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Terahertz Astronomy © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 1 20-08-2015 20:38:15 © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 2 20-08-2015 20:38:15 Terahertz Astronomy Christopher K. Walker Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 3 20-08-2015 20:38:15 CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20150413 International Standard Book Number-13: 978-1-4665-7043-6 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti- lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy- ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To my Family, who lit the path to the writing of this book © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 5 20-08-2015 20:38:16 © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 6 20-08-2015 20:38:16 CONTENTS Preface xi Author xiii About the Cover xv 1 The Interstellar Medium (ISM) at Terahertz (THz) Frequencies 1 1.1 Introduction 1 1.2 ISM Components of the Milky Way 3 1.2.1 Hot Ionized Medium (HIM) 5 1.2.2 Warm Neutral Medium (WNM) 5 1.2.3 Warm Ionized Medium (WIM) 5 1.2.4 Cool Neutral Medium (CNM) 6 1.2.5 Cold Dense Molecular Clouds (CDM) 7 1.2.6 Relationship between ISM Phases 7 1.3 Lifecycle of the ISM 10 1.4 Probing the Lifecycle of the ISM 16 1.4.1 Origin of Fine-Structure Lines 16 1.4.2 Importance of [CII] 18 1.4.3 Diffuse Gas Density 20 1.4.4 Star Formation Rate and Infrared (IR) Luminosity 23 1.4.5 Spectral Classification of Ionizing Star 25 1.4.6 THz Molecular Lines 26 1.4.6.1 Rotational Transitions 26 1.4.6.2 H O Lines 29 2 1.5 THz Spectral Energy Distributions (SEDs) 32 Conclusion 34 References 35 2 THz Radiative Transfer Basics and Line Radiation 39 2.1 Equation of Radiative Transfer 39 2.2 Solution to the Equation of Radiative Transfer under Local Thermodynamic Equilibrium (LTE) 41 2.3 Radiative Transfer of Rotational Transitions of Linear Molecules in LTE 48 2.3.1 Determining Gas Optical Depth 49 2.3.2 Derivation of Gas Excitation Temperature 51 2.3.3 Derivation of Gas Column Density with Optical Depth 55 2.3.4 Derivation of Gas Column Density in the Optically Thin Limit 56 2.3.5 Estimating Gas Density and Mass 60 2.4 Non-LTE Approach 60 Conclusion 64 References 65 vii © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 7 20-08-2015 20:38:16 3 THz Continuum Emission 67 3.1 Introduction 67 3.2 THz Spectral Energy Distributions 70 3.3 Deriving Dust Optical Depth, Column Density, and Mass 73 3.4 Temperature and Density Distributions 75 3.5 Dust Energy Balance in Clouds 77 3.6 Dust–Gas Coupling 77 3.7 Dust Polarization: Origin and Measurement 79 Conclusion 83 References 84 4 Simple Radiative Transfer Model 87 4.1 Introduction 87 4.2 Geometry 87 4.3 Source Physical Conditions 88 4.4 Lines of Sight 89 4.5 Model Equation of Transfer 89 4.6 LTE Radiative Transfer with Hydrodynamic Simulations 97 4.7 Non-LTE Radiative Transfer with Hydrodynamic Simulations 99 Going Further 102 References 102 5 THz Optical Systems 103 5.1 Introduction: Source–Beam Coupling 103 5.2 Quantum Electrodynamics (QED) and Maxwell 108 5.3 Origin of a Single-Aperture Diffraction Pattern 109 5.4 Gaussian Beam Optics 113 5.4.1 Gaussian Beam Basics 113 5.4.2 Gaussian Beam Coupling 116 5.5 Focusing Gaussian Beams 117 5.5.1 Lenses 118 5.5.2 Behavior of Light at Dielectric Interfaces 120 5.5.3 Mirrors 126 5.5.3.1 Parabola 126 5.5.3.2 Ellipsoid 127 5.5.3.3 Mirror Reflective Losses and Beam Distortion 130 5.5.4 Gaussian