Statistical Analyses of Extrasolar Planets and Other Close Companions to Nearby Stars

STATISTICAL ANALYSES OF EXTRASOLAR PLANETS AND OTHER CLOSE COMPANIONS TO NEARBY STARS

by Daniel Grether

A thesis submitted in satisfaction of the requirements for the degree of Doctor of Philosophy in the Faculty of Science.

December, 2006 Abstract

We analyse the properties of extrasolar planets, other close companions and their hosts. We start by identifying a sample of the detected extrasolar planets that is minimally affected by the selection effects of the Doppler detection method. With a simple analysis we quantify trends in the surface density of this sample in the Msini-period plane. A modest extrapolation of these trends puts Jupiter in the most densely occupied region of this parameter space, thus suggesting that Jupiter is a typical massive planet rather than an outlier. We then examine what fraction of Sun-like (∼ FGK) stars have planets. We find that at least ∼ 25% of stars possess planets when we limit our analysis to stars that have been monitored the longest and whose low surface activity allow the most precise radial velocity measurements. The true fraction of stars with planets may be as large as ∼ 100%.

We construct a sample of nearby Sun-like stars with close companions (period < 5 years). By using the same sample to extract the relative numbers of stellar, brown dwarf and planetary companions, we verify the existence of a very dry brown dwarf desert and describe it quantitatively. Approximately 16% of Sun-like stars have close companions more massive than Jupiter: 11% 3% are stellar, < 1% are brown dwarf and 5% 2% are giant planets. A comparison with the initial mass function of individual stars and free-ﬂoating brown dwarfs, suggests either a diﬀerent spectrum of gravitational fragmentation in the formation environment or post-formation migratory processes disinclined to leave brown dwarfs in close orbits.

Finally we examine the relationship between the frequency of close companions and the metallicity of their Sun-like hosts. We confirm and quantify a ∼ 4σ positive correlation between host metallicity and planetary companions. In contrast we find a ∼ 2σ anti-correlation between host metallicity and the presence of a stellar companion. Upon dividing our sample into FG and K sub-samples, we find a negligible anti-correlation in the FG sub-sample and a ∼ 3σ anti-correlation in the K subsample. A kinematic analysis suggests that this anti-correlation is produced by a combination of low-metallicity, high-binarity thick disk stars and higher-metallicity, lower-binarity thin disk stars. Statement of Originality

I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project’s design and conception or in style, presentation and linguistic expression is acknowledged.

(Signed) ...... Contents

Abstract ...... i List of Tables ...... v List of Figures ...... vii Acknowledgements ...... viii Preface ...... x

1 Introduction 1 1-1 Planets and Other Close Companions ...... 3 1-2 The Radial Velocity Method ...... 5 1-2.1 Selection Eﬀects ...... 6 1-2.2 Inclination ...... 8 1-3 Other Extrasolar Planet Detection Methods ...... 12 1-3.1 Transits ...... 13 1-3.2 Microlensing ...... 14 1-3.3 Direct Imaging ...... 15 1-3.4 Pulsar Timing ...... 17

2 How Typical is Our Solar System? 19 2-1 The Standard Model of Planet Formation ...... 20 2-2 Mass-Period Plane ...... 22 2-2.1 A Less Biased Sample ...... 22 2-2.2 Undersampling Corrections ...... 24 2-2.3 Mass and Period Histogram Fits ...... 25 2-3 Eccentricity ...... 30 Contents iii

2-4 Discussion ...... 35 2-5 Summary ...... 37

3 Extrasolar Planet Frequency 39 3-1 Introduction ...... 40 3-2 Extrasolar Planet Data ...... 41 3-2.1 Mass and Period Distribution ...... 41 3-2.2 Monitoring Duration ...... 43 3-2.3 High Doppler Precision Targets ...... 48 3-2.4 Number of Monitored Stars ...... 51 3-3 Fitting For and Extrapolating Trends ...... 55 3-3.1 Extrapolation Using Discrete Bins ...... 59 3-3.2 Extrapolation Using a Diﬀerential Method ...... 61 3-4 Fractions in K − P Parameter Space ...... 62 3-4.1 Consistency Check ...... 62 3-5 Jupiter-like Planets ...... 63 3-6 Comparison with Other Results ...... 64 3-7 Summary ...... 67

4 Extrasolar Planet - Close Companion Comparison 69 4-1 Introduction ...... 70 4-2 A Less-Biased Sample of Stars ...... 72 4-2.1 Selection Eﬀects ...... 72 4-2.2 Sample Completeness ...... 77 4-3 Close Companion Detection ...... 79 4-3.1 Inclination Distribution ...... 82 4-3.2 Companion Mass Estimates ...... 84 4-3.3 Companion Completeness ...... 85 4-4 Orbital Properties ...... 89 4-4.1 Period ...... 89 4-4.2 Eccentricity ...... 89 Contents iv

4-5 Summary ...... 93

5 The Brown-Dwarf Desert 94 5-1 Companion Mass Function ...... 95 5-1.1 Bestﬁt Trends ...... 98 5-1.2 Companion Fractions ...... 99 5-1.3 Comparison with Other Results ...... 102 5-2 Companion Mass as a Function of Host Mass ...... 103 5-3 Comparison with the Initial Mass Function ...... 108 5-4 Summary and Discussion ...... 112

6 Metallicity of Stars with Close Companions 115 6-1 Introduction ...... 116 6-2 The Sample ...... 117 6-2.1 Measuring Stellar Metallicity ...... 117 6-2.2 Selection Eﬀects and Completeness ...... 119 6-2.3 Close Companions ...... 125 6-3 Companion - Host Metallicity Correlation ...... 128 6-4 Is the Anti-Correlation Real? ...... 143 6-4.1 Comparison with a Kinematically Unbiased Sample ...... 144 6-4.2 Comparison with a Kinematically Biased Sample ...... 145 6-4.3 Probability of Galactic Population Membership ...... 153 6-4.4 Discussion ...... 154 6-5 Summary ...... 157

7 Conclusions 159

Appendices 162

A Extrasolar Planet Data 162

B Close Sun-like Sample 181

References 199 List of Tables

3.1 Doppler Surveys: Targets ...... 53 3.2 Doppler Surveys: Cumulative Numbers of Targets vs Time ...... 54 3.3 Best-Fit Trends to Mass and Period Histograms ...... 58 3.4 Exoplanet Fraction Comparison ...... 65

4.1 Sample, Doppler Targets and Detected Companions ...... 88

5.1 Companion Slopes and Companion Desert Mass Minima ...... 100 5.2 Companion Fraction Comparison ...... 101

6.1 Stellar Samples Used in Our Analysis ...... 124 6.2 Metallicity and Frequency of Hosts with Companions ...... 126 6.3 Best-ﬁt Trends for Close Companion Host Metallicity Correlation . . . . 139 6.4 Properties of the Three Stellar Populations ...... 153

A.1 Planets Detected with the Radial Velocity Method ...... 165 A.2 Planets Detected with the Transit Method ...... 177 A.3 Planets Detected with the Microlensing Method ...... 178 A.4 Planets Detected by Direct Imaging ...... 179 A.5 Planets Detected with the Pulsar Timing Method ...... 180

B.1 Sun-like 25 pc Sample ...... 181 List of Figures

1.1 Inclination Angle Diagram ...... 9 1.2 Random Inclination Distribution ...... 10 1.3 Methods of Extrasolar Planet Detection ...... 11

2.1 Less Biased Sample of Exoplanets ...... 23 2.2 Linear Mass Histogram ...... 27 2.3 Trend in Mass ...... 28 2.4 Trend in Period ...... 29 2.5 Eccentricity as a Function of Period ...... 32 2.6 Eccentricity and Proximity to Jupiter ...... 33 2.7 Comparison with our Solar System ...... 34

3.1 Mass-Period Plane ...... 44 3.2 The Fraction of Stars with Planets ...... 46 3.3 Number of Targets as a Function of Monitoring Duration ...... 47 3.4 Planet Fraction for Hosts with Low Stellar Activity ...... 49 3.5 Extrapolated Trends in Mass and Period ...... 57 3.6 Simple Method of Extrapolation to Predict Planet Numbers ...... 60 3.7 Comparison of Planetary Fractions ...... 66

4.1 Our Close Sample ...... 73 4.2 Our Far Sample ...... 74 4.3 Doppler Binaries as a Function of Absolute Magnitude ...... 76 4.4 Distance Dependence of Sample and Companions ...... 78 4.5 Brown Dwarf Desert in Mass and Period ...... 81 List of Figures vii

4.6 Astrometric Inclination Distribution ...... 83 4.7 Period Distribution of Close Companions ...... 90 4.8 Eccentricity Distribution of Close Companions ...... 91

5.1 Brown-Dwarf Desert in Close Sample ...... 96 5.2 Brown-Dwarf Desert in Far Sample ...... 97 5.3 Lower and Higher Mass Hosts in Close Sample ...... 105 5.4 Lower and Higher Mass Hosts in Far Sample ...... 106 5.5 Companion Mass as a Function of Host Mass ...... 107 5.6 Companion Mass Function Compared with to the IMF ...... 110 5.7 IMF as a Series of Power-Laws ...... 111

6.1 Exoplanet Target Stars Metallicity Comparison ...... 120 6.2 Methods of Obtaining Metallicity Comparison ...... 121 6.3 Distribution of Close Companions in Mass and Period ...... 127 6.4 Metallicity of stars in our close sample ...... 130 6.5 Linear Metallicity of stars in our close sample ...... 131 6.6 Metallicity of stars in our far sample ...... 132 6.7 Linear Metallicity of stars in our far sample ...... 132 6.8 Metallicity of stars in our FG sample ...... 136 6.9 Metallicity of stars in our K sample ...... 137 6.10 Comparison of Best-Fits ...... 141 6.11 Colour Distribution for Close Companions ...... 142 6.12 Metallicity of Stars in GC Sample ...... 146 6.13 Metallicity of FG Stars in GC Sample ...... 147 6.14 Metallicity of K Stars in GC Sample ...... 148 6.15 Combining the Three Samples ...... 150 6.16 Halo, Thick and Thin Disk Stars ...... 151 6.17 Binarity of Thick and Thin Disk Stars ...... 152 Acknowledgements

It is a delight to thank my PhD supervisor, Charles Lineweaver, for all his guidance and encouragement over the past 5 years. It has been a pleasure to continue working with Charley after my Honours year. His enthusiasm for the projects that we have worked on together never abated and he has always remained full of new ideas. With his move from UNSW to the Australian National University (ANU) in Canberra two years ago, his skill as a communicator allowed me to stay in Sydney and continue working with him even though most of our correpondence was through electronic media.

I would like to thank the many people who have contributed their time and knowledge to my research through informal discussions and correspondence. Although I have never met most of these people face-to-face, I am very grateful to William Cochran, Andrew Cumming, Debra Fischer, Chris Flynn, Scott Gaudi, Lynne Hil- lenbrand, Johan Holmberg, Hugh Jones, Sylvain Korzennik, John Norris, Christian Perrier, Penny Sackett, Ross Taylor and Stephane Udry.

I have made extensive use of the SIMBAD database, operated at CDS, Stras- bourg, France and the Washington Double Star Catalog maintained at the U.S. Naval Observatory in my research and I am very thankful to the people that main- tain these databases.

For directly and indirectly providing funds that supported the publication of my research and conference attendances, I would like to thank the Astrophysics Depart- ment at UNSW, the Australian Centre for Astrobiology at Macquarie University and the Planetary Science Institute at ANU. Thanks also to the UNSW Sports Asso- cation for awarding me a scholarship and the funds necessary to take part at the World University Games in Slovakia. I am also very grateful to Michael Whitting- ham, general manager of WIKA Australia, for oﬀering me interesting paid work with very ﬂexible hours. I appreciate the computing experience this job has given me in the private sector.

Thanks also to my fellow students at UNSW particularly Paul Beasly, Tamara Acknowledgements ix

Davis and Marton Hidas along with everyone else at the Department of Astrophysics, for providing a friendly, stimulating and helpful learning and research environment. I wish you all the best for the future.

Finally and most importantly, I thank my parents (Veronika and Rolf), my brother (Oliver) and my extended family for their love and support throughout these busy years at university. A special thanks must also go to Snowy and Flop for the support they provided in their unique ways. Preface

The content of this thesis comes from research that I have had published in a series of refereed papers and conference proceedings. Each chapter of this thesis is loosely based on these publications as outlined below.

Chapter 2:

• Lineweaver & Grether (2002), “The Observational Case for Jupiter Being a Typical Massive Planet”, (Astrobiology, 2, 325), forms the basis of this Chapter. I have updated this analysis, originally based on extrasolar planet data from November 2001, to include extrasolar planet data up to November 2006. The new data supports and strengthens our results.

Chapter 3:

• Lineweaver & Grether (2003), “What Fraction of Sun-Like Stars have Plan- ets?”, (The Astrophysical Journal, 598, 1350), forms the basis of this Chapter.

• Grether & Lineweaver (2004), “At Least a Quarter of Sun-Like Stars have Planets”, (IAU Symposium 219, 798), summarises the main results.

Chapters 4 and 5:

• Grether & Lineweaver (2006), “How Dry is the Brown Dwarf Desert? Quan- tifying the Relative Number of Planets, Brown Dwarfs, and Stellar Companions around Nearby Sun-like Stars”, (The Astrophysical Journal, 640, 1051), forms the basis of both these Chapters.

Chapter 6:

• Grether & Lineweaver (2007), “The Metallicity of Stars with Close Com- panions”, (The Astrophysical Journal, Accepted, astro-ph/0612172), forms the basis of this Chapter. Preface xi

Although I have retained the use of the ﬁrst person plural for this thesis, all of the work presented is my own. The work was largely carried out in close contact between myself and my PhD supervisor, Charles Lineweaver. This work builds on research carried out during my Honours degree in Physics at UNSW in 2001, some of which was later published as part of the work in Lineweaver & Grether (2002). Throughout the thesis, previous work and/or contributions from other researchers are described for the sake of completeness. I have endeavored to acknowledge these instances by referring to relevant papers and by referring explicitly to the researchers involved.

Numerous conference proceedings summarise the main results:

• Lineweaver, Grether, & Hidas (2003), “What Can Extrasolar Planets Tell Us About Our Solar System?”, (ASP Conference Series, 294, 161)

• Lineweaver, Grether, & Hidas (2004), “How Common are Earths? How Common are Jupiters?”, (IAU Symposium 213, 41)

• Lineweaver & Grether (2004), “How Dry is the Brown Dwarf Desert?: Quan- tifying the Relative Number of Planets, Brown Dwarfs and Stellar Companions Around Nearby Sun-like Stars”, (Bulletin of the American Astronomical Society, 36, 1153)

• Lineweaver & Grether (2005a), “How Dry is the Brown Dwarf Desert? Quantifying the Relative Number of Planets, Brown Dwarfs and Stellar Com- panions Around Nearby Sun-like Stars”, (Protostars and Planets V, 8252)

• Lineweaver & Grether (2005b), “Quantifying the Short-Period Brown Dwarf Deserts”, (Bulletin of the American Astronomical Society, 37, 1292) Chapter 1

Introduction

The observable universe contains ∼ 100 billion galaxies, each containing ∼ 100 billion stars. These 1022 stars may all potentially host planets. This raises some intriguing questions. Just how many planets are really out there? Are these planets similar to the familiar ones in our Solar System or is our planetary system in someway unique? What is a planet and how do they compare to other close companions? Until recently, only speculation has been possible because of a lack of observational evidence. This has now ﬁnally changed with the discovery of the ﬁrst planets beyond our Solar System commonly referred to as extrasolar planets or “exoplanets”.

The ﬁrst planets found beyond our Solar System were detected in 1992 around a pulsar (Wolszczan & Frail 1992). This discovery was followed in 1995 by the detection of the ﬁrst extrasolar planet orbiting a main sequence star (Mayor & Queloz 1995). This giant exoplanet orbiting 51 Peg was dubbed a “hot-Jupiter” due to the close proximity between it and its host star. This unexpected discovery provoked some early controversy and has shown us that only limited conclusions can be drawn from examining the formation of our own planetary system - a sample of one.

These early detections have prompted a ﬂood of new planet search programs, resulting in the ∼ 200 exoplanets we know today. Examining the properties of these extrasolar planets, some of which are far diﬀerent to the planets found in our Solar System, has led to some rapid progress in our understanding of planet formation. 2

Finding and analysing empirical trends in the extrasolar planetary data, such as those examined in this thesis, may be key to continuing this advancement.

In this thesis we aim to investigate the properties of extrasolar planetary systems. We do this (i) by searching for empirical trends in the distribution of the various extrasolar planet parameters, and (ii) by comparing these distributions with those obtained for other close companions such as brown dwarfs and stellar companions, and (iii) by analysing the properties of extrasolar planet hosts and comparing them with other close companion hosts. This area of research is broad so we introduce each of the topics separately at the beginning of each Chapter.

We discuss how typical our Solar System is in Chapter 2, paying particular at- tention to our most massive planet Jupiter. We identify a subsample of extrasolar planets that is minimally affected by the selection effects of the Doppler detection method. We examine the trends in extrasolar planetary mass, orbital period and eccentricity in this subsample and find that a modest extrapolation puts Jupiter in the most densely occupied region of parameter space, strongly supporting the idea that Jupiter is a typical planet. In Chapter 3 we find the frequency of extrasolar planets by analysing the target lists of the high precision Doppler extrasolar planet surveys. We conclude that at least a quarter and possibly up to 100% of the nearby Sun-like stars have planets.

In Chapter 4 we define a less biased sample of stars with planetary, brown dwarf and stellar companions. We use this sample to compare the period and eccentricity distributions of these close companions. We again use this less biased sample in Chapter 5 to examine the mass distribution of planetary, brown dwarf and stellar companions. We confirm and quantify a very dry brown dwarf desert in close companion mass. In Chapter 6 we examine the metallicity distribution of hosts with close companions. We quantify a correlation between the presence of extrasolar planetary companions and host metallicity. We also find an anti-correlation between host metallicity and binarity for low mass K stars.

The ﬁeld of extrasolar planets is rapidly developing as more and more planets are discovered using an ever expanding variety of detection techniques. This is evident 1-1. Planets and Other Close Companions 3 in this thesis as the work completed towards the end is based on a larger sample of exoplanets compared to the earlier work. More speciﬁcally, the analysis in Chapter 2 is based on current (November 2006) extrasolar planet data updated from November 2001 producing similar results but with a higher accuracy. Chapter 3 is based on extrasolar planet data detected as of June 2003. Chapters 4 and 5 are based on close companion data as of October 2005. Chapter 6 is based on close companion data as of October 2006.

Throughout this thesis we analyse close companions detected using the Doppler or radial velocity technique. We use the remainder of this Chapter to define the various types of close companions and to introduce the Doppler technique. We define planetary, brown dwarf and stellar companions in Section 1-1. The details and selection effects of the Doppler method are examined in Section 1-2. Until recently, virtually all of the known extrasolar planets were detected using the Doppler method. Thus we primarily analyse extrasolar planets and other close companions in this thesis that have been detected using this method. However we also outline other more recent proven methods for detecting extrasolar planets in Section 1-3.

The discovery and analysis of extrasolar planets has been a giant first step to finding the still elusive Earth analog and determining if the planet we inhabit is unique in its suitability for life as we know it. Hopefully within the next decade as detection methods are refined and new ones designed, we will see the detection of the first potentially habitable or perhaps even inhabited extrasolar planets.

1-1 Planets and Other Close Companions

In this Section we define the various types of close companions: planets, brown dwarfs and stellar companions. There is currently no consensus on what defines a “planet” (but see the definition given by the Working Group on Extrasolar Planets of the International Astronomical Union 1). Definitions based solely on mass, on current location or formation history and on combinations of the above have all

1http://www.ciw.edu/IAU/div3/wgesp/definition.html 1-1. Planets and Other Close Companions 4 been proposed. Without the luxury of an empirical definition, we define a planet in terms of the census of known exoplanets.

In terms of mass, we deﬁne a planet, brown dwarf and stellar companion in this thesis as follows. Stellar companions are those objects capable of thermonuclear fusion of hydrogen, i.e., those with masses above M ∼ 80MJup. Brown dwarfs are sub-stellar objects capable of deuterium fusion but below the mass limit for hydrogen fusion. Sub-stellar objects that are below the mass limit for deuterium fusion (M

< ∼ 13MJup) are called planets (e.g. Burrows et al. 1997). These limits all refer to the true mass and not the Doppler minimum mass.

Planetary mass objects are usually found in orbit around a star or stellar remnant, however they have also been observed as companions to brown dwarfs (Chauvin et al. 2005a) and as free-floating objects in young stellar clusters (Tamura et al. 1998; Zapatero Osorio et al. 2000) that may have formed in the same way as planets around stars. Most planet detection methods cannot find these unbound objects, so we will not consider them further here. Brown dwarfs have also been found as free-floating objects, as companions to stars and as companions to other brown dwarfs. Systems containing potentially a planet, brown dwarf and a star such as HD 168443 (Marcy et al. 2001b), HD 202206 (Udry et al. 2002; Correia et al. 2005), GJ 86 (Queloz et al. 2000; Els et al. 2001) and HD 41004 (Zucker et al. 2003, 2004) have also been found.

This variety has led to the following additional criteria for planetary mass objects to be called planets. A planet needs to orbit a star or stellar remnant and have a mass below that needed for deuterium fusion. Any objects above the limiting mass for thermonuclear fusion of deuterium are brown dwarfs, not planets, no matter how they formed nor where they are located. Additionally any free-ﬂoating objects with masses below the limiting mass for fusion of deuterium are also not planets. 1-2. The Radial Velocity Method 5

1-2 The Radial Velocity Method

The vast majority of close companions have been detected using the radial velocity or Doppler “wobble” method. This technique infers the existence of a planet from a small amplitude periodic variation that the companion planet induces in the radial velocity of its host star. Larger amplitude periodic variations induced in the host star by brown dwarf and stellar companions are also observable using this technique. This wobble is observed in the periodically Doppler red and blue shifted spectrum of the host star. Of all the planets in our Solar System, Jupiter creates the largest such periodic variation in the radial velocity of the Sun at ∼ 12 m/s. In contrast the Earth induces a tiny wobble of just 0.1 m/s in the Sun. Even a small stellar companion with mass ∼ 2 orders of magnitude larger than Jupiter and in a similar orbit induces a wobble of over 1 km/s in its host star. Thus, when using the Doppler method to ﬁnd planets very high precision measurements are required.

While the detection by Mayor & Queloz (1995) of a planet orbiting 51 Peg (Msini =

0.5MJup) is generally considered the ﬁrst discovery of an extrasolar planet using the Doppler technique, the Latham et al. (1989) radial velocity result for HD 114762 is also potentially a planet (Msini = 11.7MJup < 13MJup), although it is expected that once the unknown inclination is determined that the detection will actually be a brown dwarf.

Planets have been detected using the Doppler method by numerous groups. The largest and most successful of these are the “California and Carnegie Extrasolar Planet Search” and the “The Geneva Extrasolar Planet Search”. The ﬁrst of these searches incorporates the AAT: Anglo Australian Observatory, Anglo Aus- tralian Telescope, UCLES Spectrograph (e.g. Tinney et al. 2001), Lick: Lick Ob- servatory, Hamilton Spectrograph (e.g. Cumming et al. 1999) and Keck: Keck Ob- servatory, HIRES Spectrograph (e.g. Vogt et al. 2000) programs while the second incorporates the Coralie: European Southern Observatory, Euler Swiss Telescope, CORALIE Spectrograph (e.g. Queloz et al. 2000), Elodie: Haute Provence Observa- tory, ELODIE Spectrograph (e.g. Perrier et al. 2003) and Harps: European South- 1-2. The Radial Velocity Method 6 ern Observatory, HARPS Spectrograph (e.g. Pepe et al. 2004) programs. The most precise of these instruments reaches sensitivities of ∼ 1 m/s.

Various other smaller searches have also had success at detecting extrasolar planets, e.g. the AFOE: Whipple Observatory, AFOE Spectrograph (e.g. Noyes et al. 1997a), CES: European Southern Observatory, CAT Telescope, CES Spectrograph (e.g. K¨ursteret al. 2000) and McDonald: McDonald Observatory, Coud´eSpectro- graph (e.g. Cochran & Hatzes 1993) programs. Additional Doppler survey details are discussed in Section 3-2 and listed in Tables 3.1 and 3.2. A current list of all the known exoplanets is tabulated in Appendix A. While these high precision Doppler surveys are sensitive to giant planetary companions they will also detect any larger mass companions such as brown dwarfs and stellar companions amongst their monitored stars.

1-2.1 Selection Eﬀects

To detect an exoplanet, its host star must be Doppler-monitored regularly for a period Pobs greater than or comparable to the orbital period P of the planet. Thus, one selection eﬀect on the detection of exoplanets using the Doppler technique is

> Pobs ∼ P (1.1)

The relationship between the observable line-of-sight or radial velocity of the host star, K = v∗sini, the mass of the planet, M, the mass of the host star, M∗, the semimajor axis of the planet’s orbit, a, and the velocity of the planet, vp is obtained by 2 1/2 combining vp = (2π/P ) a/(1−e ) (the average velocity around an ellipse of orbital eccentricity e) with momentum conservation, M∗K = Msini vp and Kepler’s third 2 3 2 law M∗ = (4π /G) a /P (in the limit that M∗ >> M). Simultaneously solving these equations yields the induced line-of-sight velocity of the host star,

2πG 1/3 Msini 1 K = 2/3 2 1/2 . (1.2) P M∗ ! (1 − e ) 1-2. The Radial Velocity Method 7

This equation is used to ﬁnd Msini as a function of the Doppler survey observables

K,P and e, with M∗ estimated from stellar spectra. To detect an exoplanet, the radial velocity K must be greater than the instrumental noise, Ks. Thus, the Doppler technique is most sensitive to massive close-orbiting planets. The Doppler technique is limited by convective inhomogeneities in the host star along with other errors due to asteroseismological signals. Biases in detection due to sampling can depend on the survey (e.g. Cumming et al. 1999, but we do not consider them here). At shorter periods, detectability is reduced for eccentric orbits, mainly due to the sparse sampling of the periastron passage (Cumming 2004). For very short periods of a few days or less, tidal circularisation of the orbit leads to planets having zero eccentricity. Although the radial velocity amplitude is independent of the distance from the observer to the host star, signal to noise considerations limit observations to the brighter stars (typically V < 7.5, see Table 3.1).

Systems containing double-lined spectroscopic binaries (SB2s) are generally avoided as target stars for the exoplanet surveys using the Doppler method. Stars with high levels of surface activity are also avoided. High levels of chromospheric activity, fast rotation, convective inhomogeneities and time-dependent surface features all increase the velocity scatter and can even mimic small amplitude radial velocity variations. Even low levels of intrinsic stellar variability typically add a few m/s to the velocity scatter (Saar et al. 1998).

The blue regions of Fig. 1.3 partition the parameter space and represent the selection effects of the Doppler surveys. The largest observed P and the smallest observed K of the exoplanets in Fig. 1.3 are inserted into Eqs. 1.1 & 1.2 to empir- ically define the boundary between the “Being Detected” and the “Not Detected” regions in Fig. 1.3. The precision of the surveys was twice greatly improved (lowering the smallest observable K), firstly with upgrades to the original surveys and the introduction of the large Keck and Coralie surveys (see Table 3.2) and secondly with further upgrades to the existing surveys and the introduction of the current state of the art precision HARPS survey. This has lowered the smallest observable K from 25 m/s to 6 m/s to 1.5 m/s as shown in Fig. 1.3. In earlier work, such as 1-2. The Radial Velocity Method 8 that shown in Fig. 3.1, this empirical, smallest observed K boundary between the “Being Detected” and the “Not Detected” regions was set at 10 m/s instead of 6 m/s, but was subsequently improved due to refinements in the entire data reduction pipeline (Butler et al. 2006).

To deﬁne the “Detected” region of parameter space in Fig. 1.3, in which virtually all planets should have been detected (thus deﬁning a less-biased subsample of exoplanets) we consider planets with periods shorter than, and that have been observed longer than, the survey duration. The survey duration is 5 years in Fig. 1.3 and 3 years in Fig. 3.1. We also only consider planets with K > 25 m/s in Fig. 1.3

< and K > 40 m/s in Fig. 3.1 such that the instrumental noise Ks ∼ K/2, although generally K >> Ks. The 25 m/s and 40 m/s limits between the “Detected” and “Being Detected” regions are both ∼ 4σ higher than the respective 6 m/s and 10 m/s limits between the “Being Detected” and “Not Detected” regions. The Doppler method with state of the art precision of 1 m/s can reveal planets having masses as low as 10 M⊕ for periods less than 5 days around solar mass hosts (Marcy et al. 2005a). An alternative approach to ﬁnding low-mass planets is by searching low mass hosts.

