Solar Magnetism: Solar Cycle Solar Dynamo Coronal Magnetic Field

1. CSI 662 / ASTR 769 Lect. 03, February 6 Spring 2007 Solar Magnetism:Solar CycleSolar Dynamo Coronal Magnetic Field • References: • NASA/MSFC Solar Physics at http://solarscience.msfc.nasa.gov/ • Tascione 2.6-2.7, P25-P28 • Gombosi 11.4 – 11.5, P219-P225 • Aschwanden 5.2-5.3, P177-P195

2. Magnetic Induction Equation • Generalized Ohm’s Law • Tascione 1-2, P2 • Aschwanden 5.1.3, P177 • “Simplified” Ampere’s Law in Plasma • Aschwanden 5.1.2, P176-P177 • Magnetic Induction Equation • Aschwanden 5.1.4, P177-178

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

4. 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

5. 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

6. Photospheric Magnetic Field • Magnetogram: measurement of magnetic in the photosphere • Nature of sunspot: area of strong magnetic field Magnetogram Continuum Image

7. Photospheric B: Measurement • Based on Zeeman effect: the splitting of a spectral line because of the presence of magnetic field. • Δλ = 4.7 x 10-13 g λ2 B • λ: wavelength • g: Lande factor, e.g., FeI 6173Å (g=2.5)  • B: magnetic field strength

8. 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.

9. Hale’s Polarity Law + - + - + + - + - -

10. Solar Magnetic Cycle • 22 year magnetic cycle • 11 year sunspot number cycle

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

12. 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 (also see Eq 5.1.14, P177 in Aschwanden) Diffusion (turbulent + molecular) Differential rotation and meridional circulation Displacing and twisting effect by kinetic helicity

13. 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)

14. Solar Dynamo: Ω-effect • Generation of toroidal field by shearing a pre-existing poloidal field by differential rotation • (Ω-effect )

15. Solar Dynamo: α-effect (ii) Re-generation of poloidal field by lifting and twisting a toroidal flux tube by helical turbulence (α-effect) Proposed by Parker (1955) Mathematically formulated by Steenbeck, Krause & Radler (1969)

16. 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 & Charbonneau 1999, ApJ, 518, 508

17. Coronal Magnetic Field • Indirect observation • EUV and X-ray observations to infer the morphology • But can not determine the intensity and direction • Low-β plasma, the structure is dominated by magnetic field distribution TRACE March 2001 EUV movie X-ray image of Corona

18. Coronal Magnetic Field • In active regions (sunspot regions): closed magnetic loops • In (polar) coronal hole regions: open magnetic field, extended into solar wind

19. Coronal Magnetic Field • Can be calculated using Maxwell equations (Aschwanden 5.2-5.3, P177-P195) • Potential Field Model: J = 0 • Force Free Model: J || B • The input to models is the photospheric magnetic field as lower boundary condition

20. Coronal Magnetic Field • Helical magnetic field in the region close to the magnetic polarity inversion line (neutral line) • Helical structure supports the filament material • Complex magnetic field above the neutral line leads to magnetic instability, causing solar flares and CMEs

21. The End