Astrophysics : decoding the cosmos

Astrophysics: Decoding the Cosmos is an accessible introduction to the key principles and theories underlying astrophysics. This text takes a close look at the radiation and particles that we receive from astronomical objects, providing a thorough understanding of what this tells us, drawing the information together using examples to illustrate the process of astrophysics. Content: Astrophysics; Contents; Preface; Acknowledgments; Introduction; Appendix: dimensions, units and equations; PART I THE SIGNAL OBSERVED; 1 Defining the signal; 2 Measuring the signal; PART II MATTER AND RADIATION ESSENTIALS; 3 Matter essentials; 4 Radiation essentials; PART III THE SIGNAL PERTURBED; 5 The interaction of light with matter; 6 The signal transferred; 7 The interaction of light with space; PART IV THE SIGNAL EMITTED; 8 Continuum emission; 9 Line emission; PART V THE SIGNAL DECODED; 10 Forensic astronomy; Appendix A: Mathematical and geometrical relations Abstract: Astrophysics: Decoding the Cosmos is an accessible introduction to the key principles and theories underlying astrophysics. This text takes a close look at the radiation and particles that we receive from astronomical objects, providing a thorough understanding of what this tells us, drawing the information together using examples to illustrate the process of astrophysics Astrophysics 4 Contents 10 Preface 16 Acknowledgments 18 Introduction 20 Appendix: dimensions, units and equations 25 PART I THE SIGNAL OBSERVED 32 1 Defining the signal 34 1.1 The power of light - luminosity and spectral power 34 1.2 Light through a surface - flux and flux density 38 1.3 The brightness of light - intensity and specific intensity 40 1.4 Light from all angles - energy density and mean intensity 44 1.5 How light pushes - radiation pressure 47 1.6 The human perception of light - magnitudes 50 1.6.1 Apparent magnitude 50 1.6.2 Absolute magnitude 53 1.6.3 The colour index, bolometric correction, and HR diagram 54 1.6.4 Magnitudes beyond stars 55 1.7 Light aligned - polarization 56 Problems 56 2 Measuring the signal 60 2.1 Spectral filters and the panchromatic universe 60 2.2 Catching the signal - the telescope 63 2.2.1 Collecting and focussing the signal 65 2.2.2 Detecting the signal 67 2.2.3 Field of view and pixel resolution 68 2.2.4 Diffraction and diffraction-limited resolution 69 2.3 The Corrupted signal - the atmosphere 72 2.3.1 Atmospheric refraction 73 2.3.2 Seeing 74 2.3.3 Adaptive optics 76 2.3.4 Scintillation 79 2.3.5 Atmospheric reddening 79 2.4 Processing the signal 80 2.4.1 Correcting the signal 80 2.4.2 Calibrating the signal 81 2.5 Analysing the signal 81 2.6 Visualizing the signal 83 Problems 86 Appendix: refraction in the Earth's atmosphere 89 PART II MATTER AND RADIATION ESSENTIALS 94 3 Matter essentials 96 3.1 The Big Bang 96 3.2 Dark and light matter 97 3.3 Abundances of the elements 101 3.3.1 Primordial abundance 101 3.3.2 Stellar evolution and ISM enrichment 101 3.3.3 Supernovae and explosive nucleosynthesis 106 3.3.4 Abundances in the Milky Way, its star formation history and the IMF 108 3.4 The gaseous universe 113 3.4.1 Kinetic temperature and the Maxwell-Boltzmann velocity distribution 115 3.4.2 The ideal gas 119 3.4.3 The mean free path and collision rate 120 3.4.4 Statistical equilibrium, thermodynamic equilibrium, and LTE 124 3.4.5 Excitation and the Boltzmann Equation 127 3.4.6 Ionization and the Saha Equation 131 3.4.7 Probing the gas 132 3.5 The dusty Universe 135 3.5.1 Observational