The Solar Dynamo and Emerging Flux Presented by Angelo P. Verdoni Physics 681 Fall 05 George H. Fisher, Yuhong Fan, Dana W. Longcope, Mark G. Linton and Alexei A. Pevtsov

Dynamo Theory Theory that explains planetary and stellar magnetic fields in terms of rotating, conducting material flowing in an object's interior.

 1843 Samuel Heinrich Schwabe using 17 years of sunspot data discovered the sunspot cycle.  Hale’s polarity laws early 20 th century established existence of well organized toroidal magnetic field Larmor suggested that inductive actions of fluid motion were the cause of these fields.  1939 Cowling’s antidynamo theorem: a purely axisymmetric flow could not sustain an axisymmetric magnetic field against a Ohmic dissipation.  Mid 1950’s E.N. Parker implemented the effect of the Coriolis force to refute Cowling’s claim, later quantified using mean-field electrodynamics.  By the late 1970’s consensus had almost emerged as to the fundamental nature of the solar dynamo, the α-effect of mean-field electrodynamics. ………..to date the mechanism responsible for the solar dynamo is still a debatable topic Solar Dynamo: A Historical Picture 3

Location of Solar Dynamo  Flux tubes originate in the convective overshoot layer where the sun’s dynamo is thought to take place  This region happens to coincide with the ‘Tachocline’ generated using inversion methods of the rotation profile from helioseismology ( Mark S. Miesch, "Large-Scale Dynamics of the Convection Zone and Tachocline", Living Rev. Solar Phys. 2, (2005), 1. URL (cited on ):

Solar Toroidal Fields soi.stanford.edu/results/dynamo_colbig.jpg

A model of flux tube dynamics is presented and compared with observation of known active region properties:  Latitude distribution of sunspots  The tilt of active regions  Asymmetric characteristics of active regions i.e. The rapid separation of the leading spot from the magnetic neutral line  The tendency for most active regions to have a negative magnetic twist in the northern hemisphere and positive twist in the southern hemisphere  The properties of flare producing δ-spot active regions Solar Dynamo and Emerging Flux: Introduction

The Thin Flux Tube Equation of Motion The thin flux tube model is constructed using a simplification of the 3-D ideal MHD momentum equation for a thin untwisted magnetic flux tube: Where F B is the magnetic buoyant force, F T is the magnetic tension force, F D is the drag force and F C is the Coriolis force

The Thin Flux Tube Equation of Motion Field Strength of B = B eq Field Strength of B = 10B eq Animations from:

Latitude Distribution of Sunspots

Latitude Distribution of Sunspots  Choudhuri and Gilman (1987) were the first to use the thin flux tube model to study the emergence of magnetic flux rings from the base of the convection zone.  They found that for field strengths of 10 4 G the flux emerged to higher latitudes. Only flux tubes with field strengths of 10 5 G were consistent with observation.  Fan and Fisher (1996) found field strengths down to 3 X 10 4 G could be consistent with observed latitudes.  Moreno-Insertis, Schussler and Ferriz-Mas (1992) showed that if the field strength is 10 5 G or more the minimum latitude at the base of the convection zone is ≥17 o. Any greater than that, the initial latitude is too large to account for lower latitudes that appear later in the solar cycle . The conclusion is that by knowing the observed active latitudes a strict requirement is applied to the field strength at the base of the convection zone: 10 4 G < B o < 10 5 G

Active Region Tilt  Joy’s Law, similar to Hale’s Law illustrates the latitude dependence of the tilt of a bipolar active region.  The size of the tilt at 30 o latitude is roughly 7 o  The tilt of a bipolar group is a consequence of the Coriolis force.

Active Region Tilt  D’Silva and Choudhuri (1993) were the first to model active region tilts as a consequence of the Coriolis force.  A simple cartoon model (shown above) was presented by Fan, Fisher and McClymont (1994). In the model the magnetic tension force opposes the Coriolis force allowing one to arrive at a tilt angle: Where α is the tilt angle, Φ is the magnetic flux and θ is the latitude

 The tilt angle can also be expressed in terms of the separation distance between the poles d as: Active Region Tilt

Asymmetries – Field Strength, Inclinations & Spot Group Motions Along with the tilt, the Coriolis force is responsible for other asymmetric characteristics of active regions:  The asymmetry in the field strength of the leading leg of the emergent loop.  The asymmetry in magnetic field inclination and spot motions between the leading and following sides of active regions. Both of these effects are explained as a result of the same mechanism:  As the flux tube rises a Coriolis force is induced  A counter-rotation ensues to conserve angular momentum  Conservation of angular momentum results in a greater field strength in the leading leg of the loop along with a more gradual slope and a steeper descent and weaker field on the trailing leg.

Asymmetries – Field Strength, Inclinations & Spot Group Motions van Driel-Gesztelyi, L. and Petrovay, K.:1990, Solar Phys. 126, 285.

Beyond the Thin Untwisted Flux Tube Approximation & MHD Simulations  Most active regions have a modest level of twist  There is a trend: northern hemisphere spots have negative twist and southern, positive.  Longcope, Fisher and Pevtsov (1998) describe the twist using the ‘Σ-effect’ Longcope, D. W., Fisher, G. H., and Pevtsov, A. A.: 1998, Astrophys. J. 507, 417.

δ – spot Active Regions  Delta-spot active regions exhibit an unusually high amount of magnetic twist. They are highly tilted away from the E-W direction and frequently appear to rotate as they emerge

δ – spot Active Regions  Theoretical work using a ‘twisted’ flux tube model have been used to model these regions.  A criteria was established based on a comprehensive linear stability analysis of a ‘kink’ mode for an infinitely long, pressure confined twisted flux tube was presented by Linton, Longcope and Fisher (1996)  The model considers the azimuthal field component of the tube in terms of the axial and a ‘twist’ parameter q:  If q exceeds a critical twist q cr then the tube is kink unstable and the model can account for delta-spot emergence and morphology.

3D MHD Simulations

Summary  Dynamic flux tube models have been successful in reproducing many observed properties of active regions, such as: 1. Active region latitude emergence. 2. Active region tilt, ‘Joy’s Law’. 3. The asymmetries present in active regions, i.e. Field strengths, Inclinations and spot group motions. 4. The ‘twist’ of active regions and its latitude dependence 5. Delta-spot emergence

References Linton, M. G., Longcope, D. W., and Fisher, G. H.: 1996, Astrophys. J. 469, 954. Longcope, D. W., Fisher, G. H., and Pevtsov, A. A.: 1998, Astrophys. J. 507, 417. D’Silva, S. and Choudhuri, A. R.: 1993, Astron. Astrophys. 272, 621. Fan, Y., Fisher, G. H., and McClymont A. N.: 1994, Astrophys. J. 436, 907. Choudhuri, A. R. and Gilman P. A.: 1987, Astrophys. J. 316, 788. Fan, Y. and Fisher, G. H.: 1996, Solar Phys. 166, 17. Moreno-Insertis, F., Schüssler, M., and Ferriz-Mas, A: 1992, Astron. Astrophys. 264, 686.