COX & GIULI'S PRINCIPLES OF STELLAR STRUCTURE

Size: px
Start display at page:

Download "COX & GIULI'S PRINCIPLES OF STELLAR STRUCTURE"

Transcription

1 COX & GIULI'S PRINCIPLES OF STELLAR STRUCTURE Extended Second Edition A. Weiss, W. Hillebrandt, H.-C. Thomas and H. Ritter Max-Planck-lnstitut fur Astrophysik, Garching, Germany C S P

2 CONTENTS PREFACE TO THE SECOND EDITION PREFACE v vii 0. Introduction and Survey of Observations 1. Luminosities, Masses and Radii of Stars, /. 2. Stellar Time Scales, Empirical (L, T e ) Correlation: Hertzsprung-Russell Diagram, Empirical (L, M) Correlation: Empirical Mass-Luminosity Relation, Empirical (R, M) Correlation: Empirical Mass-Radius Relation, P. 6. Chemical Abundances, //. 7. Mass Loss, Close Binaries, Rotation, Magnetic Fields, IS. 11. Stellar Pulsations, 'Physical Conditions in Stellar Interiors Statement of Condition of Hydrostatic Equilibrium, Estimates of Interior Values of Pressure and Temperature, Effect of Departures from Hydrostatic Equilibrium, Radiation Theory Specific Intensity, 29. la. Integrated Intensity, 30. lb. Constancy of I v Along Every Ray Path in Free Space, 31. lc. Constancy of lj[i^ Along Every Ray Path for Variable Refractive Index, Net Flux, Energy Density of Radiation, 37. A. Average Intensity, Radiation Pressure, 39. 5a. Integrated Radiation Pressure, 42. 5b. Pressure Tensor, Mass Emission Coefficient, Mass Absorption Coefficient, Microscopic Picture of Emission and Absorption of Radiation, 50. 8a. Emission, 51. 8b. Absorption, Equation of Transfer, 65. 9a. Inclusion of the Time Derivative, 69. 9b. Equation of Transfer in Terms of Atomic Parameters, Elementary Theory of Dispersion, a. Plane Electromagnetic Waves, b. Relation Between Attenuation and "True" Absorption, Oc. Electromagnetic Field Energy in Dispersive Media, 81. lod. Lorentz-Lorenz Model for a Dielectric, The "Directional Gradient" and Some of Its Properties, Thermodynamic Equilibrium General Discussion of Thermodynamic Equilibrium, Basic Distribution Law for a System in Statistical Equilibrium, PS. 3. Statistical Weight, PP. 3a. For Discrete Energy Levels, 99. 3b. For Continuous Energy Levels, Distribution Laws for Matter, 104. XV

3 xvi CONTENTS 4a. Boltzmann Equation, b. Maxwell-Boltzmann Distribution Law, c. Saha Ionization Equation, Planck Radiation Law, Relations Among the Einstein Coefficients, Properties of Black Body Radiation, a. Integrated Planck Function, b. Energy Density of Black Body Radiation, c. Integrated Energy Density, d. Integrated Radiation Pressure, Local Thermodynamic Equilibrium (LTE) Equation of Transfer for LTE, Departure of s)n? from BJJT), Assuming LTE, Thermal and Radiative Equilibrium Thermal Equilibrium, Radiative Equilibrium, Solution of the Equation of Transfer Formal Solutions, Expressions for J' v,'fy, and p' r v in Terms of S' v for an Isotropic Source Function, Power Series Solution of the Equation of Transfer, Convergence, Conditions for LTE Equation of Transfer and the Excitation and Kinetic Temperatures, Statistically Steady State for a Two-Level Atom, Simultaneous Solution of the Equation of Transfer and the Statistically Steady State Equations for a Two-Level Atom, 168. Appendix 7-A. Solving the Equation of Transfer Grey Atmospheres, 772. la. The General Solution, 772. lb. The Eddington Approximation, 773. lc. The Method of Discrete Ordinates, Non-grey Atmospheres, a. Opacity Means, b. Multigroup Methods, c. Numerical Methods, 7 SO. 8. Radiative Temperature Gradient General Relation Between Radiation Pressure Tensor and Vector Net Flux, Rosseland Mean Mass Absorption Coefficient, 7P2. 2a. Rosseland Mean for Unity Refractive Index Everywhere, 7P2. 2b. "Modified" Rosseland Mean for Non-Unity Refractive Index, 7P5. 9. Some Thermodynamic Relations Definitions, 7PP. 2. "Zeroth" Law of Thermodynamics, First Law of Thermodynamics, Quantity of Heat, Quasi-Static

4 CONTENTS xvii (or Reversible) Process, Infinitesimal Changes, Case in Which the Pressure Tensor Does Not Reduce to a Pure Hydrostatic Pressure, Exactness, Second Law of Thermodynamics, Conditions for Thermodynamic Equilibrium, Reciprocity Relation, Chemical Equilibrium, Specific Heats, Quasi-Static Infinitesimal Adiabatic Changes, a. The Three Adiabatic Exponents (Gammas), b. Relations Between the Gammas and Specific Heats, c. Computation of the Gammas, Gammas and Specific Heats for a Simple Perfect Gas, Gammas and Specific Heats for Black Body Radiation, Gammas and Specific Heats for a Mixture of Black Body Radiation and a Simple Perfect Gas, Gammas and Specific Heats for a Mixture of Perfect Gases Undergoing Ionization, with Radiation Pressure Included, 234. Appendix 9-A. Semi-Degenerate Equations of State Semi-Degenerate Equations of State, Meaning of Degeneracy of Electron Gas, Mean Molecular Weight Per Free Electron, General Expressions for Electron Density, Pressure, Internal Energy, and Entropy, Non-Relativistic (N.R.) and Extreme Relativistic (E.R.) Regimes for Arbitrary Degree of Degeneracy, a. N.R. Regime QS «1, r] finite), b. E.R. Regime (fi» 1, JJ finite), Completely Degenerate Case (j] = oo), a. N.R. Regime (r/>3 «1, rj = oo), b. E.R. Regime (»jj8» 1,»j = oo), 27P. 6c. Partial Relativistic, Completely Degenerate Regime (r]f} ~ 1, rj = oo), Evaluation of the F t (rj, /3), a. Large Degeneracy (rj» 1), Arbitrarily Relativistic (Arbitrary P), b. Small Degeneracy (rj s 1), Arbitrarily Relativistic (Arbitrary /}), c. Partial Degeneracy, Arbitrarily Relativistic (Arbitrary /8), Criteria for Degeneracy and Regions of Degeneracy on the p-t Plane, a. Criteria for Degeneracy, b. Regions of Degeneracy on the p-r Plane, 2P3. 9. Effect of Electron-Positron Pairs, 2PS. 9a. Discussion of Degeneracy and Conditions for Neglect of e* Pairs, b. Pressure, Internal Energy, and Entropy, c. Gammas for a Mixture Consisting of e* Pairs and Black Body Radiation, Some Results of Kinetic Theory and Statistical Mechanics Pressure in a System of Non-Interacting "Particles", Internal Translational Kinetic Energy per Unit Volume, Statistical Mechanics Approach, Explicit Expressions for N, E, P, and S for Assemblies of Non-Interacting Bosons and Fermions in Statistical Equilibrium, Non-Degenerate (Maxwell-Boltzmann) Systems, Principle of the Equipartition of Energy, Application of the Equipartition Principle to Some Simple Systems, 33P. 7a. Perfect