Beam Telescope 132 5.5.5 Wire Grid Polarizers 133 5.6 Intercepting Gaussian Beams 135 5.6.1 Open-Structure Detector Optics 135 5.6.2 Transmission-Line-Mounted Detectors 136 5.6.3 Waveguide Feedhorns 145 5.6.3.1 Corrugated Horn 146 5.6.3.2 Pickett–Potter Horn 147 viii Contents © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 8 20-08-2015 20:38:16 5.6.3.3 Neilson Horn 148 5.6.3.4 Diagonal Horn 148 5.7 Illuminating THz Telescopes 150 Conclusion 154 References 156 6 THz Coherent Detection Systems 159 6.1 Introduction 159 6.2 Superheterodyne Receivers 163 6.3 Receiver Noise Temperature 167 6.4 Noise Temperature of THz Optical Systems 168 6.5 THz Mixer Architectures and Noise 172 6.5.1 Double Sideband (DSB) Mixer 172 6.5.2 Sideband Separation (2SB) Mixer 173 6.5.3 Balanced DSB Mixer 174 6.6 IF Amplifiers 175 6.7 Effective Temperature Measurement of THz Components 179 6.8 THz Mixers 182 6.8.1 Schottky Diode Mixers 183 6.8.2 Introduction to Superconductivity 189 6.8.3 Superconductor-Insulator-Superconductor (SIS) Mixers 193 6.8.4 Hot Electron Bolometer (HEB) Mixers 199 6.9 THz Local Oscillators 202 6.9.1 Frequency Multiplied Sources 205 6.9.2 Quantum Cascade Lasers (QCLs) 208 6.10 Receiver Back-Ends 210 6.10.1 Total Power Detection 211 6.10.2 Spectrometers 213 6.10.2.1 Filterbanks 214 6.10.2.2 Fast Fourier Transform (FFT) Spectrometer 215 6.10.2.3 Autocorrelator Spectrometer 216 6.11 Receiver Stability and Allan Time 220 6.12 Heterodyne Array Considerations 223 Summary 225 References 227 7 Incoherent Detectors 231 7.1 Introduction 231 7.2 Bolometer Basics 232 7.3 Semiconductor Bolometers 234 7.4 Superconducting Incoherent Detectors 242 7.4.1 Transition Edge Sensors (TES) 242 7.4.2 Microwave Kinetic Inductance Detectors (MKID) 245 7.5 Background Noise Limited Operation 250 7.6 Instrument Noise Limited Operation 252 Contents ix © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 9 20-08-2015 20:38:16 7.7 Sensitivity Requirements 253 7.8 Comparing Heterodyne and Incoherent Detector Sensitivity 254 7.9 Incoherent Array Considerations 257 Conclusion 258 References 259 8 Terahertz Observing Techniques 261 8.1 Introduction 261 8.2 Observing Strategies 263 8.2.1 Absolute Position Switching 263 8.2.2 On-the-Fly Mapping 265 8.2.3 Frequency Switching 266 8.3 Receiver Calibration 267 8.4 Estimating Atmospheric Optical Depth 273 8.5 THz Brightness Temperature of Planetary Bodies 277 8.5.1 The Moon 277 8.5.2 Mars 278 8.5.3 Venus, Jupiter, Uranus, and Neptune 278 Conclusion 281 References 282 9 THz Interferometry 285 9.1 Introduction 285 9.2 Simple Adding Interferometer 287 9.3 Phase Switched Interferometer 292 9.4 Correlation Interferometer 293 9.5 Phasor Equation for Interferometry 295 9.6 Aperture Synthesis of Extended Sources 297 9.7 Filling in uv Space 300 9.8 Transforming the Visibility Function 300 9.9 Map Noise Level 302 9.10 Phase Closure or Self-Calibration 304 9.11 Phase Error at THz Frequencies 305 References 307 Answers to Problems 309 Appendix 1: Timeline of THz Technology 313 Appendix 2: More THz Transitions of Atoms and Molecules 315 Appendix 3: Commonly Used Physical and Astronomical Quantities 317 Appendix 4: Useful Radiative Transfer Expressions 319 Appendix 5: Commonly Used Quasi-Optical Expressions 321 Appendix 6: Useful Heterodyne Receiver Expressions 323 Appendix 7: Dielectric Beamsplitters 325 Index 327 x Contents © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 10 20-08-2015 20:38:16

