1. Introduction to Space Weather
The Sun: Magnetism
Feb. 09, 2012
CSI 662 / PHYS 660
Spring, 2012
Jie Zhang
Copyright ©

2. Roadmap Part 1: Sun Part 2: Heliosphere CH1: Structure
Part 3: Magnetosphere
Part 4: Ionosphere
Part 5: Space Weather Effects
CH1: Structure
CH2: Magnetism and Dynamo
CH3: Magnetic Structure
CH4: Solar Eruptions

3. CH2: Solar Magnetism 2.1. Sunspots and Solar Cycle
CSI 662 / PHYS Feb. 07, 2012
CH2: Solar Magnetism
2.1. Sunspots and Solar Cycle
2.2. Magnetic Field Measurements
2.3. Laws of Solar Magnetism
2.4. Solar Dynamo
Plasma-2: Magnetohydrodynamic (MHD) Equations
Plasma-3: Magnetohydrokinematics
Plasma-4: MHD Dynamo

4. CH2: Solar Magnetism References and Reading Assignment:
KAL CH 3.1 and (on MHD)
KAL CH (on Magnetohydrokinematics)
KAL CH (on MHD Dynamo)
KAL CH (on Solar Cycle)

5. CH2.1 Sunspot and Solar Cycle
Galileo Sunspot Drawing: June 02, 1613

6. CH2.1 Sunspot and Solar Cycle
SDO HMI Sunspot Picture
Feb. 01, 2012

7. CH2.1 Sunspot and Solar Cycle
11-year cycle of sunspot numbers (SSN)
SSN is historically a good index of solar activity.
Correlate well with geomagnetic activities
Maunder Minimum

8. Sunspot and Climate
Thames Frost Fair, ,
By Thomas Wyke

9. Sunspot and Climate
River Thames frost fairs were held on the Tideway of the River Thames at London between the 15th and 19th centuries, during the period known as the Little Ice Age, when the river froze over. During that time the British winter was more severe than now, and the river was wider and slower.
During the Great Frost of 1683–84, the worst frost recorded in England,[1][2][3] the Thames was completely frozen for two months, with the ice reaching a thickness of 11 inches (28 cm) in London. Solid ice was reported extending for miles off the coasts of the southern North Sea (England, France and the Low Countries), causing severe problems for shipping and preventing the use of many harbours.[4] Near Manchester, the ground was frozen to 27 inches; in Somerset, to more than four feet.

10. CH2.2. Magnetic Field Measurements
SDO HMI Magnetogram Image
Feb. 01, 2012

11. CH2.2. Magnetic Field Measurements Magnetogram Continuum Image
Nature of sunspot: areas of concentration of strong magnetic field
The strength is about ~ 500 – 3000 Gauss
As a comparison, the Earth magnetic field is about 0.5 Gauss
Magnetogram Continuum Image

12. 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

13. 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)

14. CH2.3. Laws of Solar Magnetism
1. Sporer’s Law: Sunspot emerge at relatively high latitudes and move towards the equator
2. Hale’s Law: rules of magnetic polarity
3. Joy’s Law: The tilt angle of the active regions is proportional to the latitude

15. 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 -- Sporer’s Law

16. 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

17. Hale’s Polarity Law +
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+ -
+ - -

18. 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

19. Solar Magnetic Cycle 22 years Butterfly diagram of Magnetic Field
Global dipole field most of the time
Polar field reversal during the solar maximum

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

21. Solar Magnetic Cycle
The Evolution

22. CH2.4. Solar Dynamo
Solar magnetic field is generated through a dynamo process
The dynamo is driven by the differential rotation of the Sun
Electric Dynamo: DC Generator

23. CH2.4. Solar 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

24. 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 in the radial direction, the location of the generation of strong magnetic field

25. (Dikpati, de Toma, Gilman, Arge & White, 2004, ApJ, 601, 1136)
Solar 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)

26. Solar αΩ 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)

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

28. The End