CSI 769 Fall 2010 Jie Zhang

Solar and Heliospheric Physics

Magnetic FieldSep. 9 – Sep. 30, 2010

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, 131-149, 1969

•Sakurai, Takashi.,•Green’s Function Methods for Potential Magnetic Fields, Solar Physics 76, 301-321, 1982

•Schrijver, Carolus J., Derosa, Marc K., •Photospheric and Heliospheric Magnetic Fields, Solar Physics, 212: 165-200, 2003

For NLFF model•Schrijver et al. 2006, Solar Physics 235, P161-190 “Non-Linear Force Free Modeling of Coronal magnetic Fields Part 1: A Quantitative Comparison of Methods

Magnetic Fields

Corona in X-ray

•Why is the corona highly structured?

•Why is it hot?

•Why is it explosive?

Why?

Photospheric Magnetic Field•Magnetogram: measurement of magnetic in the photosphere•Nature of sunspot: areas of concentration of strong magnetic field

Magnetogram Continuum Image

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Hale’s Polarity Law

1. Sunspots are grouped in pairs of opposite polarities

2. 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

3. The leading polarity of sunspots is the same as the polarity in the polar region of the same hemisphere

4. 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

Hale’s Polarity Law

•Butterfly diagram of Magnetic Field•Global dipole field most of the time•Polar field reversal during the solar maximum

Solar Magnetic Cycle

Sporer’s Law: Sunspot emerge at relatively high latitudes and move towards the equator

Other Laws

Joy’s Law: The tilt angle of the active regions is proportional to the latitude

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

•A diagram shows the position (latitude) of sunspot with time•It describe the movement of sunspot in the time scale of solar cycle

Butterfly Diagram of Sunspot

1. Sunspots do not appear at random over the surface of the sun.2. At any time, they are concentrated in two latitude bands on

either side of the equator. But these bands move with time3. At the start of a cycle, these bands form at mid-latitudes (~30°)4. As cycle progresses, they move toward the equator.5. As cycle progresses, sunspot bands becomes wider6. At the end of cycle, sunspots are close to equator and then

disappear7. At the minimum of the cycle, old cycle spots near the equator

overlaps in time with new cycle spots at high latitudes

Butterfly Diagram of Sunspot

Coronal Magnetic Field

Schrijver & Derosa, 2003

Coronal Magnetic Field

Feb. 2, 2008

http://www.lmsal.com/

forecast/index.html

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

Single Sunspot Field•Aschwanden 5.2.1, P179-180

Result of the Analytical Model

Dipole Field•Aschwanden 5.2.2, P180 - 182

Result of the Analytical Model

Force-Free Field

•Force free field: Asch-Chap. 5.3.1•Non-Linear force free field: Asch-Chap. 5.3.3•Shear arcade: Asch-Chap. 5.3.2

•An example of linear force free field•Magnetic Nullpoints and Separators: Asch – Chap. 5.6

Loop Arcade

Loop arcade seen by TRACE (Credit: NASA)

Loop Arcade

Loop arcade seen by TRACE (Credit: NASA)

Loop Arcade

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

Loop Arcade

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

Nullpoint & Separatrix

(Asch—Fig. 5.22)

Nullpoints

2-D X-point (left) and O-point (Asch—Fig. 5.24)

Ref: Asch--Chap. 5.6.1

Priest—Chap. 1.3

The End