Fig. 1.3 shows that we are now on the verge of being able to detect planetary systems like ours using the Doppler method, i.e., Jupiter-mass planets at ∼> 5 AU from nearby Sun-like stars. We compare the distribution of extrasolar planets with our Solar System, which is dominated by Jupiter in Chapter 2.

1-2.2 Inclination

Using the Doppler method the inclination i cannot be determined. The inclination is the angle between the observer’s line of sight to the host and the normal to the orbital plane of the companion as shown in Fig. 1.1. The sini dependence of the Doppler method means that orbital systems seen face on (i = 0 deg) result in no measurable radial velocity perturbation.

Doppler measurements can only determine Msini rather than the true mass M 1-2. The Radial Velocity Method 9

Normal to Orbital Plane Planet

i Line of Sight

Host Star Observer

Figure 1.1. Inclination angle i. and hence can only provide a lower limit to the true planetary mass since the orbital inclination is generally unknown. Constraints can be placed on the inclination from astrometric measurements or sometimes even estimated from the light-curve if the planet transits its host star (see Section 1-3.1).

For the distribution Φ(y) of planetary minimum masses y = Msini where i is unknown, we can relate Φ(y) to the distribution of true masses Ψ(M) with (Jorissen et al. 2001)

∞ Φ(y) = Ψ(M)P (y|M)dM (1.3) Z0 where P (y|M) is the probability of observing y given M. Using the assumption that the planetary orbits are randomly oriented in space, the inclination angle i is distributed as sini with

y P (y|M) = 2 (1.4) 2 y 1/2 M (1 − M 2 ) The probability distribution for random inclinations P (sini) has a mean of π/4 ∼ 0.79, a median of 0.87 and a 68% conﬁdence region as shown in Fig. 1.2. Thus the true mass of a planet will only be on average 1/0.79 ∼ 1.25 as large as the minimum mass. The characteristics of the minimum mass distribution will thus not be much diﬀerent from that of the true mass distribution for planetary mass candidates. We 1-2. The Radial Velocity Method 10 discuss in Section 4-3.2 the mass distribution for larger-mass companions such as brown dwarfs and stars, where the assumption of M∗ >> M is no longer valid.

Figure 1.2. Probability distribution for random inclinations. The mean is shown as a solid line and the 68% conﬁdence region is enclosed by two dashed lines. 1-2. The Radial Velocity Method 11

Figure 1.3. Methods of extrasolar planet detection. These include the radial velocity, transit, microlensing, direct imaging and pulsar timing methods. The colour of the points as shown in the key indicates the technique used to make the initial detection. Planets connected by lines are in the same system. We tabulate all of the known extrasolar planets by detection method and detection date in Appendix A. 1-3. Other Extrasolar Planet Detection Methods 12

1-3 Other Extrasolar Planet Detection Methods

While the vast majority (87% ∼ 180/206) of the known extrasolar planets have been detected using the Doppler technique (see Section 1-2), numerous other techniques have also been successful. These include the transit, microlensing, direct imaging and pulsar timing methods. Astrometry has been used to conﬁrm and reﬁne the parameters of extrasolar planets found using the Doppler technique (e.g. Epsilon Eridani, Benedict et al. 2006). Various other as yet unsuccessful techniques have also been proposed (Perryman 2000). In this Section we examine these other four proven methods. We also compare the merits of each method, the parameter space that is monitored and the biases that are introduced. We tabulate the known extrasolar planets by detection method and detection date in Appendix A.

Detecting extrasolar planets is not an easy task due to their comparatively small mass, small radius and inherent faintness. Using Jupiter as a typical planet and the Sun as a typical host, we ﬁnd a planet to be three orders of magnitude less massive, an order of magnitude smaller in radius and up to nine orders of magnitude fainter (depending on the wavelength) than its host star. Thus most extrasolar planets have not been detected by direct imaging but by indirect observations based on the inﬂuence of the planet on its host star.

All of the 206 extrasolar planets known as of November 2006 are shown in Fig. 1.3. The colour of the points as shown in the key indicates the technique used to make the initial detection. 180 planets have been detected using the Doppler technique with 2 later confirmed as transits. A further 14 planets have been detected first as transits before being confirmed using the Doppler technique. The remaining 12 planet detections are split evenly between microlensing, direct imaging and pulsar timing.

These various detection techniques have found planets orbiting stars throughout the host stars life-cycle. Young pre-main sequence stars with planets have been detected using direct imaging. Planets orbiting main sequence stars of spectral types FGKM have been detected using the Doppler method, the transit method and 1-3. Other Extrasolar Planet Detection Methods 13 microlensing. Older stars that have moved oﬀ the main-sequence to become sub- giants and giants have also been found to have planets using the Doppler method. Even pulsars, stellar remnants at the end of a stars life-cycle, have been observed with orbiting planets.

1-3.1 Transits

Extrasolar planets can be detected by the transit method when a planet crosses the line of sight between the observer and the host star during its orbital revolution. This results in a periodic shallow dip in the observed stellar light curve. The time between transits is equal to the orbital period P of the planet. An almost perfect alignment between the observer, the planet and the star is required for a transit, making them rare. Due to the low probability of a transit, surveys must necessarily cover large numbers of stars, either through wide angle imaging or through deep imaging in smaller ﬁelds with high stellar densities.

The probability of observing a transit Ptransit for a randomly oriented planetary system is a direct relation between the stellar radius R∗ and the semi-major axes a,

Ptransit = R∗/a. Thus transits are exceedingly biased towards planets in short period orbits as shown in Fig. 1.3 where all known planets that transit Sun-like stars have P < 5 days.

The drop in luminosity ∆L for a host star of luminosity L∗ when transited by a planet of radius R is given by (Sackett 1999)

∆L R 2 = (1.5) L∗ R∗ ignoring limb darkening (a decrease in the brightness of a star at its edge compared with its center due to the line of sight passing through increasing atmospheric depths at larger stellar radii). Thus the transit method is biased towards larger planets orbiting smaller stars which maximises the dip in stellar light curve during transit. Current photometry can detect dips in the light curve of ∆L/L∗ ∼ 0.01 (Moutou & Pont 2006). 1-3. Other Extrasolar Planet Detection Methods 14

The stellar mass M∗ and radius can be estimated from other observations, speciﬁ- cally high resolution spectroscopy, the colour and magnitude of the host star or from stellar evolutionary models. With knowledge of P and M∗, the semi-major axes a can be derived from Kepler’s law and with knowledge of the stellar radius R∗ the planetary radius R can be derived from Eq. 1.5. A list of all the known exoplanets detected using the transit method is tabulated in Appendix A.

There are however several other astrophysical situations that can produce shallow light curve dips mimicking planetary transits such as grazing stellar eclipses and blended eclipsing binaries (an eclipsing binary whose light is blended with a third stars such as a foreground star or in a gravitationally bound triple system). Additionally, since planets, brown dwarfs and low mass stars all have similar radii, the transit depth by itself is insuﬃcient to distinguish between the three types of companions (Sahu et al. 2006). Radial velocity follow up of these transiting candidates has the capacity of resolving these ambiguities and ﬁnding the true nature of these systems.

1-3.2 Microlensing

Microlensing like the transit method makes use of photometry to detect extrasolar planets. Gravitational microlensing occurs when a foreground massive, compact object (the lens) passes through or very near the observer’s line of sight to a luminous background source such as a distant star. If the observer, lens and source are perfectly aligned, then the lens images the source into a ring, called the Einstein ring which has angular radius (Gaudi et al. 2002)

1/2 4GML dS − dL θE = 2 (1.6) c dSdL ! where ML is the mass of the lens and dL and dS are the distances from the observer to the lens and source respectively. This corresponds to a physical distance at the lens of rE = θEdL. The source is also magniﬁed by the lens with the amount depending on ratio θS/θE where θS is the angular separation between the source and the lens. 1-3. Other Extrasolar Planet Detection Methods 15

As an isolated lens, source and observer move relative to one another, diﬀerent portions of the lens magniﬁcation pattern are traversed by the source, resulting in a symmetric rising and falling of the light curve over a timescale of about tE = 20 days (Sackett 1999).

If the lens is orbited by a companion such as a planet with mass M, which acts as another lens with Einstein radius θp, more complicated magniﬁcation patterns are 1/2 formed. From Eq. 1.6, θp = q θE where q = M/ML is the mass ratio. If the source passes near a defect or ‘caustic’ in the lensing pattern caused by the companion, an anomalous light curve will result that deviates from the smooth, symmetric light curves of isolated lenses. Precise modelling of the anomaly allows the mass ratio q

< and projected separation b ∼ a/(θEdL) of the lens and companion to be determined (Mao & Paczynski 1991). For a Jupiter/Sun mass ratio (q ∼ 10−3), the perturbation

1/2 will have a characteristic timescale tp = q tE of less than a day (Gaudi et al. 2002).

For typical Galactic microlensing, θE ∼ 1 mas corresponding to separations of 1 − 5 AU at the lens (Sackett et al. 2004). Due to the precise alignment required between the source and lens stars, the probability of microlensing for background Galactic stars at any given time is very low ∼ 10−6. Thus microlensing searches target the Galactic bulge where the lens stars probed for planets are primarily M dwarfs at a distance of a few kpc.

1-3.3 Direct Imaging

Direct imaging of planetary companions is difficult because of the large difference between the faint companion and the close by, but much brighter star. In the visible part of the spectrum, a star is very bright while a planet emits negligible light and relies on reflection from its host star to make it observable. The ratio of the planet to stellar brightness for a Jupiter-like planet orbiting a Sun-like star is only of order 10−9 (Perryman 2000). However, in the infrared part of the spectrum, although the thermal infrared emission from the planet is not strong, it nevertheless occurs near the peak of the planetary emission spectrum whereas the infrared band is well 1-3. Other Extrasolar Planet Detection Methods 16 down from the peak of the stellar spectrum (Bracewell & MacPhie 1979). This can improve the ratio of the planet to stellar brightness by up to 5 orders of magnitude for such a system.

For a planet to be resolvable as a separate source from its host star, the angular planet-star separation α = a0/d needs to be suﬃciently large compared to the resolution of the telescope. Here a0 is the projected planet-star separation and d is the distance to the system. For a Jupiter-like planet (a ∼ 5 AU) viewed at maximum elongation from a relatively close 5 pc, the star-planet separation is already down to α = 1 arcsec. Thus only close systems with large star-planet separations are resolvable. Assuming a planet is near its maximum elongation when detected using direct imaging, the projected separation a0 will be approximately the same as the true separation a.

For a telescope of diameter D observing with wavelength λ the resolution is ∝ λ/D mainly because of its diffraction limit. However most ground-based telescopes do not have anywhere near this resolution because of the 0.5 − 1 arcsec noise arising from refraction of the light in our turbulent atmosphere, the ‘seeing’ limit. This effect of seeing can be greatly reduced by using adaptive optics (AO) such as the NACO instrument on the VLT (Rousset et al. 2003). Space-based observations also approach the diffraction limit of the telescope. Coronagraphy can also be used to suppress the brightness of the host star image (Kuchner & Spergel 2003).

Due to contraction, young sub-stellar objects are brighter than older ones. Hence young nearby stars would be the best targets for the direct imaging of planetary companions (Neuh¨auseret al. 2005). The mass of a detected planetary companion can be estimated from the observed companion magnitude and the assumed or known age and distance of the host star, using theoretical model calculations. As- trometry is required to determine if the host and planetary mass form a common proper motion pair and are thus gravitationally bound. 1-3. Other Extrasolar Planet Detection Methods 17

1-3.4 Pulsar Timing

The pulsar timing method is somewhat similar to the radial velocity method in that both methods infer the existence of a companion by measuring the variation in the emitted light due to the radial motion of a companion orbiting the light source. The pulsar timing method detects the timing perturbations from the strictly periodic pulses emitted by the pulsar. Pulsars are rapidly spinning, highly magnetized neutron stars formed during the core collapse of massive stars in a supernova explo- sion (Perryman 2000). They emit narrow beams of radio emission parallel to their magnetic dipole axis, seen as intense pulses at the object’s spin frequency due to a misalignment of the magnetic and spin axes.

For a planet orbiting a 1.35M pulsar in a circular orbit, the amplitude of the pulsar timing residuals τ are related to the planetary mass M and period P by (Wolszczan 1997)

− Msini τ P 2/3 = 0.815 (1.7) M⊕ 1ms 1year! Thus the timing residuals are greater for larger planets in larger orbits. These residuals can be measured extremely accurately with 1 ms precision for “normal” slowly rotating pulsars (with ∼ 1 second periods) and with precision of 1µs for faster rotating millisecond pulsars (Wolszczan 1999). Since an increased frequency of pulses emitted by the pulsar correlates with increased accuracy, the frequency of the pulses limits the type of planets detectable.

This technique has led to some unique detections, including the ﬁrst known extrasolar planetary system around PSR B1257+12, a 6.2 ms pulsar (Wolszczan & Frail 1992). This planetary system has three very small known planets with the smallest closer to its host and less massive than Mercury as shown in Fig. 1.3. A distant planet has also been detected in the PSR B1620-26 system consisting of a 11 ms pulsar - white dwarf binary with a period of 191 days (Sigurdsson et al. 2003).

While there are hundreds of known normal pulsars there are only ∼ 30 known millisecond pulsars that are thought to have been spin-up due to mass and angular 1-3. Other Extrasolar Planet Detection Methods 18 momentum transfer from a binary companion. Only eight of the millisecond pulsars are solitary objects that have either managed to dispose of their binary stellar companions or they have been created without the aid of binary evolution. Com- bining the standard ideas of planetary formation with the evolution of millisecond pulsars suggests that the observed planets orbiting PSR B1257+12 were probably created in a circumpulsar disk of matter from the remains of the pulsar’s binary stellar companion (Wolszczan 1999). Chapter 2

How Typical is Our Solar System?

In this Chapter we examine the region of parameter space occupied by Jupiter, the dominant planet in our Solar System. We aim to show whether or not our Solar System is typical. In Section 2-1 we introduce the standard model of planet formation and show how exoplanets differ from the planets found in our Solar System. We identify a sample of the detected extrasolar planets that is minimally affected by the selection effects of the Doppler detection method. We quantify the trends in the minimum mass-period plane of this less biased sample. A modest extrapolation of these trends puts Jupiter in the most densely occupied region of this parameter space, thus indicating that Jupiter is a typical massive planet rather than an outlier. An analysis of exoplanet eccentricity suggests that planets in longer period orbits similar to Jupiter’s, tend to have lower eccentricity more like Jupiter’s.

The data analysis method in this Chapter was originally published in Lineweaver & Grether (2002) making use of exoplanet data available as of November 2001. We have subsequently updated this analysis using November 2006 exoplanet data (See Appendix A). We obtain new results that conﬁrm our initial ﬁndings. We have also added an analysis of exoplanet eccentricity to the updated analysis of mass and period. 2-1. The Standard Model of Planet Formation 20

2-1 The Standard Model of Planet Formation

The prevalence of infrared emission from accretion disks around young stars is consistent with the idea that such disks are ubiquitous. Their disappearance on a time scale of ∼ 6 million years suggests that the dust and gas accrete into planetesimals and eventually planets (Haisch et al. 2001). Such observations support the widely accepted idea that planet formation is a common by-product of star formation (e.g. Beckwith et al. 2000). In the standard model of planet formation, Earth-like planets accrete near the host star from rocky debris depleted of volatile elements, while giant gaseous planets accrete in the ice zones ( ∼> 4 AU) around rocky cores (Lissauer 1995;

Boss 1995). When the rocky cores in the ice zones reach a critical mass (∼ 10MEarth) runaway gaseous accretion (formation of Jupiters) begins and continues until gaps form in the protoplanetary disk or the disk dissipates (Papaloizou & Terquem 1999; Habing et al. 1999), leaving one or more Jupiter-like planets at ∼ 4 − 10 AU. This runaway gaseous accretion is predicted to produce a “planet desert” for intermediate mass planets between ∼ 10 MEarth to ∼ 100 MEarth with semimajor axes less than 3 AU (Ida & Lin 2004).

We cannot yet determine how generic the pattern described above is. However, formation of terrestrial planets is thought to be less problematic than the formation of Jupiter-like planets (Wetherill 1995). Gas in circumstellar disks around young stars is lost within a few million years and it is not obvious that the rocky cores necessary to accrete the gas into a Jupiter can form on that time scale (Zuckerman et al. 1995), although migration of the forming planet may help to solve the time scale problem (e.g. Benz et al. 2006). Thus, Jupiter-like planets may be rare. Planets may not form at all if erosion, rather than growth, occurs during collisions of planetesimals (Kortenkamp & Wetherill 2000). The present day asteroid belt may be an example of such non-growth. In addition, not all circumstellar disks produce an extant planetary system. Some fraction may spawn a transitory system only to be accreted by the central star along with the disk (Ward 1997). Also, observations of star-forming regions indicate that massive stars disrupt the protoplanetary 2-1. The Standard Model of Planet Formation 21 disks around neighboring lower mass stars, aborting their eﬀorts to produce planets (Henney & O’Dell 1999). Given these uncertainties, whether planetary systems like our Solar System are common around Sun-like stars and whether Jupiter-like planets are typical of such planetary systems, are important open questions.

The frequency of Jupiter-like planets may also have implications for the frequency of life in the Universe. A Jupiter-like planet shields inner planets from an otherwise much heavier bombardment by planetesimals, comets and asteroids during the ﬁrst billion years after formation of the central star. Wetherill (1994) has estimated that Jupiter signiﬁcantly reduced the frequency of sterilizing impacts on the early Earth during the important epoch ∼ 4 billion years ago when life originated on Earth. The removal of comet Shoemaker-Levy by Jupiter in 1994, is a more recent example of Jupiter’s protective role.

To date (November 2006), 176 giant planets (Msini < 13 MJup) in close orbits

( ∼< 4 AU) around 150 nearby stars have been detected by measuring the Doppler reﬂex of the host star (See Section 1-2 and Appendix A). Twenty stars are host to multiple planets (fourteen double, four triple and two quadruple systems). The large masses, small orbits, high eccentricities and high host metallicities of these 176 exoplanets was not anticipated by theories of planet formation that were largely based on the assumption that planetary systems are ubiquitous and our Solar System is typical (Lissauer 1995).

Naef et al. (2001b) point out that none of the planetary companions detected so far resembles the giants of the Solar System. This observational fact however, is fully consistent with the idea that our Solar System is a typical planetary system. Fig. 2.1 shows explicitly that selection eﬀects can easily explain the lack of detections of Jupiter-like planets. Exoplanets detected to date can not resemble the planets of our Solar System because the Doppler technique used to detect exoplanets has not been sensitive enough to detect Jupiter-like planets. If the Sun were a target star in one of the Doppler surveys, no planet would have been detected around it.

This situation is about to change. In the next few years Doppler planet searches will be making detections in the region of parameter space occupied by Jupiter. 2-2. Mass-Period Plane 22

Thus it is timely to use the current data to estimate how densely occupied that parameter space will be. The detected exoplanets may well be the observable tail of the main concentration of massive planets of which Jupiter is typical. The main goal of this Chapter is to correct or account for selection eﬀects to the extent possible and then examine what the trends in the mass and period distributions indicate for the region of parameter space near Jupiter. Such an analysis is now possible because a statistically signiﬁcant sample is starting to emerge from which we can determine meaningful distributions in mass, period as well as in eccentricity and metallicity. Our analysis helps answer the important question: How does our planetary system compare to other planetary systems?

We present our method for identifying a less biased subsample of exoplanets in Section 2-2 which we use to identify and extrapolate the trends in mass and period. In Section 2-3 we examine the eccentricity distribution of exoplanets. We discuss our results in Section 2-4 along with other constraints that suggest that Jupiter is probably a typical planet. Finally we summarise our results in Section 2-5.

2-2 Mass-Period Plane

2-2.1 A Less Biased Sample

We define a less biased sample of exoplanets with the thick solid rectangle in Fig. 2.1. This rectangle is the largest rectangular area that approximately fits inside the “Detected” region in which virtually all planets should have been detected (see Section 1-2). The area within the rectangle subsumes the ranges 2 days < P < 5 years and 0.85 < Msini/MJup < 13 and is subdivided into a minimum number of smaller areas (12 boxes) for histogram binning convenience (see Figs. 2.3 and 2.4). Trends in Msini and P identified within this subsample are less biased than trends based on the full sample of exoplanets. This less biased rectangle contains 81 planets compared to the smaller (3 days < P < 3 years and 0.85 < Msini/MJup < 13) less biased rectangle in Lineweaver & Grether (2002) that only contained 44 planets. 2-2. Mass-Period Plane 23

Figure 2.1. Mass-Period plane for the 176 exoplanets detected to date with the Doppler method. Regions where planets are “Detected”, “Being Detected” and “Not Detected” by the Doppler surveys are shaded differently and represent the observational selection effects of the Doppler reflex technique (see Section 1-2). Four low mass brown dwarfs are also shown. The rectangle enclosing the grid of twelve boxes defines the less biased subsample of 81 planets. The numbers in the upper left of each box gives the number of planets in that box that have been observed for at least 5 years. The increasing numbers from left to right and from top to bottom are easily identified trends. Green dots are planets orbiting non-main-sequence giant stars and the orange dots are planets orbiting low mass M dwarfs. 2-2. Mass-Period Plane 24

In Fig. 2.1 the twenty exoplanetary systems are connected by thin lines. Jupiter and Saturn are in the “Not Detected” region although Jupiter is just on the bor- der with the “Being Detected” region. The upper x axis shows the distances and periods of the planets of our Solar System. The brown dwarf region is deﬁned by

Msini/MJup > 13. While most of the exoplanets have been found orbiting FGK main-sequence stars with Sun-like masses there are some exceptions. These include exoplanets orbiting non-main-sequence giant stars (green dots), which we exclude from the analysis. All of the planets found orbiting these giant stars have periods in excess of 100 days. Also excluded from the analysis are planets orbiting low mass M dwarfs (orange dots). The Doppler method is biased towards ﬁnding lower mass exoplanets orbiting these much lower mass hosts, as evident in Fig. 2.1

If Jupiter is a typical giant planet, the region around Jupiter in the Msini − P plane of Fig. 2.1 will be more densely occupied than other regions – the density of planets in the lower right will be larger than in the upper left. Although we are dealing with small number statistics, that trend is the main identiﬁable trend in Fig. 2.1, the number of exoplanets in the boxes increases from left to right and top to bottom. In Figs. 2.3 and 2.4 we quantify and extrapolate these trends into the lower mass bin and longer period bin (which includes Jupiter) enclosed by the dotted rectangles in Fig. 2.1.

2-2.2 Undersampling Corrections

Within the rectangle enclosed by the thick solid line in Fig. 2.1, one box in the lower right lies partially in the “Being Detected” region. Thus this box is partially undersampled compared to the other boxes within the rectangle. We correct for this undersampling by making the simple assumption that the detection eﬃciency is linear in the “Being Detected” region. That is, we assume that the detection eﬃciency is 100% in the “Detected” region and 0% in the “Not Detected” region and decreases linearly and perpendicularly between the “Detected” and “Not Detected” regions. Thus the decrease is linear in log(P ) for the region constrained by the survey 2-2. Mass-Period Plane 25 duration and linear in log(K) for the region constrained by the detection threshold of the Doppler survey. This linear correction produces the “+2” correction to the number of exoplanets observed in this box and produces the dotted corrections to the histograms in Figs. 2.2, 2.3 and 2.4.

Eleven planets were detected since July 2006 (Butler et al. 2006; Johnson et al. 2006a; Moutou et al. 2006; Pepe et al. 2006; Wright et al. 2006). These are distin- guished in Fig. 2.1 by crosses plotted over the dots. Eight of the eleven justify our parameter space partitions by falling as expected, in the “Being Detected” region. The other three fall unexpectedly in the “Detected” region. If this region were fully detected, newly detected planets would not fall there. However, all three of these planets have only been observed for less than 2.5 years and therefore do not qualify for our least biased sample containing only host stars that have been monitored for at least ﬁve years. Therefore, these three apparent anomalies do not undermine our parameter space partitions. Subsequent exoplanets can be similarly used to verify the accuracy of our representation of the Doppler detection selection eﬀects in the Msini − P plane.

In Fig. 2.1, the exoplanet points are coloured according to length of time that they have been observed as shown in the key. Only exoplanets observed for at least 5 years are included in the less biased sample. Note that there are many exoplanets that have been observed for less than 2.5 years that fall within the “Detected” region. These are generally exoplanets orbiting more distant host stars that have been detected by the HARPS survey (e.g. Pepe et al. 2004) that has only been operating for this shorter timescale.

2-2.3 Mass and Period Histogram Fits

The distribution of the masses of the exoplanets is shown against Msini in Fig. 2.2 and against log Msini in Fig. 2.3. The 2 planet correction (Section 2-2.2) to the Msini ∼ 1 bin in both figures is indicated by the dotted lines. In Fig. 2.2 the solid curve and the enclosing dashed curves are the best fit and 68% confidence 2-2. Mass-Period Plane 26 levels of the functional form (dN/dMsini) ∝ (Msini)α fit to the histogram of the corrected less-biased subsample (83 = 81 + 2 exoplanets). We find α = −1.500.16. This means, for example, that within the same period range there are ∼ 3 times as many MJup as 2 MJup exoplanets and similarly ∼ 3 times as many 0.5 MJup as MJup exoplanets. This slope is consistent with the α = −1.50.2 found for the November 2001 sample in (Lineweaver & Grether 2002).

In Fig. 2.3 the line is the best-fit of the functional form dN/d(log(Msini)) = a log(Msini) + b to the histogram. The best-fit slope, a = −34 9, is significantly steeper than flat. The extrapolation of this trend into the adjacent lower mass bin

(0.34 < Msini/MJup < 0.85) indicates that at least ∼ 549 exoplanets with periods in the range 2−2000 days are being hosted by the target stars now being monitored. Since 18 have been detected to date in this mass range, we predict that 36 9 more have yet to be detected. Thus we predict that the continued monitoring of the target stars that produced the current set of exoplanets will eventually yield ∼ 36 new planets in the parameter range 2 < P < 2000 days with 0.34 < Msini/MJup < 0.85 (dotted horizontal rectangle in Fig. 2.1).

The trend of increasing number of exoplanets per box as one descends in mass holds true even in the highly undersampled longest period bin (2000 < P < 10000), although the trend here is not signiﬁcant. This may be the result of small number statistics or an additional hint that a smooth curve, rather than our two straight boundaries, more accurately describes the selection eﬀects.

We estimate the number of planets that will be discovered in the ﬁrst bin to the right of the rectangle in Fig. 2.1 (2000 < P < 10000 days in the mass range

0.85 < Msini/MJup < 13) in two independent ways: 1) based on the extrapolation of the linear ﬁt to this longer period bin and 2) correcting for undersampling in the “Being Detected” region as described in Section 2-2.2. The former yields 41 4 while the later yields 52 7. We take the weighted mean of these, 44 4, as our best prediction for how many planets will be found in this longest period bin scattered over the mass range 0.85 < Msini/MJup < 13. To date (November 2006), 17 extrasolar planets have been found in this period bin. Thus we predict that 2-2. Mass-Period Plane 27

Figure 2.2. Mass histogram of the less-biased subsample (dark grey) of 81 exoplanets within the rectangle in Fig. 2.1 compared to the histogram of the complete sample of 180 exoplanets (light grey). The errors on the bin heights are Poissonian. The solid curve and the enclosing dashed curves are the best fit and 68% confidence levels from fitting the functional form (dN/dMsini) ∝ (Msini)α to the histogram of the corrected less-biased subsample (83 = 81 + 2 exoplanets). The extrapolation of this curve into the lower mass bin produces an estimate of the substantial incompleteness of this bin (arrow). The lower limit of 0.85 was chosen to match the lower limit of the logarithmic binning in Fig. 2.1. 2-2. Mass-Period Plane 28

Figure 2.3. Histogram in log(Msini) of the less-biased subsample of exoplanets within the rectangular area enclosed by the thick solid line in Fig 2.1. The difference between the solid and dotted histograms in the lowest mass bin is the correction factor due to undersampling as described in Section 2-2.2. The best-fit line is of the functional form dN/d(log(Msini)) = a log(Msini) + b. The best fit slope is a = −34 9. The extrapolation of this trend into the adjacent lower mass bin

(0.34 < Msini/MJup < 0.85) indicates that at least ∼ 549 exoplanets with periods in the range 2−2000 days are being hosted by the target stars now being monitored. This is 36 more than the 18 that have been detected to date in this mass range. 2-2. Mass-Period Plane 29

Figure 2.4. Trend in period of the corrected (dotted) and uncorrected (solid) less- biased subsample. The line is the best-fit to the corrected histogram. The functional form fitted is linear in log P , i.e., dN/d(log P ) = a log P + b. The best fit slope is a = 13 3. Extrapolation of the linear trend indicates that 27 new planets will be discovered in the highest period bin. 2-3. Eccentricity 30

27 4 more planets will be found in this period bin. Following the trend in Msini identiﬁed in Fig. 2.3, these 27 should be preferencially assigned to the lower masses in this range. Extrapolation of the trend in period into an even longer period bin, which would include Saturn, is more problematic.