effects of dust 136 3.5.2 Structure and composition of dust 140 3.5.3 The origin of dust 142 3.6 Cosmic rays 143 3.6.1 Cosmic ray composition 143 3.6.2 The cosmic ray energy spectrum 144 3.6.3 The origin of cosmic rays 148 Problems 149 Appendix: the electron/proton ratio in cosmic rays 152 4 Radiation essentials 154 4.1 Black body radiation 154 4.1.1 The brightness temperature 158 4.1.2 The Rayleigh-Jeans Law and Wien's Law 160 4.1.3 Wien's Displacement Law and stellar colour 161 4.1.4 The Stefan-Boltzmann Law, stellar luminosity and the HR diagram 163 4.1.5 Energy density and pressure in stars 165 4.2 Grey bodies and planetary temperatures 165 4.2.1 The equilibrium temperature of a grey body 167 4.2.2 Direct detection of extrasolar planets 171 Problems 174 Appendix: derivation of the Planck function 177 4.A.1 The statistical weight 177 4.A.2 The mean energy per state 178 4.A.3 The specific energy density and specific intensity 179 PART III THE SIGNAL PERTURBED 182 5 The interaction of light with matter 184 5.1 The photon redirected - scattering 185 5.1.1 Elastic scattering 188 5.1.2 Inelastic scattering 196 5.2 The photon lost - absorption 199 5.2.1 Particle kinetic energy - heating 199 5.2.2 Change of state - ionization and the Stro ̈mgren sphere 200 5.3 The wavefront redirected - refraction 203 5.4 Quantifying opacity and transparency 206 5.4.1 Total opacity and the optical depth 206 5.4.2 Dynamics of opacity – pulsation and stellar winds 206 5.5 The opacity of dust - extinction 213 Problems 214 6 The signal transferred 218 6.1 Types of energy transfer 218 6.2 The equation of transfer 220 6.3 Solutions to the equation of transfer 222 6.3.1 Case A: no cloud 222 6.3.2 Case B: absorbing, but not emitting cloud 223 6.3.3 Case C: emitting, but not absorbing cloud 223 6.3.4 Case D: cloud in thermodynamic equilibrium (TE) 224 6.3.5 Case E: emitting and absorbing cloud 224 6.3.6 Case F: emitting and absorbing cloud in LTE 225 6.4 Implications of the LTE solution 226 6.4.1 Implications for temperature 226 6.4.2 Observability of emission and absorption lines 227 6.4.3 Determining temperature and optical depth of HI clouds 231 Problems 235 7 The interaction of light with space 238 7.1 Space and time 238 7.2 Redshifts and blueshifts 241 7.2.1 The Doppler shift - deciphering dynamics 241 7.2.2 The expansion redshift 248 7.2.3 The gravitational redshift 250 7.3 Gravitational refraction 251 7.3.1 Geometry and mass of a gravitational lens 251 7.3.2 Microlensing - MACHOs and planets 256 7.3.3 Cosmological distances with gravitational lenses 257 7.4 Time variability and source size 258 Problems 259 PART IV THE SIGNAL EMITTED 264 8 Continuum emission 266 8.1 Characteristics of continuum emission – thermal and non-thermal 267 8.2 Bremsstrahlung (free-free) emission 268 8.2.1 The thermal Bremsstrahlung spectrum 268 8.2.2 Radio emission from HII and other ionized regions 273 8.2.3 X-ray emission from hot diffuse gas 276 8.3 Free–bound (recombination) emission 282 8.4 Two-photon emission 284 8.5 Synchrotron (and cyclotron) radiation 286 8.5.1 Cyclotron radiation – planets to pulsars 289 8.5.2 The synchrotron spectrum 293 8.5.3 Determining synchrotron source properties 299 8.5.4 Synchrotron sources - spurs, bubbles, jets, lobes and relics 301 8.6 Inverse Compton radiation 304 Problems 307 9 Line emission 310 9.1 The richness of the spectrum - radio waves to gamma rays 311 9.1.1 Electronic transitions - optical and UV lines 311 9.1.2 Rotational and vibrational transitions - molecules, IR and mm-wave spectra 312 9.1.3 Nuclear transitions -g-rays and high energy events 317 9.2 The line strengths, thermalization, and the critical gas density 319 9.3 Line broadening 321 9.3.1 Doppler broadening and temperature diagnostics 322 9.3.2 Pressure broadening 326 9.4 Probing physical conditions via electronic transitions 327 9.4.1 Radio recombination lines 328 9.4.2 Optical recombination lines 333 9.4.3 The 21 cm line of hydrogen 338 9.5 Probing physical conditions via molecular transitions 342 9.5.1 The CO molecule 342 Problems 344 PART V THE SIGNAL DECODED 348 10 Forensic astronomy 350 10.1 Complex spectra 350 10.1.1 Isolating the signal 350 10.1.2 Modelling the signal 352 10.2 Case studies - the active, the young, and the old 356 10.2.1 Case study 1: the Galactic Centre 357 10.2.2 Case study 2: the Cygnus star forming complex 360 10.2.3 Case study 3: the globular cluster, NGC 6397 362 10.3 The messenger and the message 366 Problems 367 Appendix A: Mathematical and geometrical relations 370 A.1 Taylor series 370 A.2 Binomial expansion 370 A.3 Exponential expansion 371 A.4 Convolution 371 A.5 Properties of the ellipse 371 Appendix B: Astronomical geometry 374 B.1 One-dimensional and two-dimensional angles 374 B.2 Solid angle and the spherical coordinate system 375 Appendix C: The hydrogen atom 378 C.1 The hydrogen spectrum and principal quantum number 378 C.2 Quantum numbers, degeneracy, and statistical weight 383 C.3 Fine structure and the Zeeman effect 384 C.4 The l 21 cm line of neutral hydrogen 385 Appendix D: Scattering processes 388 D.1 Elastic, or coherent scattering 389 D.1.1 Scattering from free electrons – Thomson scattering 389 D.1.2 Scattering from bound electrons I: the oscillator model 390 D.1.3 Scattering from bound electrons II: quantum mechanics 393 D.1.4 Scattering from bound electrons III: resonance scattering and the natural line shape 394 D.1.5 Scattering from bound electrons IV: Rayleigh scattering 397 D.2 Inelastic scattering – Compton scattering from free electrons 398 D.3 Scattering by dust 400 Appendix E: Plasmas, the plasma frequency, and plasma waves 404 Appendix F: The Hubble relation and the expanding Universe 408 F.1 Kinematics of the Universe 408 F.2 Dynamics of the Universe 414 F.3 Kinematics, dynamics and high redshifts 417 Appendix G: Tables and figures 420 References 432 Index 438 Colour insert 449 Astrophysics......Page 4 Contents......Page 10 Preface......Page 16 Acknowledgments......Page 18 Introduction......Page 20 Appendix: dimensions, units and equations......Page 25 PART I THE SIGNAL OBSERVED......Page 32 1.1 The power of light - luminosity and spectral power......Page 34 1.2 Light through a surface - flux and flux density......Page 38 1.3 The brightness of light - intensity and specific intensity......Page 40 1.4 Light from all angles - energy density and mean intensity......Page 44 1.5 How light pushes - radiation pressure......Page 47 1.6.1 Apparent magnitude......Page 50 1.6.2 Absolute magnitude......Page 53 1.6.3 The colour index, bolometric correction, and HR diagram......Page 54 1.6.4 Magnitudes beyond stars......Page 55 Problems......Page 56 2.1 Spectral filters and the panchromatic universe......Page 60 2.2 Catching the signal - the telescope......Page 63 2.2.1 Collecting and focussing the signal......Page 65 2.2.2 Detecting the signal......Page 67 2.2.3 Field of view and pixel resolution......Page 68 2.2.4 Diffraction and diffraction-limited resolution......Page 69 2.3 The Corrupted signal - the atmosphere......Page 72 