof that the corona can't be stationary:

A static corona  superficially appears  to be quite reasonable but that’s why we need to test this is so. The first one to do this was Sydney Chapman. He began by first assuming the condition for hydrostatic equilibrium applied:

dp/ dr = - r {GM_s/ r²}

where G is the usual Newtonian gravitational constant, and r defines the plasma density for the corona, while M_s is the mass of the Sun, and r the distance from the solar center:

r = n(m_p)

with n the number density for protons

The coronal pressure (P) is given by:

P = 2 n T

Provided both protons and electrons are assumed to have the same temperature.

The thermal conductivity of the corona is dominated by electron thermal conductivity and takes the form:

k = k_o T ^5/2

for typical coronal conditions the value of k is about 20 times the value of copper at room temperature.

The coronal heat flux density is:

q = -k Ñ T

A static corona means heat inputs cancel heat outputs so that the divergence:

Ñ× q = 0

Assuming a spherical symmetry for the corona one can write:

1/r² [d/dr (r² k_o T ^5/2  dT/dr)] = 0

    Obviously the preceding assumptions mean there must be some distance where the coronal temperature becomes zero.

From the above equation one should be able to show:

d(T ^7/2) = 7/2 (F T_o ^5/2)/ 4 p k_o d(1/r) = C d(1/r)

where C is a constant.

The integral is:

T_o ^7/2 - T ^7/2 = C[ 1/R_o - 1/r]

Now, set the temperature at infinity (T) to zero and obtain:

C = R_o T_o ^7/2 

which fixes the total flux at:

F = 2/7   [4 p R_o k_o T_o ]

After another step, one finds:

T(r) = T_o (R_o / r) ^2/7

    This gives the temperature T at a distance from the Sun= r. This is based on using a defined value (say T_o = 2 x 10⁶ K) at a defined distance, say R_o = 7 x 10⁸ m.

    For example, at the Earth’s distance (r = 1.5 x 10¹¹ m) one would find: T = 4.3 x 10⁵ K

    This seems fine, until one examines the pressure.

    Analogous to the temperature formalism, we have, the pressure p(r) at some distance r defined by:

p(r) =

p(R_o) exp [7/5 GM_s m_p/ 2 T(R_o) R_o {( R_o / r)^5/7 – 1}]

    Now, if one allows r to approach infinity, e.g. r ®¥ an interesting thing occurs in the equation, as we can see. That is, the denominator of the first term in the end brackets becomes so large (R_o / ¥) that the first term vanishes.

Then we are left with the expression for the pressure:

p(¥) = p(R_o) [exp – 7k/5 * 1/ T(R_o) R_o]

where ‘k’ denotes a constant composed of all the constant quantities in the previous eqn. (G, M, m_p etc)

    Substituting the given values into the above, one finds p(R_o) multiplied by a factor

exp[0] = 1

    The reason is that the exponential of a very small and negative valued magnitude ® 0

Then:

p(¥)  »  p(R_o)

But this can’t be since the pressure of the coronal base would then be the same as the value at infinity!

    This led astrophysicists to conclude an unphysical result, and that the static coronal model couldn’t be accurate.

    If the static model were accurate, the pressure at infinity should be zero, p(¥)   = 0, not a small finite pressure that’s effectively equal to the coronal base pressure. This finding led to the further investigations that disclosed a solar “wind” had to flow outwards from the corona.

Why I'm Excited About the Parker Solar Probe

Artist's conception of the Parker Solar Probe which will approach within 4 million miles of the Sun.

As a long time solar researcher, I was excited to hear the NASA announcement on Wednesday to launch an unprecedented mission directly into the solar atmosphere.  That means coming within 4 million miles of the solar surface  (photosphere) and withstanding temperatures of up to 2,500 F.  In fact, I don't remember being this revved up about a solar mission since the mid-1980s when the Solar Optical Telescope was to have made ground breaking investigations - but was scuttled as a result of budget cuts. See e.g.

http://brane-space.blogspot.com/2011/06/telescope-that-never-was.html

By contrast, the Solar Probe Plus - renamed the "Parker Solar Probe" after solar physicist Eugene Parker, is already fully funded to the tune of $1.5 billion. For perspective, this is less than half of what we waste on Afghanistan in a given month ($3.1 b).