5 xviii CONTENTS Monatomic Gases with Only Three Degrees of Freedom per Particle, 35P. 7b. More General Perfect Gases with Constant Specific Heats, 340. Appendix 10-A. Non-ideal Gas Effects Real Gases, Pressure Ionization, Coulomb Interactions, Other Effects, a. Configuration Terms, b. Degeneracy, Importance of Radiation Pressure in Stellar Interiors Polytropic Changes Stability of the Radiative Gradient Case of Uniform Chemical Composition, 359."2. Estimate of the Degree of Superadiabaticity in the Deep Interior, Case of Non- Uniform Chemical Composition, General Discussion of Stability Against Convection, 577. Appendix 13-A. Stability of the Radiative Gradient Semi-Convection, Mixing Length Theory of Convection The Four Gradients, 37P. 2. Convective Flux, Average Speed of Convecting Elements, The Net Flux, 5P0. 5. Efficiency of Convection, Upper Limits to Values of Various Quantities, Solution of the Equations When the Total Flux is Specified, Solution of the Equations When the Actual Gradient is Specified, Solution of the Equations When Supersonic Convective Velocities Are Indicated, 420. Appendix 14-A. Non-local and Time-dependent Convection Statement of the Problem, The Basic Equations, Application to Stars: Free Convection, Turbulence in Stars, The Moment Equations Approach, The Diffusion Approximation, A Few Examples, Solutions of Mixing Length Theory in Stellar Models, 435.

6 CONTENTS xix 15. lonization of Material in Stellar Interiors Mean Molecular Weight, Electron Density, Calculation of n h Excitation and lonization Energy, Electrostatic Corrections, a. Depression of the Continuum, b. Electrostatic Corrections to the Pressure Equation of State, Numerical Results for a Particular Chemical Composition, 460. Appendix 15-A. Equation of State in Stellar Interiors Standard Equations of State in Stellar Evolution Calculations, Equation of State Tables for Moderate Densities, a. The MHD Equation of State, b. The OPAL Equation of State, The EoS at High Stellar Densities, Comparison of Different EoS, Other Sources for EoS and Data, Stellar Opacity Photo Effect, Free-Free Transitions (Bremstrahlung), Thomson Scattering (Coherent Compton Effect), Monochromatic Mass Absorption Coefficient, Rosseland Mean Opacity, Approximate Formulae, a. Thomson Electron Scattering Opacity, b. Free-Free Opacity, c. Bound-Free Opacity, d. Relative Magnitudes, e. Interpolation Formulae, Electron Thermal Conduction, Other Effects, a. Bound-Bound Absorption, b. Negative Ion Absorption, c. Molecular Absorption, d. Rayleigh Scattering, e. Raman Scattering, f. Photo-Excitation to Auto-Ionizing States, g. Pair Production, A. N. Cox Opacity Results, 57S. Appendix 16-A. Stellar Opacity Atomic Data, 527. la. Line Profiles, 523. lb. Oscillator Strengths, 523. lc. Mean Opacities, 524. Id. Resulting Data, Rosseland Mean Opacities, a. Summary of OPAL Opacities, b. Sample Tables, c. Comparisons of Results, Additional Opacities, a. Molecular Opacities, b. Electron Conduction Opacities, Combined Tables Ready for Use, Successes of the New Opacities, Stellar Energy Sources Gravitational Potential Energy of a Star, The Virial Theorem, Internal Energy and Total Energy of a Star, Gravitational Contraction, Some Conditions for Gravitational Contraction, Local Energy Release from Gravitational Contraction, Nuclear Energy Production, Basic Properties of Atomic Nuclei, Bohr Picture of a Nuclear Reaction, a. Occurrence of

7 xx CONTENTS Resonances, b. Compound Nucleus, Cross Section for Nuclear Reactions, Cross Section for Low Energy Exothermic Nuclear Reactions, Thermonuclear Reaction Rate, Non-Resonant Contribution, Resonant Contribution, Electron Screening, Hydrogen Burning Reactions, Rates of Energy Production by Hydrogen Burning, a. Carbon Cycle, b. Proton Chain, Helium Burning Reactions, a. Triple Alpha Reaction, b. Further Alpha Particle Capture Reactions, c. Neon-Sodium Cycle, Carbon, Oxygen, and Neon Burning, Neutrino Energy Losses, a. Photo-Neutrino Process, b. Pair Neutrino Process, c. Plasma Neutrino Process, 655. Appendix 17-A. Stellar Energy Sources Nuclear Reactions in Stars, 663. la. Weak Interaction Reactions and Decays, 663. lb. Strong Interaction Reactions and Decays, 666. lc. Theoretical Models of Nuclear Reactions in Stars, 667. Id. The Reaction Network Equations, Nuclear Processes in Stars, a. Hydrostatic and Explosive Hydrogen Burning, b. Helium Burning and the s-process, c. Carbon, Neon, and Oxygen Burning, d. Silicon Burning and Nuclear Statistical Equilibrium, e. Explosive Nuclear Burning, f. The r-process, Neutrino Energy Losses, 6S The Sun and the Solar Model The Solar Neutrino Problem, 684. la. A Brief History, 684. lb. Solutions of the Solar Neutrino Problem, Helioseismology, Particle Diffusion, a. Physical Motivation, b. The Burgers Equations, The Standard Solar Model, a. Physics of the SSM, b. Numerical Aspects, c. Standard Solar Model Data, Resolution of the Solar Neutrino Problem, 709. APPENDICES Al. Physical and Astronomical Constants 712 REFERENCE LIST AND AUTHOR INDEX 713 ADDITIONAL BIBLIOGRAPHY 731 SUBJECT INDEX 752

Advanced Stellar Astrophysics

Advanced Stellar Astrophysics v Advanced Stellar Astrophysics William K. Rose University of Maryland College Park CAMBRIDGE UNIVERSITY PRESS Contents Preface xiii Star formation and stellar evolution: an overview 1 1 A short history

More information

Opacity. requirement (aim): radiative equilibrium: near surface: Opacity

Opacity. requirement (aim): radiative equilibrium: near surface: Opacity (Gray) Diffusion approximation to radiative transport: (assumes isotropy valid only in the deep stellar interior) - opacity is a function of frequency (wave length ). - aim: to reduce the (rather complex)

More information

THIRD-YEAR ASTROPHYSICS

THIRD-YEAR ASTROPHYSICS THIRD-YEAR ASTROPHYSICS Problem Set: Stellar Structure and Evolution (Dr Ph Podsiadlowski, Michaelmas Term 2006) 1 Measuring Stellar Parameters Sirius is a visual binary with a period of 4994 yr Its measured

More information

THE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES

THE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES THE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES DAVID F. GRAY University of Western Ontario, London, Ontario, Canada CAMBRIDGE UNIVERSITY PRESS Contents Preface to the first edition Preface to the

More information

Cambridge University Press Advanced Stellar Astrophysics William K. Rose Frontmatter More information

Cambridge University Press Advanced Stellar Astrophysics William K. Rose Frontmatter More information In the last two decades, remarkable progress has been made in understanding stars. This graduate-level textbook provides a systematic, self-contained and lucid introduction to the physical processes and

More information

11/19/08. Gravitational equilibrium: The outward push of pressure balances the inward pull of gravity. Weight of upper layers compresses lower layers

11/19/08. Gravitational equilibrium: The outward push of pressure balances the inward pull of gravity. Weight of upper layers compresses lower layers Gravitational equilibrium: The outward push of pressure balances the inward pull of gravity Weight of upper layers compresses lower layers Gravitational equilibrium: Energy provided by fusion maintains

More information

Course Descriptions. Appendix F

Course Descriptions. Appendix F Appendix F Course Descriptions Seven new courses are required to implement the Space Physics program, and their course descriptions are contained in this appendix. 51 F.1 Course Description: Physics II

More information

Charles Keeton. Principles of Astrophysics. Using Gravity and Stellar Physics. to Explore the Cosmos. ^ Springer

Charles Keeton. Principles of Astrophysics. Using Gravity and Stellar Physics. to Explore the Cosmos. ^ Springer Charles Keeton Principles of Astrophysics Using Gravity and Stellar Physics to Explore the Cosmos ^ Springer Contents 1 Introduction: Tools of the Trade 1 1.1 What Is Gravity? 1 1.2 Dimensions and Units

More information

ELECTRODYNAMICS OF CONTINUOUS MEDIA

ELECTRODYNAMICS OF CONTINUOUS MEDIA ELECTRODYNAMICS OF CONTINUOUS MEDIA by L. D. LANDAU and E. M. LIFSHITZ Institute of Physical Problems, USSR Academy of Sciences Volume 8 of Course of Theoretical Physics Translated from the Russian by

More information

Many-Body Problems and Quantum Field Theory

Many-Body Problems and Quantum Field Theory Philippe A. Martin Francois Rothen Many-Body Problems and Quantum Field Theory An Introduction Translated by Steven Goldfarb, Andrew Jordan and Samuel Leach Second Edition With 102 Figures, 7 Tables and

More information

9-1 The Sun s energy is generated by thermonuclear reactions in its core The Sun s luminosity is the amount of energy emitted each second and is

9-1 The Sun s energy is generated by thermonuclear reactions in its core The Sun s luminosity is the amount of energy emitted each second and is 1 9-1 The Sun s energy is generated by thermonuclear reactions in its core The Sun s luminosity is the amount of energy emitted each second and is produced by the proton-proton chain in which four hydrogen

More information

Astronomy 404 October 9, 2013

Astronomy 404 October 9, 2013 Nuclear reaction rate: Astronomy 404 October 9, 2013 from the tunneling increases with increasing E from the velocity distrib. decreases with increasing E The Gamow peak occurs at energy Energy generation

More information

Ay 1 Lecture 8. Stellar Structure and the Sun

Ay 1 Lecture 8. Stellar Structure and the Sun Ay 1 Lecture 8 Stellar Structure and the Sun 8.1 Stellar Structure Basics How Stars Work Hydrostatic Equilibrium: gas and radiation pressure balance the gravity Thermal Equilibrium: Energy generated =

More information

ASTROPHYSICS. K D Abhyankar. Universities Press S T A R S A ND G A L A X I E S

ASTROPHYSICS. K D Abhyankar. Universities Press S T A R S A ND G A L A X I E S ASTROPHYSICS S T A R S A ND G A L A X I E S K D Abhyankar Universities Press Contents Foreword vii Preface ix 1 Introduction 1 1.1 ' Astronomy and astrophysics 1 1.2 Importance of astronomy 2 1.3 Methods

More information

Introduction to the Sun

Introduction to the Sun Lecture 15 Introduction to the Sun Jiong Qiu, MSU Physics Department Open Q: what physics do we learn about the Sun? 1. Energy - nuclear energy - magnetic energy 2. Radiation - continuum and line emissions;

More information

The Microphysics. EOS, opacity, energy generation

The Microphysics. EOS, opacity, energy generation The Microphysics Equation of State EOS, opacity, energy generation Ideal gas: (see tutorial handout) P = nk B T = R µ ρt with ρ = nµm u ; µ: molecular weight, mass of particle per m u. Several components

More information

Physics and Chemistry of the Interstellar Medium

Physics and Chemistry of the Interstellar Medium Physics and Chemistry of the Interstellar Medium Sun Kwok The University of Hong Kong UNIVERSITY SCIENCE BOOKS Sausalito, California * Preface xi The Interstellar Medium.1.1 States of Matter in the ISM

More information

Highenergy Nuclear Optics of Polarized Particles

Highenergy Nuclear Optics of Polarized Particles Highenergy Nuclear Optics of Polarized Particles Vladimir G. Baryshevsky Research Institute for Nuclear Problems Belarusian State University 1> World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI

More information

Observable constraints on nucleosynthesis conditions in Type Ia supernovae

Observable constraints on nucleosynthesis conditions in Type Ia supernovae Observable constraints on nucleosynthesis conditions in Type Ia supernovae MPE Eurogenesis Garching, March 26, 2013 Ivo Rolf Seitenzahl Institut für Theoretische Physik und Astrophysik Julius-Maximilians-Universität

More information

Ay Fall 2004 Lecture 6 (given by Tony Travouillon)

Ay Fall 2004 Lecture 6 (given by Tony Travouillon) Ay 122 - Fall 2004 Lecture 6 (given by Tony Travouillon) Stellar atmospheres, classification of stellar spectra (Many slides c/o Phil Armitage) Formation of spectral lines: 1.excitation Two key questions:

More information

Stellar Structure. Observationally, we can determine: Can we explain all these observations?

Stellar Structure. Observationally, we can determine: Can we explain all these observations? Stellar Structure Observationally, we can determine: Flux Mass Distance Luminosity Temperature Radius Spectral Type Composition Can we explain all these observations? Stellar Structure Plan: Use our general

More information

Pre Main-Sequence Evolution

Pre Main-Sequence Evolution Stellar Astrophysics: Stellar Evolution Pre Main-Sequence Evolution The free-fall time scale is describing the collapse of the (spherical) cloud to a protostar 1/2 3 π t ff = 32 G ρ With the formation

More information

The Sun. How are these quantities measured? Properties of the Sun. Chapter 14

The Sun. How are these quantities measured? Properties of the Sun. Chapter 14 The Sun Chapter 14 The Role of the Sun in the Solar System > 99.9% of the mass Its mass is responsible for the orderly orbits of the planets Its heat is responsible for warming the planets It is the source

More information

PHAS3135 The Physics of Stars

PHAS3135 The Physics of Stars PHAS3135 The Physics of Stars Exam 2013 (Zane/Howarth) Answer ALL SIX questions from Section A, and ANY TWO questions from Section B The numbers in square brackets in the right-hand margin indicate the

More information

Opacity and Optical Depth

Opacity and Optical Depth Opacity and Optical Depth Absorption dominated intensity change can be written as di λ = κ λ ρ I λ ds with κ λ the absorption coefficient, or opacity The initial intensity I λ 0 of a light beam will be

More information

List of Comprehensive Exams Topics

List of Comprehensive Exams Topics List of Comprehensive Exams Topics Mechanics 1. Basic Mechanics Newton s laws and conservation laws, the virial theorem 2. The Lagrangian and Hamiltonian Formalism The Lagrange formalism and the principle

More information

The Physics of Fluids and Plasmas

The Physics of Fluids and Plasmas The Physics of Fluids and Plasmas An Introduction for Astrophysicists ARNAB RAI CHOUDHURI CAMBRIDGE UNIVERSITY PRESS Preface Acknowledgements xiii xvii Introduction 1 1. 3 1.1 Fluids and plasmas in the

More information

Introduction. Stellar Objects: Introduction 1. Why should we care about star astrophysics?

Introduction. Stellar Objects: Introduction 1. Why should we care about star astrophysics? Stellar Objects: Introduction 1 Introduction Why should we care about star astrophysics? stars are a major constituent of the visible universe understanding how stars work is probably the earliest major

More information

NERS 311 Current Old notes notes Chapter Chapter 1: Introduction to the course 1 - Chapter 1.1: About the course 2 - Chapter 1.

NERS 311 Current Old notes notes Chapter Chapter 1: Introduction to the course 1 - Chapter 1.1: About the course 2 - Chapter 1. NERS311/Fall 2014 Revision: August 27, 2014 Index to the Lecture notes Alex Bielajew, 2927 Cooley, bielajew@umich.edu NERS 311 Current Old notes notes Chapter 1 1 1 Chapter 1: Introduction to the course

More information

The Sun. the main show in the solar system. 99.8% of the mass % of the energy. Homework due next time - will count best 5 of 6

The Sun. the main show in the solar system. 99.8% of the mass % of the energy. Homework due next time - will count best 5 of 6 The Sun the main show in the solar system 99.8% of the mass 99.9999...% of the energy 2007 Pearson Education Inc., publishing as Pearson Addison-Wesley Homework due next time - will count best 5 of 6 The

More information

CLASSICAL ELECTRICITY

CLASSICAL ELECTRICITY CLASSICAL ELECTRICITY AND MAGNETISM by WOLFGANG K. H. PANOFSKY Stanford University and MELBA PHILLIPS Washington University SECOND EDITION ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo

More information

is the minimum stopping potential for which the current between the plates reduces to zero.

is the minimum stopping potential for which the current between the plates reduces to zero. Module 1 :Quantum Mechanics Chapter 2 : Introduction to Quantum ideas Introduction to Quantum ideas We will now consider some experiments and their implications, which introduce us to quantum ideas. The

More information

The Sun. The Sun is a star: a shining ball of gas powered by nuclear fusion. Mass of Sun = 2 x g = 330,000 M Earth = 1 M Sun