Based on extrapolations of the trends that put Jupiter in the most densely occupied region of the Msini − P region of parameter space, we ﬁnd that Jupiter is a typical planet. The detected exoplanets are probably the observable tail of the main concentration of massive planets that occupies the parameter space closer to Jupiter.

2-3 Eccentricity

A signiﬁcant diﬀerence between the detected exoplanets and Jupiter, is the high orbital eccentricities of the exoplanets. The eccentricities of the planets of our

Solar System were presumably constrained to small values (e ∼< 0.1) by the migration through, and accretion of, essentially zero eccentricity disk material. A simple model that can explain the higher exoplanet eccentricities is that in higher metallicity systems, the higher abundance of refractory material in the protoplanetary disk may lead to the production of more planetary cores in the ice zone producing multiple Jupiters which gravitationally scatter oﬀ each other. Occasionally one will be scattered in closer to the central star and become Doppler-detectable (Weidenschilling & Marzari 1996). As expected for this model, no statistically significant correlation is observed between eccentricity and metallicity (e.g. Santos et al. 2005; Fischer & Valenti 2005). Since the detected planets are scattered into Doppler detectability (which is correlated with higher metallicity), we do not expect the higher metallicity hosts to necessarily have detectable planets that have been scattered into more eccentric orbits. If that is the origin of the hot Jupiters, then the detected exoplanets may be the high metallicity tail of a distribution in which our Solar System is typical, and as longer period giant planets are found they will have lower eccentricities, comparable to Jupiter’s and Saturn’s. Thus, if Jupiter is the 2-3. Eccentricity 31 norm rather than the exception, not only will we ﬁnd more planets in the Msini−P parameter space near Jupiter as reported above, but also the eccentricities of the longer period exoplanets will be lower.

We examine the eccentricities of the exoplanets with similar masses and periods to that of Jupiter by deﬁning what we call the magnitude of proximity to Jupiter dprox. This unitless distance in log Msini − log P parameter space is deﬁned as the following

1/2 Msini 2 P 2 dprox = log + log (2.1)  MJup ! PJup !    We call dprox the “magnitude” of proximity to Jupiter because it is the diﬀerence in orders of magnitude between an exoplanet and Jupiter in log Msini−log P parameter space, i.e., all the points between 0 < dprox < 1 are less than one order of magnitude away from Jupiter in log Msini − log P space. We plot eccentricity as a function of the magnitude of proximity to Jupiter dprox in Fig. 2.6. We also bin every 20 points together and show the average eccentricity for these as red dots. Dotted concentric circles in the log Msini − log P plane show the proximity to Jupiter for this 20 point binning convention in Fig. 2.7. We ﬁnd that the average eccentricity of the 20 exoplanets in the closest proximity to Jupiter is approximately 0.5σ lower than the average eccentricity for the next four higher proximity bins of 20 exoplanets that all have similar higher average eccentricities. While this drop (0.5σ) is very marginal, it does raise the possibility that exoplanets with Jupiter-like periods may also have more Jupiter-like low eccentricities.

In Lineweaver & Grether (2002) we noted that in four out of the detected six (originally seven but the second companion to HD 83443 was shown not to be a planet) planetary systems the more distant member is less eccentric and more massive. This is what one would expect if the Solar System is a typical planetary system and Doppler-detectable exoplanets have been scattered in by more massive, less eccentric companions. For both of the planetary systems that do not conform to this pattern, the inner planet while more eccentric than the outer is also more 2-3. Eccentricity 32

Figure 2.5. Eccentricity of the orbits of exoplanets as a function of period. Planets in the same system are connected by lines. Notice that in ﬁve out of the six planetary systems with more than two members, the most distant member is less eccentric and more massive than the inner planets. This is what one would expect if the Solar System is a typical planetary system and Doppler-detectable exoplanets have been scattered in by more massive, less eccentric companions. This also suggests that the exoplanets closer to Jupiter’s region of Msini − P parameter space may share Jupiter’s low eccentricity. The dashed line indicates tidal circularisation. See Section 2-3 for a discussion of this ﬁgure. 2-3. Eccentricity 33

Figure 2.6. Eccentricity of the exoplanets as a function of the magnitude of the proximity to Jupiter in log Msini − log P space which we deﬁne in Eq. 2.1. The average eccentricity is binned for every 20 points and shown as larger red dots. The average eccentricity is lower for those exoplanets in the immediate vicinity of Jupiter than for the majority of detected exoplanets that have a proximity of ∼ 1 mag. Most of the exoplanets have been found orbiting FGK main-sequence stars with Sun-like masses and are plotted as black dots. The exceptions include exoplanets orbiting non-main-sequence giant stars (green dots) and those orbiting low mass M dwarfs (orange dots), both of which are not included in the average. 2-3. Eccentricity 34

Figure 2.7. The region of the Msini − P plane occupied by our Solar System compared to the region being sampled by Doppler surveys. Doppler surveys are on the verge of detecting Jupiter-like exoplanets. We would like to know how planetary systems in general are distributed in this plane. Extrapolations of the trends quantiﬁed in this Chapter put Jupiter in the most densely occupied region of the Msini−P parameter space. Dotted concentric circles show the proximity to Jupiter for every 20 points. The four red points are exoplanets that have been detected using microlensing. The dashed wedge-shaped contour represents the microlensing constraints discussed in the text. 2-4. Discussion 35 massive. In both of these cases a third, as yet undetected, even more massive planet may be responsible for the scattering. Thus, in planetary systems, the eccentricities of exoplanets with longer periods (like Jupiter’s) tend to also have less eccentric orbits (like Jupiter’s).

In Fig. 2.5 we note that there are now 20 multiple planetary systems. Of these systems, 2 contain four planets, 4 contain three planets and 14 contain two planets. We again examine the masses and eccentricities of these planetary systems for signs of scattering. For the systems with more than two planets we examine the two most distant members. Only in seven out of the twenty planetary systems is the more distant member the less eccentric and more massive one. This may just be a sign that we have a significant fraction of planetary systems with unknown components and not evidence against a scattering origin since in five out of the six planetary systems with three or four detected members, the outer-most planet is more massive and less eccentric than the next inner planet. Also in these systems with more than two planets, the inner-most planet is so close to the central star that its orbit has probably been tidally circularised – a complex process where the tidal torque is an r−6 effect (Halbwachs et al. 2005) indicated by the dashed line in Fig. 2.5.

2-4 Discussion

We compare the region of the Msini − P plane occupied by our Solar System compared to the region being sampled by Doppler surveys in Fig. 2.7. Doppler surveys are on the verge of detecting Jupiter-like exoplanets. If our Solar System is typical then the dispersion away from Jupiter into the Doppler-detectable region may be largely due to the eﬀect of high metallicity in producing gravitational scattering. Whether Jupiter is slightly more or less massive than the average most massive planet in a planetary system is diﬃcult to determine. However, the strong correlation between the presence of Doppler-detectable exoplanets and high host metallicity (see Chapter 6) suggests that high metallicity systems preferentially produce massive Doppler-detectable exoplanets. This further suggests (since the Sun is more 2-4. Discussion 36 metal-rich than ∼ 2/3 of local solar analogues) that Jupiter may be slightly more massive than the average most massive planet of an average metallicity, but otherwise Sun-like, star.

Results from microlensing searches are plotted as red points in Fig. 2.7. These can be used to constrain the frequency of Jupiter-mass planets. Gaudi et al. (2002) analysed 5 years worth of microlensing events (43 in total) and reported that less than 33% of the lensing objects (presumed to be Galactic bulge M-dwarfs) have planetary companions within the dashed wedge-shaped area of Fig. 2.7. The period scale, but not the AU scale, is applicable to this area. Two planets have now been detected within this wedge. Since another 5 years have elapsed since the 5 year anlysis of Gaudi et al. (2002), we assume that approximately twice the number of microlensing events have now been intensively monitored. Thus approximately 2/86 = 2% of microlensing events have planets in the wedge-shared area of Fig. 2.7. Two lower mass planets found by microlensing suggest that Neptune mass planets may be more common. Gould et al. (2006) report that the lower limit for the frequency of Neptune mass planets is 16% at the 90% conﬁdence level.

A conversion of the relative Doppler planet frequencies reported here to a fractional abundance in the wedge-shaped area yields the rough estimate that more than ∼ 3% of Doppler-surveyed Sun-like stars will be found to have companions with masses and periods in the wedge-shaped area. Thus our results are crudely consistent with current microlensing constraints. However, because of the difference in host mass, (∼ M for Doppler surveys and ∼ 0.3M for microlensing) it is not clear that such a direct comparison is justified. For example, if in the next few years Doppler and microlensing constraints appear to conflict, it may simply be that typical planetary masses scale with the mass of the host star, that is, Jupiter-mass planets at Jupiter-like orbital radii may be more common around ∼ M stars than around ∼ 0.3M stars. 2-5. Summary 37

2-5 Summary

Despite the fact that massive planets are easier to detect, the mass distribution of detected planets is strongly peaked toward the lowest detectable masses. And despite the fact that short period planets are easier to detect, the period distribution is strongly peaked toward the longest detectable periods.

To quantify these trends as accurately as possible, we have identified a less-biased subsample of exoplanets (Fig. 2.1). Within this subsample, we have identified trends in Msini and period that are less biased than trends based on the full sample of exoplanets. Straightforward extrapolations of the trends quantified here, into the area of parameter space occupied by Jupiter, indicates that Jupiter lies in a region of parameter space densely occupied by exoplanets.

These new results were obtained using a similar data analysis method to that published in Lineweaver & Grether (2002), but with November 2006 exoplanet data, conﬁrming our initial ﬁndings based on exoplanet data from November 2001.

Despite the importance of the mass distribution and the trends in it, it is the trend in period that, when extrapolated, takes us to Jupiter and the parameter space occupied by Jupiter-like exoplanets (compare Figs. 2.1 and 2.4). Long term slopes in the velocity data that have not yet been associated with planets are present in a large fraction of the target stars surveyed with the Doppler technique (Butler R.P, Mayor, M. 2001, private communication). However, quantifying the percentage of host stars showing such residual trends is diﬃcult and depends on instrumental noise, phase coverage and the signal-to-noise threshold used to decide whether there is, or is not, a long term trend.

Figure 2.7 shows that the Doppler technique has been able to sample a very speciﬁc high mass, short-period region of the log P − log Msini plane. Thus far, this sampled region does not overlap with the 10 times larger area of this plane occupied by the nine planets of our Solar System. Thus there is room in the ∼ 95% of target stars with no Doppler-detected planets, to harbour planetary systems like our Solar System. 2-5. Summary 38

The trends in the exoplanets detected thus far do not rule out the hypothesis that our Solar System is typical. They support it. The extrapolations of the trends quantiﬁed here put Jupiter in the most densely occupied region of the Msini − P parameter space. In addition long term trends in velocity, not yet identiﬁed with planets, are common. Both of these observations indicate that the detected exoplanets are the observable tail of the main concentration of massive planets of which Jupiter is likely to be a typical member rather than an outlier. Chapter 3

Extrasolar Planet Frequency

In this Chapter we examine the frequency of stars with extrasolar planets. We analyse a sample of ∼ 1800 nearby Sun-like stars being monitored by eight high- sensitivity Doppler exoplanet surveys. Approximately 90 of these stars have been found to host exoplanets massive enough to be detectable. Thus at least ∼ 5% of target stars possess planets. If we limit our analysis to target stars that have been monitored the longest (∼ 15 years), ∼ 11% possess planets. If we limit our analysis to stars monitored the longest and whose low surface activity allow the most precise velocity measurements, ∼ 25% possess planets.

In Chapter 2 we quantified the trends in extrasolar planetary mimimum mass and period from a sample of exoplanets less biased by selection effects, which we then extrapolated to show that Jupiter is a typical massive planet with respect to mass and period. Using a similar approach, and linearly extrapolating these trends into regions of parameter space that have not yet been completely sampled, we find at least ∼ 9% of Sun-like stars have planets in the mass and orbital period ranges,

Msini > 0.3MJup and P < 13 years, and at least ∼ 22% have planets in the larger range, Msini > 0.1MJup and P < 60 years. Even this larger area of the log mass - log period plane is less than 20% of the area occupied by our planetary system, suggesting that this estimate is still a lower limit to the true fraction of Sun-like stars with planets, which may be as large as ∼ 100%. 3-1. Introduction 40

This Chapter is based on work published in Lineweaver & Grether (2003) using exoplanet data available as of June 2003. As of November 2006, no new planets were detected around the stars that previously contained no detected planets for the sample that has been monitored the longest. Thus we still ﬁnd for the stars monitored the longest and whose low surface activity allow the most precise velocity measurements that ∼ 25% possess detectable planets.

3-1 Introduction

With increasingly sensitive instruments exoplanet hunters had detected more than 100 exoplanets by mid 2003. The focus of these pioneering eﬀorts has been to ﬁnd and describe new exoplanets. As more exoplanets have been found, the question: ‘What fraction of stars have planets?’ has been looked at occasionally. Estimates of the fraction of stars with planets can be simply calculated from the raw numbers of exoplanet hosts divided by the number of monitored stars. For example,

Marcy & Butler (2000) report “5% harbor companions of 0.5 to 8MJup within 3 AU”. Estimates can also be based on high precision Doppler targets in a single survey. Fischer et al. (2003a) report a fraction of 15% for high precision Doppler targets in the original Lick sample. Estimates can also be based on a semi-empirical analysis of exoplanet data (Tabachnik & Tremaine 2002).

In this Chapter we use a semi-empirical method, staying as close to the exoplanet data as possible. We use the growth and current levels of exoplanet detection to verify that sensitive and long duration surveys have been ﬁnding more planets in a predictable way. This is no surprise. However, quantitatively following the consistent increase of the lower limit to the fraction of stars with detected planets is an important new way to substantiate both current and future estimates of this fraction. Because of the growing importance of the question ‘What fraction of stars have planets?’ and our increasing ability to answer this question, such a closer scrutiny of (i) the assumptions used to arrive at the answer, (ii) the parameter space in which they are valid and (iii) the associated error bars, is timely. 3-2. Extrasolar Planet Data 41

We present the exoplanet data set in Section 3-2. We analyse the target lists and detections and show how the fraction of stars with detected planets has increased over time. In Section 3-2.3 we quantify how the fraction of stars with planets depends on the precision with which the radial velocity of individual stars can be measured. In Section 3-3 we quantify trends in exoplanet mass and period by linear and power-law ﬁts to histograms of a less-biased sub-sample of exoplanets. Based on these trends, we extrapolate into larger regions of parameter space and give estimates for the fraction of stars with planets in these regions. We compare our results with previous work in Section 3-6. We provide a brief summary and discussion in Section 3-7.

3-2 Extrasolar Planet Data

3-2.1 Mass and Period Distribution

Figure 3.1 displays the masses and periods of the 106 exoplanets detected as of June 2003 by the eight high precision Doppler surveys analysed in this paper. The region in the upper left labeled “Detected” is our estimate of the region in which the Doppler technique has detected virtually all the exoplanets with periods less than three years orbiting target stars that have been monitored for at least three years.

This region is bounded by three days on the left, three years on the right, 13MJup on the top and at the bottom by a radial velocity of 40 m/s induced in a solar- mass host star. The largest observed exoplanet period and the smallest observed radial velocity induced by a detected exoplanet are used to deﬁne the boundary between the “Being Detected” and “Not Detected” regions. The discontinuity of the “Being Detected” region near Jupiter is due to the increased sensitivity of the original Lick survey at the end of 1994. No more exoplanets should be detected in the “Detected” region unless new stars are added to the target lists. Thus, all the exoplanets marked with a ‘+’ (detected since August 2002) should fall in, or near, the “Being Detected” region. Of the 11 detections since August 2002, 8 fall in 3-2. Extrasolar Planet Data 42 the “Being Detected” region, 2 fall just inside the “Detected” region while one has P < 3 days – it was not being monitored with suﬃcient phase coverage for detection until recently.

We deﬁne a less-biased sample of planet hosts as the 49 hosts to the planets within the rectangular region circumscribed by a thin solid line (3 days < P < 3 years and 0.84 < Msini/MJup < 13) in Fig. 3.1. This rectangle is predominantly in the “Detected” region. We will use this less-biased sample as the basis for our extrapolations (Sec. 3-3).

Within the rectangle enclosed by the thick solid line in Fig. 3.1, two boxes in the lower right lie partially in the “Being Detected” region. Thus they are partially undersampled compared to the other boxes within the rectangle. We correct for this undersampling by making the simple assumption that the detection eﬃciency is linear in the “Being Detected” region. That is, we assume that the detection eﬃciency is 100% in the “Detected” region and 0% in the “Not Detected” region and decreases linearly inbetween. Thus the decrease is linear in log P for the region constrained by the survey duration and linear in log K for the region constrained by the detection threshold of the Doppler survey. This linear correction adds 4 planets giving us a corrected less-biased sample of 53(= 49 + 4) planets.

To find the correction for the section of the less-biased sample lying in the partially complete “Being Detected” region, we firstly find the completeness function, e.g. C = 1.7(log K − 1.0), where C = 1 when K = 40 m/s and C = 0 when K = 10 m/s. We then integrate the completeness function over the various bins that have regions that are partially complete or “Being Detected”. To normalise the correction we assume that the underlying planetary distribution is uniform over the whole bin that is being corrected. From this correction for regions of partial completeness, we then subtract the detected planets multiplied by a weight 1/C.

Also in Figure 3.1, the metallicity of the host stars (see Chapter 6) are indicated by the coloured points while eccentricity of the exoplanet orbits (see Section 4-4.2) are indicated by point size (see key in lower left). Thin lines connect planets orbiting the same host star. The cross-hatched square is our Jupiter-like region deﬁned 3-2. Extrasolar Planet Data 43

by MSaturn ≤ Msini ≤ 3MJupiter and Pasteroids ≤ P ≤ PSaturn and discussed in Section 3-5.

3-2.2 Monitoring Duration

The exoplanets plotted in Fig. 3.1 are the combined detections of eight Doppler surveys currently monitoring the radial velocities of ≈ 1812 nearby FGK stars (Tables 3.1 & 3.2). The top panel of Fig. 3.2 shows how the number of these target stars has increased over the past 16 years and the increasing number of them found to be hosting at least one exoplanet. 94 stars have been found to host 106 exoplanets. Of these 94, 92 fall within our selection criteria of Sun-like stars (= FGK class IV or

V) with planets (Msini < 13MJup). Six known exoplanet hosts were not included in this analysis because they were found in the context of surveys whose search strate- gies and sensitivities cannot easily be combined with results from the 8 sensitive Doppler surveys analysed here.

The exoplanet host stars in the top panel of Fig. 3.2 are binned in two ways. In the darkest histogram they are binned at the date-of-detection of the first exoplanet found orbiting the star. In the middle-grey histogram they are binned at the date- of-first-monitoring of the star. Notice the small number of target stars until the discovery of the first planet (Mayor & Queloz 1995).

The date-of-first-monitoring and the discovery date for the detected exoplanets were largely obtained from the literature and press releases (Table 3.1). In some cases the date-of-first-monitoring was estimated from the first point on the planet host’s velocity curve. The ramp-up time needed to start observing all the stars in a survey’s target list was estimated from the distribution of the date-of-first- montitoring of a survey’s detected exoplanets. That is, the ramp up time needed to start observing the detected hosts was used to estimate the ramp-up time needed to start observing all the stars on a survey’s target list. The exceptions to this were the time dependence of the original Lick target list obtained from Cumming et al. (1999) and the time dependence of the Keck target list (FGK) estimated from the 3-2. Extrasolar Planet Data 44

Figure 3.1. Our Solar System compared to the 106 exoplanets detected by eight high-sensitivity Doppler surveys. The three regions labeled “Detected”, “Being De- tected” and “Not Detected” indicate the selection effects in the log mass - log period plane due to a limited time of observation and limited radial velocity sensitivity (Sec- tions 3-2.2 and 3-2.3). The rectangular region circumscribed by the thin solid line, fits almost entirely into the “Detected” region, and contains what we call the less- biased sub-sample. This sub-sample is the basis of the trends in mass and period identified in Fig. 3.5. All of the recently detected exoplanets marked with a “+” should fall in, or near, the “Being Detected” region. The cross-hatched square is our Jupiter-like region defined by MSat ≤ Msini ≤ 3MJup and PAst ≤ P ≤ PSat. 3-2. Extrasolar Planet Data 45

FGKM histogram of Cumming et al. (2003).

By taking the ratio, in the top panel, of the darker histograms to the lightest one, we obtain the fraction of target stars hosting at least one planet (lower panel of Fig. 3.2). The two binning conventions lead to different results. Using the date- of-detection binning (darkest histogram) yields the intuitive result that the fraction of host stars starts at zero in 1995 and climbs monotonically until its current value of 5 1% (≈ 92/1812). The date-of-first-monitoring binning starts on the far left at 11 3% from the bin of target stars that has been monitored the longest. The fraction decreases as we average in more stars that have been monitored for shorter durations. The dashed line is the result of a linear fit to a sparse, and therefore more independent, sample of the non-independent points (data points used have a larger point size). This line yields 9 2% on the far left in good agreement with the single data point in the left-most bin. The last bin on the right is the same in both binning methods and includes all Sun-like target stars. Thus, ≈ 5% is an average fraction from target stars that have been monitored for times varying between 0 and 16 years, while ≈ 11% is the fraction from target stars that have been monitored the longest (≈ 15 yrs). The non-trivial task of estimating the total number of stars being monitored is described in Section 3-2.4 and summarised in Table 3.2.

Although this 11% estimate is based on the results from ∼ 85 target stars of the two longest running surveys: Lick and McDonald, it is consistent with the increasing fraction based on the monitoring duration of all target stars. This is shown in Fig. 3.3. Notice the small number of target stars (∼ 85) in the original Doppler surveys (bins on far right) and the ∼ 2 years it took to start monitoring all of them. These ∼ 85 (∼ 5% of the stars currently being monitored) are the only target stars that have been monitored long enough to begin to detect exoplanets with Jupiter-like masses in Jupiter-like (∼ 12 year) orbital periods. It will be another ﬁve years before a substantially larger fraction of target stars have been monitored long enough to detect such planets.

The fractions plotted in the lower panel of Fig. 3.3 are the ratios of the histograms in the upper panel. This panel shows the eﬀect of longer monitoring duration on the 3-2. Extrasolar Planet Data 46

Figure 3.2. The fraction of stars with planets using two different binning conventions. The date-of-detection binning yields the intuitive result that the fraction of host stars starts at zero in 1995 and climbs to 5% in 2003. The date-of-first- monitoring binning starts on the far left at 11% from the bin of target stars that has been monitored the longest and decreases as we average in more stars that have been monitored for shorter durations. See Section 3-2.2 for a discussion of this figure. 3-2. Extrasolar Planet Data 47

Figure 3.3. Number of targets as a function of how many years they have been monitored. Most targets have only been monitored for ∼ 5 years. The longer a group of target stars has been monitored, the larger the fraction of planet-possessing targets. See Sections 3-2.2 and 3-4 for discussions of this figure. 3-2. Extrasolar Planet Data 48 observed fraction of stars with planets. The fraction of target stars with detected planets increases with duration. This is distinct from the cumulative fractions shown in the lower panel of Fig. 3.2. However, the right-most bin here is the same as the left-most bin there. Calculation of the fraction of stars hosting exoplanets is described in Section 3-4. We fit a curve with the light grey 68% confidence regions to this data normalised at a duration of 15 years to the weighted average fraction of the two longest duration bins (see Section 3-4). The extrapolation of this curve (based on current sensitivity) to monitoring durations of 30 years (approximate period of Saturn) yields a fraction of ∼ 15%. This extrapolation corresponds to extending the white “Detected” region in Fig. 3.1 to the upper right, above the diagonal K = 40 m/s line.

The scatter of the data points around the smooth curve is due to small number statistics, varying instrumental sensitivities and variation in observational phase coverage. For example, the two points at durations of 7.5 and 8.5 years lie below the curve, due to the lower average sensitivity ∼> 10 m/s of AFOE and Elodie surveys in these bins. The high point at 6.5 years is the start of the sensitive Keck survey. Thus, this plot also shows the eﬀect of diﬀerent instrumental sensitivities on the fraction of stars hosting planets.

In the lower panel of Fig. 3.3, we increase the fraction for a given group of stars, not when a planet is reported, but at the duration equal to the period of the newly detected planet. For example, recent detections of short period planets increase the fraction at a duration corresponding to the short period of the newly detected planet. This smooths over artiﬁcial delays associated, for example, with not analyzing the data for the ﬁrst 8 years of observations, and enables us to trace with dotted lines the increasing fraction for each group of target stars.

3-2.3 High Doppler Precision Targets

Instrumental sensitivity is an important limit on a Doppler survey’s ability to detect planets. However, the level of stellar activity on a star’s surface is also important. 3-2. Extrasolar Planet Data 49

Figure 3.4. When stellar activity is low, high measurement precision is possible and a higher fraction of targets are found to host planets. Top: The number of targets in the original Lick survey that have been monitored for a duration of 14-16 0 years and that have an excess radial velocity dispersion σv less than the value on the x axis. The ratio (Bottom) gives the fraction of stars with planets as a function 0 of σv threshold. 3-2. Extrasolar Planet Data 50

Using the Doppler technique, planets are more easily detected around slowly rotating stars with low level chromospheric activity, little granulation or convective inhomogeneities and few time-dependent surface features. To reduce these problems, some target lists have been selected for high Doppler precision (low stellar activity) by excluding targets with high values of projected rotational velocity vsini 0 or chromospheric emission ratio RHK (Table 3.1).

By selecting target stars monitored the longest, the detected fraction of Sun-like stars possessing planets increased from 5% to 11%. By selecting from the target stars monitored the longest, the stars with the highest Doppler precision, the fraction increases still further. Fischer et al. (2003a) analysed a group of high Doppler precision target stars in the original Lick sample and found that 15% possessed planets. We extend this idea in Fig. 3.4 by plotting the fraction of target stars with planets as a function of their stellar activity as measured by their excess radial 0 0 velocity dispersion σv (Saar et al. 1998). σv is a measure of how precisely one can determine the radial velocity of the targets. The number of detections from these targets is also shown.

0 The σv of the Lick target stars have been estimated from the stellar rotational 0 1.1 periods tabulated by Cumming et al. (1999) using the relations σv = 10×(12/Prot) 0 1.3 for G and K stars and σv = 10 × (10/Prot) for F stars (Saar et al. 1998). The 0 0 γ curve is a power law (df/dσv ∝ σv ) ﬁt to a sparse sample of these non-independent points (larger point size). Thus, as we select for higher Doppler precision in the Lick sample, the fraction of targets possessing planets increases from 15% to 25% for the 0 0 stars with the highest precision (σv < 2.5 m/s). However, as we decrease the σv threshold to consider only the highest precision stars, we are using fewer target stars to infer the fraction. Thus, the error bars on the estimates increase from 15 5% on the right to 25 15% on the left. In this cumulative plot the error bars are highly correlated.

We ﬁnd that this selection increases the fraction from 15% on the far right of Fig. 3.4 to ∼ 25% on the far left for the highest Doppler precision stars. As long as high precision Doppler stars are an unbiased sample of Sun-like stars this indicates that 3-2. Extrasolar Planet Data 51 at least ∼ 25% of Sun-like stars possess planets.

