Theoretical - PowerPoint Presentation

Slide1

Theoretical

Astrophysics II

Markus Roth

Fakultät für Mathematik und PhysikAlbert-Ludwigs-Universität FreiburgKiepenheuer-Institut für Sonnenphysik

I.

Magnetohydrodynamics

(

for

astrophysics

)Slide2

Introduction

Following first part

of the lecture is intended as an

introduction to magnetohydrodynamics in astrophysics

.Pre-Conditions:Concepts of fluid dynamicsLagrangian

and

Eulerian descriptions of fluid flowVector calculusElementary special relativity

Reference: „Essential

magnetohydrodynamics

for

astrophysics

“

by

H.

SpruitSlide3

Introduction

Not much knowledge on electromagnetic

theory requiredMHD is closer in spirit to

fluid mechanics than to

electromagnetismSlide4

History

Basic astrophysical applications of MHD

were developed 1950s – 1980sPowerful tools for numerical

simulations of the MHD equations

allow now application to more realistic

astrophysical

problems.Slide5

1. Essentials

MHD describes electrically conducting

fluids in which a magnetic field is present.

Astrophys. def. (Fluid): generic

term for a gas, liquid or plasmaSlide6

1.1 Equations

1.1.1 The MHD Approximation1.1.2 Ideal MHD1.1.3 The Induction

Equation1.1.4 Geometrical meaning of

r ¢ B =01.1.5

Electric Current1.1.6 Charge Density 1.1.7 Lorentz Force, Equation

of

Motion1.1.8 The Status of Currents in MHD1.1.9 Consistency of the MHD ApproximationSlide7

1.1 Equations

1.1.4 Geometrical meaning

of r ¢ B =0Slide8

1.2 The motion of

field linesSlide9

1.2.2 Field Amplification by Fluid

Flows

1.2 The motion of field linesSlide10

1.2.2 Field Amplification by Fluid

Flows

1.2 The motion of field linesSlide11

1.2.2 Field Amplification by Fluid

Flows

1.2 The motion of field linesSlide12

1.2.2 Field Amplification by Fluid

Flows

1.2 The motion of field linesSlide13

1.3 Magnetic

force and magnetic stress

1.3.2 Magnetic stress tensor

Example

: Accretion disk

Example

: Solar

Prominence

gSlide14

1.3 Magnetic force

and magnetic stress

1.3.3 Properties of the magnetic stress. Pressure and

tension

Fright

, xSlide15

1.3 Magnetic force

and magnetic stress

1.3.4 Boundaries between regions of different field

strengthSlide16

1.3.5 Magnetic BoyancySlide17

1.4.1 Potential FieldsSlide18

1.4.1 Potential Fields

(

courtesy T. Wiegelmann, MPS)

Potential field

reconstructionTop: Observation of corona

Botton: Potential

field

reconstruction of coronaSlide19

1.4.2 Force-Free FieldsSlide20

17.5.2010

Flares

Wenn unterschiedliche Magnetfelder aufeinandertreffen: “Kurzschluss”Slide21

Flares

Bastille-FlareSlide22

Coronal Mass Ejections (CMEs)

Bastille flare: Juli 14, 2000 10:24 am

energetic particles reach Earth: 10:38 amCME mass: several billion tons

speed: 1520 km/sflight 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, SFaurorae„light bulb“ CME (not Bastille)Slide23

Earth: magnetosphere

and aurorae

Earth 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.Slide24

The Solar Dynamo

Flows 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)Slide25

The Solar Dynamo

(

Courtesy

R. Arlt, AIP)