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 Tascione , P25-P28 Gombosi 11.4 – 11.5, P219-P225 Aschwanden , 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, P

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 time 3.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 wider 6.At the end of cycle, sunspots are close to equator and then disappear 7.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 g λ 2 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 , P177 in Aschwanden) Solar Dynamo Differential rotation and meridional circulation Displacing and twisting effect by kinetic helicity 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 2001 EUV 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 , P177-P195) 1.Potential Field Model: J = 0 2.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