3-2.4 Number of Monitored Stars

To compute the total number of target stars being monitored (Fig. 3.2) we need to avoid double-counting. Target lists of six of the eight surveys considered here have been published, thus allowing the overlap in the FGK targets of these six to be eliminated by comparing target star names (Table 3.1). We removed K giants and M dwarfs before comparison. The total number monitored by these six surveys is then known (Nknown ≈ 1124). The total number of targets monitored by the Coralie and Elodie surveys is known (NC = 1100,NE = 350) but without published target lists the extent of overlap with the other surveys can only be estimated. We do this by using the statistics of duplicate detections.

Let the total number of exoplanet hosts discovered or conﬁrmed by Elodie and

Coralie be NEhosts = 16 and NChosts = 33 respectively. The number of these planet hosts that were discovered or conﬁrmed by any of the other 6 surveys are

NEoverlap = 8 and NCoverlap = 10. Since there is no overlap between the Coralie and Elodie surveys (Udry, S. 2003, private communication), these two sets of planet hosts are mutually exclusive. The fractional overlap of detections/conﬁrmations is gE = NEoverlap/NEhosts = 8/16 = 0.50 and gC = NCoverlap/NChosts = 10/33 = 0.30 (Tables 3.1 & 3.2). We use these fractional detection overlaps as estimates of the fractional target list overlaps. Thus, we estimate the total number of monitored targets (excluding overlap) as:

Ntotal ≈ Nknown + (1 − gC ) NC + (1 − gE) NE. (3.1)

However, estimated this way, Ntotal includes target stars that were found to be single line spectroscopic binaries (SB1). Exoplanet detection is diﬃcult in such systems so we correct for this by substracting the estimated fractions of SB1’s in the various surveys (between 3% and 9%, see Tables 3.1 & 3.2). After this last step we ﬁnd that

Ntotal ≈ 1812 103. The time dependence of Ntotal (see top panel of Fig. 3.2) is 3-2. Extrasolar Planet Data 52

taken from the time dependence of Nknown and from NC and NE (Table 3.2) using the approximation that gC and gE are constants. Our estimates of the error associated with this procedure are indicated by the error bars on each bin in Figs. 3.2 & 3.3.

Notes for Table 3.1. a refers to all target stars in a survey. b another 450 stars have one or more observations but have been dropped for various reasons (Butler et al. 2003). c there are 550 faster rotators in a lower priority target list (Udry, S. 2003, private communication). d combined Lick/Keck (889 stars). e Ko- rzennik, S. 2003 private communication. f the fractional CaII H and K flux corrected for the photospheric flux (see Noyes et al. 1984; Saar et al. 1998). g projected rotational velocity. h SB1: single-lined spectroscopic binaries. The AAT survey (Jones et al. 2002a) finds 18 out of 204 target stars are SB1. Nidever et al. (2002) mentions that 29 out of 889 Lick and Keck target stars are SB1. Endl et al. (2002) finds 3 out of 37. The original Lick survey has 5 out of 74 (Cumming et al. 1999). We estimate the fraction of SB1’s for the other surveys by noting a survey as either northern or southern hemipshere and taking an average of the known surveys in that hemisphere to estimate the fraction of SB1’s. SB2’s have been eliminated from the target lists. All surveys exclude binary stars when the angular separation is less 00 than 2 . i including confirmations but excluding confirmations of hosts that were known to have a planet prior to the start of observation. Thus several hosts of Lick and Elodie that are monitored by Keck and Coralie to increase phase coverage are only included in the Lick and Elodie numbers. References - 1) Jones et al. (2002a), 2) Fischer et al. (2003a), 3) Butler et al. (2003), 4) Udry et al. (2000), 5) Sivan et al. (2000), 6) Korzennik, S. 2003, private communication, 7) Endl et al. (2002), 8) Cochran & Hatzes (1993), 9) Nidever et al. (2002), 10) Fischer et al. (1999), 11) Vogt et al. (2000), 12) Mayor et al. (2003), The Geneva Extrasolar Planet Search Programmes 3-2. Extrasolar Planet Data 53 6 < ∼ 6 < ∼ YY 8 7 . 5 e < ∼ < 5 350 146 37 33 < NY 3.516 3.5 6 8.1 3.5 2 3 < 7.65 5,12 6 7 8 c c 1100 N < 4 < 9 (for 80%) 4 . 5 b − 11 d Doppler Surveys: Targets < < ∼ ∼ Y 4 . 5 − 7 . 5 d < < ∼ ∼ Table 3.1. 4 . 5 − 7 . 5 < < ∼ ∼ AAT204 Lick 360 Keck Coralie 600 Elodie AFOE CES McDonald 8.818 3.3 18 3.3 26 8.7 33 YY 1998 1987 1996 1998 1994 1995 1992 1987 1 2,9,10 3,9,11 4 i h g f ) a 0 HK (km/s) sin i Planet Host Detections log( R v FGK IV, V TargetsList Published 198 360 443 1100 350 136 32 33 Year Started Spectral TypesApparent V FGKM F7-K0 F7-M5 F8-M0 FGK FGK F8-M5 FGK Targets References Detected SB1’s % - AAT: Anglo Australian Observatory, Anglo Australian Telescope, UCLES Spectrograph; Lick: Lick Observatory, Hamilton Spectrograph; Keck: Keck Observatory, HIRES Spectrograph;Coralie Spectrograph; Coralie: Elodie: European Haute Southern Provence Observatory, Eulergraph; Observatory, Elodie Swiss CES: Spectrograph; Telescope, European AFOE: Whipple Southern Observatory, Observatory, AFOESpectrograph. CAT Spectro- See Telescope, text CES for Spectrograph; additional notes. McDonald: McDonald Observatory, Coudé Note 3-2. Extrasolar Planet Data 54 values c binning is from July to June with January at the center of bin. b 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Doppler Surveys: Cumulative Numbers of FGK IV-V Targets as a Function of Time b 0 0 0 0 0 0 0 0 0 0 66 198 198 198 198 198 – – –0 – 0 –0 0 –0 0 0 – 0 0 74 0 0 0 74 29 0 0 74 29 0 265 29 0 360 0 29 360 0 360 32 0 23 360 32 90 0 360 113 32 8 136 32 179 136 32 270 136 326 32 136 360 136 32 399 136 443 443 0 0 0 0 0 0 0 142 142 159 315 350 350 350 350 350 0 0 0 0 0 0 0 0 0 0 33 700 1000 1100 1100 1100 63 8563 87 22 87 89 2 111 0 111 210 2 263 22 413 790 0 1465 1688 99 1782 1812 53 1812 150 377 675 223 94 30 0 44 56 62 64 66 67 73 – – – – – – – – – 66 89 95 97 99 129 135 301 376 590 1150 2135 2469 2608 2652 2652 1988 20 22 33 33 – – – – – – – – – – – – – 10 – – – 33 33 33 33 33 33 33 33 – – – – – a Table 3.2. − 3 – – – – – – – – – – – 33 33 33 33 33 − ∼ c c 3 15 m/s) 10 5 10 15 5 3 ∼ − − ∼ ∼ − − ∼ σ Survey( Lick 10 Lick 3 AFOE Cumulative no overlap non-cumulativeno overlap 66 23 6 2 2 30 6 166 75 214 560 985 334 139 44 0 McDonald 10 McDonald 5 McDonald CES 8 Elodie Keck 2 AAT Coralie internal error also known as instrument sensitivity. a have been corrected for overlapping target lists and for estimated numbers of single line spectroscopic binaries (SB1). 3-3. Fitting For and Extrapolating Trends 55

3-3 Fitting For and Extrapolating Trends

We use extrapolation to estimate the fraction of stars with planets within regions of mass-period parameter space larger than the less-biased sample (Fig. 3.1). Since there is no accepted theoretical model for the functional form for the mass or period distribution functions, we make simple linear ﬁts to the histograms in log Msini and log P and we ﬁt conventional power laws to the histograms in Msini and P (Fig. 3.5). Fitting

dN/d(log(Msini)) = a log(Msini) + c (3.2) to the histogram of log Msini (Fig. 3.5 A) we obtain the slope a = −30 7. Fitting

dN/d(log P ) = b log P + d (3.3) to the histogram of log P (Fig. 3.5 B) we obtain the slope b = 19 4. These trends are shown as thick lines. The distribution of exoplanets is not flat in either log Msini or log P . That is a = −30 7 is significantly different (∼ 4σ) from a = 0 and b = 19 4 is significantly different (∼ 5σ) from b = 0. Fitting

dN/d(Msini) ∝ (Msini)α (3.4) to the histogram of Msini (Fig. 3.5 C) we obtain α = −1.7 0.2. Fitting

dN/dP ∝ P β (3.5) to the histogram of P (Fig. 3.5 D) we obtain β = −0.40.2. To check the robustness of the ﬁts we change variables to log Msini and log P which eﬀectively producing a re-binning of the data. Since d (ln x) = dx/x, the functional form

dN/d(Msini) ∝ (Msini)α (3.6) can be written as 3-3. Fitting For and Extrapolating Trends 56

dN/d(log(Msini)) ∝ (Msini)(1+α) (3.7) and similarly

dN/dP ∝ P β (3.8) can be written as

dN/d(log P ) ∝ P (1+β) (3.9)

We fit these functions to the histograms of log Msini and log P in Fig. 3.5 A & B where we find α = −1.9 0.2 and β = −0.2 0.2. These values differ by ∼ 1σ from the values of α and β found in Fig. 3.5 C & D. We attribute the differences to the different log and linear binning schemes. Combining these two estimates gives +0.3 our best estimates of α = −1.8 0.3 and β = −0.3−0.4. In the fit of panel B, we ignore the 5 exoplanets in the smallest period bin because we are interested in the overall pattern that can be most plausibly extrapolated to larger P bins, not in the pile up associated with a poorly understood stopping mechanism at P < 12 days. For consistency, these 5 exoplanets have also been removed from the smallest period bin in panel D. These values are compared to other estimates in Table 3.3.

If the distributions were flat in log Msini and log P we would find respectively α ≈ −1.0 and β ≈ −1.0. However, both the trend in mass (α) and in period (β) are significantly different (∼ 2σ) from flat. These slopes agree with our previous results (Table 3.3) and show that the evidence supporting the idea that Jupiter lies in a region of parameter space densely occupied by exoplanets, has gotten stronger in the sense that our new value b = 19 is larger than our previous estimate and our new values for a and α are more negative than our previous estimates.

The main diﬀerences between our results and previous results is that we obtain a steeper slope (more negative α) when we ﬁt the funtional form dN/d(Msini) ∝ (Msini)α to the mass histogram of the data: we get α ≈ −1.8 while other analyses 3-3. Fitting For and Extrapolating Trends 57

Figure 3.5. Trends that we extrapolate to lower mass and longer periods. His- tograms of planet mass (Top) and period (Bottom) for the less-biased sample of exoplanets within the thin solid rectangle of Fig. 3.1, compared to all exoplanet detections. Both log (Left) and linear (right) versions are shown. Histograms in log(Msini) and log P (panels A & B) are fitted with the linear functional forms dN/d(log(Msini)) = a log(Msini) + c and dN/d(log P ) = b log P + d where the best fits to the histograms yield a = −30 7, and b = 19 4. The linearly binned histograms of Msini and P (panels C & D) are fitted to the functional forms: dN/d(Msini) ∝ (Msini)α and dN/dP ∝ P β respectively and we find α = −1.70.2 and β = −0.4 0.2. 3-3. Fitting For and Extrapolating Trends 58

Table 3.3. Best-Fit Trends to Mass and Period Histograms and Comparison with Other Analyses

Source α β a b Figs. 3.5 A&Ba – – −30 7 19 4 Figs. 3.5 C&Db −1.7 0.2 −0.4 0.2 – – Figs. 3.5 A&Bc −1.9 0.2 −0.2 0.2 – – +0.3 Combined Figs. 3.5 A-D −1.8 0.3 −0.3−0.4 – – Marcy et al. (2003) −0.7d – – – Lineweaver et al. (2003) −1.6 0.2 – – 13 4 Lineweaver & Grether (2002) −1.5 0.2 – −24 4 12 3 Tabachnik & Tremaine (2002) −1.11 0.10 −0.73 0.06 – – Stepinski & Black (2000) −1.15 0.01 −0.98 0.01 – – Jorissen et al. (2001) ∼ −1 – – – Zucker & Mazeh (2001b) ∼ −1 – – – a Best fit of dN/d(log(Msini)) = a log(Msini) + c to histogram of log Msini and best fit of dN/d(log P ) = b log P + d to histogram of log P . b Best fit of dN/d(Msini) ∝ (Msini)α to histogram of Msini and best fit of dN/dP ∝ P β to histogram of P . c Best fit of dN/d(log(Msini)) ∝ (Msini)1+α to histogram of log Msini and best fit of dN/d(log P ) ∝ P 1+β to histogram of log P . d including the lowest mass bin with no completeness corrections. get α ≈ −1.1. Thus we predict more low mass planets relative to the more easily detected number of high mass planets, than do other analyses. We obtain a more shallow slope (less negative β) when we fit the funtional form dN/dP ∝ P β to the period histogram of the data. We get β ≈ −0.3 while other analyses get β ∼ −0.8. Thus, we predict more hosts of long period planets relative to the more easily detected short period planets, than do other analyses. These differences are largely due to three aspects of the analysis which include (i) the differences in the way the incompleteness in the lowest mass bin and the longest period bin are accounted 3-3. Fitting For and Extrapolating Trends 59 for, (ii) a less-biased data set and (iii) a more simple, straightforward data analysis method. The first difference can be seen, for example in the α = −0.7 reported by Marcy et al. (2003) when no correction is made for incompleteness in the lowest mass bin. When we make no completeness correction and include the lowest mass bin, we reproduce their result.

3-3.1 Extrapolation Using Discrete Bins

Based on slopes a and b, we make predictions for the fraction of Sun-like stars with planets within two regions of the log mass - log period plane. The estimated populations of the two lowest mass bins based on the slope a are indicated in Fig. 3.5 A. Similarly the estimated populations of the two largest period bins based on slope b are shown in Fig. 3.5 B. From the less-biased region (thin rectangle in Fig. 3.1) we extrapolate both in Msini and P by 1 bin. When we extrapolate in Msini or P we are doing so at a ﬁxed range in P or Msini respectively. However to estimate the fraction of stars within the thick rectangle in Fig. 3.1 (given by the Msini and P ranges 0.3 < Msini/MJup < 13 and 3 days < P < 13 years) we need to estimate the number of planets NMP ext in the bottom right-hand region (just below Jupiter, see Fig. 3.1). To do this we use Eq. 3.10 (see Fig. 3.6), where

Nlb is the number of planet hosts in the less-biased region of Fig. 3.1 and NMext and NP ext are the number of planet hosts in the ﬁrst extrapolated bin based on the slopes a and b respectively. Our estimate of the total number of planet hosts is then

Nhosts = Nlb + NMext + NP ext + NMP ext. We have Nlb = 53 7 from Fig. 3.1 and

NMext = 41 7 and NP ext = 39 6 from Fig. 3.5 A & B. Inserting these values into,

N N Mext ≈ MP ext (3.10) Nlb NP ext

(see Fig. 3.6) we obtain NMP ext = 30 8. Thus, Nhosts = 163 20 and the fraction f, of targets hosting planets is the ratio, 3-3. Fitting For and Extrapolating Trends 60

N f = hosts (3.11) Ntargets where Ntargets ∼ 1812 103 (Table 4). Finally we ﬁnd f = (163 20)/1812 103) ≈ 9 1%. Thus, using the slopes a and b to extrapolate one bin into lower masses and longer periods (thick solid rectangle in Fig. 3.1) we ﬁnd that 9 1% of the targeted Sun-like stars have planets.

Figure 3.6. The simple method of extrapolation used to predict planet numbers in under-sampled regions of the log mass - log period plane. The known value of

Nlb (number of planet hosts in the less-biased region of Fig. 3.1) and extrapolations based on the slopes a and b were used to derive NMext and NP ext. We then use Eq.

3.10 to estimate NMP ext. Our estimate of the total number of planet hosts is then

Nhosts = Nlb + NMext + NP ext + NMP ext.

Similarly and more speculatively we estimate the fraction contained within the thick dashed rectangle in Fig. 3.1 by extrapolating one more bin in mass (over the same range in period as the previous mass extrapolation) and by extrapolating one more bin in period (over the same range in mass as the previous period extrapolation). The analogous numbers are Nlb = 53 7, NMext = (41 7) + (53 10),

NP ext = (396)+(529) (where the sum of the 2 sets of numbers is the sum of the 2 separate bins). Equation 3.10 then yields NMP ext = 16145. Summing the four contributions as before yields Nhosts = 399 69 and thus f = (399 69)/1812 103) ≈ 22 4%. Thus, we estimate that 22 4% of the monitored Sun-like stars have 3-3. Fitting For and Extrapolating Trends 61

planets in the larger region (0.1 < Msini/MJup < 13 and 3 days < P < 60 years) that encompasses both Jupiter and Saturn. This larger region is less than 20% of the area of the log mass - log period plane occupied by our planetary system.

3-3.2 Extrapolation Using a Diﬀerential Method

Instead of extrapolating one or two discrete bins, we can generalize to a more flexible differential method. For example, we can use the power law functional form to integrate a differential fraction within an arbitrary range of Msini and P (Tabachnik & Tremaine 2002),

df = c(Msini)αP β d(Msini)dP (3.12)

We ﬁnd the normalisation c by inserting the known values from the less-biased +0.3 area: f = (53 7/(1812 103)) = 2.9 0.4%, α = −1.8 0.3 and β = −0.3−0.4 (Table 3.3). We integrate between the boundaries of the less-biased rectangle (3 days < P < 3 years and 0.84 < Msini/MJup < 13) and solve for the normalisation. +43.9 −5 We ﬁnd c = 8.6−6.0 × 10 .

Under the assumption that this same c, α and β hold over larger regions of parameter space, we can integrate over the larger region and solve for f. For the +26 thick solid and thick dashed regions shown in Fig. 3.1, we find f = 20−11% and +0 100−71% respectively. Using this differential method with the slopes a and b we find values nearly identical with the discrete bin extrapolations based on a and b: f = 9 1% and 22 5% respectively.

The power-law based estimates are consistent with the lower linear (a− and b−based) estimates in the sense that the large error bars on the power-law estimates overlap with the lower estimates of the linear method. The reason the power law fits yield larger fractions can be seen in Fig 3.5 A & B. In the low mass and large period regions, the dashed curves are higher than the solid lines. Without further data from less massive planets and larger periods we interpret this difference as an uncertainty associated with the inability of the data to prefer one of the two simple 3-4. Fractions in K − P Parameter Space 62 functional forms fit here. The power law fits are marginally better fits to the data. We interpret the lower values from the linear fits as conservative lower limits to the fraction f.

3-4 Fractions in K − P Parameter Space

The fractions discussed in Section 3-2 are based on exoplanet detections constrained by the Doppler technique to a trapezoidal region of the log mass - log period plane deﬁned by a minimal velocity Kmin. The fractions discussed in Section 3-3 are based on rectangular regions of the log mass - log period plane. In the lower panel of Fig. 3.3, the fractions plotted as a function of duration come from a trapezoidal region (not a rectangular region) of the log Msini - log P plane.

0 Hence, a fit of dN/dP ∝ P β to the P histogram of detected planet hosts, will produce a value of β0 slightly different from the β of Fig. 3.5 D. We find β0 = −0.5 0.2 (while β = −0.4 0.2). Such a difference is expected since the number of planets at large P will decrease more steeply in the trapezoidal region, because as P increases the “Detected” regions becomes narrower than a region defined by a constant Msini. The curve shown in the lower panel of Fig. 3.3 is the integral of 0 P β . It is normalised to the last two bins on the right. In plotting this integral we are assuming that a survey of duration Ps has observed a large fraction of its target

< stars with Doppler-detectable exoplanets of period P ∼ Ps.

3-4.1 Consistency Check

We can use the fraction ≈ 11% at a duration of 15 years in the lower panel of Fig.

3.3 as well as the known quantities Pmax, Kmin to perform an interesting consistency check of the relationships between them and the extracted values of α and β.

Assuming Mhost ≈ M >> M and low eccentricity, the relation between Msini and the semiamplitude K of radial velocity is 3-5. Jupiter-like Planets 63

Msini K ≈ A , (3.13) P 1/3 where A = 200 when K is expressed in units of m/s, Msini in MJup and P in days. We are only interested in exoplanets with Msini < 13MJup (∼ the deuterium burning limit). Using Eq. 3.13 to change variables from Msini to K we can write,

df = c(Msini)αP β d(Msini) dP (3.14)

(Eq. 3.12) as,

c 1 df = KαP β+ 3 (1+α) dK dP. (3.15) A(1+α) Under the assumption that Msini is uncorrelated with P and that α and β are approximately constant within the region of interest, we can integrate between arbi-

1/3 trary limits. The upper limit on K depends on period: Kmax(P ) = 13 A/P from Eq. 3.13. We then have,

c Pmax Pmax 1 (1+α) β (1+α) β+ 3 (1+α) f = (1+α) (13 A) P dP − Kmin P dP (3.16) (1 + α)A " Z0 Z0 # Using our best estimates α = −1.8, β = −0.3, c = 8.6 × 10−5 and f = 0.106 from the lower panel in Fig. 3.3 at 15 years, we integrate Eq. 3.16 and solve for Kmin. +7 We ﬁnd Kmin = 16−5 m/s. The weighted average internal error of the original Lick and McDonald observing programs that contain the 85 stars in these two bins is σ = 6 − 10 m/s. The minimum signal to noise of exoplanet detections is ∼ 3, so we expect Kmin ≈ 3 σ which is indeed the case.

3-5 Jupiter-like Planets

The fraction of Sun-like stars possessing Jupiter-like planets is important since Jupiter is the dominant orbiting body in our Solar System and had the most in- ﬂuence on how our planetary system formed. Exoplanets with Jupiter-like periods 3-6. Comparison with Other Results 64 and Jupiter-like masses are on the edge of the detectable region of parameter space. The cross-hatched square in Fig. 3.1 is our Jupiter-like region deﬁned by orbital periods between the period of the asteroid belt and Saturn with masses in the range

MSaturn << Msini < 3MJupiter.

We estimate the fraction of Sun-like stars hosting planets in this region using the differential method based on our best-fit values of a and b. Integrating between the limits of the cross-hatched area we find that f = 5 2% of Sun-like stars possess such a Jupiter-like planet. Using the differential method based on our best-fit values +68 for α and β we obtain f = 28−22%. As with the different f values resulting from these two methods in Section 3-3.2, these are consistent with each other and reflect the different functional forms used.

3-6 Comparison with Other Results

We compare our results for the fraction of Sun-like stars with planets to those of other published works in Table 3.4. We list the source, the range in Msini, the range in period P and the fraction estimated by these other analyses. We apply our discrete bins method (see Section 3-3.1) and our diﬀerential method (see Section 3-3.2) to these ranges in Msini and P and show that our results are consistent with, but generally higher than, these previous works.

We estimate that at least 9% of Sun-like stars have planets within the thick solid rectangle and at least 22% have planets within the thick dashed rectangle of Fig. 3.7 using the discrete bins method. We find larger values using a differential method based on power-law fits. We compare our results with other published estimates in Fig. 3.7. The papers, estimates and the regions of the log Msini - log P plane associated with these estimates are indicated. 3-6. Comparison with Other Results 65 b +21 − 8 +25 − 11 +4 − 2 6 100 (%) 18 19 Our Fraction a 1 +19 − 15 +4 − 3 +4 − 3 ) 3.7 15 9 (%) (%) c 4 AU) 6 9 Fraction Comparison (see Fig. Range Period Range Fraction Our Fraction Jup i . M 0.3-10 0.03-11.2 yrs 0.25-15 0-8 yrs ( < β sin b . M and Table 3.4. and ) 1 - 10) 2 days - 10 0.003-10 yrs 2 days - 4 10 yrs 18 4 45 α a ( 2002 ( 2002 ) ( 2002 ) ( 2002 Source Tabachnik & Tremaine Liu et al. Armitage et al. Tabachnik & Tremaine Differential method based on slopes Differential method based on powers Corresponds to 0.1 - 5 AU. a b c 3-6. Comparison with Other Results 66

Figure 3.7. We estimate that at least 9% of Sun-like stars have planets within the thick solid rectangle and at least 22% have planets within the thick dashed rectangle (Sec. 3-3.1). We find larger values using a differential method based on power-law fits (Sec. 3-3.2). Here, we compare our results with other published estimates of the fraction of stars with planets. The papers, estimates and the regions of the log Msini - log P plane associated with these estimates are indicated. Our results are consistent with, but generally higher than, previous work (Table 3.4). 3-7. Summary 67

3-7 Summary

We have analysed the results of eight Doppler surveys to help answer the question: ‘What fraction of stars have planets?’. We use the number of targets and the number of detected planet hosts to estimate the fraction of stars with planets. Quantitatively following the consistent increase of this fraction is an important new way to substantiate both current and future estimates of this fraction. We show how the naive fraction of ∼ 5% increases to ∼ 11% when only long-duration targets are included. We extend the work of Fischer et al. (2003a) by plotting the fraction as a function of excess dispersion and show how this ∼ 11% increases to ∼ 25% when only long-duration Lick targets with the lowest excess in radial velocity dispersion are considered.

We have identified trends in the exoplanet data based on a less-biased sub-sample. We find stronger support than found previously for the idea that Jupiter-like planets are common in planetary systems (Table 3.3). We estimate the fraction of Sun-like stars hosting planets in a well-defined Jupiter-like region to be ∼ 5%.

We have extrapolated these trends into unsampled or undersampled regions of the log mass - log period plane. We ﬁnd at least ∼ 9% of target stars will be found to host an exoplanet within the thick rectangle of Fig. 3.1 and that more speculatively at least ∼ 22% of target stars will be found to host an exoplanet within the larger thick dashed rectangle. Our results for the fraction of Sun-like stars with planets are consistent with but are, in general, larger than previous estimates (Table 3.4, Fig. 3.7).

The largest uncertainty in this analysis is that we may be extrapolating trends derived from a small region of log mass - log period into regions of parameter space in which the trends are slightly or substantially diﬀerent. This uncertainty is why we did not extrapolate beyond the dashed region in Fig. 3.1 that contains from our Solar System, only Jupiter and Saturn.

It is sometimes implicitly assumed that most planetary systems will be like ours and that Earth-like planets will be common in the Universe. However, as we descend 3-7. Summary 68 in scale from galaxy, to star, to planetary system to terrestrial planet we run more of a risk of self-selection. That is, the factors that are responsible for our origin may have selected a non-typical location. Thus, answering the question “What fraction of stars have planets?” must rely on the continued analysis of the statistical distributions of exoplanets detected by the increasingly precise and ground-breaking Doppler surveys.

The hypothesis that ∼ 100% of stars have planets is consistent with both the observed exoplanet data which probes only the high-mass, close-orbiting exoplanets and with the observed frequency of circumstellar disks in both single and binary stars (e.g. Lada et al. 2006). The observed fractions f that we have derived from current exoplanet data are lower limits that are consistent with a true fraction of

< < stars with planets ft, in the range 0.25 ∼ ft ∼ 1. If the fraction of Sun-like stars that possess planets is representative of all stars, our result means that out of the ∼ 300 billion stars in our Galaxy there are between ∼ 75 and ∼ 300 billion planetary systems. Chapter 4

Extrasolar Planet - Close Companion Comparison

Sun-like stars have stellar, brown dwarf and planetary companions. In this Chapter we compare the extrasolar planet population with that of the close orbiting (orbital period < 5 years) stellar and brown dwarf companion populations to help constrain their formation and migration scenarios. We deﬁne a less-biased sample of Sun-like stars from which to extract the stellar, brown dwarf and planetary companions. The selection eﬀects and completeness of the detected close companions in this sample are discussed in detail.

The period and eccentricitry distributions of close-orbiting companion stars are different from those of the planetary companions. Planets tend to be more abundant at longer periods and are less frequent at very low and very high eccentricities than stellar companions. The period and eccentricity distributions of close-orbiting companions may be more a result of post-formation migration and gravitational jostling than representive of the relative number of companions that are formed at a specific distance and with a specific eccentricity from their hosts. The companion mass distribution examined in Chapter 5 is more fundamental than the period and eccentricity distributions and should provide better constraints on formation models.

This Chapter is based on work published in Grether & Lineweaver (2006) using 4-1. Introduction 70 close exoplanet, brown dwarf and stellar companion data available as of October 2005.

