An Introduction to

Distance Measurement in Astronomy

Richard de Grijs

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An Introduction to Distance Measurem

ent in Astronomy

de GrijsAn Introduction toDistance Measurement in AstronomyRichard de Grijs, Kavli Institute for Astronomy and Astrophysics, Peking University, China

An Introduction to Distance Measurement in Astronomy delves into the physical processes and properties underlining the methods used for distance determinations, travelling from our local solar neighbourhood to the edge of the Universe and defi ning the milestones along the way. Accurate distance measurements are of prime importance to our understanding of the fundamental properties of not only the Universe as a whole, but also of the large variety of astrophysical objects contained within it. This book illustrates the interdependence of measurements across radically different scales and provides a clear introductory overview of the many subfi elds of relevance to this topic. It outlines the links between distance determination techniques and many other areas of astrophysics and cosmology, including;

• stellar types, star clusters and their life cycles• stellar content, dynamics and evolution of galaxies• the expansion, geometry and history of the Universe

The focus of this text is on the physics behind distance determination methods, highlighting the effectiveness of modern techniques including up-to-date results with accounts of recent progress and detailed discussions of the uncertainties and pitfalls associated with all methods. This enables the reader to build a framework for understanding how to place observations into an astrophysical context and recognize that some key issues are open-ended.

This highly valuable and practical book is not only appropriate for undergraduate and postgraduate students but also includes technical and detailed material for the more advanced reader.

An Introduction to Distance Measurementin Astronomy

An Introduction toDistance Measurement

in AstronomyRICHARD DE GRIJS |

Kavli Institute for Astronomy and Astrophysics,Peking University, China

This edition first published 2011© 2011 John Wiley & Sons Ltd

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Library of Congress Cataloging-in-Publication Data

De Grijs, Richard, 1969-An introduction to distance measurement in astronomy / Richard de Grijs.

p. cm.Includes bibliographical references and index.ISBN 978-0-470-51179-4 (cloth) – ISBN 978-0-470-51180-0 (paper) – ISBN

978-1-119-97818-3 (ePDF) – ISBN 978-1-119-97817-6 (ebook) – ISBN978-1-119-97980-7 (ePub) – ISBN 978-1-119-97981-4 (eMobi)

1. Cosmological distances–Measurement. 2. Astronomy–Methodology. I. Title.QB991.C66D34 2011522.87–dc23

2011014927

A catalogue record for this book is available from the British Library.

Print ISBN: 9780470511794 (H/B) 9780470511800 (P/B)ePDF ISBN: 9781119978183oBook ISBN: 9781119978176ePub ISBN: 9781119979807eMobi ISBN: 9781119979814Set in 10/12 pt Times-Roman by Thomson Digital, Noida, India

Printed and bound in Singapore by Markono Print Media Pvt. Ltd.

To (Jie)

for her unconditional love and support throughout the years

Contents

Preface xi

1 The Importance of Astrophysical Distance Measurements 11.1 The Distance to the Galactic Centre 2

1.1.1 Early Determinations of R0 31.1.2 Modern Results 6

1.2 The Distance to the Large Magellanic Cloud 111.3 Benchmarks Beyond the Magellanic Clouds: the 3D Universe on

Large(r) Scales 15Bibliography 22

2 The Solar Neighbourhood 312.1 Geometric Parallax Measurements 31

2.1.1 Trigonometric Parallax 312.1.2 Astrometric Advances: Space-Based Missions and Interferometry 332.1.3 Secular and Statistical Parallaxes: Moving Groups Method 39

2.2 Dynamical Parallax 422.2.1 Mass–Luminosity Relations 46

2.3 Spectroscopic and Photometric Parallaxes 50Bibliography 55

3 From the Milky Way to the Local Group 633.1 Basic Stellar Physics as the Key to Understanding Distance Measurements

to Local Group Galaxies 633.1.1 Stellar Evolution Through the Hertzsprung–Russell Diagram 633.1.2 From Two to Multiple Stellar Populations 68

3.2 Open and Globular Cluster Hertzsprung–Russell Diagrams 703.2.1 Main-Sequence and Subdwarf Fitting 703.2.2 Red Clump Stars 723.2.3 The (Zero-Age) Horizontal Branch Level 74

3.3 Giants and Supergiants as Standard Candles 763.3.1 The Tip of the Red Giant Branch 763.3.2 The Red Giant Branch Bump 783.3.3 Supergiants as Standard Candles 80

3.4 White Dwarf Sequences 833.5 Period–Density Relations 84

3.5.1 The Baade–Wesselink Method 853.5.2 Classical Cepheid Variables 87

viii Contents

3.5.3 Mira Variables 903.5.4 W Virginis and Other ‘Population II’ Cepheids 933.5.5 RR Lyrae Stars 953.5.6 Dwarf and Anomalous Cepheids 97

3.6 Novae as Standard Candles 983.7 Geometric Methods 100

3.7.1 Planetary Nebula Expansion Parallaxes 1013.7.2 Supernova Light Echoes 1023.7.3 Eclipsing Binary Stars 1063.7.4 Maser-Based Distance Determinations 108

