Solar and Heliospheric Physics Magnetic Field Sep. 9 – Sep. 30, 2010 CSI 769 Fall 2010 Jie Zhang

Magnetic Fields References: Aschwanden: Chap. 5.1 – 5.6 Supplement articles for PFSS model Altschuler, Martin D., Newkirk, Gordon, Jr., Magnetic Fields and the Structure of the Solar Corona, Solar Physics 9, 131-149, 1969 Sakurai, Takashi., Green’s Function Methods for Potential Magnetic Fields, Solar Physics 76, 301-321, 1982 Schrijver, Carolus J., Derosa, Marc K., Photospheric and Heliospheric Magnetic Fields, Solar Physics, 212: 165-200, 2003 For NLFF model Schrijver et al. 2006, Solar Physics 235, P161-190 “Non-Linear Force Free Modeling of Coronal magnetic Fields Part 1: A Quantitative Comparison of Methods

Why? Why is the corona highly structured? Why is it hot? Why is it explosive? Why highly structured? Holes, loop arcades, s-shaped loops, flux rope stricutre Why is hot? That leads to expansion into solar wind Why is explosive, leading to flares and CMEs, the sources of space weather Corona in X-ray

Photospheric Magnetic Field Magnetogram Continuum Image Magnetogram: measurement of magnetic in the photosphere Nature of sunspot: areas of concentration of strong magnetic field Magnetogram Continuum Image

Hale’s Polarity Law + - + - + + - + - -

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. The Hale cycle is 22 years, while the sunspot cycle is 11 years

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

Other Laws Sporer’s Law: Sunspot emerge at relatively high latitudes and move towards the equator Joy’s Law: The tilt angle of the active regions is proportional to the latitude

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

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

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

Coronal Magnetic Field Schrijver & Derosa, 2003 Magnetogam image, coronal loops, extrapolated coronal magnetic field

Coronal Magnetic Field Feb. 2, 2008 http://www.lmsal.com/forecast/index.html Synoptic calculation Surface magnetogram used data assimilation to take into account the evolution on the backside of the Sun.

Potential Field Aschwanden 5.2 Unipolar field Dipole field Potential field calculation methods Green’s function methods Eigenfunction expansion methods PFSS model

Result of the Analytical Model Single Sunspot Field Aschwanden 5.2.1, P179-180 Result of the Analytical Model

Result of the Analytical Model Dipole Field Aschwanden 5.2.2, P180 - 182 Result of the Analytical Model

Force-Free Field Force free field: Asch-Chap. 5.3.1 Non-Linear force free field: Asch-Chap. 5.3.3 Shear arcade: Asch-Chap. 5.3.2 An example of linear force free field Magnetic Nullpoints and Separators: Asch – Chap. 5.6

Loop Arcade Loop arcade seen by TRACE (Credit: NASA)

Loop Arcade Loop arcade seen by TRACE (Credit: NASA)

Loop Arcade Loop arcade, shear motion, and formation of prominence (Van Ballegooijen & Martens, 1989)

Loop Arcade Force Free Field of a Sheared Arcade – Analytic Solution (Asch—Fig. 5.4)

Nullpoint & Separatrix (Asch—Fig. 5.22)

Nullpoints 2-D X-point (left) and O-point (Asch—Fig. 5.24) Ref: Asch--Chap. 5.6.1 Priest—Chap. 1.3

The End