Thomas Zurbuchen, associate administrator for the agency's Science Mission Directorate in Washington, said in the accompanying announcement:

"This is the first time NASA has named a spacecraft for a living individual. It's a testament to the importance of his body of work, founding a new field of science that also inspired my own research and many important science questions NASA continues to study and further understand every day. I'm very excited to be personally involved honoring a great man and his unprecedented legacy."

NASA had previously named about 20 spacecraft after distinguished researchers, including major space telescopes like Hubble, Chandra and Spitzer, as well as smaller missions like Fermi.  However until now NASA had never named a spacecraft after a researcher during their lifetime.

Why is Eugene Parker so special ?  Well, to many of us who've invested segments of our lives into solar research he is seen as the father of solar physics. It was while Dr. Parker was still a budding young astrophysicist at the University of Chicago that he wrote a seminal paper in 1958 about the solar wind and its association with the interplanetary magnetic field. (Parker, E.N. : Dynamics of the interplanetary gas and magnetic fields,” 128, 664, Astrophys. J., 1958.)

The paper can be accessed in full here:

http://adsabs.harvard.edu/full/1958ApJ...128..664P

Fast forward some 21 years, to ca. 1979. Measurements over decades 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.

The full paper can be accessed here:

http://articles.adsabs.harvard.edu//full/1979ApJ...230..905P/0000905.000.html


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 of this served as an immensely useful guide when I wrote my thesis relating sunspot morphology to the occurrence of a special type of solar flare. Indeed, Parker's multiple flux tube model figured into the essential morphological characteristics when I invoked magnetic classes as one barometer for flare frequency.

From all these points of view, the use of Eugene Parker's name for this novel spacecraft is welcome and quite understandable. Indeed, the mission is a culmination of Prof. Parker's research in the fields of solar physics and heliophysics (the latter distinguished from the former on the basis of the extent of the solar wind, e.g. into the heliosphere - or the magnetically affected region that extends beyond Pluto's orbit).

The dynamics for the probe are now known in essence and entail entering a preliminary solar orbit, followed by seven flybys of Venus using its gravity to edge closer to the Sun, ultimately reaching the atmosphere at a distance of 3.8 million miles. At its peak the probe will be moving at 430,000 mph and will then commence near orbits of the Sun, making varied measurements as well as taking images - at least many of which are hopefully of coronal loops - increasing dramatically the existing resolution.  We already have a generic, hypothetical  profile for such loops, e.g.

 But we really need to refine it in order to narrow down the origin of any instability that might occur, say to release a loop flare.  Most experts on coronal loops I've spoken to at assorted solar conferences believe we need a resolution of at least 0."40 or better.  This is roughly equal to the separation of a close binary star system. (Slightly larger than the separation for Beta Cygni.)

Naturally, I'm excited because if such coronal observations are also made they would be what my own (1980s) research lacked because of the untimely scuttling of the Solar Optical Telescope owing to budget cuts. This occurred just as my research was wrapping up.

Also critical - and which I look forward to - is the enhancement of space weather forecasting potential.  Space weather phenomena include: solar flares and especially coronal mass ejections, e.g.

http://brane-space.blogspot.com/2016/12/coronal-mass-ejections-successfully.html


As we know these violent events can affect everything from electrical grids and GPS systems to the navigation controls of aircraft.  If a monster flare triggered a "central meridian"  CME we could expect adverse effects on all GPS positioning satellites. Bear in mind that GPS, besides providing directions for road users, allows synchronized cell phone conversations, as well as orchestrates air traffic not to mention 'date stamping' most financial transactions and guiding the dynamic positioning of the majority of deep sea oil drilling and gas operations.

Imagine then the same deep sea operations and financial transactions (say if you wish to redeem mutual fund shares) occurring when erroneous GPS info is received because a monster flare's radiation has knocked the timing off by even 1 millionth of a second (given the geo-spatial positioning measures accuracy to a few billionths of a second accuracy)? The resulting hundred fold or more time divergence would have catastrophic consequences.


For many of us who've been deeply involved in solar physics research, the Parker Solar Probe can't take off soon enough.

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.