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Terahertz Astronomy © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 1 20-08-2015 20:38:15 © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 2 20-08-2015 20:38:15 Terahertz Astronomy Christopher K. Walker Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 3 20-08-2015 20:38:15 CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20150413 International Standard Book Number-13: 978-1-4665-7043-6 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti- lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy- ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To my Family, who lit the path to the writing of this book © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 5 20-08-2015 20:38:16 © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 6 20-08-2015 20:38:16 CONTENTS Preface xi Author xiii About the Cover xv 1 The Interstellar Medium (ISM) at Terahertz (THz) Frequencies 1 1.1 Introduction 1 1.2 ISM Components of the Milky Way 3 1.2.1 Hot Ionized Medium (HIM) 5 1.2.2 Warm Neutral Medium (WNM) 5 1.2.3 Warm Ionized Medium (WIM) 5 1.2.4 Cool Neutral Medium (CNM) 6 1.2.5 Cold Dense Molecular Clouds (CDM) 7 1.2.6 Relationship between ISM Phases 7 1.3 Lifecycle of the ISM 10 1.4 Probing the Lifecycle of the ISM 16 1.4.1 Origin of Fine-Structure Lines 16 1.4.2 Importance of [CII] 18 1.4.3 Diffuse Gas Density 20 1.4.4 Star Formation Rate and Infrared (IR) Luminosity 23 1.4.5 Spectral Classification of Ionizing Star 25 1.4.6 THz Molecular Lines 26 1.4.6.1 Rotational Transitions 26 1.4.6.2 H O Lines 29 2 1.5 THz Spectral Energy Distributions (SEDs) 32 Conclusion 34 References 35 2 THz Radiative Transfer Basics and Line Radiation 39 2.1 Equation of Radiative Transfer 39 2.2 Solution to the Equation of Radiative Transfer under Local Thermodynamic Equilibrium (LTE) 41 2.3 Radiative Transfer of Rotational Transitions of Linear Molecules in LTE 48 2.3.1 Determining Gas Optical Depth 49 2.3.2 Derivation of Gas Excitation Temperature 51 2.3.3 Derivation of Gas Column Density with Optical Depth 55 2.3.4 Derivation of Gas Column Density in the Optically Thin Limit 56 2.3.5 Estimating Gas Density and Mass 60 2.4 Non-LTE Approach 60 Conclusion 64 References 65 vii © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 7 20-08-2015 20:38:16 3 THz Continuum Emission 67 3.1 Introduction 67 3.2 THz Spectral Energy Distributions 70 3.3 Deriving Dust Optical Depth, Column Density, and Mass 73 3.4 Temperature and Density Distributions 75 3.5 Dust Energy Balance in Clouds 77 3.6 Dust–Gas Coupling 77 3.7 Dust Polarization: Origin and Measurement 79 Conclusion 83 References 84 4 Simple Radiative Transfer Model 87 4.1 Introduction 87 4.2 Geometry 87 4.3 Source Physical Conditions 88 4.4 Lines of Sight 89 4.5 Model Equation of Transfer 89 4.6 LTE Radiative Transfer with Hydrodynamic Simulations 97 4.7 Non-LTE Radiative Transfer with Hydrodynamic Simulations 99 Going Further 102 References 102 5 THz Optical Systems 103 5.1 Introduction: Source–Beam Coupling 103 5.2 Quantum Electrodynamics (QED) and Maxwell 108 5.3 Origin of a Single-Aperture Diffraction Pattern 109 5.4 Gaussian Beam Optics 113 5.4.1 Gaussian Beam Basics 113 5.4.2 Gaussian Beam Coupling 116 5.5 Focusing Gaussian Beams 117 5.5.1 Lenses 118 5.5.2 Behavior of Light at Dielectric Interfaces 120 5.5.3 Mirrors 126 5.5.3.1 Parabola 126 5.5.3.2 Ellipsoid 127 5.5.3.3 Mirror Reflective Losses and Beam Distortion 130 5.5.4 Gaussian Beam Telescope 132 5.5.5 