4-1 Introduction

The formation of a binary star via molecular cloud fragmentation and collapse, and the formation of a massive planet via accretion around a core in a protoplanetary disk both involve the production of a binary system, but are usually recognised as distinct processes, e.g. Heacox (1999); Kroupa & Bouvier (2003), see however Boss (2002). The formation of companion brown dwarfs, with masses in between the stellar and planetary mass ranges, may have elements of both or some new mechanism (Bate 2000; Rice et al. 2003; Jiang et al. 2004). For the purposes of our analysis brown dwarfs can be conveniently deﬁned as bodies massive enough to burn

> < deuterium (M ∼ 13 MJup), but not massive enough to burn hydrogen M ∼ 80 MJup, e.g. (Burrows et al. 1997). Since fusion does not turn on in gravitationally collapsing fragments of a molecular cloud until the ﬁnal masses of the fragments are largely in place, gravitational collapse, fragmentation and accretion should produce a spectrum of masses that does not know about these deuterium and hydrogen burning boundaries. Thus, these mass boundaries should not necessarily correspond to transitions in the mode of formation. The physics of gravitational collapse, fragmentation, accretion disk stability and the transfer of angular momentum, should be responsible for the relative abundances of objects of diﬀerent masses, not fusion onset limits.

However, there seems to be a brown dwarf desert – a deficit in the frequency of brown dwarf companions either relative to the frequency of less massive planetary companions (Marcy & Butler 2000) or relative to the frequency of more massive stellar companions to Sun-like hosts. The goal of this Chapter and that of Chapter 5 is (i) to verify that this desert is not a selection effect due to our inability to detect brown dwarfs or due to some exoplanet search programs not publishing the orbits of larger mass companions such as brown dwarfs and stellar companions that they 4-1. Introduction 71 detect, and (ii) to quantify the brown dwarf desert more carefully with respect to both stars and planets. By selecting a single sample of nearby stars as potential hosts for all types of companions, we can better control selection effects and more accurately determine the relative number of companions more and less massive than brown dwarfs.

Various models have been suggested for the formation of companion stars, brown dwarfs and planets (e.g. Bate 2000; Boss 2002; Kroupa & Bouvier 2003; Larson 2003; Rice et al. 2003; Matzner & Levin 2005). All models involve gravitational collapse and a mechanism for the transfer of energy and angular momentum away from the collapsing material. To help constrain their formation and migration scenarios, we examine the mass, period and eccentricity distributions for companion stars, brown dwarfs and planets.

Observations of giant planets in close orbits have challenged the conventional view in which giant planets form beyond the ice zone and stay there (e.g. Udry et al. 2003c). Various types of migration have been proposed to meet this challenge. The most important factors in determining the result of the migration is the time of formation and mass of the secondary and its relation to the mass and time evolution of the disk (e.g. Armitage & Bonnell 2002). We may be able to constrain the above models by quantitative analysis of the brown dwarf desert. For example, if two distinct processes are responsible for the formation of stellar and planetary secondaries, we would expect well-deﬁned slopes of the mass function in these mass ranges to meet in a sharp brown dwarf valley.

In Section 4-2 we deﬁne a less-biased sample of Sun-like stars from which to extract the stellar, brown dwarf and planetary companions. We examine the selections eﬀects and completeness of the detected close companions in Section 4-3. The properties of the close companion distributions are compared in Section 4-4 apart from the companion mass distributions which we examine in Chapter 5. We provide a brief summary and discussion in Section 4-5. 4-2. A Less-Biased Sample of Stars 72

4-2 A Less-Biased Sample of Stars

4-2.1 Selection Eﬀects

High precision Doppler surveys are monitoring Sun-like stars for planetary companions and are necessarily sensitive enough to detect brown dwarfs and stellar companions within the same range of orbital period. However, to compare the relative abundances of stellar, brown dwarf and planetary companions, we cannot select our potential hosts from a non-overlapping union of the FGK spectral type target stars of the longest running, high precision Doppler surveys that are being monitored for planets (Table 3.1). This is because Doppler survey target selection criteria often exclude close binaries (separation < 2”) from the target lists, and are not focused on detecting stellar companions. Some stars have also been left oﬀ the target lists because of high stellar chromospheric activity (Fischer et al. 1999). These surveys are biased against ﬁnding stellar mass companions. We correct for this bias by identifying the excluded targets and then including in our sample any stellar companions from other Doppler searches found in the literature.

Our sample selection is illustrated in a Hertzsprung-Russell diagram, Fig. 4.1 and detailed in Appendix B for stars closer than 25 pc and Fig. 4.2 for stars closer than 50 pc. The grey parallelogram is the region of MV -(B − V ) space that contains the highest fraction (as shown by the triangles) of Hipparcos stars that are being monitored for exoplanets. This monitored or target fraction needs to be as high as possible to minimise selection eﬀects potentially associated with companion frequency. The target fraction is calculated from the number of main sequence stars, i.e., the number of stars in each bin between the two dashed lines. Fig. 4.1 contains 1509 Hipparcos stars, of which 627 are Doppler target stars. The Sun-like region contains 464 Hipparcos stars, of which 384 are target stars. Thus, the target fraction in the Sun-like grey parallelogram of Fig. 4.1 is ∼ 83%(= 384/464).

Most Doppler survey target stars come from the Hipparcos catalogue because host stars need to be both bright and have accurate masses for the Doppler method 4-2. A Less-Biased Sample of Stars 73

Figure 4.1. Our close sample. Hertzsprung-Russell diagram for Hipparcos stars closer than 25 pc. Small black dots are Hipparcos stars not being monitored for possible companions by one of the 8 high precision Doppler surveys considered here (Table 3.1). Larger blue dots are the subset of Hipparcos stars that are being monitored (“Target Stars”) but have as yet no known planetary companions. The still larger red dots are the subset of target stars hosting detected planets (“Planet

Host Stars”) and the green dots are those hosts with larger mass (M2 > 13MJup) companions (“Other Host Stars”). Only companions in our less-biased sample (P <

−3 5 years and M2 > 10 M ) are shown (see Section 4-3). Our Sun is shown as the black cross. Additional details of this plot are discussed in Section 4-2.1. 4-2. A Less-Biased Sample of Stars 74

Figure 4.2. Our far sample. Same as Fig. 4.1 but for all Hipparcos stars closer than 50 pc. The major reason the target fraction (∼ 61%, triangles) is lower than in the 25 pc sample (∼ 83%) is that K stars become too faint to include in many of the high precision Doppler surveys where the apparent magnitude is limited to V < 7.5 (see Table 3.1). This plot contains 6924 Hipparcos stars, of which 2351 are target stars. The grey parallelogram contains 3296 Hipparcos stars, of which 2001 are high precision Doppler target stars (61% ∼ 2001/3296). The stars below the main sequence and the stars to the right of the M dwarfs are largely due to uncertainties in the Hipparcos parallax or B − V determinations. 4-2. A Less-Biased Sample of Stars 75 to be useful in determining the companion’s mass. One could imagine that the Hipparcos catalogue would be biased in favor of binarity since hosts with bright close-orbiting stellar companions would be over-represented. We have checked for this over-representation by looking at the absolute magnitude dependence of the frequency of stellar binarity for systems closer than 25 and 50 pc (Fig. 4.3). We found no signiﬁcant decrease in the fraction of binaries in the dimmer stellar systems for the 25 pc sample and only a small decrease in the 50 pc sample. Thus, the Hipparcos catalogue provides a good sample of potential hosts for our analysis, since it (i) contains the Doppler target lists as subsets (ii) is volume-limited for Sun- like stars out to ∼ 25 pc (Reid 2002) and (iii) it allows us to identify and correct for stars and stellar systems that were excluded.

We limit our selection to Sun-like stars (0.5 ≤ B − V ≤ 1.0) or approximately those with a spectral type between F7 and K3. Following Udry, S. (2004, private communication) and the construction of the Coralie target list, we limit our anaylsis to main sequence stars, or those between -0.5 and +2.0 dex (below and above) an average main sequence value as deﬁned by 5.4(B−V )+2.0 ≤ MV ≤ 5.4(B−V )−0.5. This sampled region, which we will call our “Sun-like” region of the HR diagram, is shown by the grey parallelograms in Figs. 4.1 & 4.2.

The Hipparcos sample is essentially complete to an absolute visual magnitude of MV = 8.5 (Reid 2002) within 25 pc of the Sun. Thus the stars in our 25 pc Sun-like sample represent a complete, volume-limited sample. In our sample we make corrections in companion frequency for stars that are not being targeted by Doppler surveys as well as corrections for mass and period companion detection selection effects (see Section 4-3). The result of these corrections is our less-biased distribution of companions to Sun-like stars within 25 pc. We also analyse a much larger sample of stars out to 50 pc to understand the effect of distance on target selection and companion detection. Although less complete, with respect to the relative number of companions of different masses, the results from the 50 pc sample are similar to the results from the 25 pc sample (Chapter 5). 4-2. A Less-Biased Sample of Stars 76

Figure 4.3. Fraction of stars that are known to be close (P < 5 years) Doppler binaries as a function of absolute magnitude. For the 25 pc Sun-like sample (large dots), ∼ 11% of stars are binaries and within the error bars, brighter stars do not appear to be signiﬁcantly over-represented. If we include the extra stars to make the 50 pc Sun-like sample (small dots), the stellar binary fraction is lower and decreases as the systems get fainter. 4-2. A Less-Biased Sample of Stars 77

4-2.2 Sample Completeness

Stars in our nearby Sun-like region are plotted as a function of distance in Fig. 4.4. Each histogram bin represents an equal volume spherical shell hence a sample complete in distance would produce a ﬂat histogram. Also shown are the target stars, which are the subset of Hipparcos stars that are being monitored for planets by one of the 8 high precision Doppler surveys (Table 3.1) analysed here. The triangles in Fig. 4.4 represent this number as a fraction of Hipparcos stars. This fraction needs to be as large as possible to minimise distance dependent selection eﬀects in the target sample potentially associated with companion frequency. Also shown are the number of Hipparcos stars that have one or more companions in the

−3 mass range 10 < M/M < 1, and those that host planets. Only those companions

−3 in the less-biased sample, P < 5 years and M2 > 10 M are shown (Section 4-3).

Since nearly all of the high precision Doppler surveys have apparent magnitude limited target lists (often V < 7.5), we investigate the eﬀect this has on the total target fraction as a function of distance. The fraction of stars having an apparent magnitude V brighter (lower) than a given value are shown by the 5 dotted lines for V < 7.5 to V < 9.5. For a survey, magnitude limited to V = 7.5, 80% of the Sun-like Hipparcos stars will be observable between 0 pc and 25 pc. This rapidly drops to only 20% for stars between 48 and 50 pc. Thus the major reason why the target fraction drops with increasing distance is that the stars become too faint for the high precision Doppler surveys to monitor. The fact that the target fraction (triangles) lie near the V < 8.0 line indicates that on average V ∼ 8.0 is the eﬀective limiting magnitude of the targets monitored by the 8 combined high precision Doppler surveys.

In Fig. 4.1, 80(= 464 − 384) or 17% of Hipparcos Sun-like stellar systems are not present in any of the Doppler target lists. The triangles in Fig. 4.1 indicate that the ones left out are spread more or less evenly in B − V space spanned by the grey parallelogram. Similarly in Fig. 4.2, 1295(= 3296 − 2001) or 39% are not included in any Doppler target list, but the triangles show that more K stars compared to FG stars have not been selected, again pointing out that the lower K dwarf stellar 4-2. A Less-Biased Sample of Stars 78

Figure 4.4. Distance dependence of sample and companions. Each histogram bin represents the stars in an equal volume spherical shell. Hence, a sample that is complete in distance out to 50 pc would produce a ﬂat histogram (indicated by the horizontal dashed line). The lightest shade of grey represents Hipparcos Sun- like Stars that fall within the parallelogram of Fig. 4.2. The next darker shade of grey represents Hipparcos stars that are being monitored for planets using the high precision Doppler techniques. Also shown (darker grey) are the number of Hipparcos

−3 stars that have one or more companions in the mass range 10 < M/M < 1 and those that host planets (darkest grey). The triangles represent this number as a fraction of Hipparcos stars. The fraction of stars having an apparent magnitude V brighter (lower) than a given value are shown by the 5 dotted lines for V < 7.5 to V < 9.5. 4-3. Close Companion Detection 79 brightness is the dominant reason for the lower target fraction, not an eﬀect strongly biased with respect to one set of companions over another.

In the Sun-like region of Fig. 4.1 we use the target number (384) as the mother population for planets and brown dwarfs and the Hipparcos number (464) as the mother population for stars. To achieve the same normalisations for planetary, brown dwarf and stellar companions we assume that the fraction of these 384 targets that have exoplanet or brown dwarf companions is representative of the fraction of the 464 Hipparcos stars that have exoplanet or brown dwarf companions. Thus we renormalise the planetary and brown dwarf companions which have the target sample as their mother population to the Hipparcos sample by 464/384 = 1.21 (“renormalisation”). Since close-orbiting stellar companions are anti-correlated with close-orbiting sub-stellar companions and the 384 have been selected to exclude separations of < 2”, the results from the sample of 384 may be a slight over-estimate of the relative frequency of sub-stellar companions. However, this over-estimate will be less than ∼ 11% because this is the frequency of close-orbiting stellar secondaries.

A non-overlapping sample of the 8 high precision Doppler surveys is used as the exoplanet target list where the Elodie target list was kindly provided by Perrier, C. (2004, private communication) and additional information to construct the Coralie target list from the Hipparcos catalogue was obtained from Udry, S. (2004, private communication). The Keck and Lick target lists are those of Nidever et al. (2002), since ∼ 7% of the targets in Wright et al. (2004) have not been observed over the full 5 year baseline used in this analysis. For more details about the sample sizes, observational durations, selection criteria and sensitivities of the 8 surveys see Table 3.1.

4-3 Close Companion Detection

The companions to the above Sun-like sample of host stars have primarily been detected using the Doppler technique (but not exclusively high precision exoplanet Doppler surveys) with some of the stellar pairs also being detected as astrometric 4-3. Close Companion Detection 80 or visual binaries. Thus we need to consider the selection effects of the Doppler method in order to define a less-biased sample of companions (see Section 3-2.1). As a consequence of the exoplanet surveys’ limited monitoring duration we select only those companions with an orbital period P < 5 years. To reduce the selection effect due to the Doppler sensitivity we also limit our less-biased sample to companions of mass M2 > 0.001M . See Section 4-3.2 for a discussion on estimating the mass M from the Doppler detectable minimum mass Msini.

Fig. 4.5 shows all of the Doppler companions to the Sun-like 25 pc and 50 pc samples within the mass and period range considered here. Our less-biased companions are enclosed by the thick solid rectangle. Given a ﬁxed number of targets, the “Detected” region should contain all companions that will be found for this region of mass-period space. The “Being Detected” region should contain some but not all companions that will be found in this region and the “Not Detected” region contains no companions since the current Doppler surveys are either not sensitive enough or have not been observing for a long enough duration. To avoid the incomplete “Being Detected” region, we limit our sample of companions to M2 >

0.001M . In Section 3-2.1 we describe a crude method for making a completeness correction for the lower right corner of the solid rectangle falling within the “Being Detected” region. The result for the d < 25 pc sample is a one planet correction to the lowest mass bin and for the d < 50 pc sample, a six planet correction to the lowest mass bin (see Table 4.1 - footnote c).

The companions in Fig. 4.5 all have radial velocity (Doppler) solutions. Some of the companions also have additional photometric, interferometric, astrometric or visual solutions. The exoplanet Doppler orbits are taken from the Extrasolar Planets Catalog (Schneider 2005). Only the planet orbiting the star HIP 108859 (HD 209458) has an additional photometric solution but this companion falls outside our less-biased region (M2 < MJup). For the stellar companion data, the single- lined (SB1) and double-lined (SB2) spectroscopic binary orbits are primarily from the Ninth Catalogue of Spectroscopic Binary Orbits (Pourbaix et al. 2004) with additional interferometric, astrometric or visual solutions from the 6th Catalog of 4-3. Close Companion Detection 81

Figure 4.5. Estimated companion mass M2 versus orbital period for the companions to Sun-like stars of our two samples: companions with hosts closer than 25 pc (large symbols) and those with hosts closer than 50 pc, excluding those closer than 25 pc (small symbols). The companions in the thick solid rectangle are deﬁned by

−3 < periods P < 5 years, and masses 10 < M2 ∼ M , and form our less-biased sample of companions. The stellar (open circles), brown dwarf (grey circles) and planetary (ﬁlled circles) companions are separated by dashed lines at the hydrogen and deuterium burning onset masses of 80 MJup and 13 MJup respectively. This plot clearly shows the brown dwarf desert for the P < 5 year companions. The companion mass estimates are derived from M2sini measurements corrected for inclination as shown in Section 4-3.2. 4-3. Close Companion Detection 82

Orbits of Visual Binary Stars (Washington Double Star Catalog, Hartkopf & Mason 2004). Many additional SB1s come from Halbwachs et al. (2003). Stellar binaries and orbital solutions also come from Endl et al. (2004); Halbwachs et al. (2000); Mazeh et al. (2003); Tinney et al. (2001); Jones et al. (2002a); Vogt et al. (2002); Zucker & Mazeh (2001a).

4-3.1 Inclination Distribution

We examine the inclination distribution for the 30 Doppler companions (d < 50 pc) with an astrometric or visual solution. We ﬁnd that 24 of these 30 companions have a minimum mass larger than 80MJup (Doppler stellar candidates) and that 6 of these

30 companions have a minimum mass between 13MJup and 80MJup (Doppler brown dwarf candidates). These 6 Doppler brown dwarf candidates with an astrometric solution are a subset of the 16 Doppler brown dwarf candidates in the far sample. They have an astrometric orbit derived with a conﬁdence level greater than 95% from Hipparcos measurements (Halbwachs et al. 2000; Zucker & Mazeh 2001a) and are thus assumed to have an astrometric orbit.

As shown in Fig. 4.6, the inclination distribution is approximately random for the 24 companions with a minimum mass in the stellar regime whereas it is biased towards low inclinations for the 6 companions in the brown dwarf regime. All 6 of the Doppler brown dwarf candidates with an astrometric determination of their inclination have a true mass in the stellar regime. This includes all 3 of the Doppler brown dwarf candidates that are companions to stars in our close sample (d < 25 pc) thus leaving an empty brown dwarf regime.

Also shown in Fig. 4.6, is the distribution of the maximum values of sini that would put the true masses of the remaining 10 Doppler brown dwarf candidates with unknown inclinations in the stellar regime. This distribution is substantially less- biased than the observed sini distribution, strongly suggesting that the remaining 10 Doppler brown dwarf candidates will also have masses in the stellar regime. Thus astrometric corrections leave us with no solid candidates with masses in the brown 4-3. Close Companion Detection 83

Figure 4.6. Astrometric inclination distribution for close companions (d < 50 pc) with a minimum mass larger than 80MJup (Doppler stellar candidates - Top) and between 13MJup and 80MJup (Doppler brown dwarf candidates - Bottom). The inclination distribution is approximately random for companions with a minimum mass in the stellar regime whereas it is biased towards low inclinations for companions in the brown dwarf regime. All 6 astrometric determinations of sini for brown dwarf candidates put their true mass in the stellar regime. See Section 4-3.1 for a discussion on estimating the true mass of the brown dwarf candidates with unknown inclinations. 4-3. Close Companion Detection 84 dwarf regime from the 16 Doppler brown dwarf candidates in the far sample (d < 50 pc), consistent with the result obtained for the close sample.

Two weak brown dwarf candidates are worth mentioning. HD 114762 has a minimum mass below 13MJup. However, to convert minimum mass to mass, we have assumed random inclinations and have used hsinii ≈ 0.785. This conversion

> puts the estimated mass of HD 114762 in the brown dwarf regime (M2 ∼ 13MJup). In Fig. 4.5, this is the only companion lying in the brown dwarf regime. Another weak brown dwarf candidate is the only candidate that requires a sini < 0.2 to place its mass in the stellar regime.

4-3.2 Companion Mass Estimates

The Doppler method for companion detection cannot give us the mass of a companion without some additional astrometric or visual solution for the system or by making certain assumptions about the unknown inclination except in the case where a host star and its stellar companion have approximately equal masses and a double-lined solution is available. Thus to ﬁnd the companion mass M2 that induces a radial velocity K1 in a host star of mass M1 we use (see Heacox 1999)

1/3 2πG M2sini 1 K1 = ( ) 2/3 1/2 (4.1) P (M1 + M2) (1 − e2) This equation can be expressed in terms of the mass function f(M)

3 3 3 2 3/2 M2 sin (i) PK1 (1 − e ) f(M) = 2 = (4.2) (M1 + M2) 2πG Eq. 4.2 can then be expressed in terms of a cubic equation in the mass ratio q = M2/M1, where Y = f(M)/M1.

q3sin3(i) − Y q2 − 2Y q − Y = 0 (4.3)

For planets (M1 >> M2) we can simplify Eq. 4.2 and directly solve for M2sini but this is not true for larger mass companions such as brown dwarfs and stars. We use 4-3. Close Companion Detection 85

Cox (2000) to relate host mass to spectral type. When a double-lined solution is available, the companion mass can be found from q = M2/M1 = K1/K2 where K2 is the induced radial velocity in the companion mass.

For all single-lined Doppler solutions, where the inclination i of a companion’s orbit is unknown (no astrometric or visual solution), we assume a random distribution P (i) for the orientation of the orbit with respect to our line of sight,

P (i)di = sin(i)di (4.4)

From this we can ﬁnd probability distributions for sini and sin3(i). Heacox (1995) and others suggest using either the Richardson-Lucy or Mazeh-Goldberg algorithms to approximate the inclination distribution. However, Hogeveen (1991) and Trimble (1990) argue that for low number statistics, the simple mean method produces similar results to the more complicated methods. We have large bin sizes and small number statistics, hence we use this method. The average values of the sini and sin3(i) distributions assuming a random inclination are hsinii = 0.785 and hsin3(i)i = 0.589, which are used to estimate the mass for planets and other larger single- lined spectroscopic binaries respectively. For example, in Fig. 4.5, of the 198 mass estimates in the 50 pc sample, 53 (27%) come from visual double-lined Doppler solutions, 6 (3%) come from infrared double-lined Doppler solutions (Mazeh et al. 2003), 18 (9%) come from knowing the inclination (astrometric or visual solution also available for system), 10 (5%) come from assuming that Doppler brown dwarf candidates have low inclinations, 55 (28%) come from assuming hsinii = 0.785 and 56 (28%) from assuming hsin3(i)i = 0.589.

4-3.3 Companion Completeness

The size of the 25 pc and 50 pc samples, the extent to which they are being targeted for planets, and the number and types of companions found along with any associated corrections are summarised in Table 4.1. For the stars closer than 25 pc, 59 have companions in the less-biased region (rectangle circumscribed by thick line) of 4-3. Close Companion Detection 86

Fig. 4.5. Of these, 19 are exoplanets, 0 are brown dwarfs and 40 are of stellar mass. Of the stellar companions, 25 are SB1s and 15 are SB2s. For the stars closer than 50 pc, 198 have companions in the less-biased region. Of these, 54 are exoplanets, 1 is a brown dwarf and 143 are stars. Of the stellar companions, 90 are SB1s and 53 are SB2s.

We ﬁnd an asymmetry in the north/south declination distribution of the Sun-like stars with companions, probably due to undetected or unpublished stellar companions in the south. The number of hosts closer than 25 pc with planetary or brown dwarf companions are symmetric in north/south declination to within one sigma Poisson error bars, but because more follow up work has been done in the north, more of the hosts with stellar companions with orbital solutions are in the northern hemisphere (30) compared with the southern (10). A comparison of our northern sample of hosts with stellar companions to the similarly selected approximately complete sample of Halbwachs et al. (2003) indicates that our 25 pc northern sample of hosts with stellar companions is also approximately complete. Under this assumption, the number of stellar companions missing from the south can be estimated by making a minimal correction up to the one sigma error level below the expected number, based on the northern follow up results. Of the 464 Sun-like stars closer than 25 pc, 211 have a southern declination (Dec < 0◦) and 253 have a northern declination (Dec ≥ 0◦) and thus ∼ 25(25/211 ≈ 30/253) stars in the south should have a stellar companion when fully corrected or 20 if we make a minimal correction. Thus we estimate that we are missing at least ∼ 10(= 20 − 10) stellar companions in the south, 7 of which have been detected by Jones et al. (2002a) under the plau- sible assumption that the orbital periods of the companions detected by Jones et al. (2002a) are less than 5 years. Although these 7 SB1 stellar companions detected by Jones et al. (2002a) have as yet no published orbital solutions, we assume that the SB1 stellar companions detected by Jones et al. (2002a) have P < 5 years since they have been observed as part of the high Doppler precision program at the Anglo- Australian Observatory (started in 1998) for a duration of less than 5 years before being announced. The additional estimated stellar companions are assumed to have 4-3. Close Companion Detection 87 the same mass distribution as the other stellar companions.

We can similarly correct the declination asymmetry in the sample of Sun-like stars closer than 50 pc. We ﬁnd that there should be, after a minimal correction, an additional 55 stars that are stellar companion hosts in the southern hemisphere. 14 of these 55 stellar companions are assumed to have been detected by Jones et al. (2002a). An asymmetry found in the planetary companion fraction in the 50 pc sample due to the much larger number of stars being monitored less intensively for exoplanets in the south (∼ 2% = 33/1525) compared to the north (∼ 4% = 21/476) results in a correction of 19 planetary companions in the south. The results given in Table 5.1 are done both with and without the asymmetry corrections.

Unlike the 25 pc sample, for which we are conﬁdent that the small corrections made to the number of companions will result in a reliable estimate of a census, correcting the 50 pc sample for the large number of missing companions is less reliable. This is so because if it were complete, the 50 pc sample would have approximately 8 times the number of companions as the 25 pc sample, since the 50 pc sample has 8 times the volume of the 25 pc sample. However, the incomplete 50 pc sample has only ∼ 7(= 3296/464) times the number of Hipparcos stars, ∼ 5(= 2001/384) times as many exoplanet targets and ∼ 3 times as many companions as the 25 pc sample. Thus rather than correcting both planetary and stellar companions by large amounts we show in Section 3 that the relative number and distribution of the observed planetary and stellar companions (plus a small completeness correction for the “Being Detected” region of 6 planets and an additional 14 probable stellar companions from Jones et al. (2002a) - see Table 4.1) remains approximately unchanged when compared to the corrected companion distribution of the 25 pc sample. Anal- yses both with and without a correction for the north/south asymmetry produce similar results for the brown dwarf desert (Table 5.1). 4-3. Close Companion Detection 88 ) d ). 4-3 g g ( 2002a g g g g Jones et al. 2 (1) 15 (8) 13 (7) 12 (2) 53 (12) 41 (10) g g g g g g Jones et al. -- -- Completeness correction in Stars ) 90 (18) ) 27 (7) f c f )) 25 (9) 8 (3) f f ). ,+41 ,+3 ,+3 ,+41 e e e e - - 4-3.1 Total SB1 SB2 143 (+14 h 0 39 (+14 Companions ) 1 ) 0 40 (+7 f d f ,+4 ,+19 c c 9 0 30 17 (6) 10 0 10 (+7 21 1 104 63 (11) 22 - 58 - is unknown (see Section i 33 (+19) 19 (+1 Total of corrections c through to f. 54 (+6 b b b b b = 0 . 785 when Sample, Doppler Targets and Detected Companions h sin i a Number of these spectroscopic binaries with an additional astrometric or visual solution g ). Table 4.1. 4-3.3 Number % Correction for north/south declination asymmetry in companion fraction after correcting for f Result from assuming 211253 211 173 100% 20 (+10) 68% 39 16471649 1525 93% 476 72 (+74) 29% 126 Correction based on the most likely scenario that the southern stellar companions from h Number Target Total Planets BDs e ). ). 5 years. ◦ ◦ ◦ ◦ 0 0 0 0 < 4-3.2 < < ≥ ≥ 4-2.2 25 pc 1509 62750 pc 42% 6924 - 2351 34% - Sample Hipparcos Doppler Sun-like 464 384 83% 59 (+15) Sun-like 3296 2001 61% 198 (+80) ) detections (see Section Dec Dec Dec Dec d < d < Percentage of Hipparcos stars that are Doppler targets. a Renormalisation for planetary target population (384)in being Section less than stellar companion mother population (464) (see discussion have periods (see Section ( 2002a the lowest mass bin for the lower right corner of our sample in Fig. 5 lying in the “Being Detected” region (see Section 4-4. Orbital Properties 89

4-4 Orbital Properties

4-4.1 Period

The period distribution for close companions is shown in Fig. 4.7 for both the close (d < 25 pc) and far (d < 50 pc) samples. Fig. 4.7 is a projection of Fig. 4.5 onto the period axis. In Section 4-3.1 we show that the Doppler brown dwarf candidates only have a minimum mass in the brown dwarf regime and a probable true mass in the stellar regime. This eﬀectively empties the brown dwarf region, leaving just stellar and planetary companions.

