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Theoretical Astrophysics II Markus Roth Fakultät für Mathematik und Physik Albert-Ludwigs-Universität Freiburg Kiepenheuer-Institut für Sonnenphysik I. Magnetohydrodynamics (for astrophysics)

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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

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Introduction Not much knowledge on electromagnetic theory required MHD is closer in spirit to fluid mechanics than to electromagnetism

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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.

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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

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1.1 Equations The MHD Approximation Ideal MHD The Induction Equation Geometrical meaning of r ¢ B = Electric Current Charge Density Lorentz Force, Equation of Motion The Status of Currents in MHD Consistency of the MHD Approximation

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1.1 Equations Geometrical meaning of r ¢ B =0

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1.2 The motion of field lines

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1.2.2 Field Amplification by Fluid Flows 1.2 The motion of field lines

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1.2.2 Field Amplification by Fluid Flows 1.2 The motion of field lines

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1.2.2 Field Amplification by Fluid Flows 1.2 The motion of field lines

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1.2.2 Field Amplification by Fluid Flows 1.2 The motion of field lines

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1.3 Magnetic force and magnetic stress Magnetic stress tensor Example: Accretion disk Example: Solar Prominence g

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1.3 Magnetic force and magnetic stress Properties of the magnetic stress. Pressure and tension F right, x

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1.3 Magnetic force and magnetic stress Boundaries between regions of different field strength

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1.3.5 Magnetic Boyancy

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1.4.1 Potential Fields

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(courtesy T. Wiegelmann, MPS) Potential field reconstruction Top: Observation of corona Botton: Potential field reconstruction of corona

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1.4.2 Force-Free Fields

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Flares Wenn unterschiedliche Magnetfelder aufeinandertreffen: “Kurzschluss”

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Flares Bastille-Flare

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Coronal Mass Ejections (CMEs) Bastille flare: Juli 14, :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)

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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.

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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)

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The Solar Dynamo (Courtesy R. Arlt, AIP)

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