2.3.1 Atmospheric refraction......Page 73 2.3.2 Seeing......Page 74 2.3.3 Adaptive optics......Page 76 2.3.5 Atmospheric reddening......Page 79 2.4.1 Correcting the signal......Page 80 2.5 Analysing the signal......Page 81 2.6 Visualizing the signal......Page 83 Problems......Page 86 Appendix: refraction in the Earth's atmosphere......Page 89 PART II MATTER AND RADIATION ESSENTIALS......Page 94 3.1 The Big Bang......Page 96 3.2 Dark and light matter......Page 97 3.3.2 Stellar evolution and ISM enrichment......Page 101 3.3.3 Supernovae and explosive nucleosynthesis......Page 106 3.3.4 Abundances in the Milky Way, its star formation history and the IMF......Page 108 3.4 The gaseous universe......Page 113 3.4.1 Kinetic temperature and the Maxwell-Boltzmann velocity distribution......Page 115 3.4.2 The ideal gas......Page 119 3.4.3 The mean free path and collision rate......Page 120 3.4.4 Statistical equilibrium, thermodynamic equilibrium, and LTE......Page 124 3.4.5 Excitation and the Boltzmann Equation......Page 127 3.4.6 Ionization and the Saha Equation......Page 131 3.4.7 Probing the gas......Page 132 3.5 The dusty Universe......Page 135 3.5.1 Observational effects of dust......Page 136 3.5.2 Structure and composition of dust......Page 140 3.5.3 The origin of dust......Page 142 3.6.1 Cosmic ray composition......Page 143 3.6.2 The cosmic ray energy spectrum......Page 144 3.6.3 The origin of cosmic rays......Page 148 Problems......Page 149 Appendix: the electron/proton ratio in cosmic rays......Page 152 4.1 Black body radiation......Page 154 4.1.1 The brightness temperature......Page 158 4.1.2 The Rayleigh-Jeans Law and Wien's Law......Page 160 4.1.3 Wien's Displacement Law and stellar colour......Page 161 4.1.4 The Stefan-Boltzmann Law, stellar luminosity and the HR diagram......Page 163 4.2 Grey bodies and planetary temperatures......Page 165 4.2.1 The equilibrium temperature of a grey body......Page 167 4.2.2 Direct detection of extrasolar planets......Page 171 Problems......Page 174 4.A.1 The statistical weight......Page 177 4.A.2 The mean energy per state......Page 178 4.A.3 The specific energy density and specific intensity......Page 179 PART III THE SIGNAL PERTURBED......Page 182 5 The interaction of light with matter......Page 184 5.1 The photon redirected - scattering......Page 185 5.1.1 Elastic scattering......Page 188 5.1.2 Inelastic scattering......Page 196 5.2.1 Particle kinetic energy - heating......Page 199 5.2.2 Change of state - ionization and the Stro ̈mgren sphere......Page 200 5.3 The wavefront redirected - refraction......Page 203 5.4.2 Dynamics of opacity – pulsation and stellar winds......Page 206 5.5 The opacity of dust - extinction......Page 213 Problems......Page 214 6.1 Types of energy transfer......Page 218 6.2 The equation of transfer......Page 220 6.3.1 Case A: no cloud......Page 222 6.3.3 Case C: emitting, but not absorbing cloud......Page 223 6.3.5 Case E: emitting and absorbing cloud......Page 224 6.3.6 Case F: emitting and absorbing cloud in LTE......Page 225 6.4.1 Implications for temperature......Page 226 6.4.2 Observability of emission and absorption lines......Page 227 6.4.3 Determining temperature and optical depth of HI clouds......Page 231 Problems......Page 235 7.1 Space and time......Page 238 7.2.1 The Doppler shift - deciphering dynamics......Page 241 7.2.2 The expansion redshift......Page 248 7.2.3 The gravitational redshift......Page 250 7.3.1 Geometry and mass of a gravitational lens......Page 251 7.3.2 Microlensing - MACHOs and