Bartelmann, M. L.
Theoretical Astrophysics : An Introduction. - 1st ed. - 1 online resource (342 pages)
Theoretical Astrophysics -- Contents -- Preface -- Acknowledgements -- Colour Plates -- 1 Theoretical Foundations -- 1.1 Units -- 1.1.1 Lengths, Masses, Times, and Temperatures -- 1.1.2 Charges and Electromagnetic Fields -- 1.1.3 Natural Constants -- 1.2 Lorentz Invariance -- 1.2.1 The Special Lorentz Transform -- 1.2.2 Minkowski Space -- 1.2.3 Some Properties of the Minkowski World -- 1.2.4 Relativistic Dynamics -- 1.3 Electromagnetism -- 1.3.1 Field Tensor and Sources -- 1.3.2 Lorentz Transform of the Electromagnetic Field -- 1.3.3 Maxwell's Equations -- 1.3.4 Energy-Momentum Conservation -- 1.3.5 Liénard-Wiechert Potentials and the Larmor Formula -- 1.3.6 The Lorentz Force -- 1.4 Elementary Kinetic Theory -- 1.4.1 The BBGKY Hierarchy and the Boltzmann Equation -- 1.4.2 Collision Terms -- 1.4.3 Diffusion in Phase-Space: The Fokker-Planck Approximation -- 1.4.4 Diffusion in Absolute Momentum -- 1.4.5 Calculation of the Diffusion Coefficient D2 -- Further Reading -- 2 Radiation Processes -- 2.1 Thomson Scattering -- 2.2 Spectra -- 2.3 Synchrotron Radiation -- 2.3.1 Larmor Frequency and Relativistic Focussing -- 2.3.2 Synchrotron Power -- 2.3.3 Synchrotron Spectrum -- 2.4 Bremsstrahlung -- 2.4.1 Orbit of an Electron Scattering off an Ion -- 2.4.2 Fourier Transform of the Orbit -- 2.4.3 Integration over Impact Parameters -- 2.4.4 Average over Electron Velocities, Thermal Bremsstrahlung -- 2.5 Radiation Damping -- 2.5.1 Damping Force -- 2.5.2 Transfer of Energy from a Moving Charge to a Radiation Field -- 2.6 Compton Scattering -- 2.6.1 Energy Change in the Scattering Process -- 2.6.2 Net Energy Transfer -- 2.6.3 The Kompaneets Equation -- 2.7 Radiative Quantum Transitions -- 2.7.1 Transition Probability -- 2.7.2 Perturbing Hamiltonian -- 2.7.3 Decomposition of the Electromagnetic Field -- 2.7.4 Dipole Approximation -- 2.7.5 Cross Sections. 2.7.6 Photoionisation Cross Section -- 2.8 Shapes of Spectral Lines -- 2.8.1 Natural Line Width -- 2.8.2 Collisional Broadening -- 2.8.3 Doppler Broadening of Spectral Lines -- 2.8.4 The Voigt Profile -- 2.8.5 Equivalent Widths and Curves-of-Growth -- 2.9 Radiation Quantities -- 2.9.1 Specific Intensity -- 2.9.2 Moments of the Intensity -- 2.9.3 Relativistic Invariance of I/3 -- 2.10 The Planck Spectrum and Einstein Coefficients -- 2.10.1 The Planck Spectrum -- 2.10.2 Transition Balance and the Einstein Coefficients -- 2.11 Absorption and Emission -- 2.11.1 Absorption Coefficients and Emissivity -- 2.11.2 Radiation Transport in a Simple Case -- 2.11.3 Emission and Absorption in the Continuum Case -- 2.11.4 Energy Transport Through Absorbing Media -- Further Reading -- 3 Hydrodynamics -- 3.1 The Equations of Ideal Hydrodynamics -- 3.1.1 Particle-Current Density and Energy-Momentum Tensor -- 3.1.2 Collisional Invariants and the Fluid Approximation -- 3.1.3 The Equations of Ideal Hydrodynamics -- 3.2 Relativistic Hydrodynamics -- 3.2.1 Hydrodynamic Equations -- 3.2.2 Hydrodynamics in a Weak Gravitational Field -- 3.2.3 Gravitational Field Equation -- 3.2.4 The Combined Set of Equations -- 3.2.5 Perturbative Analysis -- 3.3 Viscous Hydrodynamics -- 3.3.1 Diffusion of Particles, Momentum and Internal Energy -- 3.3.2 The Equations of Viscous Hydrodynamics -- 3.3.3 Entropy -- 3.3.4 Fluids in a Gravitational Field -- 3.3.5 The Tensor Virial Theorem -- 3.3.6 Transformation to Cylindrical or Spherical Coordinates -- 3.4 Flows under Specific Circumstances -- 3.4.1 Sound Waves -- 3.4.2 Polytropic Equation of State -- 3.4.3 Hydrostatic Equilibrium -- 3.4.4 Vorticity and Kelvin's Circulation Theorem -- 3.4.5 Bernoulli's Constant -- 3.4.6 Bondi Accretion -- 3.4.7 Bernoulli's Law for Irrotational, Non-Stationary Flows -- 3.4.8 Diffusion of Vorticity. 3.4.9 The Reynolds Number -- 3.4.10 Hagen-Poiseulle Flow -- 3.5 Shock Waves -- 3.5.1 The Method of Characteristics -- 3.5.2 Steepening of Sound Waves -- 3.5.3 The Rankine-Hugoniot Shock Jump Conditions -- 3.5.4 Shock Velocity -- 3.5.5 The Sedov Solution -- 3.6 Instabilities -- 3.6.1 Gravity Waves -- 3.6.2 The Rayleigh-Taylor Instability -- 3.6.3 The Kelvin-Helmholtz Instability -- 3.6.4 Thermal Instability -- 3.6.5 Heat Conduction -- 3.6.6 Convection -- 3.6.7 Turbulence -- Further Reading -- 4 Fundamentals of Plasma Physics and Magneto-Hydrodynamics -- 4.1 Collision-Less Plasmas -- 4.1.1 Shielding and the Debye Length -- 4.1.2 The Plasma Frequency -- 4.2 Electromagnetic Waves in Media -- 4.2.1 Polarisation and Dielectric Displacement -- 4.2.2 Structure of the Dielectric Tensor -- 4.3 Dispersion Relations -- 4.3.1 General Form of the Dispersion Relations -- 4.3.2 Transversal and Longitudinal Waves -- 4.3.3 Longitudinal and Transversal Dielectricities -- 4.3.4 Landau Damping -- 4.4 Electromagnetic Waves in Thermal Plasmas -- 4.4.1 Longitudinal and Transversal Dielectricities -- 4.4.2 Dispersion Measure and Damping -- 4.5 The Magneto-Hydrodynamic Equations -- 4.5.1 Assumptions -- 4.5.2 The Induction Equation -- 4.5.3 Euler's Equation -- 4.5.4 Energy and Entropy -- 4.5.5 Incompressible Flows -- 4.5.6 Magnetic Advection and Diffusion -- 4.6 Generation of Magnetic Fields -- 4.7 Ambipolar Diffusion -- 4.7.1 Velocity-Averaged Scattering Cross Section -- 4.7.2 Friction Force and Diffusion Coefficient -- 4.8 Waves in Magnetised Cold Plasmas -- 4.8.1 The Dielectric Tensor -- 4.8.2 Contribution by Ions -- 4.8.3 Dispersion Relations in a Cold, Magnetised Plasma -- 4.8.4 Longitudinal and Transverse Waves -- 4.8.5 Faraday Rotation -- 4.9 Hydromagnetic Waves -- 4.9.1 Linearised Perturbation Equations -- 4.9.2 Alfvén Waves -- 4.9.3 Slow and Fast Hydro-Magnetic Waves. Further Reading -- 5 Stellar Dynamics -- 5.1 The Jeans Equations and Jeans' Theorem -- 5.1.1 Collision-Less Motion in a Gravitational Field -- 5.1.2 The Relaxation Time Scale -- 5.1.3 The Jeans Equations -- 5.1.4 Jeans Equations in Cylindrical and Spherical Coordinates -- 5.1.5 Application to Spherical Systems -- 5.1.6 The Tensor Virial Theorem in Stellar Dynamics -- 5.1.7 Jeans' Theorem -- 5.2 Equilibrium and Stability -- 5.2.1 The Isothermal Sphere -- 5.2.2 Equilibrium and Relaxation -- 5.2.3 Linear Analysis and the Jeans Swindle -- 5.2.4 Jeans Length and Jeans Mass -- 5.2.5 Disk Potentials -- 5.2.6 Fluid Equations for Two-Dimensional Systems -- 5.2.7 Dispersion Relation -- 5.2.8 Toomre's Criterion -- 5.3 Dynamical Friction -- 5.3.1 Deflection of Point Masses -- 5.3.2 Velocity Changes -- 5.3.3 Chandrasekhar's Formula -- Further Reading -- 6 Brief Summary and Concluding Remarks -- Index.
Beginning from first principles and adopting a modular structure, this book develops the fundamental physical methods needed to describe and understand a wide range of seemingly very diverse astrophysical phenomena and processes. For example, the discussion of radiation processes including their spectra is based on Larmor's equation and extended by the photon picture and the internal dynamics of radiating quantum systems, leading to the shapes of spectral lines and the ideas of radiation transport. Hydrodynamics begins with the concept of phase-space distribution functions and Boltzmann's equation and develops ideal, viscous and magneto-hydrodynamics all from the vanishing divergence of an energy-momentum tensor, opening a natural extension towards relativistic hydrodynamics. Linear stability analysis is introduced and used as a common and versatile tool throughout the book. Aimed at students at graduate level, lecturers teaching courses in theoretical astrophysics or advanced topics in modern astronomy, this book with its abundant examples and exercises also serves as a reference and an entry point for more advanced researchers wanting to update their knowledge of the physical processes that govern the behavior and evolution of astronomical objects.
9783527669783
Astrophysics.
Hydrodynamics.
Electronic books.
QB461
523.01
Theoretical Astrophysics : An Introduction. - 1st ed. - 1 online resource (342 pages)
Theoretical Astrophysics -- Contents -- Preface -- Acknowledgements -- Colour Plates -- 1 Theoretical Foundations -- 1.1 Units -- 1.1.1 Lengths, Masses, Times, and Temperatures -- 1.1.2 Charges and Electromagnetic Fields -- 1.1.3 Natural Constants -- 1.2 Lorentz Invariance -- 1.2.1 The Special Lorentz Transform -- 1.2.2 Minkowski Space -- 1.2.3 Some Properties of the Minkowski World -- 1.2.4 Relativistic Dynamics -- 1.3 Electromagnetism -- 1.3.1 Field Tensor and Sources -- 1.3.2 Lorentz Transform of the Electromagnetic Field -- 1.3.3 Maxwell's Equations -- 1.3.4 Energy-Momentum Conservation -- 1.3.5 Liénard-Wiechert Potentials and the Larmor Formula -- 1.3.6 The Lorentz Force -- 1.4 Elementary Kinetic Theory -- 1.4.1 The BBGKY Hierarchy and the Boltzmann Equation -- 1.4.2 Collision Terms -- 1.4.3 Diffusion in Phase-Space: The Fokker-Planck Approximation -- 1.4.4 Diffusion in Absolute Momentum -- 1.4.5 Calculation of the Diffusion Coefficient D2 -- Further Reading -- 2 Radiation Processes -- 2.1 Thomson Scattering -- 2.2 Spectra -- 2.3 Synchrotron Radiation -- 2.3.1 Larmor Frequency and Relativistic Focussing -- 2.3.2 Synchrotron Power -- 2.3.3 Synchrotron Spectrum -- 2.4 Bremsstrahlung -- 2.4.1 Orbit of an Electron Scattering off an Ion -- 2.4.2 Fourier Transform of the Orbit -- 2.4.3 Integration over Impact Parameters -- 2.4.4 Average over Electron Velocities, Thermal Bremsstrahlung -- 2.5 Radiation Damping -- 2.5.1 Damping Force -- 2.5.2 Transfer of Energy from a Moving Charge to a Radiation Field -- 2.6 Compton Scattering -- 2.6.1 Energy Change in the Scattering Process -- 2.6.2 Net Energy Transfer -- 2.6.3 The Kompaneets Equation -- 2.7 Radiative Quantum Transitions -- 2.7.1 Transition Probability -- 2.7.2 Perturbing Hamiltonian -- 2.7.3 Decomposition of the Electromagnetic Field -- 2.7.4 Dipole Approximation -- 2.7.5 Cross Sections. 