The Biermann Lectures: Adventures in Theoretical Astrophysics
Theoretical Astrophysics II
description
Transcript of Theoretical Astrophysics II
![Page 1: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/1.jpg)
Theoretical Astrophysics II
Markus RothFakultät für Mathematik und PhysikAlbert-Ludwigs-Universität Freiburg
Kiepenheuer-Institut für Sonnenphysik
I. Magnetohydrodynamics(for astrophysics)
![Page 2: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/2.jpg)
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
![Page 3: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/3.jpg)
Introduction
• Not much knowledge on electromagnetic theory required
• MHD is closer in spirit to fluid mechanics than to electromagnetism
![Page 4: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/4.jpg)
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.
![Page 5: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/5.jpg)
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
![Page 6: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/6.jpg)
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
![Page 7: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/7.jpg)
1.1 Equations
• 1.1.4 Geometrical meaning of r ¢ B =0
![Page 8: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/8.jpg)
1.2 The motion of field lines
![Page 9: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/9.jpg)
• 1.2.2 Field Amplification by Fluid Flows
1.2 The motion of field lines
![Page 10: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/10.jpg)
• 1.2.2 Field Amplification by Fluid Flows
1.2 The motion of field lines
![Page 11: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/11.jpg)
• 1.2.2 Field Amplification by Fluid Flows
1.2 The motion of field lines
![Page 12: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/12.jpg)
• 1.2.2 Field Amplification by Fluid Flows
1.2 The motion of field lines
![Page 13: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/13.jpg)
1.3 Magnetic force and magnetic stress• 1.3.2 Magnetic stress tensor
Example: Accretion disk
Example: Solar Prominence
g
![Page 14: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/14.jpg)
1.3 Magnetic force and magnetic stress
• 1.3.3 Properties of the magnetic stress. Pressure and tension
Fright, x
![Page 15: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/15.jpg)
1.3 Magnetic force and magnetic stress
• 1.3.4 Boundaries between regions of different field strength
![Page 16: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/16.jpg)
1.3.5 Magnetic Boyancy
![Page 17: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/17.jpg)
1.4.1 Potential Fields
![Page 18: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/18.jpg)
1.4.1 Potential Fields
(courtesy T. Wiegelmann, MPS)
Potential field reconstruction
Top: Observation of coronaBotton: Potential field reconstruction of corona
![Page 19: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/19.jpg)
1.4.2 Force-Free Fields
![Page 20: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/20.jpg)
17.5.2010
Flares
Wenn unterschiedliche Magnetfelder aufeinandertreffen: “Kurzschluss”
![Page 21: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/21.jpg)
Flares
Bastille-Flare
![Page 22: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/22.jpg)
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)
![Page 23: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/23.jpg)
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.
![Page 24: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/24.jpg)
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)
![Page 25: Theoretical Astrophysics II](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815ecf550346895dcd5b85/html5/thumbnails/25.jpg)
The Solar Dynamo
(Courtesy R. Arlt, AIP)