Both stellar and planetary companions are more frequent at larger periods than at shorter periods as shown in Fig. 4.7. However planets are more abundant at longer periods than are stellar companions. The Doppler planet detection method is not biased against short period planets. This would be a selection effect with no significance if the efficiency of finding short period stellar companions with the low precision Doppler technique used to find spectroscopic binaries, was much higher than the efficiency of finding exoplanets with high precision spectroscopy. Konacki et al. (2004) and Pont et al. (2004) conclude that the fact that the transit photometry method has found planets in sub 2.5 day periods (while the Doppler method has found none) is due to higher efficiency for small periods and many more target stars and thus that these two observations do not conflict. Thus there seems to be a real difference in the period distributions of stellar and planetary companions.

Low mass stellar companions (M ∼< 0.3M ) appear to be under-abundant at very short periods (P ∼< 10 days) compared to higher mass stellar companions as shown in Fig. 4.5.

4-4.2 Eccentricity

The eccentricity distribution for close companions is shown in Fig. 4.8 for both the close (d < 25 pc) and far (d < 50 pc) samples. At short periods, detectability is reduced for eccentric orbits, mainly due to the sparse sampling of the periastron 4-4. Orbital Properties 90

Figure 4.7. Period distribution of close companions for the 25 pc (dark grey) and 50 pc (light grey) samples. Planets are more abundant at longer periods than are stellar companions. The Doppler planet detection method is not biased against short period planets. The Doppler stellar companion detections are not signiﬁcantly biased for shorter periods or against longer periods in our samples analysis range (period < 5 years) since Doppler instruments of much lower precision than those used to detect exoplanets are able to detect any Doppler companions of stellar mass. Thus this represents a real diﬀerence in period distributions. 4-4. Orbital Properties 91

Figure 4.8. Eccentricity distribution of close companions for the 25 pc (dark grey) and 50 pc (light grey) samples. Both planetary and stellar companions have distributions that decrease towards higher eccentricity. The Doppler stellar companion detections should be largely unbiased towards eccentricity but the Doppler planetary companion detections may be biased against eccentric orbits. We find a difference in the starting point of the decrease, with stellar companions having a significant difference between the lowest two eccentricity bins whereas the planetary companions are statistically the same. Thus there seems to be a real difference in the eccentricity distributions of lower eccentricity stellar and planetary companions. 4-4. Orbital Properties 92

passage. This lost sensitivity at short orbital periods can be recovered for e ∼< 0.6, but there remain signiﬁcant selection eﬀects against eccentric orbits for extrasolar planets with e ∼> 0.6 (Cumming 2004). This is may be shown in Fig. 4.8 by the small number of highly eccentric planets discovered so far.

The stellar companions in our samples have been detected using instruments with a large range in precision, potentially introducing an eccentricity bias against the lower mass stellar companions. However, generally as stellar companion mass or Doppler detectability decreases, instrument sensitivity increases, thus providing evidence against an eccentricity bias, i.e., the higher stellar companion masses were typically detected using the lowest precision instruments (e.g. SB2s that are not monitored by the high precision Doppler surveys). Additionally the very short period stellar and planetary companions will be tidally circularised increasing their detectability. Thus a selection eﬀect against high eccentricity should be minimal for the stellar companions.

In Fig. 4.8 we find that both stellar and planetary companions are more frequent at low eccentricities and that both stellar and planetary companions become increasingly less frequent as eccentricity increases. For the stellar companion distribution the lowest eccentricity bin has significantly more stellar companions than the next lowest bin, but for the planetary companions both the lowest eccentricity bins contain similar numbers of planetary companions with the difference insignificant for Poisson statistics. Thus the eccentricity distribution for stellar companions appears to decrease at a lower eccentricity than that for planetary companions even before we consider that the bins of higher eccentricity for the extrasolar planet distribution may be empty because of the reduced detectability selection effect. Hence we find a real difference between the eccentricity distribution of stellar and planetary companions. 4-5. Summary 93

4-5 Summary

The period and eccentricitry distributions of close-orbiting (P < 5 years) companion stars are diﬀerent from that of the planetary companions. The close-in stellar companions are fairly evenly distributed over log P with planets tending to be more abundant at longer periods. While both stellar and planetary companions are more frequent at lower eccentricities, the decrease in the eccentricity distribution towards higher eccentricities appears to occur sooner for stellar companions compared to planetary companions.

The period and eccentricity distributions of close-orbiting companions may be more a result of post-formation migration and gravitational jostling than representive of the relative number of companions that are formed at a speciﬁc distance and with a speciﬁc eccentricity from their hosts. The companion mass distribution is more fundamental than the period and eccentricity distributions and should provide better constraints on formation models, but our ability to sample the mass distribution is only for P < 5 years. Chapter 5

The Brown-Dwarf Desert

In Chapter 4 we deﬁned a less-biased sample of Sun-like stars from which we extracted the stellar, brown dwarf and planetary companions. We also examined the period and eccentricity distribution of this close companion sample. In this Chapter we examine the close companion mass distribution.

We verify the existence of a very dry brown-dwarf desert and describe it quantitatively. With decreasing mass, the companion mass function drops by almost two orders of magnitude from 1 M stellar companions to the brown dwarf desert and then rises by more than an order of magnitude from brown dwarfs to Jupiter-mass planets. The slopes of the planetary and stellar companion mass functions are of opposite sign and are incompatible at the 3 sigma level, thus yielding a brown-dwarf desert. The minimum number of companions per unit interval in log mass (the +25 driest part of the desert) is at M = 31 −18 MJup. Approximately 16% of Sun-like stars have close (P < 5 years) companions more massive than Jupiter: 11% 3% are stellar, < 1% are brown dwarf and 5% 2% are giant planets.

Linear fits to the companion mass function marginally suggest that the driest part of the desert scales with host mass and we predict a Jupiter-mass desert and a stellar companion desert for hosts of mass < 0.5 M and > 2 M respectively. However, we find no evidence that companion mass scales with host mass in general. The steep decline in the number of companions in the brown dwarf regime, 5-1. Companion Mass Function 95 compared to the initial mass function of individual stars and free-floating brown dwarfs, suggests either a different spectrum of gravitational fragmentation in the formation environment or post-formation migratory processes disinclined to leave brown dwarfs in close orbits.

This Chapter is based on work published in Grether & Lineweaver (2006) using close companion data available as of October 2005.

5-1 Companion Mass Function

The close-companion mass function to Sun-like stars clearly shows a brown-dwarf desert for both the 25 pc and the 50 pc samples as seen in Figs. 5.1 and 5.2 respectively. The numbers of both the planetary and stellar mass companions decrease toward the brown dwarf mass range. Both plots contain the detected Doppler companions, shown as the grey histogram, within our less-biased sample of companions

−3 (P < 5 years and M2 > 10 M , see Section 4-3). The white histogram contains our corrections to this less-biased sample and are discussed in Sections 4-2 and 4-3. We expect no other substantial biases to aﬀect the relative amplitudes of the stellar companions on the right-hand side (RHS) and the planetary companions on the left-hand side (LHS).

In Fig. 5.1, the corrected version of the less-biased sample, shown as the white histogram, includes an extra seven probable SB1 stars from (Jones et al. 2002a) (Table 5.2 - footnote e) and an extra three stars from an asymmetry in the host declination distribution (Table 5.2 - footnote f). The planetary mass companions are also renormalised to account for the small number of Hipparcos Sun-like stars that are not being Doppler monitored (21% renormalisation, Table 5.2 - footnote d) and a 1 planet correction for the undersampling of the lowest mass bin due to the overlap with the “Being Detected” region (Table 5.2 - footnote c). Fig. 5.2 contains most of these same corrections, apart from the asymmetry correction for the planetary and stellar companions discussed in Section 4-3.3 and shown in Table 5.2. 5-1. Companion Mass Function 96

Figure 5.1. Brown-dwarf desert in our close sample. Histogram of the companions to Sun-like stars closer than 25 pc plotted against mass. The grey histogram is made up of Doppler detected companions in our less-biased (P < 5 years and

−3 M > 10 M ) sample. The white histogram contains corrections as discussed in Section 5-1. The hatched histogram is the subset of detected companions to hosts that are not included on any of the exoplanet search target lists and hence shows the extent to which the exoplanet target lists are biased against the detection of stellar companions. We expect no other substantial biases to aﬀect the relative amplitudes of the stellar companions on the right-hand side (RHS) and the planetary companions on the left-hand side (LHS). The brown dwarf mass range is empty. 5-1. Companion Mass Function 97

Figure 5.2. Same as Fig. 5.1 but for the larger 50 pc sample renormalised to the size of the 25 pc sample. Fitting straight lines using a weighted least squares fit to the 3 bins on the LHS and RHS, gives us gradients of −9.1 2.9 and 24.1 4.7 respectively (solid lines). Hence the brown-dwarf desert is significant at more than the 3 sigma level. These LHS and RHS slopes agree to within about 1 sigma of those in Fig. 5.1. The ratio of the number of companions on the LHS to the RHS is also about the same for both samples. Hence the relative number and distribution of companions is approximately the same as in Fig. 5.1. The separate straight line +14 fits to the 3 bins on the LHS and RHS intersect at M = 43 −23MJup beneath the abscissa. 5-1. Companion Mass Function 98

The hatched histograms at large mass in Figs. 5.1 and 5.2, show the subset of the stellar companions that are not included in any of the exoplanet Doppler surveys. A large bias against stellar companions would have been present if we had only included companions found by the exoplanet surveys. For multiple companion systems, we select the most massive companion in our less-biased sample to represent the system. We put the few companions (3 in the 25 pc sample, 6 in the 50 pc sample) that have a mass slightly larger than 1M in the largest mass bin in the companion mass distributions.

5-1.1 Bestﬁt Trends

To aid in comparison we renormalise the mass distribution in Fig. 5.2 by comparing each bin in this figure with its corresponding bin in Fig. 5.1 and scaling the vertical axis of Fig. 5.2 so that the difference in height between the bins is on average a minimum. We find that the optimum renormalisation factor is 0.33.

Fitting straight lines using a weighted least squares method to the 3 bins on the left-hand side (LHS) and right-hand side (RHS) of the brown dwarf region of the mass histograms of Figs. 5.1 and 5.2, gives us gradients of −15.2 5.6 (LHS) and 22.08.8 (RHS) for the 25 pc sample and −9.12.9 (LHS) and 24.14.7 (RHS) for the 50 pc sample. Since the slopes have opposite signs, they form a valley which is the brown-dwarf desert. The presence of a valley between the negative and positive sloped lines is signiﬁcant at more than the 3 sigma level.

The ratio of the corrected number of companions in the less-biased sample on the LHS to the RHS along with their poisson error bars is (249)/(5013) = 0.480.22 with no companions in the middle 2 bins for the 25 pc sample. For the larger 50 pc sample the corrected less-biased LHS/RHS ratio is (6014)/(15722) = 0.380.10, with 1 brown dwarf companion in the middle 2 bins. Thus the LHS and RHS slopes agree to within about 1 sigma and so do the LHS/RHS ratios, indicating that the companion mass distribution for the larger 50 pc sample is not significantly different from the more complete 25 pc sample and that the relative fraction of planetary, 5-1. Companion Mass Function 99 brown dwarf and stellar companions is approximately the same. A comparison of the relative number of companions in each bin in Fig. 5.1 with its corresponding bin in Fig. 5.2 produces a bestfit of reduced χ2 = 1.9 with seven degrees of freedom.

To ﬁnd the driest part of the desert, we ﬁt separate straight lines to the 3 bins on either side of the brown dwarf desert (solid lines) in Figs. 5.1 and 5.2. The deepest part of the valley where the straight lines cross beneath the abscissa is at +25 +14 M = 31 −18MJup and M = 43 −23MJup for the 25 and 50 pc samples respectively. These results are summarised in Table 5.1. The driest part of the desert is virtually the same for both samples even though we see a bias in the stellar binarity fraction of the 50 pc sample (Fig. 4.3). We have done the analysis with and without the minimal declination asymmetry correction. The position of the brown dwarf minimum and the slopes are robust to this correction (see Table 5.1).

5-1.2 Companion Fractions

The smaller 25 pc Sun-like sample contains 464 stars with 16.0% 5.2% of these having companions in our corrected less-biased sample. Of these ∼ 16% with companions, 5.2% 1.9% are of planetary mass and 10.8% 2.9% are of stellar mass. None is of brown dwarf mass. This agrees with previous estimates of stellar binarity such as that found by Halbwachs et al. (2003) of 14% for a sample of G-dwarf companions with a slightly larger period range (P < 10 years). The planet fraction agrees with the fraction 4% 1% (see Table 3.4) found in Chapter 3 when most of the known exoplanets are considered.

The 50 pc sample has a large incompleteness due to the lower fraction of monitored stars (Fig. 4.4) but as shown in Section 5-1.1, the relative number of companion planets, brown dwarfs and stars is approximately the same as for the 25 pc sample. The 50 pc sample has a total companion fraction of 15.6% 2.8%, where +0.2 4.3% 1.0% of the companions are of planetary mass, 0.1−0.1% are of brown dwarf mass and 11.2% 1.6% are of stellar mass. Table 5.2 summarises these companion fractions. 5-1. Companion Mass Function 100 a ) +25 − 18 +25 − 17 +15 − 24 +14 − 23 +17 − 9 +9 − 23 +28 − 26 +21 − 21 Jup ( M 8 . 31 4 . 7 43 4 . 6 44 8 . 5 30 11 . 4 39 10 . 7 18 10 . 9 50 10 . 4 45 5 . 6 22 . 0 5 . 4 19 . 4 9 . 2 20 . 0 8 . 2 21 . 1 5 . 6 20 . 7 5 . 1 25 . 2 2 . 9 24 . 1 3 . 0 24 . 3 − 5 . 9 − 9 . 1 − 9 . 4 − 15 . 2 − 17 . 5 − 12 . 4 − 12 . 2 − 15 . 2 5.1 5.3 5.3 5.4 5.4 5.2 No No No No Yes Yes Yes Yes Correction Asymmetry Figure LHS slope RHS slope Slope Minima

Companion Slopes and Companion Desert Mass Minima 1 M 1 M 1 M 1 M < < ≥ ≥ 1 1 1 1 M M M M Table 5.1. 25 pc 25 pc 50 pc 50 pc 25 pc and 50 pc and 25 pc and 50 pc and Sample d < d < d < d < d < d < d < d < values of mass where the best-ﬁtting lines, to the LHS and RHS, intersect. The errors given are from the range between the a two intersections with the abscissa. 5-1. Companion Mass Function 101 2 . 9 2 . 7 1 . 6 1 . 6 3 . 5 3 . 9 3 . 5 3 . 4 9 . 4 9 . 4 10 . 8 10 . 1 11 . 1 11 . 2 11 . 8 12 . 8 +0 . 4 − 0 . +0 . 4 − 0 . +0 . 2 − 0 . 1 +0 . 2 − 0 . 1 +0 . 4 − 0 . +0 . 4 − 0 . 2 +0 . 4 − 0 . +0 . 4 − 0 . 1 . 9 0 . 1 . 9 0 . 3 . 1 0 . 1 . 0 0 . 1 1 . 7 0 . 2 2 . 9 0 . 1 . 9 0 . 1 . 0 0 . 1 5 . 2 5 . 2 5 . 8 4 . 2 7 . 0 6 . 2 . 8 4 . 3 6 . 0 2 . 6 6 . 7 6 . 2 5 . 0 5 . 2 2 . 8 4 . (%) (%) (%) (%) 16 . 0 16 . 0 16 . 0 15 . 6 15 . 6 15 . 6 15 . 3 15 . 6 5.1 5.3 5.3 5.2 5.4 5.4 Companion Fraction Comparison No No No No Yes Yes Yes Yes Correction Asymmetry Figure Total Planetary Brown Dwarf Stellar Table 5.2.

1 M 1 M 1 M 1 M < < ≥ ≥ 1 1 1 1 M M M M 25 pc 50 pc 50 pc and 50 pc and 25 pc 50 pc 25 pc and 25 pc and d < d < d < d < Sample d < d < d < d < 5-1. Companion Mass Function 102

Surveys of the multiplicity of nearby Sun-like stars yield the relative numbers of single, double and multiple star systems. According to Duquennoy & Mayor (1991), 51% of star systems are single stars, 40% are double star systems, 7% are triple and 2% are quadruple or more. Of the 49%(= 40 + 7 + 2) which are stellar binaries or multiple star systems, 11% have stellar companions with periods less than 5 years and thus we can infer that the remaining 38% have stellar companions with P > 5 years. Among the 51% without stellar companions, we ﬁnd that ∼ 5% have close

(P < 5 years) planetary companions with 1 < M/MJup < 13, while < 1% have close brown dwarfs companions.

5-1.3 Comparison with Other Results

Although there are some similarities, the companion mass functions found by Heacox (1999); Zucker & Mazeh (2001b); Mazeh et al. (2003) are generally flatter for both planetary and stellar companions from that shown in Figs. 5.1 and 5.2. Our approach was to normalise the companion numbers to a well-defined sub-sample of Hipparcos stars whereas these authors use two different samples of stars, one to find the planetary companion mass function and another to find the stellar companion mass function, which are then normalised to each other. The different host star properties and levels of completeness of the two samples may make this method more prone than our method, to biases in the frequencies of companions.

Both Heacox (1999) and Zucker & Mazeh (2001b) combined the companions of the stellar mass sample of Duquennoy & Mayor (1991) with the known substellar companions, but identified different mass functions for the planetary mass regime below 10 MJup and similar flat distributions in logarithmic mass for brown dwarf and stellar mass companions. Heacox (1999) found that the logarithmic mass function in the planetary regime is best fit by a power-law (dN/d log M ∝ M Γ) with index Γ between 0 and -1 whereas Zucker & Mazeh (2001b) find an approximately flat distribution (power-law with index 0). Our work here and in Section 3-3 suggests that neither the stellar nor the planetary companion distributions are flat (Γ = 5-2. Companion Mass as a Function of Host Mass 103

−0.8). Rather, they both slope down towards the brown-dwarf desert, more in agreement with the results of Heacox (1999).

The work most similar to ours is probably (Mazeh et al. 2003) who looked at a sample of main sequence stars with primaries in the range 0.6 − 0.85 M and P < 3000 days using infrared spectroscopy and combined them with the known substellar companions of these main sequence stars and found that in logarithmic mass the stellar companions reduce in number towards the brown dwarf mass range. This agrees with our results for the shape of the stellar mass companion function. However, they identify a ﬂat distribution for the planetary mass companions in contrast to our non-zero slope (see Table 5.1). Mazeh et al. (2003) found the frequency of stellar and planetary companions (M > 1 MJup) to be 15% (for stars below 0.7 M ) and 3% respectively. This compares with our estimates of 8% (for stars below 0.7 M ) and 5%. The larger period range used by Mazeh et al. (2003) can account for the diﬀerence in stellar companion fractions.

5-2 Companion Mass as a Function of Host Mass

We split the 25 and 50 pc samples into companions to hosts with masses above and below 1 M (Figs. 5.3 and 5.4) and scale these smaller samples to the size of the full 25 and 50 pc samples (Figs. 5.1 and 5.2) respectively. As seen in Figs. 5.3 and 5.4, lower mass hosts have more stellar companions and fewer giant planet companions while higher mass hosts have fewer stellar companions and more giant planet companions.

The Doppler method should preferentially ﬁnd planets around lower mass stars where a greater radial velocity is induced. This is the opposite of what is observed. The Doppler technique is also a function of B − V colour (Saar et al. 1998) with the level of systematic errors in the radial velocity measurements, decreasing as we move from high mass to low mass (B − V = 0.5 to B − V = 1.0) through our two samples, peaking for late K spectral type stars before increasing for the lowest mass M type stars again. Hence again ﬁnding planets around the lower mass stars (early 5-2. Companion Mass as a Function of Host Mass 104

K spectral type) in our sample should be easier.

We ﬁnd that the minimum of the companion mass desert is a function of host mass with lower mass hosts having a lower companion mass desert. We plot the linear slope minima (intersections) of the lower and higher mass samples of the 0 < d < 25 pc and 25 < d < 50 pc samples together with the corresponding average host mass for these 4 samples as 4 crosses in Fig. 5.5. The squares represent the linear slope minima of the lower and higher mass samples of the complete 0 < d < 50 pc sample. The linear best-ﬁt to these crosses (thick line) shows the driest part of the companion mass distribution as a function of host mass and can be described by:

1.81.8 MHost MDriest ≈ 40 MJup (5.1) M ! Thus, for hosts of half a solar mass, the short period (P < 5 years) desert minimum would be for 10 MJup objects – a “Jupiter Desert”, and for 2 solar mass hosts, the short period desert minimum would be for 140 MJup objects – a low mass “Stellar Desert”. Both of these “deserts” are outside the brown dwarf mass regime as shown in Fig. 5.5. A speculative extrapolation of this trend by an additional factor of ﬁve down to small M dwarf hosts (0.1 M ) suggests that the minimum of the short period desert would occur well into the planetary regime at 0.6 MJup. However there seems to be no theoretical backing for such an extrapolation.

Although our claim that the location of the brown-dwarf desert is a function of host star mass is marginal, Gizis et al. (2003) find a larger abundance of brown dwarfs orbiting M dwarfs compared to FGK dwarfs and Bonfils et al. (2005) find that close exoplanets are smaller and rarer around M dwarfs than around FGK dwarfs. We find no evidence against our proposed stellar desert for higher mass hosts from the small number of additional stellar companions to larger mass Hip- parcos main sequence hosts from the Ninth Catalogue of Spectroscopic Binary Orbits

(Pourbaix et al. 2004) closer than 25 pc. The mass ratio q(= M2/M1) distribution should also show a drop in frequency at q < 0.1 for higher mass hosts where we pro- 5-2. Companion Mass as a Function of Host Mass 105

Figure 5.3. Same as Fig. 5.1 but for the 25 pc sample split into companions to lower mass hosts (M1 < 1M ) and companions to higher mass hosts (M1 ≥ 1M ). The lower mass hosts have 4.2% planetary, 0.0% brown dwarf and 11.8% stellar companions. The higher mass hosts have 6.6% planetary, 0.0% brown dwarf and 9.4% stellar companions. The Doppler method should preferentially ﬁnd planets around lower mass stars where a greater radial velocity is induced. This is the opposite of what we observe. To aid comparison, both samples are scaled such that they contain the same number of companions as the full corrected less-biased 25 pc sample of Fig. 5.1. 5-2. Companion Mass as a Function of Host Mass 106

Figure 5.4. Same as Fig. 5.2 but for the 50 pc sample split into companions to lower mass hosts (M1 < 1M ) and companions to higher mass hosts (M1 ≥ 1M ). Both samples are scaled such that they contain the same number of companions as the corrected less-biased 50 pc sample of Fig. 5.2. Also shown are the linear best-ﬁts to the planetary and stellar companions of the two populations. 5-2. Companion Mass as a Function of Host Mass 107

Figure 5.5. We ﬁnd the average companion mass (triangles) for each of the four host mass bins for stellar and planetary companions in our Sun-like 50 pc sample (large dots are closer than 25 pc and smaller dots are between 25 and 50 pc) to investigate any host-mass/companion-mass correlation. The companion mass appears uncorrelated with host mass for either stellar or planetary companions. The grey histogram of host masses is also shown. The 4 crosses represent the linear slope minima of the lower and higher mass sub-samples of the 0 < d < 25 pc and 25 < d < 50 pc samples together with their corresponding average host masses. The squares represent the linear slope minima of the lower and higher mass samples of the d < 50 pc sample. The linear best-ﬁt to these crosses (thick line) shows the driest part of the companion mass distribution as a function of host mass. 5-3. Comparison with the Initial Mass Function 108 pose a low stellar companion mass desert. Halbwachs et al. (2003) observe a higher companion fraction at q < 0.4 for the less massive K spectral type host stars than for the more massive F7-G host stars.

Although the driest part of the companion mass desert appears to be a function of host mass we ﬁnd no evidence for a direct correlation between host mass and companion mass. This is shown in Fig. 5.5 by the distribution of the average mass for stellar and planetary companions for the 50 pc sample (triangles). The hashed region of stellar companions at the top of the ﬁgure is ignored in the analysis of the correlation between M1 and M2 to avoid introducing a bias.

5-3 Comparison with the Initial Mass Function

Brown dwarfs found as free-floating objects in the solar neighbourhood and as members of young star clusters have been used to extend the initial mass function (IMF) well into the brown dwarf regime. Comparing the mass function of our sample of close-orbiting companions of Sun-like stars to the IMF of single stars indicates how the environment of a host affects stellar and brown dwarf formation and/or migration. Here we quantify how different the companion mass function is from the IMF (Halbwachs et al. 2000).

The galactic IMF appears to be remarkably universal and independent of environment and metallicity with the possible exception of the substellar mass regime. A weak empirical trend with metallicity is suggested for very low mass stars and brown dwarfs where more metal rich environments may be producing relatively more low mass objects (Kroupa 2002). This is consistent with an extrapolation up in mass from the trend found in exoplanet hosts. The IMF is often represented as a power- law, although this only appears to be accurate for stars with masses above ∼ 1M (Hillenbrand 2004). The stellar IMF slope gets ﬂatter towards lower masses and extends smoothly and continously into the substellar mass regime where it appears to turn over. 5-3. Comparison with the Initial Mass Function 109

Free ﬂoating brown dwarfs may be formed either as ejected stellar embryos or from low mass protostellar cores that have lost their accretion envelopes due to photo- evaporation from the chance proximity of a nearby massive star (Kroupa & Bouvier 2003). This hypothesis may explain their occurence in relatively rich star clusters such as the Orion Nebula cluster and their virtual absence in pre-main sequence stellar groups such as Taurus-Auriga.

We compare the mass function of companions to Sun-like stars with the IMF of cluster stars in Figs. 5.6 and 5.7. The mass function for companions to Sun-like stars is shown by the green dots from Figs. 5.1 and 5.2 (bigger dots are the d < 25 pc sample and smaller dots are the d < 50 pc sample). For clarity the smaller green dots are shifted slightly to the right in Fig. 5.6. The linear slopes from Fig. 5.1 and their one sigma confidence region are also shown. The power-law fit for exoplanets derived in Section 3-3 and shown in Fig. 5.7 as the green dot with a horizontal line indicating the range over which the slope applies is consistent with these fits.

We ﬁnd that between log(M/M ) ≈ −1.0 and −0.5 (0.1M < M < 0.3M ) the slopes are similar for the mass function of companions to Sun-like stars compared with the IMF. However, above 0.3M and below 0.1M the slopes become inconsis- tent. Above 0.3M the slopes, while of similar magnitude are of opposite sign and below 0.1M the companion slope is much steeper than the IMF slope. The IMF for young clusters (yellow dots) is statistically indistinguishable from that of older stars (blue dots) and follows the average IMF.