3.8 Pulsars: Distance Measurements Outside the ‘Classical’Wavelength Range 110

Bibliography 114

4 Reaching Virgo Cluster Distances and Beyond 1354.1 The Hubble Space Telescope Key Project 1354.2 Surface Brightness Fluctuations 1364.3 The Globular Cluster Luminosity Function 140

4.3.1 Elliptical Versus Spiral Galaxy GCLFs 1414.3.2 The Stellar Population Mix 1444.3.3 GCLF and GCMF Universality Through Dynamical Evolution 144

4.4 The Planetary Nebulae Luminosity Function 1484.4.1 Applicability 1494.4.2 Physical Basis 150

4.5 The Tully–Fisher Relation 1514.5.1 Wavelength Dependence 1524.5.2 The Scatter in the Tully–Fisher Relation 154

4.6 Distance Indicators Specific to Elliptical Galaxies 1564.7 The Colour–Magnitude Relation 1614.8 Hii Regions as Distance Indicators? 164Bibliography 165

5 From Nearby Galaxy Clusters to Cosmological Distances 1755.1 Cosmological Redshifts 175

5.1.1 Determination of the Current Expansion Rate of the Universe 1755.1.2 Redshift Surveys and Peculiar Velocities 1765.1.3 The Prevailing Cosmological Model 179

5.2 Supernovae as Beacons 1865.2.1 Type Ia Supernovae 1885.2.2 Type II-P Supernovae 1975.2.3 A Link to Gamma-Ray Bursts as Standard Candles? 207

5.3 Indirect Techniques to Measure H0 2105.3.1 Gravitational Lensing: Time Delays 2105.3.2 The Sunyaev–Zel’dovich Effect 2155.3.3 Anisotropies in the Cosmic Microwave Background 2225.3.4 The Drive for Improved Accuracy 225

Bibliography 227

Contents ix

6 Systematic Uncertainties and Common Pitfalls 2436.1 Common Biases 244

6.1.1 Extinction: Spatial Distribution and Wavelength Dependence 2446.1.2 Parallaxes: Lutz–Kelker Bias 2466.1.3 Malmquist Bias 251

6.2 High Versus Low Values of the Hubble Constant:Science or Philosophy? 255

Bibliography 259

7 Promises and Prospects 2677.1 The Way Forward: Where Are Significant Gains Achievable? 2677.2 The Pleiades Distance Controversy 2707.3 X-Ray Scattering Haloes 2737.4 Standard Sirens: Listening to Gravitational Waves 2767.5 Three-Dimensional Mapping of Redshifted Neutral Hydrogen 2807.6 The Present-Day Distance Ladder 283Bibliography 285

Glossary 293Figure Credits 305Index 309

Preface

Knowing the distance of an astrophysical object is key to understanding it: without anaccurate distance, we do not know how bright it is, how large it is, or even (for greatdistances) when it existed. But astronomical distance measurements are difficult. Distancesto stars were first measured in 1838 by Bessel, Struve and Henderson, and accurate distancesto other galaxies – even the nearest – date only from the 1950s. This is not really surprising,since the only information we have about any object beyond our solar system is its position(perhaps as a function of time), its brightness (as a function of wavelength and time) andperhaps its radial velocity or chemical composition. Yet, from this unpromising startingpoint, modern astronomers have developed methods of measuring distances which cantake us from the nearest star to the most distant galaxy, using techniques that vary fromthe mundane (the astronomical equivalent of the surveyor’s theodolite) to the exotic (thebending of light in general relativity, wiggles in the spectrum of the cosmic microwavebackground). Nevertheless, the most accurate optical and near-infrared (near-IR) methodsof distance determination, from the solar neighbourhood to the highest redshifts, in usetoday rely heavily on having access to accurate spectroscopy, supplemented by astrometricmeasurements in the Milky Way and slightly beyond.

In 1997, the Hipparcos space mission provided (for the first time) a significant numberof absolute trigonometric parallaxes at milli-arcsecond-level precision across the wholesky, which had a major impact on all fields of astrophysics. In addition, during the past10 years, the use of ground-based 8–10 m-class optical and near-IR telescopes (includ-ing the Keck Observatory, the Very Large Telescope, the twin Gemini telescopes and theJapanese Subaru telescope) and space observatories (such as the Hubble Space Telescope,the Spitzer Space Telescope, the Chandra X-ray Observatory and the European XMM–Newton satellite) have provided an unprecedented wealth of accurate photometric andspectroscopic data for stars and galaxies in the local Universe. Radio observations, par-ticularly with the Very Large Baseline Array and the Japanese VERA (VLBI Exploration ofRadio Astrometry, where VLBI stands for Very Long Baseline Interferometry) array, haveachieved 10 micro-arsecond astrometric accuracy. Moreover, stellar models and numericalsimulations are providing accurate predictions of a broad range of physical phenomena,which can now – in principle – be tested using accurate spectroscopic and astromet-ric observations (including measurements of e.g. spectral line ratios and shapes, spectralslopes, radial velocities and velocity dispersions). However, at present, comparisons oftheory and observations are mainly hampered by precision (or lack thereof) in distancemeasurements/estimates.

