1. Radio Astronomical Fundamentals ............................. 1
1.1. On the Role of Radio Astronomy in Astrophysics ........ 1
1.2. The Radio Window ...................................... 3
1.3. Some Basic Definitions ................................ 5
1.4. Radiative Transfer .................................... 7
1.5. Black Body Radiation and the Brightness
Temperature .......................................... 10
1.6. The Nyquist Theorem and the Noise Temperature ........ 15
Problems ............................................. 16
2. Electromagnetic Wave Propagation Fundamentals .............. 19
2.1. Maxwell's Equations .................................. 19
2.2. Energy Conservation and the Poynting Vector .......... 20
2.3. Complex Field Vectors ................................ 22
2.4. The Wave Equation .................................... 23
2.5. Plane Waves in Nonconducting Media ................... 25
2.6. Wave Packets and the Group Velocity .................. 28
2.7. Plane Waves in Conducting Media ...................... 30
2.8. The Dispersion Measure of a Tenuous Plasma ........... 32
Problems ............................................. 35
3. Wave Polarization .......................................... 39
3.1. Vector Waves ......................................... 39
3.2. The Poincare Sphere and the Stokes Parameters ........ 43
3.3. Quasi-Monochromatic Plane Waves ...................... 47
3.4. The Stokes Parameters for Quasi-Monochromatic
Waves ................................................ 48
3.5. Faraday Rotation ..................................... 49
Problems ............................................. 53
4. Signal Processing and Receivers: Theory .................... 55
4.1. Signal Processing and Stationary Stochastic
Processes ............................................ 55
4.1.1. Probability Density, Expectation Values
and Ergodicity ............................... 55
4.1.2. Autocorrelation and Power Spectrum ........... 56
4.1.3. Linear Systems ............................... 59
4.1.4. Filters ...................................... 61
4.1.5. Digitization and Sampling .................... 62
4.1.6. Gaussian Random Variables .................... 65
4.1.7. Square Law Detectors ......................... 65
4.2. Limiting Receiver Sensitivity ........................ 66
4.2.1. Noise Uncertainties due to Random
Processes .................................... 68
4.2.2. Receiver Stability ........................... 69
4.2.3. Receiver Calibration ......................... 73
Problems ..................................... 75
5. Practical Receiver Systems ................................. 79
5.1. Historical Introduction .............................. 79
5.1.1. Bolometer Radiometers ........................ 80
5.1.2. The Noise Equivalent Power of a Bolometer .... 81
5.1.3. Currently Used Bolometer Systems ............. 83
5.2. Coherent Receivers ................................... 85
5.2.1. The Minimum Noise in a Coherent System ....... 85
5.2.2. Basic Components: Passive Devices ............ 86
5.2.3. Basic Components: Active Devices ............. 87
5.2.4. Semiconductor Junctions ...................... 92
5.2.5. Practical HEMT Devices ....................... 95
5.2.6. Superconducting Mixers ....................... 97
5.2.7. Hot Electron Bolometers ...................... 99
5.3. Summary of Front Ends Presently in Use .............. 100
5.3.1. Single Pixel Receiver Systems ............... 100
5.3.2. Multibeam Systems ........................... 101
5.4. Back Ends: Correlation Receivers, Polarimeters and
Spectrometers ....................................... 102
5.4.1. Correlation Receivers and Polarimeters ...... 103
5.4.2. Spectrometers ............................... 105
5.4.3. Fourier and Autocorrelation Spectrometers ... 106
5.4.4. Pulsar Back Ends ............................ 115
Problems .................................... 117
6. Fundamentals of Antenna Theory ............................ 121
6.1. Electromagnetic Potentials .......................... 121
6.2. Green's Function for the Wave Equation .............. 123
6.3. The Hertz Dipole .................................... 126
6.3.1. Arrays of Emitters .......................... 131
6.3.2. Arrays of Hertz Dipoles ..................... 133
6.4. Radiation Fields of Filled Antennas ................. 134
6.4.1. Two Dimensional Far Field ................... 134