In Fig. 5.6, data for the number of stars and brown dwarfs in the Orion Nebula Cluster (ONC) (circles), Pleiades cluster (triangles) and M35 cluster (squares) come from Hillenbrand & Carpenter (2000); Slesnick et al. (2004), Moraux et al. (2003) and Barrado y Navascu´eset al. (2001) respectively and are normalised such that they overlap for masses larger than 1M where a single power-law slope applies. The absolute normalisation of cluster stars is arbitrary, while the companion mass function is normalised to the IMF of the cluster stars by scaling the three companion points of stellar mass to be on average ∼ 7% for P < 5 years (derived from the stellar multiplicity of Duquennoy & Mayor (1991) discussed in Section 5-1.2, combined with 5-3. Comparison with the Initial Mass Function 110

Figure 5.6. The mass function of companions to Sun-like stars (lower left) compared to the initial mass function (IMF) of cluster stars (upper right). Our mass function of the companions to Sun-like stars is shown by the green dots (bigger dots are the d < 25 pc sample, smaller dots are the d < 50 pc sample). The linear slopes we fit to the data in Fig. 5.1 are also shown along with their error. The average power-law IMF is shown as larger red dots along with two thin red lines showing the error. If the turn down in the number of brown dwarfs of the IMF is due to a selection effect because it is hard to detect brown dwarfs, then the two distributions are even more different from each other. 5-3. Comparison with the Initial Mass Function 111

Figure 5.7. The initial mass function (IMF) for clusters represented by a series of power-law slopes (Hillenbrand 2004). Each point represents the power-law slope claimed to apply within the mass range indicated by the horizontal lines. Although the IMF is represented by a series of power-laws, the IMF is not a power-law for masses less than 1M where the slope continually changes. The green dots show the slope of the companion mass function to Sun-like stars between the bins of Figs. 5.1 & 5.2 with the larger and smaller dots respectively. The linear ﬁts to the data in Fig. 5.1 and their associated error are shown by the curves inside the grey regions. The larger red dots with error bars represent the average power-law IMF with a root-mean-square error. 5-4. Summary and Discussion 112 our estimate that 11% of Sun-like stars have stellar secondaries). The data for the average power-law IMF comes from various values of the slope of the IMF quoted in the literature (Hillenbrand 2004).

In Fig. 5.7, where we represent the IMF as a series of power-laws, Γ and −α are the respective logarithmic and linear slopes of the mass function. The logarithmic mass power-law distribution is dN/d log M ∝ M Γ and the linear mass power-law distribution is dN/dM ∝ M −α where Γ = 1 − α. Note that the errors on the ﬁts of

−3 Fig. 5.1 (green dots) get smaller in Fig. 5.7 at M ∼ 10 M and M ∼ 1 M since as log(M/M ) tends to ∞, Γ tends to 0. This can also be seen in Fig. 5.6 where the slopes of the upper and lower contours become increasingly similar.

5-4 Summary and Discussion

We analyse the close-orbiting (P < 5 years) planetary, brown dwarf and stellar companions to Sun-like stars to help constrain their formation and migration scenarios. We use the same sample to extract the relative numbers of planetary, brown dwarf and stellar companions and verify the existence of a brown-dwarf desert. Both planetary and stellar companions reduce in number towards the brown dwarf mass range. We ﬁt the companion mass function over the range that we analyse

(0.001 < M/M ∼< 1.0) by two separate straight lines ﬁt separately to the planetary and stellar data points. The straight lines intersect in the brown dwarf regime, at +25 M = 31 −18 MJup. This result is robust to the declination asymmetry correction (Table 5.1).

We find marginal evidence that the minimum of the companion mass desert is a function of host mass with lower mass hosts having a lower mass companion desert, but we find no evidence for a direct correlation between host mass and companion mass. We compare the companion mass function to the IMF for bodies in the brown dwarf and stellar regime. We find that starting at 1 M and decreasing in mass, stellar companions continue to reduce in number into the brown dwarf regime, while cluster stars increase in number before reaching a maximum just before the 5-4. Summary and Discussion 113 brown dwarf regime. This leads to a difference of at least 1.5 orders of magnitude between the much larger number of brown dwarfs found in clusters to those found as close-orbiting companions to Sun-like stars.

We show in Figs. 5.3 and 5.4 that lower mass hosts have more stellar companions and fewer giant planet companions while higher mass hosts have fewer stellar companions but more giant planet companions. The brown-dwarf desert is generally thought to exist at close separations ∼< 3 AU (or equivalently P ≤ 5 years) (Marcy & Butler 2000) but may disappear at wider separations. Gizis et al. (2001) suggests that at very large separations (> 1000 AU) brown dwarf companions may be more common. However, McCarthy & Zuckerman (2004) in their observation of 280 GKM stars ﬁnd only 1 brown dwarf between 75 and 1200 AU. Gizis et al. (2003) reports that 15% 5% of M/L dwarfs are brown dwarf binaries with separations in the range 1.6 − 16 AU. This falls to 5% 3% of M/L dwarfs with separations less than 1.6 AU and none with separations greater than 16 AU. This diﬀers greatly from the brown dwarfs orbiting Sun-like stars but is consistent with our host/minimum- companion-mass relationship, i.e., we expect no short period brown dwarf desert around M or L type stars.

Three systems containing both a companion with a minimum mass in the planetary regime and a companion with a minimum mass in the brown dwarf regime are known - HD 168443 (Marcy et al. 2001b), HD 202206 (Udry et al. 2002; Correia et al. 2005) and GJ 86 (Queloz et al. 2000; Els et al. 2001). Our analysis suggests that both the Msin(i)-brown dwarfs orbiting HD 168443 and HD 202206 are probably stars (see Section 4-3.1 for our false positive brown dwarf correction). If the Msini planetary companions in these 2 systems are coplanar with the larger companions then these “planets” may be brown dwarfs or even stars. GJ 86 contains a possible brown dwarf detected orbiting at ∼ 20 AU (P > 5 years) and so was not part of our analysis. However this does suggest that systems containing stars, brown dwarfs and planets may be possible.

We ﬁnd that approximately 16% of Sun-like stars have a close companion more massive than Jupiter. Of these 16%, 11%3% are stellar, < 1% are brown dwarf and 5-4. Summary and Discussion 114

5% 2% are planetary companions (Table 5.2). Although in Section 3-2.3 we show that the fraction of Sun-like stars with planets is greater than 25%, this is for target stars that have been monitored the longest (∼ 15 years) and at optimum conditions (stars with low-level chromospheric activity or slow rotation) using the high precision Doppler method. When we limit this analysis to planetary companions with periods of less than 5 years and masses larger than Jupiter, we ﬁnd the same value that we calculate here. When we split our sample of companions into those with hosts above and below 1M , we ﬁnd that for the lower mass hosts: 11.8% have stellar, < 1% have brown dwarf and 4.2% have planetary companions and that for the higher mass hosts: 9.4% have stellar, < 1% have brown dwarf and 6.6% have planetary companions respectively (Table 5.2). More massive hosts have more planets and fewer stellar companions than less massive hosts. These are marginal results but are seen in both the 25 and 50 pc samples.

The constraints that we have identified for the companions to Sun-like stars indicate that close orbiting brown dwarfs are very rare. The fact that there is a close-orbiting brown-dwarf desert but no free floating brown-dwarf desert suggests that post-collapse migration mechanisms may be responsible for this relative dearth of observable brown dwarfs rather than some intrinsic minimum in fragmentation and gravitational collapse in the brown dwarf mass regime (Ida & Lin 2004). What- ever migration mechanism is responsible for putting hot Jupiters in close orbits, its effectiveness may depend on the mass ratio of the object to the disk mass. Since there is evidence that disk mass is correlated to host mass, the migratory mechanism may be correlated to host mass, as proposed by Armitage & Bonnell (2002). Chapter 6

Metallicity of Stars with Close Companions

In this Chapter we examine the relationship between the frequency of close companions (stellar and planetary companions with orbital periods < 5 years) and the metallicity of their Sun-like (∼ FGK) hosts. We principally use the less-biased sample of stars with close companions deﬁned in Chapter 4 for this analysis.

We confirm and quantify a ∼ 4σ positive correlation between host metallicity and planetary companions. We find little or no dependence on spectral type or distance in this correlation. In contrast to the metallicity dependence of planetary companions, stellar companions tend to be more abundant around low metallicity hosts. At the ∼ 2σ level we find an anti-correlation between host metallicity and the presence of a stellar companion. Upon dividing our sample into FG and K sub-samples, we find a negligible anti-correlation in the FG sub-sample and a ∼ 3σ anti-correlation in the K sub-sample. A kinematic analysis suggests that this anti- correlation is produced by a combination of low-metallicity, high-binarity thick disk stars and higher-metallicity, lower-binarity thin disk stars.

This Chapter is based on work accepted for publication in Grether & Lineweaver (2007) using close companion data available as of October 2006. 6-1. Introduction 116

6-1 Introduction

With the detection to date of more than 160 exoplanets using the Doppler technique, the observation of Gonzalez (1997) that giant close–orbiting exoplanets have host stars with relatively high stellar metallicity compared to the average ﬁeld star has gotten stronger (Reid 2002; Santos et al. 2004b; Fischer & Valenti 2005; Bond et al. 2006). To understand the nature of this correlation between high host metallicity and the presence of Doppler-detectable exoplanets, we investigate whether this correlation extends to stellar mass companions.

There has been a widely held view that metal-poor stellar populations possess few stellar companions (Batten 1973; Latham et al. 1988; Latham 2004). This may have been largely due to the difficulty of finding binary stars in the galactic halo, e.g. Gunn & Griffin (1979). Duquennoy & Mayor (1991) investigated the properties of stellar companions amongst Sun-like stars but did not report a relationship between stellar companions and host metallicity. Latham et al. (2002) and Carney et al. (2005) reported a lower binarity for stars on retrograde Galactic orbits compared to stars on prograde Galactic orbits but found no dependence between binarity and metallicity within those two kinematic groups. Dall et al. (2005) speculated that the frequency of host stars with stellar companions may be correlated with metallicity in the same way that host stars with planets are.

In this paper we describe and characterize the correlation between host metallicity and the fraction of planetary and stellar companions. In Section 6-2 we define our sample of close planetary and stellar companions and we describe the variety of techniques used to obtain metallicities of stars that do not have spectroscopic metallicities from Doppler searches. In Section 6-3 we analyse the distribution of planetary and stellar companions as a function of host metallicity. We confirm and quantify the correlation between planet-hosts and high metallicity and we find a new anti-correlation between the frequency of stellar companions and high metallicity. In Section 6-4 we compare our stellar companion results to analogous analyses of the Nordströmet al. (2004) and Carney et al. (2005) samples. 6-2. The Sample 117

6-2 The Sample

We analyse the distribution of the metallicities of FGK main-sequence stars with close companions (period < 5 years). For this we use the sample of stars deﬁned in Chapter 4. This subset of ‘Sun-like’ stars in the Hipparcos catalog, is deﬁned by

0.5 ≤ B − V ≤ 1.0 and 5.4(B − V ) + 2.0 ≤ MV ≤ 5.4(B − V ) − 0.5. This forms a parallelogram -0.5 and 2.0 mag, below and above an average main-sequence in the HR diagram. The stars range in spectral type from approximately F7 to K3 and in absolute magnitude in V band from 2.2 to 7.4. From this we deﬁne a more complete closer (d < 25 pc) sample of stars and an independent more distant (25 < d < 50 pc) sample. See Chapter 4 for additional details about the sample deﬁnition. The stars in the close sample are tabulated in Appendix B.

6-2.1 Measuring Stellar Metallicity

The metallicity of most of the extrasolar planet hosts have been determined spectroscopically. We analyse the metallicity data from three of these groups: (1) the McDonald observatory (hereafter, McD) group (e.g. Gonzalez et al. 2001; Laws et al. 2003), (2) the European Southern Observatory (hereafter, ESO) group (e.g. Santos et al. 2004b, 2005), and (3) the Keck, Lick and Anglo-Australian observatory (hereafter, KLA) group (Fischer & Valenti 2005; Valenti & Fischer 2005).

All three of these groups find similar metallicities for the extrasolar planet target stars that they have all observed as shown by the comparisons in Fig. 6.1. The 59 red dots compare the ESO to the McD values of exoplanet target metallicity that these groups have in common. We find that the ESO values are on average 0.01 dex smaller than the McD values with a dispersion of 0.05 dex. Similarly the 99 green dots compare the KLA values to the average 0.01 dex smaller ESO values with a dispersion of 0.06 dex. The 56 blue dots compare the KLA to the average 0.01 dex larger McD values with a dispersion of 0.06 dex. A solid black line shows the slope-one line with dashed lines at 0.1 dex. The three linear best-fits for these three comparisons are nearly identical to the slope-one line and almost all scatter is 6-2. The Sample 118 contained within 0.1 dex as shown in Fig. 6.1.

Apart from the ∼ 1000 KLA target stars analysed with a consistently high precision by Valenti & Fischer (2005), many nearby (d < 50 pc) FGK stars lack precise metallicities if they have any published measurement at all. A smaller sample of precise spectroscopic metallicities has also been published by the ESO group for non-planet hosting stars (Santos et al. 2005).

Since the large sample of KLA stars has been taken from exoplanet target lists it also has the same biases. This includes selection eﬀects (i) against high stellar chromospheric activity (ii) towards more metal-rich stars that have a greater probability of being a planetary host and (iii) against most stars with known close (θ < 200) stellar companions. We need to correct for or minimise these biases to determine quantitatively not only how the planetary distribution varies with host metallicity but also how the close stellar companion distribution varies with host metallicity, that is, we need metallicities of all stars in our sample in order to compare companion-hosting stars to non-companion-hosting stars, and to compare the metallicities of planet–hosting stars to the metallicities of stellar–companion–hosting stars.

In addition to the metallicities reported by the McD, ESO and KLA groups, we use a variety of other sources and techniques to determine stellar metallicity although with somewhat less precision. These include other sources of spectroscopic metallicities such as the Cayrel de Strobel et al. (2001) (hereafter, CdS) catalog, metallicities derived from uvby narrow-band photometry or broad-band photometry and metallicities derived from a star’s position in the HR diagram. The precision of the spectroscopic metallicity values in the CdS catalog are not well quantiﬁed. However, many of the stars in the catalog have several independent metallicity values which we average, excluding obvious outliers. To derive metallicities from uvby narrow-band photometry, we apply the calibration of Martell & Smith (2004) to the Hauck & Mermilliod (1998) catalog. We also use values of metallicity derived from broad-band photometry in (Ammons et al. 2006). For stars with 5.5 < MV < 7.3 (K dwarfs) the relationship between stellar luminosity and metallicity is very tight 6-2. The Sample 119

(Kotoneva et al. 2002). Using this relationship, we derive metallicities for some K dwarfs from their position in the HR diagram.

To quantify the precision of their metallicities, we compare in Fig. 6.2 the different methods of determining metallicity. We use the high precision exoplanet target spectroscopic metallicities from the McD, ESO and KLA surveys (or the average when a star has two or more values) as the reference sample. We compare these metallicities with metallicities of the following test samples: (1) CdS spectroscopic metallicities, (2) uvby photometric metallicities, (3) broad-band photometric metallicities and (4) HR Diagram K dwarf metallicities. The mean differences between the test and the reference sample metallicities ([Fe/H]test − [Fe/H]ref ) are −0.05, −0.08, 0.01, and −0.10 dex respectively, with dispersions of 0.08, 0.11, 0.14 and 0.14 dex respectively. Comparing these mean differences and dispersions we find that the mean differences are within 1σ of the solid black slope-one line and thus we regard the systematic offsets as marginal. The four linear best-fits for these four comparisons (shown by the four coloured lines in Fig. 6.2) do not show significant deviation from the slope-one line (black) except for the metallicities derived using broad-band photometry (dark blue line).

The result of this comparison is that the uncertainties associated with the high quality exoplanet target spectroscopic metallicities of McD, ESO and KLA groups are the smallest, with the CdS spectroscopic metallicities only slightly more un- certain. The uncertainties associated with the uvby photometric metallicities are intermediate with broad-band photometric and HR diagram K dwarf metallicities being the least certain.

6-2.2 Selection Eﬀects and Completeness

To minimise the scatter in the measurement of stellar metallicity while including as many stars in our samples as possible, we choose the metallicity source from one of the ﬁve groups based upon minimal dispersion. Thus we primarily use the spectroscopic exoplanet target metallicities. If no such value for metallicity is available for a 6-2. The Sample 120

Figure 6.1. Exoplanet target stars metallicity comparison. We compare the spectroscopic exoplanet target metallicities of the McD, ESO and KLA groups. The relationship between the McD and ESO values is very close with a marginally looser relationship to the KLA values. These values for exoplanet target metallicity are consistent at the ∼ 0.1 dex level. 6-2. The Sample 121

Figure 6.2. Metallicity values from exoplanet spectroscopy compared to four other methods of obtaining stellar metallicities. We compare the exoplanet target spectroscopic metallicities (plotted on the x axis as a ‘reference’) with the following test samples plotted on the y axis: (1) CdS spectroscopic metallicities (red dots), (2) uvby photometric metallicities (green dots) (3) broad-band photometric metallicities (blue dots) and (4) HR diagram K dwarf metallicities (aqua dots). 6-2. The Sample 122 star in our sample we use a spectroscopic value taken from the CdS catalog, followed by a uvby photometric value, a broad-band value and lastly a HR diagram K dwarf value for the metallicity. We use the dispersions discussed above as estimates of the uncertainties of the metallicity measurements.

Almost all (453/464 = 98%) of the close (d < 25 pc) sample and 2745/2832 = 97% of the more distant (25 < d < 50 pc) sample thus have a value for metallicity. Given the diﬀerent uncertainties associated with the ﬁve sources of metallicity, the close sample has more precise values of metallicity than the more distant sample. The dispersion for the close and far sample are 0.07 and 0.10 dex respectively. See Table 6.1 for details.

We also investigate the colour or host mass dependence of the host metallicity distributions. Thus we split our close and far samples which are deﬁned by 0.5 ≤ B − V ≤ 1.0 into 2 groups, those with 0.5 ≤ B − V ≤ 0.75 which we call FG dwarfs and those with 0.75 < B − V ≤ 1.0 which we call K dwarfs. This split is shown in Table 6.1. In this table we also show the total number of stars in the sample that have a known value of metallicity and the fraction that are close binaries, exoplanet target stars and exoplanet hosts.

In order to determine whether there is a real physical correlation between the presence of stellar or planetary companions and host metallicity we need to show that there are only negligible selection eﬀects associated with the detection and measurement of these two quantities that could cause a spurious correlation. In Section 6-2.3 we show that the planetary companion fraction should be complete for planetary companions with periods less than 5 years for the sample of target stars that are being monitored for exoplanets. This completeness helps assure minimal spurious correlation between the probability of detecting planetary companions and host metallicity.

The stellar companion sample is made up of two subsamples: those companions detected as part of an exoplanet survey and those that were not. The target list for exoplanets is biased against stellar binarity as discussed in Chapter 4. We show that there is negligible bias between the probability of detecting stellar companions 6-2. The Sample 123 and host metallicity in two ways: (1) by showing that our close sample of stellar companions is nearly complete and (2) by using the Geneva-Copenhagen survey (hereafter, GC) of the Solar neighbourhood (Nordstr¨omet al. 2004) sample of stars, containing similar types of stars to those found in our sample, as an independent check on our results.

The GC sample of stars which contains F0-K3 stars is expected to be complete for stars with stellar companions closer than d < 40 pc. For the close sample of stars (d < 25 pc), the northern hemisphere of stars with close stellar companions is approximately complete. The southern hemisphere of stars is also nearly complete if we include the binary stars from Jones et al. (2002a) that are likely to fall within our sample (see Chapter 4). We then ﬁnd that ∼ 10% of stars have stellar companions with periods shorter than 5 years. If we make a small asymmetry correction (to account for the southern hemisphere not being as well monitored for binaries) we ﬁnd that ∼ 11 3% of stars have stellar companions within this period range (see Chapter 4). We also compare our sample with that of the “Carney-Latham” survey (hereafter, CL) of proper-motion stars (Carney & Latham 1987; Carney et al. 1994) in Section 6-4. The CL sample also contains ∼ 11% of stars with stellar companions with periods shorter than 5 years (Latham et al. 2002). We tabulate the properties of all these samples in Table 6.1.

Notes for Table 6.1. For notes e - j, “HP Spec.” is high precision exoplanet target spectroscopy, “CdS Spec.” is Cayrel de Strobel et al. (2001) spectroscopy, “uvby Phot.” is uvby photometry, “BB Phot.” is broad-band photometry and “HR K Dwarf” is the method for obtaining metallicities for K dwarfs from their position in the HR diagram (Kotoneva et al. 2002). e 63% HP Spec., 12% CdS Spec., 20% uvby Phot., 1% BB Phot., 4% HR K Dwarf. f 19% HP Spec., 5% CdS Spec., 55% uvby Phot., 17% BB Phot., 4% HR K Dwarf. g 63% HP Spec., 18% CdS Spec., 19% uvby Phot. h 26% HP Spec., 7% CdS Spec., 61% uvby Phot., 6% BB Phot., < 1% HR K Dwarf. i 64% HP Spec., 5% CdS Spec., 20% uvby Phot., 3% BB Phot., 8% HR K Dwarf. 6-2. The Sample 124 j i f h e g Phot. Phot. Phot. Phot. Spec. uvby uvby uvby uvby [Fe/H] Source d – – – – – Planet Hosts c Targets Subset of target stars that are exoplanet hosts (“P” in Fig. b Subset of total stars that are exoplanet target stars (“T” in Stars with [Fe/H] Measurements d c Subset of total stars that are hosts to stellar companions (“S” in b Binary ). 6.4 a 963 254 (26.4%) – 196 18 (9.2%) 151 (77%) 6 (4.0%) Mostly Spec. 172 55 (32.0%) – 983 31 (3.2%) 430 (44%) 4 (0.9%) Mostly Phot. 453 45 (9.9%)257 379 (84%) 27 (10.5%) 19 (5.0%) 228 (89%) Mostly Spec. 13 (5.7%) Mostly Spec. 1289 346 (26.8%) – 1375 378 (27.5%) – 2745 107 (3.9%) 1597 (58%) 36 (2.3%) Mostly Phot. 1762 76 (4.3%) 1167 (66%) 32 (2.7%) Mostly Phot. 1117 291 (26.1%) – Stellar Samples Used in Our Analysis Total 50 50 50 40 40 25 25 40 25 40 (pc) < d < < d < < d < Range Table 6.1. d < d < d < d < d < d < d < 1 . 0 25 1 . 0 1 . 0 1 . 0 25 1 . 0 V 1 . 0 1 . 0 1 . 0 – 0 . 75 25 0 . 75 0 . 75 − − − − − − − − − − − − B 0 . 5 0 . 5 0 . 5 0 . 75 FGK 0 . 3 AFGK 0 . k l GC K 0 . 75 Our K 0 . 75 Sample GC FG 0 . 5 Our FG 0 . 5 Our FGK 0 . 5 GC CL ). The percentages given correspond to the fraction T/H. ). The percentages given correspond to the fraction S/H. 6.4 6.4 ). The percentages given correspond to the fraction P/T. See text for additional notes. Total number of Hipparcos sun-like stars (“H” in Fig. a Fig. 6.4 Fig. 6-2. The Sample 125 j 6% HP Spec., 3% CdS Spec., 44% uvby Phot., 36% BB Phot., 11% HR K Dwarf. k “GC” is the Geneva-Copenhagen survey of the Solar neighbourhood sample (Nordstr¨omet al. 2004). We only include those binaries observed by CORAVEL between 2 and 10 times (see Section 6-4). l “CL” is the Carney-Latham survey of proper-motion stars (Carney et al. 2005). We only include those stars on prograde Galactic orbits (V > −220 km/s). The CL sample also includes 231 stars from the sample of Ryan (1989).

6-2.3 Close Companions

The close companions included in our d < 25 pc and 25 < d < 50 pc samples are enclosed in a rectangle of mass-period space shown in Fig. 6.3. These companions have primarily been detected using the Doppler technique but the stellar companions have been detected with a variety of techniques not exclusively from high precision exoplanet Doppler surveys. Thus we need to consider the selection effects of the Doppler method in order to define a less-biased sample of companions (see Chapter 4). Given a fixed number of targets, the “Detected” region should contain all companions that will be found for this region of mass-period space. The “Being Detected” region should contain some but not all companions that will be found in this region and the “Not Detected” region contains no companions since the current Doppler surveys are either not sensitive enough or have not been observing for a long enough duration to detect companions in this regime. Thus as a consequence of the exoplanet surveys’ limited monitoring duration and sensitivity for our sample we only select those companions with an orbital period P < 5 years and mass M2 > 0.001M .

In Section 4-3.1 we found that companions with a minimum mass in the brown dwarf mass regime were likely to be low mass stellar companions seen face on, thus producing a very dry brown dwarf desert. We also included the 14 stellar companions from Jones et al. (2002a) that have no published orbital solutions but are assumed to orbit within periods of 5 years. We ﬁnd one new planet and no new stars in our 6-2. The Sample 126 less biased rectangle when compared with the data used in Chapter 4. This new planet HD 20782 (HIP 15527) (indicated by a vertical line through the point in Fig. 6.3), has been monitored for well over 5 years but only has a period of ∼ 1.6 years and a minimum mass of 1.8MJup placing it just between the “Detected” and “Being Detected” regions. While most planets are detected within a time frame comparable to the period, the time needed to detect this planet was much longer than its period because of its unusually high eccentricity of 0.92 (Jones et al. 2006). We thus have two groups of close companions to analyse as a function of host metallicity - giant planets and stars.

In Fig. 6.3 we split the close companion sample into 3 groups deﬁned by the metallicity of their host star: metal-poor ([Fe/H] < −0.1), Sun-like (−0.1 ≤ [Fe/H] ≤ 0.1) and metal-rich ([Fe/H] > 0.1) which are plotted as white, grey and black dots respectively. Fig. 6.3 suggests that the hosts of planetary companions are generally metal-rich whereas the hosts of stellar companions are generally metal-poor. Table 6.2 and Fig. 6.4 conﬁrm the correlation between exoplanets and high-metallicity and indicate an anti-correlation between stellar companions and high metallicity.

Table 6.2. Metallicity and Frequency of Hosts with Close Planetary and Stellar Companions

Companions Range Total Metal-poor Sun-like Metal-rich Planets d < 25 19 2 (11%) 5 (26%) 12 (63%) Stars d < 25 45a 25 (56%) 14 (31%) 6 (13%) Planets 25 < d < 50 36 3 (8%) 9 (25%) 24 (67%) Stars 25 < d < 50 107b 55 (51%) 36 (34%) 16 (15%) a An additional 2 hosts with unknown metallicity have stellar companions. b An additional 3 hosts with unknown metallicity have stellar companions. 6-2. The Sample 127

Figure 6.3. Masses and periods of close companions to stellar hosts of FGK spectral type. We split the close companion sample into 3 groups deﬁned by the metallicity of their host star: metal-poor ([Fe/H] < −0.1), Sun-like (−0.1 ≤ [Fe/H] ≤ 0.1) and metal-rich ([Fe/H] > 0.1) which are plotted as white, grey and black dots respectively. The larger points are companions orbiting stars in the more complete d < 25 pc sample, while the smaller points are companions to stars at distances between 25 < d < 50 pc. For multiple companion systems, we select the most massive companion in our less-biased sample to represent the system. 6-3. Companion - Host Metallicity Correlation 128

We divide the stellar companions into those not monitored by one of the exoplanet search programs (shown with an ‘X’ behind the point) and those that are monitored in Fig. 6.3. Both groups of stellar companions are distributed over the entire less- biased region (enclosed by thick line). Hence any missing stellar companions should be randomly distributed.

6-3 Companion - Host Metallicity Correlation

We examine the distribution of close companions as a function of stellar host metallicity in our two samples. We do this quantitatively by ﬁtting exponential functions to the metallicity data expressed both linearly and logarithmically. We deﬁne the logarithmic [Fe/H] and linear Z/Z metallicity as follows:

[Fe/H] = log(Fe/H) − log(Fe/H) = log(Z/Z ) (6.1) where Fe and H are the number of iron and hydrogen atoms respectively and Z =

Fe/H. We examine the close planetary companion probability Pplanet and the close stellar companion probability Pstar as a function of [Fe/H] in Figs. 6.4 and 6.6 for the d < 25 and 25 < d < 50 pc samples respectively. Similarly we also examine

Pplanet and Pstar as a function of Z/Z in Fig. 6.5 and 6.7, which is effectively just a re-binning of the data in Fig. 6.4 and Fig. 6.6. We then find the linear best-fits to the planetary and stellar companion fraction distributions as shown by the dashed lines in Figs. 6.4-6.7.

We also ﬁt an exponential to the [Fe/H] planetary (as in Fischer & Valenti 2005) and stellar companion fraction distributions in Figs. 6.4 and 6.6 and equivalently a power-law to the data points for the Z/Z plots, Figs. 6.5 and 6.7. The two linear parameterizations that we ﬁt to the data are:

Plin Fe/H = a [Fe/H] + P (6.2)

Plin Z/Z0 = A (Z/Z ) + (P − A) (6.3) 6-3. Companion - Host Metallicity Correlation 129 and the two non-linear parameterizations are:

α [Fe/H] PEP = P 10 (6.4)

α = P (Z/Z ) (6.5) where P is the fraction of stars of solar metallicity (i.e. [Fe/H] = 0 and Z/Z = 1) with companions.

