An Introduction to Astronomy and Astrophysics

A n I n t r o d u c t i o n t o

ASTRONOMY AND

ASTROPHYSICS

K14003_FM.indd 1 3/10/15 5:44 PM

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A n I n t r o d u c t i o n t o

ASTRONOMY AND

ASTROPHYSICS

Pankaj Jain

Indian Institute of Technolog y

Kanpur, India

K14003_FM.indd 3 3/10/15 5:44 PM

CRC Press

Taylor & Francis Group

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Contents

Preface xiii

1 Introduction 1

1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Scales and Dimensions . . . . . . . . . . . . . . . . . . . . . 2

1.3 Night Sky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Constellations . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 Earth, Sun, and the Solar System . . . . . . . . . . . . . . . 11

1.5.1 Retrograde Motion of Planets . . . . . . . . . . . . . . 12

1.6 Sidereal Time . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.7 Astronomical Catalogs and Software . . . . . . . . . . . . . . 15

2 Observations 17

2.1 Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . . 18

2.2 Electromagnetic Spectrum . . . . . . . . . . . . . . . . . . . 20

2.3 Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.1 Refractor Telescope . . . . . . . . . . . . . . . . . . . 24

2.3.2 Reflecting Telescope . . . . . . . . . . . . . . . . . . . 27

2.4 Observations at Visible Frequencies . . . . . . . . . . . . . . 29

2.4.1 Theoretical Limit on Resolution . . . . . . . . . . . . 31

2.4.2 Seeing . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.5 Mounting of Telescope . . . . . . . . . . . . . . . . . . . . . 33

2.5.1 Equatorial Mount . . . . . . . . . . . . . . . . . . . . 33

2.5.2 Azimuthal Mount . . . . . . . . . . . . . . . . . . . . 33

2.6 Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.7 Observations at Other Wavelengths . . . . . . . . . . . . . . 34

3 Astrometry 37

3.1 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . 41

3.1.1 The Horizontal System . . . . . . . . . . . . . . . . . . 42

3.1.2 Equatorial Coordinate System . . . . . . . . . . . . . 43

3.1.3 Ecliptic System . . . . . . . . . . . . . . . . . . . . . . 44

3.1.4 Galactic Coordinate System . . . . . . . . . . . . . . . 44

3.1.5 Supergalactic Coordinate System . . . . . . . . . . . . 44

3.2 Space Velocity and Proper Motion of Stars . . . . . . . . . . 44

3.2.1 Doppler Effect . . . . . . . . . . . . . . . . . . . . . . 46

vii

viii Contents

3.3 Parallax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.4 Aberration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.5 Coordinate Transformations . . . . . . . . . . . . . . . . . . 51

3.5.1 Transformation between Equatorial and Ecliptic Coor￾dinate Systems . . . . . . . . . . . . . . . . . . . . . . 54

3.5.2 Precession of Equinoxes . . . . . . . . . . . . . . . . . 55

3.5.3 Equatorial Mounting of a Telescope . . . . . . . . . . 56

4 Photometry 59

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2 Flux Density and Intensity . . . . . . . . . . . . . . . . . . . 61

4.3 Blackbody Radiation . . . . . . . . . . . . . . . . . . . . . . 66

4.4 Energy Density in an Isotropic Radiation Field . . . . . . . . 70

4.5 Magnitude Scale . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.5.1 Apparent Magnitude . . . . . . . . . . . . . . . . . . . 72

4.5.2 Absolute Magnitude . . . . . . . . . . . . . . . . . . . 73

4.5.3 The Color Index . . . . . . . . . . . . . . . . . . . . . 74

4.5.4 Bolometric Magnitude . . . . . . . . . . . . . . . . . . 74

4.6 Stellar Temperatures . . . . . . . . . . . . . . . . . . . . . . 75

4.6.1 Effective Temperature . . . . . . . . . . . . . . . . . . 75

4.6.2 Color Temperature . . . . . . . . . . . . . . . . . . . . 75

4.7 Appendix: Solid Angle . . . . . . . . . . . . . . . . . . . . . 77

5 Gravitation and Kepler’s Laws 81

5.1 Two-Body Problem . . . . . . . . . . . . . . . . . . . . . . . 82

5.2 Application to Solar System . . . . . . . . . . . . . . . . . . 85

5.3 Virial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.4 Tidal Forces and Roche Limit . . . . . . . . . . . . . . . . . 88

6 Stars, Stellar Spectra, and Classification 93

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.2 Stellar Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.3 Harvard Classification of Stellar Spectra . . . . . . . . . . . . 99