6.4.2. Three Dimensional Far Field ................. 135
6.4.3. Circular Apertures .......................... 137
6.4.4. Antenna Taper Related to Power Pattern ...... 140
6.5. The Reciprocity Theorem ............................. 141
6.6. Summary ............................................. 141
Problems ............................................ 142
7. Practical Aspects of Filled Aperture Antennas ............. 145
7.1. Descriptive Antenna Parameters ...................... 145
7.1.1. The Power Pattern H(υ, φ) ................... 145
7.1.2. The Main Beam Solid Angle ................... 146
7.1.3. The Effective Aperture ...................... 148
7.1.4. The Concept of Antenna Temperature .......... 150
7.2. Primary Feeds ....................................... 151
7.2.1. Prime Focus Feeds: Dipole and Reflector ..... 152
7.2.2. Horn Feeds Used Today ....................... 152
7.2.3. Multiple Reflector Systems .................. 154
7.3. Antenna Tolerance Theory ............................ 157
7.4. The Practical Design of Parabolic Reflectors ........ 161
7.4.1. General Considerations ...................... 161
7.4.2. Specific Telescopes ......................... 163
7.5. Summary ............................................. 168
Problems ............................................ 169
8. Single Dish Observational Methods ......................... 173
8.1. The Earth's Atmosphere .............................. 173
8.2. Calibration Procedures .............................. 177
8.2.1. General ..................................... 177
8.2.2. Compact Sources ............................. 178
8.2.3. Extended Sources ............................ 180
8.2.4. Calibration of cm Wavelength Telescopes ..... 181
8.2.5. Calibration of mm and sub-mm Wavelength
Telescopes for Heterodyne Systems ........... 182
8.2.6. Bolometer Calibrations ...................... 185
8.3. Continuum Observing Strategies ...................... 185
8.3.1. Point Sources ............................... 185
8.3.2. Imaging of Extended Continuum Sources ....... 186
8.4. Additional Requirements for Spectral Line
Observations ........................................ 188
8.4.1. Radial Velocity Settings .................... 188
8.4.2. Stability of the Frequency Bandpass ......... 190
8.4.3. Instrumental Frequency Baselines ............ 190
8.4.4. The Effect of Stray Radiation ............... 192
8.4.5. Spectral Line Observing Strategies .......... 194
8.5. The Confusion Problem ............................... 196
8.5.1. Introduction ................................ 196
Problems ............................................ 197
9. Interferometers and Aperture Synthesis .................... 201
9.1. The Quest for Angular Resolution .................... 201
9.1.1. The Two Element Interferometer .............. 201
9.2. Two-Element Interferometers ......................... 203
9.2.1. Hardware Requirements ....................... 205
9.2.2. Calibration ................................. 206
9.2.3. Responses of Interferometers ................ 207
9.3. Aperture Synthesis .................................. 210
9.3.1. An Appropriate Coordinate System ............ 210
9.3.2. Historical Development ...................... 214
9.3.3. Interferometric Observations ................ 218
9.3.4. Improving Visibility Functions .............. 220
9.3.5. Multi-Antenna Array Calibrations ............ 221
9.3.6. Data Processing ............................. 221
9.4. Advanced Image Improvement Methods .................. 225
9.4.1. Self-Calibration ............................ 225
9.4.2. Applying CLEAN to the Dirty Map ............. 226
9.4.3. Maximum Entropy Deconvolution Method
(MEM) ....................................... 226
9.5. Interferometer Sensitivity .......................... 227
9.6. Very Long Baseline Interferometers .................. 230
9.7. Interferometers in Astrometry and Geodesy ........... 232
Problems ............................................ 234
10. Emission Mechanisms of Continuous Radiation ............... 239
10.1. The Nature of Radio Sources ......................... 239
10.1.1. Black Body Radiation from Astronomical
Objects ..................................... 241
10.2. Radiation from Accelerated Electrons ................ 243
10.3. The Frequency Distribution of Bremsstrahlung for
an Individual Encounter ............................. 245
10.4. The Radiation of an Ionized Gas Cloud ............... 248
10.5. Nonthermal Radiation Mechanisms ..................... 252
10.6. Review of the Lorentz Transformation ................ 253
10.7. The Synchrotron Radiation of a Single Electron ...... 255
10.7.1. The Total Power Radiated .................... 257
10.7.2. The Angular Distribution of Radiation ....... 258
10.7.3. The Frequency Distribution of the
Emission .................................... 259
10.8. The Spectrum and Polarization of Synchrotron
Radiation ........................................... 261
10.9. The Spectral Distribution of Synchrotron
Radiation from an Ensemble of Electrons ............. 263
10.9.1. Homogeneous Magnetic Field .................. 266
10.9.2. Random Magnetic Field ....................... 268
10.10.Energy Requirements of Synchrotron Sources .......... 269
10.11.Low-Energy Cut-Offs in Nonthermal Sources ........... 271
10.12.Inverse Compton Scattering .......................... 272
10.12.1.The Sunyaev-Zeldovich Effect ................ 272
10.12.2.Energy Loss from High-Brightness Sources .... 273
Problems ............................................ 274
11. Some Examples of Thermal and Nonthermal Radio Sources ..... 277
11.1. The Quiet Sun ....................................... 277
11.2. Radio Radiation from Н II Regions ................... 281
11.2.1. Thermal Radiation ........................... 281
11.2.2. Radio Radiation from Ionized Stellar
Winds ....................................... 283
11.3. Supernovae and Supernova Remnants ................... 284
11.4. The Hydrodynamic Evolution of Supernova Remnants .... 285
11.4.1. The Free-Expansion Phase .................... 286
11.4.2. The Second Phase: Adiabatic Expansion ....... 288
11.5. The Radio Evolution of Older Supernova Remnants ..... 293
11.6. Pulsars ............................................. 295
11.6.1. Detection and Source Nature ................. 295
11.6.2. Distance Estimates and Galactic
Distribution ................................ 296
11.6.3. Intensity Spectrum and Pulse Morphology ..... 298
11.6.4. Pulsar Timing ............................... 301
11.6.5. Rotational Slowdown and Magnetic Moment ..... 303
11.6.6. Binary Pulsars and Millisecond Pulsars ...... 305
11.6.7. Radio Emission Mechanism .................... 308
11.7. Extragalactic Sources ............................... 310
11.7.1. Radio Galaxies: Cygnus A .................... 310
11.7.2. An Example of the Sunyaev-Zeldovich
Effect: Clusters of Galaxies ................ 312
11.7.3. Relativistic Effects and Time Variability ... 312
Problems ............................................ 315
12. Spectral Line Fundamentals ................................ 319
12.1. The Einstein Coefficients ........................... 319
12.2. Radiative Transfer with Einstein Coefficients ....... 321
12.3. Dipole Transition Probabilities ..................... 323
12.4. Simple Solutions of the Rate Equation ............... 325
Problems ............................................ 327
13. Line Radiation of Neutral Hydrogen ........................ 329
13.1. The 21 cm Line of Neutral Hydrogen .................. 330
13.2. The Zeeman Effect ................................... 333
13.3. Spin Temperatures ................................... 333
13.4. Emission and Absorption Lines ....................... 335
13.4.1. The Influence of Beam Filling Factors and
Source Geometry ............................. 336
13.5. The Physical State of the Diffuse Interstellar
Gas ................................................. 339
13.6. Differential Velocity Fields and the Shape of
Spectral Lines ...................................... 341
13.7. The Galactic Velocity Field in the Interstellar
Gas ................................................. 344
13.8. Atomic Lines in External Galaxies ................... 348
13.8.1. Virial Masses ............................... 350
13.8.2. The Tully-Fisher Relation ................... 352
Problems ............................................ 354
14. Recombination Lines ....................................... 359
14.1. Emission Nebulae .................................... 359
14.2. Photoionization Structure of Gaseous Nebulae ........ 360
14.2.1. Pure Hydrogen Nebulae ....................... 360
14.2.2. Hydrogen and Helium Nebulae ................. 363
14.2.3. Actual НII Regions .......................... 364
14.3. Rydberg Atoms ....................................... 365
14.4. Line Intensities Under LTE Conditions ............... 367
14.5. Line Intensities when LTE Conditions do not Apply ... 370
14.5.1. Collisional Broadening ...................... 376
14.6. The Interpretation of Radio Recombination Line
Observations ........................................ 378
14.6.1. Anomalous Cases ............................. 379
14.7. Recombination Lines from Other Elements ............. 380
Problems ............................................ 381
15. Overview of Molecular Basics .............................. 387
15.1. Basic Concepts ...................................... 387
15.2. Rotational Spectra of Diatomic Molecules ............ 389
15.2.1. Hyperfine Structure in Linear Molecules ..... 392
15.3. Vibrational Transitions ............................. 393
15.4. Line Intensities of Linear Molecules ................ 394
15.4.1. Total Column Densities of CO Under LTE
Conditions .................................. 396
15.5. Symmetric Top Molecules ............................. 400
15.5.1. Energy Levels ............................... 400
15.5.2. Spin Statistics ............................. 402
15.5.3. Hyperfine Structure ......................... 402
15.5.4. Line Intensities and Column Densities ....... 405
15.6. Asymmetric Top Molecules ............................ 407
15.6.1. Energy Levels ............................... 407
15.6.2. Spin Statistics and Selection Rules ......... 408
15.6.3. Line Intensities and Column Densitiess ...... 408
15.6.4. Electronic Angular Momentum ................. 412
15.6.5. Molecules with Hindered Motions ............. 413
Problems ............................................ 415
16. Molecules in Interstellar Space ........................... 419
16.1. Introduction ........................................ 419
16.1.1. History ..................................... 420
16.2. Molecular Excitation ................................ 423
16.2.1. Excitation of a Two-Level System ............ 423
16.2.2. Maser Emission Processes in One Dimension ... 426
16.2.3. Non-LTE Excitation of Molecules ............. 430
16.3. Models of Radiative Transfer ........................ 432
16.3.1. The Large Velocity Gradient Model ........... 432
16.4. Spectral Lines as Diagnostic Tools .................. 439
16.4.1. Kinetic Temperatures ........................ 440
16.4.2. Linewidths, Radial Motions and Intensity
Distributions ............................... 441
16.4.3. Determination of H2 Densities ............... 442
16.4.4. Estimates of H2 Column Densities ............ 442
16.4.5. Masses of Molecular Clouds from
Measurements of 12C16O ...................... 443
16.4.6. The Correlation of CO and H2 Column
Densities ................................... 444
16.4.7. Mass Estimates and Cloud Stability .......... 446
16.4.8. Signatures of Cloud Collapse ................ 448
16.5. A Selected Sample of Results ........................ 448
16.6. Chemistry ........................................... 449
16.6.1. Clouds for which the UV Field can be
Neglected ................................... 451
16.6.2. Models of Photon Dominated Regions .......... 451
16.6.3. Results ..................................... 452
16.6.4. Ion-Molecule Chemistry ...................... 454
16.6.5. Grain Chemistry ............................. 458
16.6.6. Searches for New Molecules .................. 458
Problems ............................................ 460
A Some Useful Vector Relations .............................. 463
В The Fourier Transform ..................................... 467
С The Van Vleck Clipping Correction: One Bit
Quantization .............................................. 469
D The Reciprocity Theorem ................................... 473
E The Hankel Transform ...................................... 477
F A List of Calibration Radio Sources ....................... 479
G The Mutual Coherence Function and van Cittert-Zernike
Theorem ................................................... 483
G1 The Mutual Coherence Function .......................... 483
G2 The Coherence Function of Extended Sources: The van
Cittert-Zernike Theorem ................................ 484
Bibliography .................................................. 489
Index ......................................................... 503
|
