Solar Magnetism:Solar Cycle

Solar Dynamo Coronal Magnetic Field

CSI 662 / ASTR 769 Lect. 03, February 6 Spring 2007

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

Magnetic Induction Equation

1. Generalized Ohm’s Law• Tascione 1-2, P2• Aschwanden 5.1.3, P177

2. “Simplified” Ampere’s Law in Plasma• Aschwanden 5.1.2, P176-P177

3. Magnetic Induction Equation– Aschwanden 5.1.4, P177-178

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

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

Magnetogram Continuum Image

•Based on Zeeman effect: the splitting of a spectral line because of the presence of magnetic field.

Photospheric B: Measurement

•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

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.

Hale’s Polarity Law

+

-

- +- +

+ -+ -

Hale’s Polarity Law

•22 year magnetic cycle •11 year sunspot number cycle

Solar Magnetic Cycle

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

Solar Magnetic Cycle

•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)

Solar Dynamo

Differential rotationand meridional circulation

Displacing andtwisting effect

by kinetic helicity

, BBBUB

ηαt

Diffusion(turbulent + molecular)

• 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)

Solar Differential Rotation

(i) Generation of toroidal field by shearing a pre-existing

poloidal field by differential rotation

(Ω-effect )

Solar Dynamo: Ω-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)

Solar Dynamo: α-effect

Dikpati & Charbonneau 1999, ApJ, 518, 508

• 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

Solar Dynamo: Meridional Flow

•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

Coronal Magnetic Field

X-ray image of Corona

TRACE March 2001EUV movie

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

Coronal Magnetic Field

• Can be calculated using Maxwell equations (Aschwanden 5.2-5.3, P177-P195)1. Potential Field Model: J = 02. Force Free Model: J || B

• The input to models is the photospheric magnetic field as lower boundary condition

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

Coronal Magnetic Field

The End