2.7.6 Photoionisation Cross Section -- 2.8 Shapes of Spectral Lines -- 2.8.1 Natural Line Width -- 2.8.2 Collisional Broadening -- 2.8.3 Doppler Broadening of Spectral Lines -- 2.8.4 The Voigt Profile -- 2.8.5 Equivalent Widths and Curves-of-Growth -- 2.9 Radiation Quantities -- 2.9.1 Specific Intensity -- 2.9.2 Moments of the Intensity -- 2.9.3 Relativistic Invariance of I/3 -- 2.10 The Planck Spectrum and Einstein Coefficients -- 2.10.1 The Planck Spectrum -- 2.10.2 Transition Balance and the Einstein Coefficients -- 2.11 Absorption and Emission -- 2.11.1 Absorption Coefficients and Emissivity -- 2.11.2 Radiation Transport in a Simple Case -- 2.11.3 Emission and Absorption in the Continuum Case -- 2.11.4 Energy Transport Through Absorbing Media -- Further Reading -- 3 Hydrodynamics -- 3.1 The Equations of Ideal Hydrodynamics -- 3.1.1 Particle-Current Density and Energy-Momentum Tensor -- 3.1.2 Collisional Invariants and the Fluid Approximation -- 3.1.3 The Equations of Ideal Hydrodynamics -- 3.2 Relativistic Hydrodynamics -- 3.2.1 Hydrodynamic Equations -- 3.2.2 Hydrodynamics in a Weak Gravitational Field -- 3.2.3 Gravitational Field Equation -- 3.2.4 The Combined Set of Equations -- 3.2.5 Perturbative Analysis -- 3.3 Viscous Hydrodynamics -- 3.3.1 Diffusion of Particles, Momentum and Internal Energy -- 3.3.2 The Equations of Viscous Hydrodynamics -- 3.3.3 Entropy -- 3.3.4 Fluids in a Gravitational Field -- 3.3.5 The Tensor Virial Theorem -- 3.3.6 Transformation to Cylindrical or Spherical Coordinates -- 3.4 Flows under Specific Circumstances -- 3.4.1 Sound Waves -- 3.4.2 Polytropic Equation of State -- 3.4.3 Hydrostatic Equilibrium -- 3.4.4 Vorticity and Kelvin's Circulation Theorem -- 3.4.5 Bernoulli's Constant -- 3.4.6 Bondi Accretion -- 3.4.7 Bernoulli's Law for Irrotational, Non-Stationary Flows -- 3.4.8 Diffusion of Vorticity. 3.4.9 The Reynolds Number -- 3.4.10 Hagen-Poiseulle Flow -- 3.5 Shock Waves -- 3.5.1 The Method of Characteristics -- 3.5.2 Steepening of Sound Waves -- 3.5.3 The Rankine-Hugoniot Shock Jump Conditions -- 3.5.4 Shock Velocity -- 3.5.5 The Sedov Solution -- 3.6 Instabilities -- 3.6.1 Gravity Waves -- 3.6.2 The Rayleigh-Taylor Instability -- 3.6.3 The Kelvin-Helmholtz Instability -- 3.6.4 Thermal Instability -- 3.6.5 Heat Conduction -- 3.6.6 Convection -- 3.6.7 Turbulence -- Further Reading -- 4 Fundamentals of Plasma Physics and Magneto-Hydrodynamics -- 4.1 Collision-Less Plasmas -- 4.1.1 Shielding and the Debye Length -- 4.1.2 The Plasma Frequency -- 4.2 Electromagnetic Waves in Media -- 4.2.1 Polarisation and Dielectric Displacement -- 4.2.2 Structure of the Dielectric Tensor -- 4.3 Dispersion Relations -- 4.3.1 General Form of the Dispersion Relations -- 4.3.2 Transversal and Longitudinal Waves -- 4.3.3 Longitudinal and Transversal Dielectricities -- 4.3.4 Landau Damping -- 4.4 Electromagnetic Waves in Thermal