If the ﬁts for the parameters a, A and α are consistent with zero then there is no correlation between the fraction of stars with companions and metallicity. On the other hand, a non-zero value, several sigma away from zero suggests a signiﬁcant correlation (a, A or α > 0) or anti-correlation (a, A or α < 0).

The best-ﬁt parameters a, A and P (but not α) depend upon the period range and completeness of the sample. In order to compare the slopes from diﬀerent samples, we parametrize this dependence in terms of the average companion fraction

Pavg for the sample, i.e., if the average companion fraction for a sample is twice as large as for another sample, the best-fit slopes a and A as well as the fraction of stars of solar metallicity P will also be twice as large. To compare samples with different Pavg, we scale the best-fit Eqs. 6.2-6.5 to a common average companion fraction by dividing each equation by Pavg. Thus, we scale the best-fit parameters a, A and P by dividing each by Pavg. These scaled parameters are then referred 0 0 0 to as a = a/Pavg, A = A/Pavg and P = P /Pavg. We list the unscaled best-fit parameters a, A, P , α along with Pavg for each sample in Table 6.3.

In Fig. 6.4, and its re-binned equivalent Fig. 6.5, we ﬁnd an anti-correlation between the presence of stellar companions and host metallicity. The linear stellar

2 companion best-fits have gradients of a = −0.14 0.06 (χred = 3.00) and A = 2 −0.06 0.03 (χred = 0.91) respectively, both significant at the ∼ 2σ level. The non-linear best-fit to the stellar companions as a function of [F e/H] in Fig. 6.4 is

2 α = −0.86 0.10 (χred = 1.33) and the non-linear best-fit to the stellar companions 2 as a function of Z/Z in Fig. 6.5 is α = −0.47 0.18 (χred = 0.40) or on average −0.8 0.4 which is significant at the ∼ 2σ level. All these best-fits are summarised 6-3. Companion - Host Metallicity Correlation 130

Figure 6.4. Metallicities ([Fe/H]) of 453 stars in our close d < 25 pc sample. Top: The histograms are shaded as shown in the key. In the Bottom plot, the fraction of target stars, stellar companion hosts and planetary companion hosts are shown by squares, triangles and circles respectively. The linear best-ﬁt to the target fraction is shown by a dotted line. The linear and exponential best-ﬁts to the stellar and planetary companion fractions are shown by dashed and solid lines respectively. 6-3. Companion - Host Metallicity Correlation 131

Figure 6.5. Same as Fig. 6.4 except that metallicity is plotted linearly as Z/Z .

All of the metal-rich (Z/Z > 1.8) sample stars are being monitored for exoplanets but as the stellar metallicity decreases so does the fraction being monitored. This is because of a bias towards selecting more metal-rich target stars for observation due to an increased probability of planetary companions orbiting metal-rich host stars. 6-3. Companion - Host Metallicity Correlation 132

Figure 6.6. Same as Fig. 6.4 except for the 2745 stars in the more distant 25 < d < 50 pc sample. It is harder to detect distant planets because of signal to noise considerations which limit observations to the brighter stars. This fainter, more distant sample relies more on photometric metallicity determinations. The fraction of stars being monitored for exoplanets is much lower than in Fig. 6.4.

Figure 6.7. Same as Fig. 6.6 except that metallicity is plotted linearly as Z/Z analogous to Fig. 6.5. In this more distant sample we ﬁnd the same trends as in Fig. 6.5 but they are not as prominent. 6-3. Companion - Host Metallicity Correlation 133 in Table 6.3.

We consistently find in Figs. 6.4 and 6.6 that metal-rich stars are being monitored more extensively for exoplanets than metal-poor stars as quantified by the “Target Stars” / “Hipparcos Sun-like Stars” ratio. This is because of a bias towards selecting more metal-rich stars for observation due to an increased probability of planetary companions orbiting metal-rich host stars. Note that this bias is well-represented by a linear trend as shown by the dotted best-fit line in these figures, and is not just a case of a few high metallicity stars being added to the highest metallicity bins. We correct for this bias by calculating “P/T” not “P/H” for each metallicity bin.

We ﬁnd a correlation between [Fe/H] and the presence of planetary companions in

2 Fig. 6.4. The linear best-fit (Eq. 6.2) has a gradient of a = 0.18 0.07 (χred = 1.21) and thus the correlation is significant at the 2σ level. The non-linear best-fit (Eq.

2 6.4) is α = 2.090.54 (χred = 0.16) and thus the correlation is signiﬁcant at slightly more than the 3σ level.

Similarly we ﬁnd a correlation between linear metallicity Z/Z and the presence of planetary companions in the same data re-binned in Fig. 6.5. The linear best-

2 fit (Eq. 6.3) has a gradient of A = 0.07 0.03 (χred = 1.25) and the non-linear 2 best-fit (Eq. 6.5) has an exponent of α = 2.22 0.39 (χred = 1.00) which are non-zero at the ∼ 2σ and ∼ 5σ significance levels respectively. These results are summarised in Table 6.3. We can compare the non-linear best-fit (Eq. 6.5) for linear metallicity Z/Z and the non-linear best-fit (Eq. 6.4) for log metallicity [Fe/H] since

2 2 both contain the parameter α. As shown by the χ per degree of freedom χred, the non-linear goodness of fit is better than the linear goodness of fit. We rely on the best fitting functional form which is the non-linear parameterization of our results although we use both parameterizations in our analysis.

We combine these two non-independent, non-linear best-fit estimates by computing their weighted average. We assign an error to this average by adding in quadrature (1) the difference between the two estimates and (2) the nominal error on the average. Thus our best estimate is α = 2.2 0.5. Hence the correlation between the presence of planetary companions and host metallicity is significant at the 6-3. Companion - Host Metallicity Correlation 134

∼ 4σ level for a non-linear best-fit and at the ∼ 2σ level with a lower goodness-of-fit for a linear best-fit in our close, most complete sample.

In Fig. 6.4, and its re-binned equivalent Fig. 6.5, we ﬁnd an anti-correlation between the presence of stellar companions and host metallicity. The linear stellar

2 α = −0.86 0.10 (χred = 1.33) and the non-linear best-fit to the stellar companions 2 as a function of Z/Z in Fig. 6.5 is α = −0.47 0.18 (χred = 0.40). Averaging these two as above we obtain, −0.8 0.4, which is significant at the ∼ 2σ level. All these best-fits are summarised in Table 6.3.

Having found a correlation for planetary companions and an anti-correlation for stellar companions in our close sample and having found them to be robust to different metallicity binnings, we perform various other checks to conﬁrm their reality. We check the robustness of both results to (i) distance and (ii) spectral type (∼ mass) of the host star.

To check if these anti-correlations have a distance dependence, we repeat this analysis for the less complete 25 < d < 50 pc sample. As shown by the best-fits in Figs. 6.6 and 6.7 and summarised in Table 6.3 we find only a marginal anti- correlation between the presence of stellar companions and host metallicity for the linear best-fits. The non-linear best-fits however still suggest an anti-correlation with α = −0.590.12 for log metallicity [Fe/H] and α = −0.440.12 for linear metallicity

Z/Z , which are significant at the 4σ and 3σ levels respectively. Combining these two estimates we find the weighted average as above of α = −0.5 0.2 significant at the 2σ level in the 25 < d < 50 pc sample.

The correlation between the presence of planetary companions and host metallicity for the less complete 25 < d < 50 pc is significant at the 4σ and 3σ levels for the linear best-fits a and A respectively. The non-linear best-fit correlation has α = 2.56 0.45 for log metallicity [Fe/H] and α = 3.00 0.46 for linear metallicity

Z/Z which are significant at the 5σ and 6σ levels respectively. Combining these 6-3. Companion - Host Metallicity Correlation 135 two estimates we find the weighted average as above of α = 2.8 0.6 significant at the 4σ level.

Having found the correlation for planetary companions and the anti-correlation for stellar companions robust to binning but less robust in the less-complete more distant sample, we test for spectral type (∼ host mass) dependence. We split our sample into bluer and redder subsamples to investigate the eﬀect of spectral type on the close-companion/host-metallicity relationship. We deﬁne the higher host mass subsample by B − V ≤ 0.75 (FG spectral type stars) and the lower host mass subsample by B − V > 0.75 (K spectral type stars). Since B − V has a metallicity dependence, a cut in B − V will not be a true mass cut, but a diagonal cut in mass vs metallicity. Thus, interpreting a B − V cut as a pure cut in mass introduces a spurious anti-correlation between mass and metallicity.

The linear best-fit to the stellar companions of the FG sample (d < 25 pc) has a normalised gradient of a0 = (−0.01 0.08)/10.5% = −0.1 0.8 and the non- linear best-fit is α = −0.2 0.4 as shown in Fig. 6.8. Both of these best-fits are consistent with the frequency of stellar companions being independent of host metallicity. The linear best-fit to the stellar companions of the K sample has a gradient of a0 = (−0.27 0.07)/9.2% = 2.9 0.8 and the non-linear best-fit is α = −1.0 0.1 as shown in Fig. 6.9 for the close d < 25 pc stars. Both of these best-fits show an anti-correlation between the presence of stellar companions and host metallicity at above the 3σ level. Less significant results are obtained for the 25 < d < 50 FG and K spectral type samples with stellar companions as shown in Table 6.3.

0 The parameters a = a/Pavg and α of the different samples are compared in Fig. 6.10. This plot is a graphical version of Table 6.3, whose notes also apply to the plot. All of the best-fits are from [Fe/H] plots except for our FGK stars where α is the average of the best-fits to both the [Fe/H] and Z/Z plots. The P values plotted in the vertical panel on the right refer to the corresponding best-fit normalisation at solar metallicity (Eqs. 6.2-6.5).

These results suggest that the observed anti-correlation between close binarity 6-3. Companion - Host Metallicity Correlation 136

Figure 6.8. Same as Fig. 6.4 for the stars in our close d < 25 pc sample but only for FG dwarfs (B − V ≤ 0.75). All stars have known metallicity in this sample. There is no apparent anti-correlation between metallicity and the presence of stellar companions. 6-3. Companion - Host Metallicity Correlation 137

Figure 6.9. Same as Fig. 6.4 for the stars in our close d < 25 pc sample but only for K dwarfs (B − V > 0.75). This plot shows a strong anti-correlation between metallicity and the presence of stellar companions. 6-3. Companion - Host Metallicity Correlation 138 and host metallicity is either (i) real and stronger for K spectral type stars than for FG stars or (ii) due to a spectral-type dependent selection eﬀect.

Under the hypothesis that the anti-correlation between host metallicity and binarity is real for K dwarfs, there is a possible selection effect limited to F and G stars that could explain why we do not see the anti-correlation as strongly in them. Doppler broadening of the line profile, due to random thermal motion in the stellar atmosphere and stellar rotation, both increase in more massive F and G stars due to their higher effective temperature and faster rotation speeds compared with less massive K stars. This wider line profile for F and G stars results in fewer observable shifting lines thus lowering the spectroscopic binary detection efficiency, although not significantly (Santos et al. 2002). However we directly examine the stellar companion fraction as a function of spectral type or colour B − V in Fig. 6.11. For both single-lined and double-lined spectroscopic binaries, if the binary detection efficiency was systemically higher for K dwarfs then the anti-correlation could be a selection effect. However, we find that it is fairly independent of spectral type. Thus the anti-correlation does not appear to be a spectral-type dependent selection effect.

We also examine the spectral type (∼ mass) dependence of the correlation between planetary companions and host metallicity. The linear best-fit to the planetary companions of the FG sample has a gradient of a0 = (0.22 0.09)/5.7% = 3.9 1.6 and the non-linear best-fit is α = 2.3 0.6 as shown in Fig. 6.8 for the close d < 25 pc stars. These are significant at the 2 and 3 σ levels respectively. The linear best-fit to the planetary companions of the K sample has a gradient of a0 = (0.11 0.10)/4.0% = 2.8 2.5 and the non-linear best-fit is α = 1.6 0.9 as shown in Fig. 6.9 for the close d < 25 pc stars. These are both significant at between the 1 and 2 σ levels. The K sample contains fewer planetary and stellar companions compared to the FG sample. Both the linear and non-linear fits are consistent between the FG and K samples suggesting that the correlation between the presence of planetary companions and host metallicity is independent of spectral type and consequently host mass. The fraction of planetary companions is also fairly independent of spectral type as shown in Fig. 6.11. 6-3. Companion - Host Metallicity Correlation 139 b avg P 2 . 1 10 . 5 0 . 5 2 . 3 0 . 4 3 . 9 1 . 3 5 . 0 1 . 3 9 . 1 . 7 5 . 7 1 . 4 5 . 0 0 . 4 2 . 3 1 . 5 9 . 0 . 4 3 . 9 0 . 6 4 . 3 0 . 6 2 . 7 [%] [%] )

6.10 0 . 4 –0 . 12 3 . 5 – 0 . 10 7 . 8 0 . 37 10 . 7 0 . 2 – – 0 . 18 8 . 0 . 12 3 . 6 0 . 18 4 . 7 0 . 5 – – 0 . 6 – – 0 . 45 2 . 3 0 . 54 4 . 5 0 . 62 5 . 0 0 . 39 5 . 3 0 . 46 2 . 0 0 . 46 2 . 8 Non-Linear α P − 0 . 8 − 0 . 5 − 0 . 59 − 0 . 86 − 0 . 18 − 0 . 47 − 0 . 44 − 0 . 09 2 . 0 0 . 4 1 . 4 0 . 4 2 . 56 1 . 2 2 . 09 1 . 7 2 . 33 2 . 5 2 . 22 0 . 6 3 . 00 3 . 5 0 . 8 0 . 6 0 . 5 2 . 63 [%] – 2 . – – – 2 . 8

0 . 02 3 . 0 . 06 7 . 3 0 . 08 10 . 3 0 . 03 8 . 0 . 01 3 . 4 AP 0 . 01 1 . 6 0 . 07 4 . 8 0 . 09 6 . 3 0 . 03 3 . 8 0 . 01 2 . 0 0 . 02 4 . 0 . 02 2 . 0 – – or a − 0 . 00 − 0 . 14 − 0 . 01 − 0 . 06 − 0 . 01 Stars Stars Stars Stars Stars Planets 0 . 04 Planets 0 . 18 Planets 0 . 22 Planets 0 . 07 Planets 0 . 03 6.6 6.4 6.8 6.6 6.4 6.8 6.5 6.5 6.7 6.7 Figure Companions Linear Fig. Fig. Fig. Fig. ] – Stars 0 . 04 ] Fig. ] Fig. ] – Planets 0 . 05 ] Fig. ] Fig. a

Z/Z Z/Z Best-ﬁt Trends for Close-Companion Host-Metallicity Correlation (see Fig. 50 [ F e/H 50 50 [ F e/H 50 Avg.50 Avg. – – Planets Stars – 50 [ F e/H 50 50 [ F e/H 25 Z / 25/ H] [Fe Fig. 25 Z / 25 Avg. – Planets – 25 [ F e/H 25/ H] [Fe Fig. 25 [ F e/H 25 Avg. – Stars (pc) < d < < d < < d < < d < < d < < d < < d < < d < Table 6.3. d < d < d < d < d < d < d < d < 25 25 25 25 25 25 FG 25 Our Our FGK 25 Sample Range Type continued on next page. . . 6-3. Companion - Host Metallicity Correlation 140 25 avg A/P b = avg 0 P ) A and for data , a 6.10 avg 1 . 4 26 . 8 1 . 6 26 . 1 3 . 9 32 . 0 1 . 2 25 . 7 3 . 1 25 . 7 3 . 1 4 . 0 2 . 3 9 . 2 0 . 5 3 . 2 1 . 0 0 . 9 [%] [%]

a/P = 0 a 0 . 14 7 . 1 0 . 07 23 . 9 0 . 10 25 . 5 0 . 11 23 . 7 0 . 05 20 . 7 0 . 19 2 . 0 0 . 09 21 . 6 0 . 85 5 . 1 2 . 16 1 . 3 Non-Linear α P Combined sample of (i) our ( d < − 0 . 95 − 0 . 28 − 0 . 08 − 0 . 52 − 0 . 22 − 1 . 12 − 0 . 12 c ). ) sample and (iii) the prograde Galactic 1 . 5 1 . 6 3 . 6 1 . 3 3 . 4 1 . 9 2 . 0 1 . 57 0 . 5 0 . 6 2 . 10 6-3 [%] 6.12

Linear 0 . 05 24 . 0 0 . 06 25 . 1 0 . 10 22 . 3 0 . 07 5 . 7 0 . 03 20 . 5 0 . 06 21 . 3 0 . 02 2 . 0 which are then referred to by AP 0 . 10 3 . 6 0 . 03 0 . 9

or P a . For data binned in/ H] [Fe the linear slope is − 0 . 15 − 0 . 05 − 0 . 46 − 0 . 27 − 0 . 10 − 0 . 07 − 0 . 06

and 40 pc F7-K3, Fig. ” is defined as the number of stars with stellar companions divided a, A avg “ P Stars Stars Stars Stars Stars b Planets 0 . 11 ). - 6.5 6.9 6.9 6.2 6.12 6.13 6.14 6.15 shows all three datasets. Figure Companions 6.15 ] Fig. ] Fig. ] – Stars ] Fig. ] Fig. ] – Stars ] Fig. ] – Planets 0 . 03 ] Fig. a (see Eqs. A ). Fig. 50 [ F e/H 50 [ F e/H ( 2005 25 [ F e/H 40 [ F e/H 25 [ F e/H 40 [ F e/H 40 [ F e/H .continued Best-fit Trends for Close–Companion Host–Metallicity Correlation (see Fig. –[ F e/H – (pc) < d < < d < d < d < d < d < d < ) sample, (ii) the volume-limited GC ( d < and can be compared between different samples (see text Section 25 6.4 the linear slope is avg c

Carney et al. Table. 6.3 K 25 P Our GC K Sample Range Type GC FG = GC FGK CL AFGK – [ F e/H Combined 0

P “Type” refers to whether the data is binned in/ H] [Fe or in Z / by the total number of stars. We use this parameter to scale a and pc F7-K3, Fig. orbits from binned in Z / 6-3. Companion - Host Metallicity Correlation 141

Figure 6.10. We compare the normalised linear a0 (triangles) and non-linear α (circles) parameterizations for the various samples listed in Table 6.3. The red points are the best-fits to planetary companions and the green points the best-fits to stellar companions. The fact that the red planet values for α are significantly larger than zero confirms and quantifies the metallicity/planet correlation. The fact that the green stellar values for α are predominantly less than zero, significantly so only for K dwarfs, is a surprising new result. The labels on the RHS refer to the samples for which the best-fit parameterizations are valid. We normalise the linear parametrization by dividing the best-fit gradient a by the average companion fraction Pavg (see text). The P values plotted in the vertical panel on the right refer to the corresponding best-fit normalisation at solar metallicity (Eqs. 6.2-6.5). 6-3. Companion - Host Metallicity Correlation 142

Figure 6.11. Colour (B − V ) distribution for double-lined (squares) and single- lined (triangles) spectroscopic binaries (SB2s and SB1s respectively) and exoplanets (circles) in our close d < 25 pc sample. The linear best-fit gradient for SB2s is 0.00 0.06, for SB1s it is −0.08 0.08 and for exoplanets it is −0.05 0.08. All three of these gradients are only significant at ∼< 1σ level. There is no significant correlation between SB1, SB2 or planetary fraction for either FG (B − V ≤ 0.75) stars or for K (B − V > 0.75) stars. 6-4. Is the Anti-Correlation Real? 143

Thus our results suggest that the correlation between the presence of planetary companions and host metallicity is significant at the ∼ 4σ level and that the anti-correlation between the presence of stellar companions and host metallicity is significant at the ∼ 2σ for the d < 25 pc FGK sample. Splitting both samples into FG and K spectral type stars suggests that the correlation between the presence of planetary companions and host metallicity is independent of spectral type but that the anti-correlation between the presence of stellar companions and host metallicity is a strong function of spectral type with the anti-correlation disappearing for the bluer FG host stars (see Fig. 6.10). We find no spectral-type dependent binary detection efficiency bias that can explain this anti-correlation.

6-4 Is the Anti-Correlation Real?

We further examine the relationship between stellar metallicity and binarity by comparing our sample with that of the Geneva and Copenhagen survey (GC) of the solar neighbourhood (Nordstr¨omet al. 2004) that has been selected as a magnitude- limited sample, a volume-limited portion (d < 40 pc) of which we analyse. This selection criteria infers that the sample is kinematically unbiased, i.e., the sample contains the same proportion of thin, thick and halo stars as is found in the solar neighbourhood. We also compare our sample with that of the “Carney-Latham” survey (CL) that has been kinematically selected to have high proper motion stars (Carney & Latham 1987), i.e., it contains a larger proportion of halo stars compared to disk stars than is observed for the solar neighbourhood.

Our sample is based on the Hipparcos sample that has a limiting magnitude for completeness of V = 7.9 + 1.1 sin |b| (Reid 2002) where b is Galactic latitude. Thus the Hipparcos sample is more complete for stars at higher Galactic latitudes where the proportion of halo stars to disk stars increases. Hence our more distant (25 < d < 50 pc) sample will have a small kinematic bias in that it will have an excess of halo stars, whereas our closer (d < 25 pc) sample will be less kinematically biased. 6-4. Is the Anti-Correlation Real? 144

6-4.1 Comparison with a Kinematically Unbiased Sample

The GC sample contains primarily F and G dwarfs with apparent visual magnitudes

V ∼< 9 and is complete in volume for d < 40 pc for F0-K3 spectral type stars. Unlike our sample analysed in Section 6-3, it also includes early F spectral type stars. The GC sample colour range is deﬁned in terms of b − y not B − V like our samples. We remove these early F stars with b−y < 0.3 (B −V ∼< 0.5, Cox 2000) from the sample so that the GC sample spectral type range is similar to ours. The GC sample then ranges from 0.3 ≤ b − y ≤ 0.6 (0.5 ∼< B − V ∼< 1.0) with those stars above b − y = 0.5 (B − V ∼ 0.75) referred to as K stars. We also exclude suspected giants from the GC sample.

For the GC sample, we only include those binaries observed by CORAVEL between 2 and 10 times so as to avoid a potential bias where low metallicity stars were observed more often, thus leading to a higher efficiency for finding binaries around these stars. This homogenizes the binary detection efficiency such that any real signal will not be removed by such a procedure. Unlike our sample for which we only include binaries with P < 5 years, the GC sample also includes much longer period visual binaries in addition to short period spectroscopic binaries such that the total binary fraction of all types corresponds to ∼ 25%. Comparing this with the period distribution for G dwarf stars of Duquennoy & Mayor (1991) this binary fraction corresponds to binary systems with periods less than ∼ 105 days.

For the volume limited d < 40 pc sample we again find an anti-correlation between binarity and stellar host metallicity as shown in Fig. 6.12. Both the linear and non- linear best-fits listed in Table 6.3 are significant at or above the 3σ level. We also split the GC sample into FG and K spectral type stars in Figs. 6.13 and 6.14 respectively. The anti-correlation between the presence of stellar companions and host metallicity is significant at less than the 1σ level for FG stars but significant at the ∼ 4σ level for K stars.

These results are qualitatively the same as those found for our sample but quantitatively weaker as shown in Fig. 6.10 (confer rows of points labeled GC). This may 6-4. Is the Anti-Correlation Real? 145 be due to the higher fraction of late F and early G spectral type stars compared to our samples or the larger range (∼ 105 days) in binary periods contained in the GC sample compared to our sample where P < 5 years. Another way of interpreting this anti-correlation between binarity and metallicity may be in terms of the age and nature of diﬀerent components of the Galaxy described by stellar kinematics, i.e., F stars are generally younger than K stars and thus are more likely to belong to the younger thin disk star population than the older thick disk star population. Hence we examine our results in terms of stellar kinematics.

6-4.2 Comparison with a Kinematically Biased Sample

We also compare our samples and that of the GC survey with the Carney & Latham (1987) high proper motion survey (CL). The CL survey contains all of the A, F and early G, many of the late G and some of the early K dwarfs from the Lowell Proper Motion Catalog (Giclas et al. 1971, 1978) and which were also contained in the NLTT Catalog (Luyten 1979, 1980). The number of stars in this distribution increases as the stellar colours become redder, peaking at about B − V = 0.65, following which the numbers of stars begin to decrease (Carney et al. 1994). This group has also obtained data for a smaller number of stars from the sample of Ryan (1989) who sampled sub-dwarfs (metal-poor stars beneath the main-sequence) that have a high fraction of halo stars in the range 0.35 < B − V < 1.0. We refer to this combined sample as outlined in Carney et al. (2005) as the CL sample. This CL sample contains all binaries detected as spectroscopic binaries, visual binaries or common proper motion pairs.

In Fig. 6.15 we plot the binary fraction of stars on prograde and retrograde Galactic orbits as shown in Fig. 3 of Carney et al. (2005). All of the CL stars have [Fe/H] ≤ 0.0. The CL distribution contains a small subset of metal-poor [Fe/H] ≤ −0.2 stars from Ryan (1989) that has a one-third lower prograde binary fraction due to fewer observations. Thus stars with metallicities of between −0.2 and 0.0 have a higher binary fraction than the rest of the CL distribution. We make a 6-4. Is the Anti-Correlation Real? 146

Figure 6.12. Histogram of stars in the complete volume limited GC sample (d < 40 pc). We only include those stars that have between 2 and 10 radial velocity measurements with the CORAVEL spectrograph. We ﬁnd an anti-correlation between binarity and host metallicity as shown by the linear and non-linear best-ﬁts represented by the dashed and solid lines respectively. 6-4. Is the Anti-Correlation Real? 147

Figure 6.13. Same as Fig. 6.12 but only for the FG dwarfs in the GC sample of stars (d < 40 pc). We define FG dwarfs as those with b−y < 0.5 (B −V ∼< 0.75). We find only a marginal anti-correlation between binarity and host metallicity as shown by the linear best-fit with gradient a = −0.050.06 and the non-linear best-fit with α = −0.11 0.10. 6-4. Is the Anti-Correlation Real? 148

Figure 6.14. Same as Fig. 6.12 but only for the K dwarfs in the GC sample of stars (d < 40 pc). We deﬁne K dwarfs as those with b − y > 0.5 (B − V ∼> 0.75). We ﬁnd a very strong anti-correlation between binarity and host metallicity. Comparing this plot with Fig. 6.13 suggests that the anti-correlation between binarity and host metallicity is stronger for redder stars. 6-4. Is the Anti-Correlation Real? 149 small correction for this bias in the binary fraction in the range −0.2 < [Fe/H] < 0.0 by lowering the 2 highest metallicity prograde points of the CL distribution by 2%.

We note an anti-correlation between the binary fraction and metallicity for −1.3 < [Fe/H] < 0.0 range of prograde disk stars of the CL distribution as shown in Fig. 6.15. We find that the linear best-fit to this anti-correlation has a gradient of a = −0.07 0.06 and the non-linear best-fit has α = −0.12 0.09, which are both significant at slightly above the 1σ level. For consistency we exclude the two lowest metallicity points from this best-fit so that we analyse the same region of metallicity as our samples and the GC sample and because these two low metallicity points will probably contain a significant fraction of halo stars. The average binary fraction is Pavg = 26% for the disk-dominated part of the prograde CL distribution. Carney et al. (2005) found no correlation between binarity and host metallicity for the retrograde halo stars.

We overplot our d < 25 pc binary fraction (from Fig. 6.4) along with the GC d < 40 pc binary fraction (from Fig. 6.12) onto the prograde CL sample in Fig. 6.15. All three of these samples have different binary period ranges and levels of completeness. We scale our sample and the GC sample to the size of the Carney et al. (2005) sample by scaling the distributions to contain the same number of binary stars at solar metallicity. The most metal-poor point in our close binary distribution is scaled above 100%, hence we set this point to 100%. The combined three sample distribution shows an anti-correlation between binarity and metallicity. The normalised linear best-fit to this is a0 = (−0.10 0.03)/25.7% = −0.39 0.12 and the non-linear best-fit is α = −0.22 0.05 which are both significant at or above the ∼ 3σ level (see last row of Table 6.3). This combined result is our best estimate and indicates a strong anti-correlation between stellar companions and metallicity for [Fe/H] > −1.3. 6-4. