Theoretical Astrophysics II

Markus RothFakultät für Mathematik und PhysikAlbert-Ludwigs-Universität Freiburg

Kiepenheuer-Institut für Sonnenphysik

I. Magnetohydrodynamics(for astrophysics)

Introduction

• Following first part of the lecture is intended as an introduction to magnetohydrodynamics in astrophysics.

• Pre-Conditions:– Concepts of fluid dynamics• Lagrangian and Eulerian descriptions of fluid flow

– Vector calculus– Elementary special relativity

Reference: „Essential magnetohydrodynamics for astrophysics“ by H. Spruit

Introduction

• Not much knowledge on electromagnetic theory required

• MHD is closer in spirit to fluid mechanics than to electromagnetism

History

• Basic astrophysical applications of MHD were developed 1950s – 1980s

• Powerful tools for numerical simulations of the MHD equations allow now application to more realistic astrophysical problems.

1. Essentials

• MHD describes electrically conducting fluids in which a magnetic field is present.

Astrophys. def. (Fluid): generic term for a gas, liquid or plasma

1.1 Equations

• 1.1.1 The MHD Approximation• 1.1.2 Ideal MHD• 1.1.3 The Induction Equation• 1.1.4 Geometrical meaning of r ¢ B =0• 1.1.5 Electric Current• 1.1.6 Charge Density • 1.1.7 Lorentz Force, Equation of Motion• 1.1.8 The Status of Currents in MHD• 1.1.9 Consistency of the MHD Approximation

1.1 Equations

• 1.1.4 Geometrical meaning of r ¢ B =0

1.2 The motion of field lines

• 1.2.2 Field Amplification by Fluid Flows

1.2 The motion of field lines

• 1.2.2 Field Amplification by Fluid Flows

1.2 The motion of field lines

• 1.2.2 Field Amplification by Fluid Flows

1.2 The motion of field lines

• 1.2.2 Field Amplification by Fluid Flows

1.2 The motion of field lines

1.3 Magnetic force and magnetic stress• 1.3.2 Magnetic stress tensor

Example: Accretion disk

Example: Solar Prominence

g

1.3 Magnetic force and magnetic stress

• 1.3.3 Properties of the magnetic stress. Pressure and tension

Fright, x

1.3 Magnetic force and magnetic stress

• 1.3.4 Boundaries between regions of different field strength

1.3.5 Magnetic Boyancy

1.4.1 Potential Fields

1.4.1 Potential Fields

(courtesy T. Wiegelmann, MPS)

Potential field reconstruction

Top: Observation of coronaBotton: Potential field reconstruction of corona

1.4.2 Force-Free Fields

17.5.2010

Flares

Wenn unterschiedliche Magnetfelder aufeinandertreffen: “Kurzschluss”

Flares

Bastille-Flare

Coronal Mass Ejections (CMEs)

• Bastille flare: Juli 14, 2000 10:24 am• energetic particles reach Earth: 10:38 am• CME mass: several billion tons• speed: 1520 km/s• flight time: 28 hours

Effects on Earth:• several satellites lose orientation;

ASCA satellite (Japan) permanently• radio communication and GPS affected• some air planes for 80 min without radio contact• power blackouts in USA, UK, SF• aurorae

„light bulb“ CME (not Bastille)

Earth: magnetosphere and auroraeEarth is protected by its magnetic field. If it is perturbed by solar eruptions, charged particles can penetrate near the poles down to the upper air layers aurorae.

The Solar DynamoFlows inside the Sun are important for solar dynamo action:

A possible solar/stellar dynamo

• At cycle minimum:a dipolar field threads through a shallow layer below the surface.

• Differential rotation shears out this dipolar field to produce a strong toroidal field (first at the mid-latitudes then progressively lower latitudes).

• Around solar maximum:Buoyant fields erupt through the photosphere forming, e.g. sunspots and active regions

• The meridional flow away from the mid-latitudes gives reconnection at the poles and equator.

The Sun’s internal rotation and meridional flow need to be measured

(Babcock, 1961; and later developments)

The Solar Dynamo

(Courtesy R. Arlt, AIP)