1. Introduction to Space Weather
The Sun:
Solar Magnetism
Sep. 17, 2009
CSI 662 / PHYS 660
Fall, 2009
Jie Zhang
Copyright ©

2. Roadmap Part 1: The Sun Part 1: The Sun Part 2: The Heliosphere
The Structure of the Sun: Interior and Atmosphere
Solar Magnetism: Sunspots, Solar Cycle, and Solar Dynamo
Solar Corona: Magnetic Structure, Active Regions, Coronal Heating
Major Solar Activities: Flares and Coronal Mass Ejections
Part 1: The Sun
Part 2: The Heliosphere
Part 3: The Magnetosphere
Part 4: The Ionsophere
Part 5: Space Weather Effects

3. Solar Magnetism: Sunspot, Solar Cycle, and Solar Dynamo
CSI 662 / PHYS September
Solar Magnetism: Sunspot, Solar Cycle, and Solar Dynamo
References:
Kallenrode: Chap 2.1, Chap. 3, and Chap. 6
NASA/MSFC Solar Physics at

4. Plasma Physics 1. Maxwell’s Equations and Generalized Ohm’s Law
Kallenrode: Chap 2.1
Aschwanden: Chap 5.1
2. Magnetohydrokinematics: Magnetic Induction Equation and Frozen-in Magnetic Field
Kallenrode: Chap 3.4
Aschwanden; Chap 5.1
3. MHD Dynamo
Kallenrode: Chap 3.6

5. 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

6. Zeeman Effect
Photospheric measurement is based on Zeeman effect: the splitting of a spectral line because of the presence of magnetic field.
Δλ = 4.7 x λ02 gB
λ0: original wavelength
g: Lande factor, e.g., FeI 6173Å (g=2.5) 
B: magnetic field strength

7. Zeeman Effect Longitudinal magnetic field: circular polarization
SOHO (1995) / MDI (Michelson Doppler Imager)
Transverse magnetic field: linear polarization
SDO (2010) / HMI (Helioseismic and Magnetic Imager)

8. Hale’s Polarity Law +
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9. 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

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

11. 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

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

13. 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

14. 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

15. Solar Magnetic Cycle 22 year magnetic cycle
11 year sunspot number cycle

16. Solar Magnetic Cycle
The Evolution

17. Solar α-Ω Dynamo
Solar dynamo is a process by which the magnetic field in an electrically conducting fluid is maintained against Ohmic dissipation
It is mathematically described by the magnetic induction equation (see Eq in Kallenrode)
Differential rotation
and meridional circulation
Diffusion caused by turbulance
Diffusion caused by electric resistivity
α effect of turbulence twisting the field

18. Solar Differential Rotation
Surface Latitudinal Differential Rotation:
rotation at equator (25 days) is faster than the higher latitudes, progressively slower, at poles (35 days)
Radial Differential Rotation
At equatorial region, interior rotates slower than surface
At polar region, interior rotates faster than surface
Tachocline: at the bottom of convection zone, have the largest shear motion, the location of the generation of strong magnetic field

19. Solar Dynamo: Meridional Flow
The flow of material along meridian lines from the equator toward the poles at the surface and from the poles to the equator deep insid
Dynamo cycle primarily governed by meridional flow speed
(Dikpati, de Toma, Gilman, Arge & White, 2004, ApJ, 601, 1136)

20. Solar Dynamo: Ω-effect
Generation of toroidal field by shearing a pre-existing poloidal field by differential rotation (Ω-effect )
Proposed by Parker (1955)
Mathematically formulated by Steenbeck, Krause & Radler (1969)

21. Solar Dynamo: α-effect
(ii) Re-generation of poloidal field by lifting and twisting a toroidal flux tube by helical turbulence (α-effect)

22. The End