The Sun. The Sun is a star: a shining ball of gas powered by nuclear fusion. Mass of Sun = 2 x g = 330,000 M Earth = 1 M Sun The Sun The Sun is a star: a shining ball of gas powered by nuclear fusion. Mass of Sun = 2 x 10 33 g = 330,000 M Earth = 1 M Sun Radius of Sun = 7 x 10 5 km = 109 R Earth = 1 R Sun Luminosity of Sun =

More information

Stellar atmospheres: an overview

Stellar atmospheres: an overview Stellar atmospheres: an overview Core M = 2x10 33 g R = 7x10 10 cm 50 M o 20 R o L = 4x10 33 erg/s 10 6 L o 10 4 (PN) 10 6 (HII) 10 12 (QSO) L o Photosphere Envelope Chromosphere/Corona R = 200 km ~ 3x10

More information

Nuclear Astrophysics. Lecture 10 Thurs. Jan. 12, 2012 Prof. Shawn Bishop, Office 2013, Ex

Nuclear Astrophysics. Lecture 10 Thurs. Jan. 12, 2012 Prof. Shawn Bishop, Office 2013, Ex Nuclear Astrophysics Lecture 10 Thurs. Jan. 12, 2012 Prof. Shawn Bishop, Office 2013, Ex. 12437 shawn.bishop@ph.tum.de 1 Summary of Reaction Rate 2 Energy Generation & Standard Model Let us consider a

More information

Today The Sun. Events

Today The Sun. Events Today The Sun Events Last class! Homework due now - will count best 5 of 6 Final exam Dec. 20 @ 12:00 noon here Review this Course! www.case.edu/utech/course-evaluations/ The Sun the main show in the solar

More information

Fundamental Stellar Parameters. Radiative Transfer. Stellar Atmospheres

Fundamental Stellar Parameters. Radiative Transfer. Stellar Atmospheres Fundamental Stellar Parameters Radiative Transfer Stellar Atmospheres Equations of Stellar Structure Basic Principles Equations of Hydrostatic Equilibrium and Mass Conservation Central Pressure, Virial

More information

The Sun Our Extraordinary Ordinary Star

The Sun Our Extraordinary Ordinary Star The Sun Our Extraordinary Ordinary Star 1 Guiding Questions 1. What is the source of the Sun s energy? 2. What is the internal structure of the Sun? 3. How can astronomers measure the properties of the

More information

An Overview of the Details

An Overview of the Details The Sun Our Extraordinary Ordinary Star 1 Guiding Questions 1. What is the source of the Sun s energy? 2. What is the internal structure of the Sun? 3. How can astronomers measure the properties of the

More information

Foundations of Astrophysics

Foundations of Astrophysics Foundations of Astrophysics Barbara Ryden The Ohio State University Bradley M. Peterson The Ohio State University Preface xi 1 Early Astronomy 1 1.1 The Celestial Sphere 1 1.2 Coordinate Systems on a Sphere

More information

Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases

Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases Bahram M. Askerov Sophia R. Figarova Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases With im Figures Springer Contents 1 Basic Concepts of Thermodynamics and Statistical Physics...

More information

9.1 Introduction. 9.2 Static Models STELLAR MODELS

9.1 Introduction. 9.2 Static Models STELLAR MODELS M. Pettini: Structure and Evolution of Stars Lecture 9 STELLAR MODELS 9.1 Introduction Stars are complex physical systems, but not too complex to be modelled numerically and, with some simplifying assumptions,

More information

From Last Time: We can more generally write the number densities of H, He and metals.

From Last Time: We can more generally write the number densities of H, He and metals. From Last Time: We can more generally write the number densities of H, He and metals. n H = Xρ m H,n He = Y ρ 4m H, n A = Z Aρ Am H, How many particles results from the complete ionization of hydrogen?

More information

2. Stellar atmospheres: Structure

2. Stellar atmospheres: Structure 2. Stellar atmospheres: Structure 2.1. Assumptions Plane-parallel geometry Hydrostatic equilibrium, i.e. o no large-scale accelerations comparable to surface gravity o no dynamically significant mass loss

More information

Life and Death of a Star 2015

Life and Death of a Star 2015 Life and Death of a Star 2015 Name Date 1. In the main-sequence, the core is slowly shrinking because A. the mass of the star is slowly increasing B. hydrogen fusing to helium makes the core more dense

More information

Mar 22, INSTRUCTIONS: First ll in your name and social security number (both by printing

Mar 22, INSTRUCTIONS: First ll in your name and social security number (both by printing ASTRONOMY 0089: EXAM 2 Class Meets M,W,F, 1:00 PM Mar 22, 1996 INSTRUCTIONS: First ll in your name and social security number (both by printing and by darkening the correct circles). Sign your answer sheet

More information

Chapter 2: Equation of State

Chapter 2: Equation of State Introduction Chapter 2: Equation of State The Local Thermodynamic Equilibrium The Distribution Function Black Body Radiation Fermi-Dirac EoS The Complete Degenerate Gas Application to White Dwarfs Temperature

More information

ASTR-3760: Solar & Space Physics...Spring 2017

ASTR-3760: Solar & Space Physics...Spring 2017 ASTR-3760: Solar & Space Physics...Spring 2017 Review material for midterm exam (March 22, 2017) Although I m not recommending full-on memorization of everything in this document, I do think it s important

More information

An Overview of the Details

An Overview of the Details Guiding Questions The Sun Our Extraordinary Ordinary Star 1. What is the source of the Sun s energy? 2. What is the internal structure of the Sun? 3. How can astronomers measure the properties of the Sun

More information

O WILEY- MODERN NUCLEAR CHEMISTRY. WALTER D. LOVELAND Oregon State University. DAVID J. MORRISSEY Michigan State University

O WILEY- MODERN NUCLEAR CHEMISTRY. WALTER D. LOVELAND Oregon State University. DAVID J. MORRISSEY Michigan State University MODERN NUCLEAR CHEMISTRY WALTER D. LOVELAND Oregon State University DAVID J. MORRISSEY Michigan State University GLENN T. SEABORG University of California, Berkeley O WILEY- INTERSCIENCE A JOHN WILEY &