Plasmas -- 4.4.1 Longitudinal and Transversal Dielectricities -- 4.4.2 Dispersion Measure and Damping -- 4.5 The Magneto-Hydrodynamic Equations -- 4.5.1 Assumptions -- 4.5.2 The Induction Equation -- 4.5.3 Euler's Equation -- 4.5.4 Energy and Entropy -- 4.5.5 Incompressible Flows -- 4.5.6 Magnetic Advection and Diffusion -- 4.6 Generation of Magnetic Fields -- 4.7 Ambipolar Diffusion -- 4.7.1 Velocity-Averaged Scattering Cross Section -- 4.7.2 Friction Force and Diffusion Coefficient -- 4.8 Waves in Magnetised Cold Plasmas -- 4.8.1 The Dielectric Tensor -- 4.8.2 Contribution by Ions -- 4.8.3 Dispersion Relations in a Cold, Magnetised Plasma -- 4.8.4 Longitudinal and Transverse Waves -- 4.8.5 Faraday Rotation -- 4.9 Hydromagnetic Waves -- 4.9.1 Linearised Perturbation Equations -- 4.9.2 Alfvén Waves -- 4.9.3 Slow and Fast Hydro-Magnetic Waves. Further Reading -- 5 Stellar Dynamics -- 5.1 The Jeans Equations and Jeans' Theorem -- 5.1.1 Collision-Less Motion in a Gravitational Field -- 5.1.2 The Relaxation Time Scale -- 5.1.3 The Jeans Equations -- 5.1.4 Jeans Equations in Cylindrical and Spherical Coordinates -- 5.1.5 Application to Spherical Systems -- 5.1.6 The Tensor Virial Theorem in Stellar Dynamics -- 5.1.7 Jeans' Theorem -- 5.2 Equilibrium and Stability -- 5.2.1 The Isothermal Sphere -- 5.2.2 Equilibrium and Relaxation -- 5.2.3 Linear Analysis and the Jeans Swindle -- 5.2.4 Jeans Length and Jeans Mass -- 5.2.5 Disk Potentials -- 5.2.6 Fluid Equations for Two-Dimensional Systems -- 5.2.7 Dispersion Relation -- 5.2.8 Toomre's Criterion -- 5.3 Dynamical Friction -- 5.3.1 Deflection of Point Masses -- 5.3.2 Velocity Changes -- 5.3.3 Chandrasekhar's Formula -- Further Reading -- 6 Brief Summary and Concluding Remarks -- Index.
Beginning from first principles and adopting a modular structure, this book develops the fundamental physical methods needed to describe and understand a wide range of seemingly very diverse astrophysical phenomena and processes. For example, the discussion of radiation processes including their spectra is based on Larmor's equation and extended by the photon picture and the internal dynamics of radiating quantum systems, leading to the shapes of spectral lines and the ideas of radiation transport. Hydrodynamics begins with the concept of phase-space distribution functions and Boltzmann's equation and develops ideal, viscous and magneto-hydrodynamics all from the vanishing divergence of an energy-momentum tensor, opening a natural extension towards relativistic hydrodynamics. Linear stability analysis is introduced and used as a common and versatile tool throughout the book. Aimed at students at graduate level, lecturers teaching courses in theoretical astrophysics or advanced topics in modern astronomy, this book with its abundant examples and exercises also serves as a reference and an entry point for more advanced researchers wanting to update their knowledge of the physical processes that govern the behavior and evolution of astronomical objects.
9783527669783
Astrophysics.
Hydrodynamics.
Electronic books.
QB461
523.01