Wire Grid Polarizers 133 5.6 Intercepting Gaussian Beams 135 5.6.1 Open-Structure Detector Optics 135 5.6.2 Transmission-Line-Mounted Detectors 136 5.6.3 Waveguide Feedhorns 145 5.6.3.1 Corrugated Horn 146 5.6.3.2 Pickett–Potter Horn 147 viii Contents © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 8 20-08-2015 20:38:16 5.6.3.3 Neilson Horn 148 5.6.3.4 Diagonal Horn 148 5.7 Illuminating THz Telescopes 150 Conclusion 154 References 156 6 THz Coherent Detection Systems 159 6.1 Introduction 159 6.2 Superheterodyne Receivers 163 6.3 Receiver Noise Temperature 167 6.4 Noise Temperature of THz Optical Systems 168 6.5 THz Mixer Architectures and Noise 172 6.5.1 Double Sideband (DSB) Mixer 172 6.5.2 Sideband Separation (2SB) Mixer 173 6.5.3 Balanced DSB Mixer 174 6.6 IF Amplifiers 175 6.7 Effective Temperature Measurement of THz Components 179 6.8 THz Mixers 182 6.8.1 Schottky Diode Mixers 183 6.8.2 Introduction to Superconductivity 189 6.8.3 Superconductor-Insulator-Superconductor (SIS) Mixers 193 6.8.4 Hot Electron Bolometer (HEB) Mixers 199 6.9 THz Local Oscillators 202 6.9.1 Frequency Multiplied Sources 205 6.9.2 Quantum Cascade Lasers (QCLs) 208 6.10 Receiver Back-Ends 210 6.10.1 Total Power Detection 211 6.10.2 Spectrometers 213 6.10.2.1 Filterbanks 214 6.10.2.2 Fast Fourier Transform (FFT) Spectrometer 215 6.10.2.3 Autocorrelator Spectrometer 216 6.11 Receiver Stability and Allan Time 220 6.12 Heterodyne Array Considerations 223 Summary 225 References 227 7 Incoherent Detectors 231 7.1 Introduction 231 7.2 Bolometer Basics 232 7.3 Semiconductor Bolometers 234 7.4 Superconducting Incoherent Detectors 242 7.4.1 Transition Edge Sensors (TES) 242 7.4.2 Microwave Kinetic Inductance Detectors (MKID) 245 7.5 Background Noise Limited Operation 250 7.6 Instrument Noise Limited Operation 252 Contents ix © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 9 20-08-2015 20:38:16 7.7 Sensitivity Requirements 253 7.8 Comparing Heterodyne and Incoherent Detector Sensitivity 254 7.9 Incoherent Array Considerations 257 Conclusion 258 References 259 8 Terahertz Observing Techniques 261 8.1 Introduction 261 8.2 Observing Strategies 263 8.2.1 Absolute Position Switching 263 8.2.2 On-the-Fly Mapping 265 8.2.3 Frequency Switching 266 8.3 Receiver Calibration 267 8.4 Estimating Atmospheric Optical Depth 273 8.5 THz Brightness Temperature of Planetary Bodies 277 8.5.1 The Moon 277 8.5.2 Mars 278 8.5.3 Venus, Jupiter, Uranus, and Neptune 278 Conclusion 281 References 282 9 THz Interferometry 285 9.1 Introduction 285 9.2 Simple Adding Interferometer 287 9.3 Phase Switched Interferometer 292 9.4 Correlation Interferometer 293 9.5 Phasor Equation for Interferometry 295 9.6 Aperture Synthesis of Extended Sources 297 9.7 Filling in uv Space 300 9.8 Transforming the Visibility Function 300 9.9 Map Noise Level 302 9.10 Phase Closure or Self-Calibration 304 9.11 Phase Error at THz Frequencies 305 References 307 Answers to Problems 309 Appendix 1: Timeline of THz Technology 313 Appendix 2: More THz Transitions of Atoms and Molecules 315 Appendix 3: Commonly Used Physical and Astronomical Quantities 317 Appendix 4: Useful Radiative Transfer Expressions 319 Appendix 5: Commonly Used Quasi-Optical Expressions 321 Appendix 6: Useful Heterodyne Receiver Expressions 323 Appendix 7: Dielectric Beamsplitters 325 Index 327 x Contents © 2016 by Taylor & Francis Group, LLC K16489_Book.indb 10 20-08-2015 20:38:16

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