More information

ACTIVE GALACTIC NUCLEI: FROM THE CENTRAL BLACK HOLE TO THE GALACTIC ENVIRONMENT

ACTIVE GALACTIC NUCLEI: FROM THE CENTRAL BLACK HOLE TO THE GALACTIC ENVIRONMENT Julian H. Krolik ACTIVE GALACTIC NUCLEI: FROM THE CENTRAL BLACK HOLE TO THE GALACTIC ENVIRONMENT PRINCETON UNIVERSITY PRESS Princeton, New Jersey Preface Guide for Readers xv xix 1. What Are Active Galactic

More information

Outline. Today we will learn what is thermal radiation

Outline. Today we will learn what is thermal radiation Thermal Radiation & Outline Today we will learn what is thermal radiation Laws Laws of of themodynamics themodynamics Radiative Radiative Diffusion Diffusion Equation Equation Thermal Thermal Equilibrium

More information

Astronomy. Stellar Evolution

Astronomy. Stellar Evolution Astronomy A. Dayle Hancock adhancock@wm.edu Small 239 Office hours: MTWR 10-11am Stellar Evolution Main Sequence star changes during nuclear fusion What happens when the fuel runs out Old stars and second

More information

The Stellar Opacity. F ν = D U = 1 3 vl n = 1 3. and that, when integrated over all energies,

The Stellar Opacity. F ν = D U = 1 3 vl n = 1 3. and that, when integrated over all energies, The Stellar Opacity The mean absorption coefficient, κ, is not a constant; it is dependent on frequency, and is therefore frequently written as κ ν. Inside a star, several different sources of opacity

More information

Rb, which had been compressed to a density of 1013

Rb, which had been compressed to a density of 1013 Modern Physics Study Questions for the Spring 2018 Departmental Exam December 3, 2017 1. An electron is initially at rest in a uniform electric field E in the negative y direction and a uniform magnetic

More information

ASTR 5110 Atomic & Molecular Physics Fall Stat Mech Midterm.

ASTR 5110 Atomic & Molecular Physics Fall Stat Mech Midterm. ASTR 5110 Atomic & Molecular Physics Fall 2013. Stat Mech Midterm. This is an open book, take home, 24 hour exam. When you have finished, put your answers in the envelope provided, mark the envelope with

More information

Energy transport: convection

Energy transport: convection Outline Introduction: Modern astronomy and the power of quantitative spectroscopy Basic assumptions for classic stellar atmospheres: geometry, hydrostatic equilibrium, conservation of momentum-mass-energy,

More information

An Introduction to. Nuclear Physics. Yatramohan Jana. Alpha Science International Ltd. Oxford, U.K.

An Introduction to. Nuclear Physics. Yatramohan Jana. Alpha Science International Ltd. Oxford, U.K. An Introduction to Nuclear Physics Yatramohan Jana Alpha Science International Ltd. Oxford, U.K. Contents Preface Acknowledgement Part-1 Introduction vii ix Chapter-1 General Survey of Nuclear Properties

More information

Star Formation and Protostars

Star Formation and Protostars Stellar Objects: Star Formation and Protostars 1 Star Formation and Protostars 1 Preliminaries Objects on the way to become stars, but extract energy primarily from gravitational contraction are called

More information

Chapter IX: Nuclear fusion

Chapter IX: Nuclear fusion Chapter IX: Nuclear fusion 1 Summary 1. General remarks 2. Basic processes 3. Characteristics of fusion 4. Solar fusion 5. Controlled fusion 2 General remarks (1) Maximum of binding energy per nucleon

More information

Environment of the Radiation Field ...

Environment of the Radiation Field ... Copyright (2003) Geroge W. Collins, II 11 Environment of the Radiation Field... Thus far, we have said little or nothing about the gas through which the radiation is flowing. This constitutes the second

More information

Astronomy 1504 Section 002 Astronomy 1514 Section 10 Midterm 2, Version 1 October 19, 2012

Astronomy 1504 Section 002 Astronomy 1514 Section 10 Midterm 2, Version 1 October 19, 2012 Astronomy 1504 Section 002 Astronomy 1514 Section 10 Midterm 2, Version 1 October 19, 2012 Choose the answer that best completes the question. Read each problem carefully and read through all the answers.

More information

MAJOR NUCLEAR BURNING STAGES

MAJOR NUCLEAR BURNING STAGES MAJOR NUCLEAR BURNING STAGES The Coulomb barrier is higher for heavier nuclei with high charge: The first reactions to occur are those involving light nuclei -- Starting from hydrogen burning, helium burning

More information

7. The Evolution of Stars a schematic picture (Heavily inspired on Chapter 7 of Prialnik)

7. The Evolution of Stars a schematic picture (Heavily inspired on Chapter 7 of Prialnik) 7. The Evolution of Stars a schematic picture (Heavily inspired on Chapter 7 of Prialnik) In the previous chapters we have seen that the timescale of stellar evolution is set by the (slow) rate of consumption

More information

The Sun. Nearest Star Contains most of the mass of the solar system Source of heat and illumination

The Sun. Nearest Star Contains most of the mass of the solar system Source of heat and illumination The Sun Nearest Star Contains most of the mass of the solar system Source of heat and illumination Outline Properties Structure Solar Cycle Energetics Equation of Stellar Structure TBC Properties of Sun

More information

PHYS3113, 3d year Statistical Mechanics Tutorial problems. Tutorial 1, Microcanonical, Canonical and Grand Canonical Distributions

PHYS3113, 3d year Statistical Mechanics Tutorial problems. Tutorial 1, Microcanonical, Canonical and Grand Canonical Distributions 1 PHYS3113, 3d year Statistical Mechanics Tutorial problems Tutorial 1, Microcanonical, Canonical and Grand Canonical Distributions Problem 1 The macrostate probability in an ensemble of N spins 1/2 is

More information

NANO/MICROSCALE HEAT TRANSFER

NANO/MICROSCALE HEAT TRANSFER NANO/MICROSCALE HEAT TRANSFER Zhuomin M. Zhang Georgia Institute of Technology Atlanta, Georgia New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore

More information

Isotopic yields from supernova light curves

Isotopic yields from supernova light curves Isotopic yields from supernova light curves Astrophysics and Nuclear Structure Hirschegg, January 29, 2013 Ivo Rolf Seitenzahl Institut für Theoretische Physik und Astrophysik Julius-Maximilians-Universität

More information

CONTENTS. vii. CHAPTER 2 Operators 15

CONTENTS. vii. CHAPTER 2 Operators 15 CHAPTER 1 Why Quantum Mechanics? 1 1.1 Newtonian Mechanics and Classical Electromagnetism 1 (a) Newtonian Mechanics 1 (b) Electromagnetism 2 1.2 Black Body Radiation 3 1.3 The Heat Capacity of Solids and

More information

Nuclear Reactions and Solar Neutrinos ASTR 2110 Sarazin. Davis Solar Neutrino Experiment

Nuclear Reactions and Solar Neutrinos ASTR 2110 Sarazin. Davis Solar Neutrino Experiment Nuclear Reactions and Solar Neutrinos ASTR 2110 Sarazin Davis Solar Neutrino Experiment Hydrogen Burning Want 4H = 4p è 4 He = (2p,2n) p è n, only by weak interaction Much slower than pure fusion protons

More information

Statistical Mechanics

Statistical Mechanics Franz Schwabl Statistical Mechanics Translated by William Brewer Second Edition With 202 Figures, 26 Tables, and 195 Problems 4u Springer Table of Contents 1. Basic Principles 1 1.1 Introduction 1 1.2

More information

Substellar Atmospheres. PHY 688, Lecture 18 Mar 9, 2009

Substellar Atmospheres. PHY 688, Lecture 18 Mar 9, 2009 Substellar Atmospheres PHY 688, Lecture 18 Mar 9, 2009 Outline Review of previous lecture the Kepler mission launched successfully results P < 1 month planets by September 09 giant planet interiors comparison

More information

Chapter 19: The Evolution of Stars

Chapter 19: The Evolution of Stars Chapter 19: The Evolution of Stars Why do stars evolve? (change from one state to another) Energy Generation fusion requires fuel, fuel is depleted [fig 19.2] at higher temperatures, other nuclear process

More information

Stellar Evolution Stars spend most of their lives on the main sequence. Evidence: 90% of observable stars are main-sequence stars.

Stellar Evolution Stars spend most of their lives on the main sequence. Evidence: 90% of observable stars are main-sequence stars. Stellar Evolution Stars spend most of their lives on the main sequence. Evidence: 90% of observable stars are main-sequence stars. Stellar evolution during the main-sequence life-time, and during the post-main-sequence

More information

Stellar Interiors - Hydrostatic Equilibrium and Ignition on the Main Sequence.

Stellar Interiors - Hydrostatic Equilibrium and Ignition on the Main Sequence. Stellar Interiors - Hydrostatic Equilibrium and Ignition on the Main Sequence http://apod.nasa.gov/apod/astropix.html Outline of today s lecture Hydrostatic equilibrium: balancing gravity and pressure

More information

Guiding Questions. The Deaths of Stars. Pathways of Stellar Evolution GOOD TO KNOW. Low-mass stars go through two distinct red-giant stages

Guiding Questions. The Deaths of Stars. Pathways of Stellar Evolution GOOD TO KNOW. Low-mass stars go through two distinct red-giant stages The Deaths of Stars 1 Guiding Questions 1. What kinds of nuclear reactions occur within a star like the Sun as it ages? 2. Where did the carbon atoms in our bodies come from? 3. What is a planetary nebula,

More information

The Deaths of Stars 1

The Deaths of Stars 1 The Deaths of Stars 1 Guiding Questions 1. What kinds of nuclear reactions occur within a star like the Sun as it ages? 2. Where did the carbon atoms in our bodies come from? 3. What is a planetary nebula,

More information

Stars AS4023: Stellar Atmospheres (13) Stellar Structure & Interiors (11)

Stars AS4023: Stellar Atmospheres (13) Stellar Structure & Interiors (11) Stars AS4023: Stellar Atmospheres (13) Stellar Structure & Interiors (11) Kenneth Wood, Room 316 kw25@st-andrews.ac.uk http://www-star.st-and.ac.uk/~kw25 What is a Stellar Atmosphere? Transition from dense

More information

Lecture 1. Overview Time Scales, Temperature-density Scalings, Critical Masses

Lecture 1. Overview Time Scales, Temperature-density Scalings, Critical Masses Lecture 1 Overview Time Scales, Temperature-density Scalings, Critical Masses I. Preliminaries The life of any star is a continual struggle between the force of gravity, seeking to reduce the star to a

More information

Lecture 1. Overview Time Scales, Temperature-density Scalings, Critical Masses. I. Preliminaries

Lecture 1. Overview Time Scales, Temperature-density Scalings, Critical Masses. I. Preliminaries I. Preliminaries Lecture 1 Overview Time Scales, Temperature-density Scalings, Critical Masses The life of any star is a continual struggle between the force of gravity, seeking to reduce the star to a

More information

TRANSFER OF RADIATION

TRANSFER OF RADIATION TRANSFER OF RADIATION Under LTE Local Thermodynamic Equilibrium) condition radiation has a Planck black body) distribution. Radiation energy density is given as U r,ν = 8πh c 3 ν 3, LTE), tr.1) e hν/kt

More information

PHYSICS (PHYS) Physics (PHYS) 1. PHYS 5880 Astrophysics Laboratory

PHYSICS (PHYS) Physics (PHYS) 1. PHYS 5880 Astrophysics Laboratory Physics (PHYS) 1 PHYSICS (PHYS) PHYS 5210 Theoretical Mechanics Kinematics and dynamics of particles and rigid bodies. Lagrangian and Hamiltonian equations of motion. PHYS 5230 Classical Electricity And

More information

Stellar Evolution: The Deaths of Stars. Guiding Questions. Pathways of Stellar Evolution. Chapter Twenty-Two

Stellar Evolution: The Deaths of Stars. Guiding Questions. Pathways of Stellar Evolution. Chapter Twenty-Two Stellar Evolution: The Deaths of Stars Chapter Twenty-Two Guiding Questions 1. What kinds of nuclear reactions occur within a star like the Sun as it ages? 2. Where did the carbon atoms in our bodies come

More information

Guiding Questions. The Deaths of Stars. Pathways of Stellar Evolution GOOD TO KNOW. Low-mass stars go through two distinct red-giant stages

Guiding Questions. The Deaths of Stars. Pathways of Stellar Evolution GOOD TO KNOW. Low-mass stars go through two distinct red-giant stages The Deaths of Stars Guiding Questions 1. What kinds of nuclear reactions occur within a star like the Sun as it ages? 2. Where did the carbon atoms in our bodies come from? 3. What is a planetary nebula,

More information

Chapter 14 Our Star A Closer Look at the Sun. Why was the Sun s energy source a major mystery?

