Solar Magnetism:Solar CycleSolar Dynamo Coronal Magnetic FieldCSI 662 / ASTR 769 Lect. 03, February 6 Spring 2007References: NASA/MSFC Solar Physics at http://solarscience.msfc.nasa.gov/Tascione 2.6-2.7, P25-P28Gombosi 11.4 11.5, P219-P225 Aschwanden 5.2-5.3, P177-P195

Magnetic Induction EquationGeneralized Ohms LawTascione 1-2, P2Aschwanden 5.1.3, P177

Simplified Amperes Law in PlasmaAschwanden 5.1.2, P176-P177

Magnetic Induction EquationAschwanden 5.1.4, P177-178

Solar Cycle11-year cycle of sunspot number (SSN)SSN is historically a good index of solar activity.Correlate well with geomagnetic activities

Butterfly Diagram of SunspotA diagram shows the position (latitude) of sunspot with timeIt describe the movement of sunspot in the time scale of solar cycle

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 timeAt 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 widerAt the end of cycle, sunspots are close to equator and then disappearAt 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 FieldMagnetogram: measurement of magnetic in the photosphereNature of sunspot: area of strong magnetic fieldMagnetogram Continuum Image

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

Photospheric B: Measurement = 4.7 x 10-13 g 2 B

: wavelengthg: Lande factor, e.g., FeI 6173 (g=2.5) B: magnetic field strength

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.

Hales Polarity Law

+-- +- ++ -+ -Hales Polarity Law

22 year magnetic cycle 11 year sunspot number cycleSolar Magnetic Cycle

Butterfly diagram of Magnetic FieldGlobal dipole field most of the timePolar field reversal during the solar maximumSolar Magnetic Cycle

Solar dynamo is a process by which the magnetic field in an electrically conducting fluid is maintained against Ohmic dissipationIt is mathematically described by the magnetic induction equation (also see Eq 5.1.14, P177 in Aschwanden)Solar DynamoDifferential rotationand meridional circulationDisplacing andtwisting effectby kinetic helicityDiffusion(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 RotationAt 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

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

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

Dikpati & Charbonneau 1999, ApJ, 518, 508The flow of material along meridian lines from the equator toward the poles at the surface and from the poles to the equator deep insidDynamo cycle primarily governed by meridional flow speedSolar Dynamo: Meridional Flow

Indirect observationEUV and X-ray observations to infer the morphologyBut can not determine the intensity and directionLow- plasma, the structure is dominated by magnetic field distribution

Coronal Magnetic FieldX-ray image of CoronaTRACE March 2001EUV movie

In active regions (sunspot regions): closed magnetic loopsIn (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)Potential Field Model: J = 0Force Free Model: J || B

The input to models is the photospheric magnetic field as lower boundary conditionCoronal Magnetic Field

Helical magnetic field in the region close to the magnetic polarity inversion line (neutral line)Helical structure supports the filament materialComplex magnetic field above the neutral line leads to magnetic instability, causing solar flares and CMEsCoronal Magnetic Field

The End