6.4 Saha Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.5 Derivation of the Saha Equation . . . . . . . . . . . . . . . . 105

6.5.1 Number of States of a Free Particle in a Box . . . . . 108

6.6 HR Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.7 Star Clusters and Associations . . . . . . . . . . . . . . . . . 112

6.8 Distance and Age Determination of Clusters Using Color￾Magnitude Diagram . . . . . . . . . . . . . . . . . . . . . . . 113

7 Radiation from Astronomical Sources 117

7.1 Continuous Spectra . . . . . . . . . . . . . . . . . . . . . . . 118

7.1.1 Synchrotron Radiation . . . . . . . . . . . . . . . . . . 118

7.1.2 Bremsstrahlung . . . . . . . . . . . . . . . . . . . . . . 121

7.1.3 Compton Scattering . . . . . . . . . . . . . . . . . . . 122

Contents ix

7.1.4 Bound-Free Transitions . . . . . . . . . . . . . . . . . 123

7.2 Absorption and Emission Line Spectrum . . . . . . . . . . . 124

7.2.1 Radial Velocity Due to Doppler Effect . . . . . . . . . 128

7.2.2 Causes of Finite Width of Spectral Lines . . . . . . . 129

7.3 Molecular Band Spectra . . . . . . . . . . . . . . . . . . . . . 129

7.4 Extinction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7.4.1 Extinction Coefficient . . . . . . . . . . . . . . . . . . 135

7.4.2 Color Excess . . . . . . . . . . . . . . . . . . . . . . . 136

8 Stellar Structure 139

8.1 Pressure Gradient . . . . . . . . . . . . . . . . . . . . . . . . 140

8.2 Mass Distribution . . . . . . . . . . . . . . . . . . . . . . . . 143

8.3 Energy Production . . . . . . . . . . . . . . . . . . . . . . . 143

8.4 Temperature Gradient . . . . . . . . . . . . . . . . . . . . . . 144

8.4.1 Radiative Transport . . . . . . . . . . . . . . . . . . . 144

8.4.2 Convective Transport . . . . . . . . . . . . . . . . . . 146

8.5 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 148

8.6 Rosseland Mean Opacity . . . . . . . . . . . . . . . . . . . . 149

8.7 Equation of State . . . . . . . . . . . . . . . . . . . . . . . . 152

8.7.1 Ideal Gas Law . . . . . . . . . . . . . . . . . . . . . . 153

8.7.1.1 Derivation of the Ideal Gas Law . . . . . . . 154

8.7.1.2 Radiation Pressure . . . . . . . . . . . . . . . 158

8.8 Energy Production in Stars . . . . . . . . . . . . . . . . . . . 159

8.9 Appendix: Maxwell–Boltzmann Distribution . . . . . . . . . 161

9 Stellar Nuclear Reactions 165

9.1 Fundamental Interactions . . . . . . . . . . . . . . . . . . . . 166

9.2 Fundamental Particles . . . . . . . . . . . . . . . . . . . . . . 167

9.3 A Brief Introduction to Neutrinos . . . . . . . . . . . . . . . 168

9.4 PP Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

9.5 Nuclear Reaction Rate . . . . . . . . . . . . . . . . . . . . . 170

9.5.1 Nuclear Reaction Rate: Derivation . . . . . . . . . . . 175

9.5.2 Nuclear Cross Section . . . . . . . . . . . . . . . . . . 177

9.5.3 Estimating the Nuclear Reaction Rate . . . . . . . . . 177

9.6 Energy Released in Nuclear Reactions . . . . . . . . . . . . . 181

9.7 Standard Solar Model . . . . . . . . . . . . . . . . . . . . . . 186

10 Star Formation and Stellar Evolution 189

10.1 Early Stage of Star Formation . . . . . . . . . . . . . . . . . 190

10.1.1 Fragmentation . . . . . . . . . . . . . . . . . . . . . . 192

10.2 Evolution on the Main Sequence . . . . . . . . . . . . . . . . 193

10.3 Degenerate Free Electron Gas . . . . . . . . . . . . . . . . . 194

10.4 Evolution beyond the Main Sequence . . . . . . . . . . . . . 196

10.5 Population I and II Stars . . . . . . . . . . . . . . . . . . . . 198

10.6 White Dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . 199

x Contents

10.7 Neutron Star . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

10.8 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

10.9 Supernova . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

11 The Sun 207

11.1 Solar Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . 208

11.1.1 Photosphere . . . . . . . . . . . . . . . . . . . . . . . . 208

11.1.2 Chromosphere . . . . . . . . . . . . . . . . . . . . . . 210

11.1.3 Corona . . . . . . . . . . . . . . . . . . . . . . . . . . 211

11.2 Dynamo Mechanism for Magnetic Field Enhancement . . . . 214

11.3 Sunspots and the Solar Cycle . . . . . . . . . . . . . . . . . . 216

11.4 Some Transient Phenomena . . . . . . . . . . . . . . . . . . . 220

12 The Solar System 223

12.1 Orbital Properties of Planets . . . . . . . . . . . . . . . . . . 224

12.2 Retrograde Motion of Planets . . . . . . . . . . . . . . . . . 226

12.3 Albedo and Temperature of Planets . . . . . . . . . . . . . . 230

12.4 Terrestrial Planets: Interior Structure . . . . . . . . . . . . . 232

12.5 Jovian Planets . . . . . . . . . . . . . . . . . . . . . . . . . . 236

12.6 The Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

12.6.1 Eclipses and Occultations . . . . . . . . . . . . . . . . 240

12.7 Why Did Pluto Lose Its Planetship? . . . . . . . . . . . . . . 241

12.8 Formation of the Solar System . . . . . . . . . . . . . . . . . 242

13 Binary Stars 247

13.1 Kinematics of a Binary Star System . . . . . . . . . . . . . . 247

13.2 Classification of Binary Stars . . . . . . . . . . . . . . . . . . 250

13.3 Mass Determination . . . . . . . . . . . . . . . . . . . . . . . 254

13.4 Mass Transfer in Binary Systems . . . . . . . . . . . . . . . . 257

14 The Milky Way 265

14.1 The Distance Ladder . . . . . . . . . . . . . . . . . . . . . . 266

14.2 Distribution of Matter in the Milky Way . . . . . . . . . . . 270

14.3 Differential Rotation of the Milky Way . . . . . . . . . . . . 273

14.4 Mapping the Galactic Disk with Radio Waves . . . . . . . . 276

14.5 Formation of the Spiral Arms . . . . . . . . . . . . . . . . . . 279

15 Galaxies 283

15.1 Elliptical Galaxies . . . . . . . . . . . . . . . . . . . . . . . . 286

15.2 Spiral Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . 289

15.3 Evidence for Dark Matter . . . . . . . . . . . . . . . . . . . . 292

15.4 Galaxy Clusters . . . . . . . . . . . . . . . . . . . . . . . . . 293

Contents xi

16 Cosmology 295

16.1 Euclidean Space . . . . . . . . . . . . . . . . . . . . . . . . . 296

16.2 Curved Space . . . . . . . . . . . . . . . . . . . . . . . . . . 296

16.3 Minkowski Space-Time . . . . . . . . . . . . . . . . . . . . . 298

16.4 Big Bang Cosmology . . . . . . . . . . . . . . . . . . . . . . 299

16.4.1 Cosmological Redshift and Hubble’s Law . . . . . . . 299

16.4.2 FRW Line Element . . . . . . . . . . . . . . . . . . . . 301

16.4.3 Matter and Radiation . . . . . . . . . . . . . . . . . . 303

16.4.4 Cosmological Evolution Equations . . . . . . . . . . . 305

16.4.5 Accelerating Universe and Dark Energy . . . . . . . . 306

16.5 The Early Universe . . . . . . . . . . . . . . . . . . . . . . . 311

16.5.1 Primordial Nucleosynthesis . . . . . . . . . . . . . . . 315

16.5.2 Recombination . . . . . . . . . . . . . . . . . . . . . . 320

16.5.3 Structure Formation . . . . . . . . . . . . . . . . . . . 321

16.5.4 Cosmic Microwave Background Radiation (CMBR) . . 322

17 Active Galaxies 325

17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

17.2 Active Galactic Nuclei: Some Basic Properties . . . . . . . . 326

17.2.1 Size of AGNs . . . . . . . . . . . . . . . . . . . . . . . 328

17.2.2 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . 329

17.2.3 Superluminal Motion . . . . . . . . . . . . . . . . . . . 330

17.3 Classification of Active Galaxies . . . . . . . . . . . . . . . . 331

17.3.1 Seyfert Galaxies . . . . . . . . . . . . . . . . . . . . . 331

17.3.2 Radio Galaxies . . . . . . . . . . . . . . . . . . . . . . 332

17.3.3 Quasars . . . . . . . . . . . . . . . . . . . . . . . . . . 334

17.3.4 Blazars . . . . . . . . . . . . . . . . . . . . . . . . . . 336

17.4 Unified Model of AGNs . . . . . . . . . . . . . . . . . . . . . 336

Appendix Fundamental Constants and Conversion of Units 339

References 341

Index 343