Chapter 14 Our Star A Closer Look at the Sun. Why was the Sun s energy source a major mystery? Chapter 14 Our Star 14.1 A Closer Look at the Sun Our goals for learning Why was the Sun s energy source a major mystery? Why does the Sun shine? What is the Sun s structure? Why was the Sun s energy source

More information

Research paper assignment

Research paper assignment Research paper assignment Review of research that interests you, more focused than discussions in class Include references and figures Final format should be PDF (try LaTeX!) Concise! < 5000 words Steps:

More information

Chapter 1 Some Properties of Stars

Chapter 1 Some Properties of Stars Chapter 1 Some Properties of Stars This chapter is assigned reading for review. 1 2 CHAPTER 1. SOME PROPERTIES OF STARS Chapter 2 The Hertzsprung Russell Diagram This chapter is assigned reading for review.

More information

ASTR-1020: Astronomy II Course Lecture Notes Section VI

ASTR-1020: Astronomy II Course Lecture Notes Section VI ASTR-1020: Astronomy II Course Lecture Notes Section VI Dr. Donald G. Luttermoser East Tennessee State University Edition 4.0 Abstract These class notes are designed for use of the instructor and students

More information

Stellar Interior: Physical Processes

Stellar Interior: Physical Processes Physics Focus on Astrophysics Focus on Astrophysics Stellar Interior: Physical Processes D. Fluri, 29.01.2014 Content 1. Mechanical equilibrium: pressure gravity 2. Fusion: Main sequence stars: hydrogen

More information

Star Formation and Evolution

Star Formation and Evolution Star Formation and Evolution Low and Medium Mass Stars Four Components of the Interstellar Medium Component Temperature Density (K) (atoms/cm 3 ) HI Clouds 50 150 1 1000 Intercloud Medium 10 3-10 4 0.01

More information

Theory of optically thin emission line spectroscopy

Theory of optically thin emission line spectroscopy Theory of optically thin emission line spectroscopy 1 Important definitions In general the spectrum of a source consists of a continuum and several line components. Processes which give raise to the continuous

More information

IoP. An Introduction to the Science of Cosmology. Derek Raine. Ted Thomas. Series in Astronomy and Astrophysics

IoP. An Introduction to the Science of Cosmology. Derek Raine. Ted Thomas. Series in Astronomy and Astrophysics Series in Astronomy and Astrophysics An Introduction to the Science of Cosmology Derek Raine Department of Physics and Astronomy University of Leicester, UK Ted Thomas Department of Physics and Astronomy

More information

Contents. Preface to the First Edition Preface to the Second Edition

Contents. Preface to the First Edition Preface to the Second Edition Contents Preface to the First Edition Preface to the Second Edition Notes xiii xv xvii 1 Basic Concepts 1 1.1 History 1 1.1.1 The Origins of Nuclear Physics 1 1.1.2 The Emergence of Particle Physics: the

More information

Internal conversion electrons and SN light curves

Internal conversion electrons and SN light curves Internal conversion electrons and SN light curves International School of Nuclear Physics 32nd Course: Particle and Nuclear Astrophysics September 23, 2010, Erice Ivo Rolf Seitenzahl DFG Emmy Noether Research

More information

ASTM109 Stellar Structure and Evolution Duration: 2.5 hours

ASTM109 Stellar Structure and Evolution Duration: 2.5 hours MSc Examination Day 15th May 2014 14:30 17:00 ASTM109 Stellar Structure and Evolution Duration: 2.5 hours YOU ARE NOT PERMITTED TO READ THE CONTENTS OF THIS QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY

More information

13 Synthesis of heavier elements. introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1

13 Synthesis of heavier elements. introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1 13 Synthesis of heavier elements introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1 The triple α Reaction When hydrogen fusion ends, the core of a star collapses and the temperature can reach

More information

Limb Darkening. Limb Darkening. Limb Darkening. Limb Darkening. Empirical Limb Darkening. Betelgeuse. At centre see hotter gas than at edges

Limb Darkening. Limb Darkening. Limb Darkening. Limb Darkening. Empirical Limb Darkening. Betelgeuse. At centre see hotter gas than at edges Limb Darkening Sun Betelgeuse Limb Darkening Stars are both redder and dimmer at the edges Sun Limb Darkening Betelgeuse Limb Darkening Can also be understood in terms of temperature within the solar photosphere.

More information

Students are required to pass a minimum of 15 AU of PAP courses including the following courses:

Students are required to pass a minimum of 15 AU of PAP courses including the following courses: School of Physical and Mathematical Sciences Division of Physics and Applied Physics Minor in Physics Curriculum - Minor in Physics Requirements for the Minor: Students are required to pass a minimum of

More information

Chapter 14 Lecture. Chapter 14: Our Star Pearson Education, Inc.

Chapter 14 Lecture. Chapter 14: Our Star Pearson Education, Inc. Chapter 14 Lecture Chapter 14: Our Star 14.1 A Closer Look at the Sun Our goals for learning: Why does the Sun shine? What is the Sun's structure? Why does the Sun shine? Is it on FIRE? Is it on FIRE?

More information

MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont

MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont McGRAW-HILL, INC. New York St. Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico Milan Montreal New Delhi

More information