Solar Magnetic Field, Solar Cycle, and Solar Dynamo

1. CSI 769-001/PHYS 590-001 Solar Atmosphere Fall 2004 Lecture 04 Sep. 22, 2004 Solar Magnetic Field, Solar Cycle, and Solar Dynamo

2. Magnetic Field is the governing force • Govern the structure of the outer atmosphere • No magnetic field, no corona and possibly no chromosphere • Govern the solar activity • Govern the heliospheric structure and space weather

3. Sunspot Observed in continuum visible light as Galileo did

4. Photosphere: Sunspot (cont.) • A phenomenological description of something we see • Been noticed in ancient time • Since 1700, systematic record of sunspot number • Sunspot was found to be a magnetic feature in 1930 • Sunspot is half the brightness. • B = σT4 ,Or T ~ B 1/4 • Tspot/Tsun=(Lspot/Lsun)1/4=(0.5)1/4 = 0.84 • Tsun = 5700 K • Tspot = 5700 * 0.84 = 4788 K • Sunspot is about 1000 K cooler than surrounding

5. Sunspot: balancing (ctnl.) • Pext = Pint + Pmag • Pext: external thermal pressure • Pext = Next * K *Text • N: particle density • K: Boltzmann;s constant • T: temperature • Pint: internal thermal pressure • Pint= Nint * K * Tint • Pmag: magnetic pressure inside sunspot • Pmag = B2/8π • B: magnetic field strength in the sunspot • Pext > P int, because Text > T int, but B helps the balance

6. Sunspot: structure (ctnl.) • Sunspots show two main structures: • Umbra: a central dark region, • Penumbra: surrounding region of a less darker and filamentary zone SOHO/MDI 2004/10/24

7. Mangetic Field of Sunspot Observed by a magnetogram

8. Magnetic Field: Measurement (ctnl.) • Zeeman effect • The splitting of a spectral line because the presence of magnetic field. • The electrons moving along different magnetic direction may have different energy

9. Magnetic Field: Measurement (ctnl.) • A magnetograph measures the wavelength shift of certain spectral lines; the shift is proportional to the wavelength as • Δλ = 4.7 x 10-13 g λ2 H • λ: wavelength • g: Lande factor • H: magnetic field strength • Reference: Zirin (1966), P. 368

10. Magnetic Field: (ctnl.) • 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.

11. Magnetic Field: (ctnl.) • Hale’s polarity law + - + - + + - + - -

12. Solar Cycle • Solar Cycle of Sunspot: 11 year http://science.nasa.gov/ssl/pad/solar/sunspots.htm

13. Solar Cycle (ctnl.) • Butterfly diagram of Sunspot http://science.nasa.gov/ssl/pad/solar/sunspots.htm

14. Solar Cycle: Butterfly Diagram (ctnl.) • Butterfly diagram of Sunspot shows position of sunspots as well as their numbers • Sunspots do not appear at random over the surface of the sun but are concentrated in two latitude bands on either side of the equator • these bands first form at mid-latitudes, widen, and then move toward the equator as each cycle progresses • The cycles overlap at the time of sunspot cycle minimum with old cycle spots near the equator and new cycle spots at high latitudes

15. Solar Cycle (ctnl.)

16. Solar Cycle (ctnl.) 22 year magnetic cycle versus 11 year sunspot number cycle

17. Solar Cycle (ctnl.) Mixed Hale polarity during solar minimum Also see textbook Figure 4.5, P102

18. Solar Cycle (ctnl.) • Maunder Minimum from 1645 to 1715 • Associated with Little Ice Age • Possible connection between solar activity and terrestrial climate http://science.nasa.gov/ssl/pad/solar/sunspots.htm

19. Solar Cycle (ctnl.) • Solar Cycle of X-ray corona

20. Solar Cycle (ctnl.) • Magnetogram: 1995 versus 2001

21. Solar Cycle (ctnl.) • Coronal at EUV (EIT 195 Å, 1.5 MK): 1995 versus 2001

22. Solar Cycle (ctnl.) • Chromosphere (EIT 304 Å, 0.08 MK): 1995 versus 2001

23. Solar Cycle (ctnl.) • Outer corona (LASCO C2): 1995 versus 2001

24. Solar Cycle (ctnl.) • Solar activities strongly follow the 11-year solar cycle • Flare: 1/day at minimum, 10/day at maximum • CME: 0.4/day at minimum, 4/day at maximum 3. As well as Geomagnetic Storms and Solar Energetic Particle events

25. Solar Dynamo • Generation of Solar Magnetic Field: • magnetic dynamo theory

26. Solar Dynamo (ctnl.) • Maxwell Equations • Faraday’s law of Induction • Ampere’s Law • Gauss’s Law • Law of no magnetic Charges • Generalized Ohm’s Law • Equation of Magnetic Induction

27. Solar Dynamo (ctnl.) • 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(27 days) rotates slower than surface (25 days) • At polar region, interior (27 days) rotates faster than surface (35 days) • (See textbook Figure 4.14 at P. 122)

28. Solar Dynamo (ctnl.) • Poloidal field stretched to toroidal field and strenghened • (also See textbook Figure 4.15 at P. 123)

29. Solar Dynamo (ctnl.) • Poloidal field rises and turns into toroidal field • (also See textbook Figure 4.16 at P. 124)

30. Solar Dynamo • Summary of the α-ω dynamo (P121—P126) • Initial poloidal field is stretched becoming toroidal field, wound up and strengthened, at the bottom of convection zone • Toroidal field, which becomes sufficiently strong, rises through the convection zone because of magnetic buoyancy force • As the magnetic flux tube rises, the Coriolis force has the so-called “helical convection” effect that take some E-W oriented field and turn it into N-S oriented poloidal field (Fi • This process forms the cycle of poloidal field – toroidal field and poloidal field again. More importantly, the new poloidal field is directed opposite to the field which started the cycle