planets......Page 256 7.3.3 Cosmological distances with gravitational lenses......Page 257 7.4 Time variability and source size......Page 258 Problems......Page 259 PART IV THE SIGNAL EMITTED......Page 264 8 Continuum emission......Page 266 8.1 Characteristics of continuum emission – thermal and non-thermal......Page 267 8.2.1 The thermal Bremsstrahlung spectrum......Page 268 8.2.2 Radio emission from HII and other ionized regions......Page 273 8.2.3 X-ray emission from hot diffuse gas......Page 276 8.3 Free–bound (recombination) emission......Page 282 8.4 Two-photon emission......Page 284 8.5 Synchrotron (and cyclotron) radiation......Page 286 8.5.1 Cyclotron radiation – planets to pulsars......Page 289 8.5.2 The synchrotron spectrum......Page 293 8.5.3 Determining synchrotron source properties......Page 299 8.5.4 Synchrotron sources - spurs, bubbles, jets, lobes and relics......Page 301 8.6 Inverse Compton radiation......Page 304 Problems......Page 307 9 Line emission......Page 310 9.1.1 Electronic transitions - optical and UV lines......Page 311 9.1.2 Rotational and vibrational transitions - molecules, IR and mm-wave spectra......Page 312 9.1.3 Nuclear transitions -g-rays and high energy events......Page 317 9.2 The line strengths, thermalization, and the critical gas density......Page 319 9.3 Line broadening......Page 321 9.3.1 Doppler broadening and temperature diagnostics......Page 322 9.3.2 Pressure broadening......Page 326 9.4 Probing physical conditions via electronic transitions......Page 327 9.4.1 Radio recombination lines......Page 328 9.4.2 Optical recombination lines......Page 333 9.4.3 The 21 cm line of hydrogen......Page 338 9.5.1 The CO molecule......Page 342 Problems......Page 344 PART V THE SIGNAL DECODED......Page 348 10.1.1 Isolating the signal......Page 350 10.1.2 Modelling the signal......Page 352 10.2 Case studies - the active, the young, and the old......Page 356 10.2.1 Case study 1: the Galactic Centre......Page 357 10.2.2 Case study 2: the Cygnus star forming complex......Page 360 10.2.3 Case study 3: the globular cluster, NGC 6397......Page 362 10.3 The messenger and the message......Page 366 Problems......Page 367 A.2 Binomial expansion......Page 370 A.5 Properties of the ellipse......Page 371 B.1 One-dimensional and two-dimensional angles......Page 374 B.2 Solid angle and the spherical coordinate system......Page 375 C.1 The hydrogen spectrum and principal quantum number......Page 378 C.2 Quantum numbers, degeneracy, and statistical weight......Page 383 C.3 Fine structure and the Zeeman effect......Page 384 C.4 The l 21 cm line of neutral hydrogen......Page 385 Appendix D: Scattering processes......Page 388 D.1.1 Scattering from free electrons – Thomson scattering......Page 389 D.1.2 Scattering from bound electrons I: the oscillator model......Page 390 D.1.3 Scattering from bound electrons II: quantum mechanics......Page 393 D.1.4 Scattering from bound electrons III: resonance scattering and the natural line shape......Page 394 D.1.5 Scattering from bound electrons IV: Rayleigh scattering......Page 397 D.2 Inelastic scattering – Compton scattering from free electrons......Page 398 D.3 Scattering by dust......Page 400 Appendix E: Plasmas, the plasma frequency, and plasma waves......Page 404 F.1 Kinematics of the Universe......Page 408 F.2 Dynamics of the Universe......Page 414 F.3 Kinematics, dynamics and high redshifts......Page 417 Appendix G: Tables and figures......Page 420 References......Page 432 Index......Page 438 Colour insert......Page 449

