Theoretical Astrophysics II

1. TheoreticalAstrophysics II I. Magnetohydrodynamics(forastrophysics) Markus Roth Fakultät für Mathematik und PhysikAlbert-Ludwigs-Universität Freiburg Kiepenheuer-Institut für Sonnenphysik

2. Introduction Reference: „Essential magnetohydrodynamicsforastrophysics“ by H. Spruit • Followingfirstpartofthelectureisintendedas an introductiontomagnetohydrodynamics in astrophysics. • Pre-Conditions: • Conceptsof fluid dynamics • LagrangianandEuleriandescriptionsof fluid flow • Vectorcalculus • Elementaryspecialrelativity

3. Introduction • Not muchknowledge on electromagnetictheoryrequired • MHD iscloser in spiritto fluid mechanicsthantoelectromagnetism

4. History • Basic astrophysicalapplicationsof MHD weredeveloped 1950s – 1980s • Powerful toolsfornumericalsimulationsofthe MHD equationsallownowapplicationtomorerealisticastrophysicalproblems.

5. 1. Essentials • MHD describeselectricallyconductingfluids in which a magneticfieldispresent. Astrophys. def. (Fluid): generictermfor a gas, liquid orplasma

6. 1.1 Equations • 1.1.1 The MHD Approximation • 1.1.2 Ideal MHD • 1.1.3 The InductionEquation • 1.1.4 Geometricalmeaningofr¢ B =0 • 1.1.5 ElectricCurrent • 1.1.6 Charge Density • 1.1.7 Lorentz Force, Equationof Motion • 1.1.8 The Status ofCurrents in MHD • 1.1.9 Consistencyofthe MHD Approximation

7. 1.1 Equations • 1.1.4 Geometricalmeaningofr¢ B =0

8. 1.2 The motionoffieldlines

9. 1.2 The motionoffieldlines • 1.2.2 Field Amplificationby Fluid Flows

10. 1.2 The motionoffieldlines • 1.2.2 Field Amplificationby Fluid Flows

11. 1.2 The motionoffieldlines • 1.2.2 Field Amplificationby Fluid Flows

12. 1.2 The motionoffieldlines • 1.2.2 Field Amplificationby Fluid Flows

13. 1.3 Magneticforceandmagnetic stress • 1.3.2 Magnetic stress tensor Example: Accretiondisk Example: Solar Prominence g

14. 1.3 Magneticforceandmagnetic stress • 1.3.3 Properties ofthemagnetic stress. Pressureandtension Fright, x

15. 1.3 Magneticforceandmagnetic stress • 1.3.4 Boundariesbetweenregionsof different fieldstrength

16. 1.3.5 MagneticBoyancy

17. 1.4.1 Potential Fields

18. 1.4.1 Potential Fields Potential fieldreconstruction Top: Observation ofcorona Botton: Potential fieldreconstructionofcorona (courtesy T. Wiegelmann, MPS)

19. 1.4.2 Force-Free Fields

20. Flares Wenn unterschiedliche Magnetfelder aufeinandertreffen: “Kurzschluss”

21. Flares Bastille-Flare

22. 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)

23. Earth: magnetosphereandaurorae Earth isprotectedbyitsmagneticfield. Ifitisperturbedby solar eruptions, chargedparticlescanpenetratenearthepoles down totheupperairlayers aurorae.

24. 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)

25. The Solar Dynamo (Courtesy R. Arlt, AIP)