1. Lecture 4 The Corona, Solar Cycle, Solar Activity, Coronal Mass Ejections, and Flares
ESS 154/200C

2. Date Day Topic Instructor Due
ESS 200C Space Plasma Physics ESS 154 Solar Terrestrial Physics M/W/F 10:00 – 11:15 AM Geology Instructors: C.T. Russell (Tel. x-53188; Office: Slichter 6869) R.J. Strangeway (Tel. x-66247; Office: Slichter 6869)
Date Day Topic Instructor Due
1/4 M A Brief History of Solar Terrestrial Physics CTR
1/6 W Upper Atmosphere / Ionosphere CTR
1/8 F The Sun: Core to Chromosphere CTR
1/11 M The Corona, Solar Cycle, Solar Activity
Coronal Mass Ejections, and Flares CTR PS1
1/13 W The Solar Wind and Heliosphere, Part 1 CTR
1/15 F The Solar Wind and Heliosphere, Part 2 CTR
1/20 W Physics of Plasmas RJS PS2
1/22 F MHD including Waves RJS
1/25 M Solar Wind Interactions: Magnetized Planets YM PS3
1/27 W Solar Wind Interactions: Unmagnetized Planets YM
1/29 F Collisionless Shocks CTR
2/1 M Mid-Term PS4
2/3 W Solar Wind Magnetosphere Coupling I CTR
2/5 F Solar Wind Magnetosphere Coupling II;
The Inner Magnetosphere I CTR
2/8 M The Inner Magnetosphere II CTR PS5
2/10 W Planetary Magnetospheres CTR
2/12 F The Auroral Ionosphere RJS
2/17 W Waves in Plasmas 1 RJS PS6
2/19 F Waves in Plasmas 2 RJS
2/26 F Review CTR/RJS PS7
2/29 M Final

3. The Corona over a Solar Cycle
The magnetic field of the Sun varies over the course of the solar cycle.
This variation expresses itself in the sunspots, in the polar magnetic fields and most visibly (at solar eclipses) in the Thompson scattering of sunlight by the coronal electrons.
Here we can see helmet streamers and coronal holes.

4. Temperature Profile of Solar Atmosphere
The Corona
Total Solar Eclipse
EUV
Soft x-rays
Temperature Profile of Solar Atmosphere
The high coronal temperature moves the line emissions from UV to EUV to x-ray energies. The photospheric spectral intensity is weaker at these wavelengths than the corona is, so that the corona can be imaged on the disk.
The white light corona is produced by Thompson scattering of light from electrons. It can be seen during eclipse (as here) when the moon blocks the light from the photosphere.
The Corona can be seen more routinely with coronagraphs with occulting disks to block the photosphere on the ground or on spacecraft.

5. Some Notes on Coronal Field Topology
The ‘open’ field regions are not strictly open because the quiet Sun fields make the magnetic carpet of low-lying loops between open field lines/flux tubes. Very high order Potential Field Source Surface (PFSS) models capture these small loops at the bases of the coronal holes.
The closed field regions of Pseudostreamers are common.
Only the Helmet Streamer Belt has an associated current sheet that originates at its cusps. Pseudostreamers have cusps and magnetic null points only, and separate open fields of the same polarity.

6. Corona in EUV and X-rays
SDO AIA EUV Image (12 Jan 2012)
Hinode XRT soft X-ray Image (5 Jan, 2012)
Temperature of gas emitting seen in EUV is 1,504,000 K.
Structure is associated with magnetic field. Coronal holes at poles appear dark because of the relatively low density and temperature there. The polar plumes seen in EUV are associated with small scale dipolar regions in the magnetic carpet there.
Hottest regions are the strongest active regions closed field lines that also emit x-rays (on right).
Darkest regions are coronal holes where the magnetic field is open.
Coronal holes produce most of the high speed solar wind and are present at the poles except near solar maximum.

7. Potential Field Source Surface (PFSS) Model
The PFSS model is based on the solution of Laplace’s equation for the coronal vector magnetic field in the volume between the photosphere and a spherical source surface outer boundary at ~ Rsun…in terms of a spherical harmonic expansion.
The radial field at the photospheric inner boundary is usually described by synoptic maps constructed from sequences of full-disk magnetograms. The coronal field is assumed to become radial at the source surface.
The PFSS model is similar to spherical harmonic expansions for the Earth’s magnetic field. It isn’t perfect, but much can be learned from it. In particular, because the corona is controlled by the magnetic field it allows us to view its effective ‘skeleton’ to which the plasma is constrained at any time.

8. 3D and synoptic projections:
Examples of PFSS Model Field Solutions
Helmet streamer
belt
Open fields
Coronal holes
3D and synoptic projections:
GONG website
(link at gong.nso.edu)
Source surface neutral line

9. Force-Free Magnetic Fields: Twisted Flux Ropes
Solar magnetic structures in equilibrium can be described by
j B g
Along the magnetic field, there is no contribution from magnetic forces so pressure gradients balance gravity.
If magnetic forces dominate them, j x B = 0. Such fields are called force-free.
Force-free fields have currents parallel to the magnetic field so where α is a scalar function of position.
Taking the divergence, we obtain so that α is constant along a field line.
If α is uniform, then , whose solutions are Bessel functions.
These structures are flux ropes.
Force free field descriptions are often use to describe active region fields which are inferred to be nonpotential by the twisted appearance (‘sigmoids’) of their associated coronal loops.

10. The Corona with Plasma: MHD picture
Open fields/coronal holes
Coronal streamer
Figure from (Pneuman
and Kopp, Sol. Phys,
1971)
Ultimately, one must consider the plasma in the corona and how it affects the field. This requires an MHD approach. This Figure from an early MHD calculation shows what hot plasma pressure does to a dipole field in a vacuum. Notice the production of several domains: closed almost dipolar field loops, stretched closed field loops, open fields. Plasma escapes on the open field. Closed regions can contain the gas pressure via magnetic field forces.

11. The Role of the Magnetic Field: Forces
The momentum equation is u t j B g
The first term is the effect of thermal pressure and the second the effect of magnetic pressure and curvature.
The third term is gravity which is important near the Sun.
If magnetic forces predominate, then we can rewrite or
Therefore, , the Alfven speed.
If plasma is static and the thermal pressure is balanced by gravity, then nkT/L = ρg and L = RT/g = H the scale height.
The magnetic force can be decomposed into
The first term is the magnetic pressure gradient force and the second the curvature or tension force.
We can rewrite as
where the first term on the right is where R is the radius of curvature and n is the normal to the field line in the plane containing the field. The second term cancels the pressure gradient along the field so that there is no j x B force along the field.

12. Coronal Heating
The question of what heats the corona in the first place is an area of intense current research that includes observations and modeling. The favored candidates involve currents or waves. The relevant currents may be at the boundaries of flux tubes which ‘braid’ around each other due to photospheric convection at their footpoints. These dissipate via reconnection and/or produce joule heating. The relevant waves may be Alfven waves produced by the same convective footpoint motions that are reflected in the transition region/corona gradients. The interacting outgoing and ingoing waves may produce plasma turbulence including shocks and their associated heating. This topic is recommended for further reading. This cartoon illustrates the challenge.

13. Solar Cycle: Proxies
The solar cycle is manifested at all altitudes from the photosphere to the corona.
Each altitude produces its own signature most often in phase but not always of similar amplitude.
Measurements from the north and south hemispheres may not be in sync.

14. The Structure of the Corona Evolves with Solar Cycle
The Corona evolves with solar cycle, being simplest near solar minimum. It is organized by the coronal magnetic field.
Coronal holes are low density or dark regions here seen most clearly above the poles.
A bright extended regions that taper with radial distance are coronal streamers
Prominences can be seen on the southeast limb.
Solar Eclipse October 1994 near sunspot minimum
Other HAO eclipse images from 1980, 1991, 1998

15. The Solar Cycle: Sunspot Cycle
Sunspot number is the most widely known signature of the solar cycle. At the beginning of a solar cycle, sunspots appear at northern and southern latitudes ~35 deg., usually before the sunspots of the previous solar cycle have disappeared. Sunspots may disappear just after they emerge or may last for months.
The latitude band where sunspots appear drifts with time toward the equator in both hemispheres so that a ‘Butterfly’ diagram (top) results when the locations at any time are plotted. Each ‘wing’ coincides with a sunspot number cycle. Old and new cycle spots may be present together for awhile as one cycle ends while another begins at the higher latitudes.
A single sunspot cycle has phases referred to as minimum, rising phase, maximum, declining phase. Sunspot cycles typically last ~10-13 years and have longer declining than rising phases. The number of sunspots also varies from cycle to cycle, especially around maximum.

16. Sunspot Cycle: Long-term Behavior
Sunspot number is not a simple calculation. Sunspot group is often used instead of individual spots. The definition of a group can be ambiguous.
Records were not always preserved since the discovery of sunspots.
Were low sunspot counts due to low solar activity, bad weather, wars, lack of interest?
The records during the Maunder minimum are controversial, but the Dalton minimum is probably real.
We note that the sunspot count is quite variable, especially at maximum.
We must remember sunspot number is only one measure of solar activity, and that active regions are often present on the solar surface that do not have associated sunspots if their magnetic fields are weaker than some threshold.

17. The Solar Magnetic Cycle: 22 years
Hale first noticed that the leading and trailing polarities of the fields in active regions switch every cycle, so that the solar magnetic cycle is actually ~22 years and not ~11 years. This ‘Hale Cycle’ also includes the reversal of the high latitude/polar quiet Sun fields that are out of phase with the sunspot number, having maximum strength at solar minimum.
Latitude averages of the field, polar region field averages, and sunspot number

18. Solar Flares: Ribbons
Flares appear in H-alpha, visible and EUV. All can have the two ribbon structure.
They can last only minutes and times and can change dramatically over time.

19. Solar Flare: Standard Model
Magnetic reconnection.
Particles accelerated downward hit the solar surface; upward acceleration releases energetic particles into interplanetary space.

20. Solar Flares: Radio Bursts and X-Rays
Long wavelength solar emissions, radio waves are well correlated with short wavelength gamma and x-rays. There are simultaneous radio waves and those that follow later as the shock wave advances away from the Sun.

21. Coronograph Images of CMEs
These images show CMEs during eruption.
It is clear that these events involve twisted magnetic fields and the expenditure of much energy.
They are usually accompanied by the acceleration of energetic particles as the bottom right slide shows as ‘snow’ in the camera image.

22. Model of a CME Eruption
While the mechanisms that produce coronal mass ejections are still under debate, everyone agrees the process produces twisted magnetic fields.

23. CME Statistics
Coronal mass ejections advance into the solar wind at a variety of speeds, sometimes very, very quickly, over 2000 km/s.
When such disturbances reach the Earth’s magnetosphere, they can cause much damage.

24. Summary
The corona is very hot, over a million degrees, and has a structured magnetic field with “coronal holes” formed by open magnetic field lines mainly over the poles.
The magnetic fields store energy and can accelerate ionized matter. Ropes can be formed that are self-balancing – called force-free magnetic structures.
Magnetic field of Sun varies over the solar cycle as does solar activity.
Solar flares accelerate energetic charged particles.
Coronal mass ejections lead to geomagnetic storms.