astrophysics: Decoding The Cosmos Is An Accessible Introduction To The Key Principles And Theories Underlying The Subject. It Takes A Close Look At The Radiation And Particles That We Receive From Astronomical Objects And Provides A Thorough Understanding Of What These Information-bearers Tell Us. Chapters Are Dedicated To Complex Physical Processes Described In An Accessible Manner And Pull Together Relevant Background Material That , With Many Examples, Places The Physics Firmly Into An Astronomical Context.

• an Accessible Student-friendly Guide To The Key Theories And Principles Of Astrophysics

• includes Numerous Illustrations, Examples And End-of-chapter Problems To Enhance Student Understanding

• focuses On The 'how' Of Astronomy- How Densities, Temperatures, Masses And Energies Are Actually Determined

• a 'tool Chest' For Undergraduate Astronomers Providing Key Background Information To The Subject

• describes The Physics First, Then Moves On To Provide Examples Of The Theory In Practice

this Book Will Be Invaluable For Students Taking Courses In Astrophysics, Physics And Astronomy And Will Also Be A Useful Reference For Graduate Students Looking For An Overview Of The Subject.

Astrophysics: Decoding the Cosmos is an accessible introduction to the key principles and theories underlying the subject. It takes a close look at the radiation and particles that we receive from astronomical objects and provides a thorough understanding of what these information-bearers tell us. Chapters are dedicated to complex physical processes described in an accessible manner and pull together relevant background material that , with many examples, places the physics firmly into an astronomical context.

• an accessible student-friendly guide to the key theories and principles of astrophysics
• includes numerous illustrations, examples and end-of-chapter problems to enhance student understanding
• focuses on the 'how' of astronomy- how densities, temperatures, masses and energies are actually determined
• a 'tool chest' for undergraduate astronomers providing key background information to the subject
• describes the physics first, then moves on to provide examples of the theory in practice

This book will be invaluable for students taking courses in astrophysics, physics and astronomy and will also be a useful reference for graduate students looking for an overview of the subject.

Astrophysics: Decoding the Cosmos is an accessible introduction to the key principles and theories underlying astrophysics. This text takes a close look at the radiation and particles that we receive from astronomical objects, providing a thorough understanding of what this tells us, drawing the information together using examples to illustrate the process of astrophysics. Chapters dedicated to objects showing complex processes are written in an accessible manner and pull relevant background information together to put the subject firmly into context. The intention of the author is that the book will be a'tool chest'for undergraduate astronomers wanting to know the how of astrophysics. Students will gain a thorough grasp of the key principles, ensuring that this often-difficult subject becomes more accessible.Dr Judith Ann Irwin, Department of Physics, Queen's University, Kingston Ontario, Canada

Astrophysics: Decoding the Cosmos is an accessible introduction to the key principles and theories underlying astrophysics.

This text takes a close look at the radiation and particles that we receive from astronomical objects, providing a thorough understanding of what this tells us, drawing the information together using examples to illustrate the process of astrophysics. Chapters dedicated to objects showing complex processes are written in an accessible manner and pull relevant background information together to put the subject firmly into context.

The intention of the author is that the book will be a 'tool chest' for undergraduate astronomers wanting to know the how of astrophysics. Students will gain a thorough grasp of the key principles, ensuring that this often-difficult subject becomes more accessible.

Astrophysics: Decoding the Cosmos is an accessible introduction to the key principles and theories underlying astrophysics. This text takes a close look at the radiation and particles that we receive from astronomical objects, providing a thorough understanding of what this tells us, drawing the information together using examples to illustrate the process of astrophysics. Chapters dedicated to objects showing complex processes are written in an accessible manner and pull relevant background information together to put the subject firmly into context. The intention of the author is that the book will be a 'tool chest' for undergraduate astronomers wanting to know the how of astrophysics. Students will gain a thorough grasp of the key principles, ensuring that this often-difficult subject becomes more accessible. Laser Chemistry: Spectroscopy, Dynamics and Applications provides a basic introduction to the subject, written for students and other novices. It assumes little in the way of prior knowledge, and carefully guides the reader through the important theory and concepts whilst introducing key techniques and applications. Providing a basic introduction to laser chemistry, this title assumes little in the way of prior knowledge, and guides the reader through the important theory and concepts whilst introducing key techniques and applications.