This is a very exciting time for numerous fields relying on astronomical distance determi-nations. VLBI sensitivity is being expanded, allowing (for example) direct measurement ofdistances throughout the Milky Way and even to Local Group galaxies. The field will likelymake a major push forward into the era of Gaia, optical interferometer and Extremely LargeTelescope-driven science, which (for example) will allow us to determine Coma cluster

xii Preface

distances without having to rely on secondary distance indicators, thus finally making theleap to accurate distance measurements well beyond the Local Group of galaxies.

In this book, we combine various aspects of distance determinations and, most impor-tantly, the underlying physics enabling this (without being restrictive in areas wherestatistical and observational approaches are more relevant), from the solar neighbourhood tothe edge of the Universe, exploring on the way the various methods employed to define themilestones along the road. We will emphasize recent advances made to further our physicalinsights. We aim to provide a snapshot of the field of distance measurement, offering notonly up-to-date results and a cutting-edge account of recent progress but also full discussionof the pitfalls encountered and the uncertainties which remain. We aim to provide a roadmapfor future efforts in this field, both theoretically and observationally. This book is aimed atsenior undergraduate and postgraduate students, as well as researchers in the various fieldstouched upon by the plethora of techniques covered here. For that reason, we have tried toboth explain basic physical concepts which may not necessarily be intuitively obvious andprovide extensive referencing to the primary literature for follow-up reading and research.

Although our focus is on techniques of distance determination, this is intimately linkedto many other aspects of astrophysics and cosmology. On our journey from the solar neigh-bourhood to the edge of the Universe, we shall encounter stars of all types, alone, in pairsand in clusters, their life cycles, and their explosive ends: binary stars, in particular, play animportant role both in this context, e.g. in pinning down accurate distances to the Pleiadesopen cluster and Local Group galaxies, and in future ground- and space-based surveys(including Gaia, rave: the Radial Velocity Experiment, and others); the stellar content,dynamics and evolution of galaxies and groups of galaxies; the gravitational bending ofstarlight; and the expansion, geometry and history of the Universe. As a result, this bookoffers not only a comprehensive study of distance measurement but also a tour of manyrecent and exciting advances in astrophysics.

It has taken significant time and effort to collect and shape the contents of this book.Along the way, numerous people generously assisted or gave their time, answering myquestions, providing me with feedback on earlier drafts of (parts of) chapters, keepingmy imagination in check, and helping me put my thoughts (and the book’s outline) inorder. I would specifically like to express my gratitude to (in alphabetical order) GiuseppeBono, Susan Cartwright, (Zuhui Fan), Stefan Gillessen, Stephen Justham, MichaelMerrifield, Brent Miszalski, Goran Ostlin, Mike Reid, Stephen Smartt, Nial Tanvir, MaxTegmark, Floor van Leeuwen and (Renxin Xu), as well as to my publishing contactsat Wiley, particularly Andy Slade, Jenny Cossham, John Peacock, Sarah Tilley and JanineMaer, for believing despite all odds that this project would eventually materialize. Finally,I acknowledge partial funding from the National Natural Science Foundation of Chinathrough grants 11043006 and 11073001.

Richard de GrijsBeijing ,

February 2011

1The Importance of Astrophysical

Distance Measurements

When we try to pick out anything by itself, we find it hitched to everything else in the Universe.– John Muir (1838–1914), American naturalist and explorer

Each problem that I solved became a rule, which served afterwards to solve other problems.– Rene Descartes (1596–1650), French philosopher

Accurate distance measurements are of prime importance for our understanding of thefundamental properties of both the Universe as a whole and the large variety of astrophysicalobjects contained within it. But astronomical distance measurement is a challenging task:the first distance to another star was measured as recently as 1838, and accurate distances toother galaxies – even the nearest – date only to the 1950s, despite evidence of the existenceof ‘spiral nebulae’ as early as Lord Rosse’s observations in the mid-nineteenth century.This is not surprising, since the only information we have about any object beyond our solarsystem includes its position (perhaps as a function of time), its brightness (as a function ofwavelength and time) and possibly its radial velocity and chemical composition.

While we can determine highly accurate distances to objects in our solar system usingactive radar measurements, once we leave the Sun’s immediate environment, most distancemeasurements depend on inferred physical properties and are, therefore, fundamentallyuncertain. Yet at the same time, accurate distance measurements on scales of galaxies andbeyond are crucial to get a handle on even the most basic questions related to the ageand size of the Universe as a whole as well as its future evolution. The primary approachto obtaining distance measurements at increasingly greater distances is by means of theso-called distance ladder, where – in its most simplistic form – each rung is calibratedusing the rung immediately below it. It is, therefore, of paramount importance to reduce the

An Introduction to Distance Measurement in Astronomy, First Edition. Richard de Grijs.© 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd.