1. Solar and Heliospheric Physics
Magnetic Field
Sep. 9 – Sep. 30, 2010
CSI Fall Jie Zhang

2. Magnetic Fields References: Aschwanden: Chap. 5.1 – 5.6
Supplement articles for PFSS model
Altschuler, Martin D., Newkirk, Gordon, Jr.,
Magnetic Fields and the Structure of the Solar Corona, Solar Physics 9, , 1969
Sakurai, Takashi.,
Green’s Function Methods for Potential Magnetic Fields, Solar Physics 76, , 1982
Schrijver, Carolus J., Derosa, Marc K.,
Photospheric and Heliospheric Magnetic Fields, Solar Physics, 212: , 2003
For NLFF model
Schrijver et al. 2006, Solar Physics 235, P
“Non-Linear Force Free Modeling of Coronal magnetic Fields Part 1: A Quantitative Comparison of Methods

3. Why? Why is the corona highly structured? Why is it hot?
Why is it explosive?
Why highly structured? Holes, loop arcades, s-shaped loops, flux rope stricutre
Why is hot? That leads to expansion into solar wind
Why is explosive, leading to flares and CMEs, the sources of space weather
Corona in X-ray

4. Photospheric Magnetic Field Magnetogram Continuum Image
Magnetogram: measurement of magnetic in the photosphere
Nature of sunspot: areas of concentration of strong magnetic field
Magnetogram Continuum Image

5. Hale’s Polarity Law +
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+ -
+ - -

6. Hale’s Polarity Law
Sunspots are grouped in pairs of opposite polarities
The ordering of leading polarity/trailing polarity with respect to the east-west direction (direction of rotation) is the same in a given hemisphere, but is reversed from northern to southern hemisphere
The leading polarity of sunspots is the same as the polarity in the polar region of the same hemisphere
From one sunspot cycle to the next, the magnetic polarities of sunspot pairs undergo a reversal in each hemisphere. The Hale cycle is 22 years, while the sunspot cycle is 11 years

7. Solar Magnetic Cycle Butterfly diagram of Magnetic Field
Global dipole field most of the time
Polar field reversal during the solar maximum

8. Other Laws
Sporer’s Law: Sunspot emerge at relatively high latitudes and move towards the equator
Joy’s Law: The tilt angle of the active regions is proportional to the latitude

9. Solar Cycle 11-year cycle of sunspot number (SSN)
SSN is historically a good index of solar activity.
Correlate well with geomagnetic activities

10. Butterfly Diagram of Sunspot
A diagram shows the position (latitude) of sunspot with time
It describe the movement of sunspot in the time scale of solar cycle

11. Butterfly Diagram of Sunspot
Sunspots do not appear at random over the surface of the sun.
At any time, they are concentrated in two latitude bands on either side of the equator. But these bands move with time
At the start of a cycle, these bands form at mid-latitudes (~30°)
As cycle progresses, they move toward the equator.
As cycle progresses, sunspot bands becomes wider
At the end of cycle, sunspots are close to equator and then disappear
At the minimum of the cycle, old cycle spots near the equator overlaps in time with new cycle spots at high latitudes

12. Coronal Magnetic Field
Schrijver & Derosa, 2003
Magnetogam image, coronal loops, extrapolated coronal magnetic field

13. Coronal Magnetic Field
Feb. 2, 2008
Synoptic calculation
Surface magnetogram used data assimilation to take into account the evolution on the backside of the Sun.

14. Potential Field Aschwanden 5.2 Unipolar field Dipole field
Potential field calculation methods
Green’s function methods
Eigenfunction expansion methods
PFSS model

15. Result of the Analytical Model
Single Sunspot Field
Aschwanden 5.2.1, P
Result of the Analytical Model

16. Result of the Analytical Model
Dipole Field
Aschwanden 5.2.2, P
Result of the Analytical Model

17. Force-Free Field Force free field: Asch-Chap. 5.3.1
Non-Linear force free field: Asch-Chap
Shear arcade: Asch-Chap
An example of linear force free field
Magnetic Nullpoints and Separators: Asch – Chap. 5.6

18. Loop Arcade
Loop arcade seen by TRACE (Credit: NASA)

19. Loop Arcade
Loop arcade seen by TRACE (Credit: NASA)

20. Loop Arcade
Loop arcade, shear motion, and formation of prominence (Van Ballegooijen & Martens, 1989)

21. Loop Arcade
Force Free Field of a Sheared Arcade – Analytic Solution (Asch—Fig. 5.4)

22. Nullpoint & Separatrix
(Asch—Fig. 5.22)

23. Nullpoints 2-D X-point (left) and O-point (Asch—Fig. 5.24)
Ref: Asch--Chap
Priest—Chap. 1.3

24. The End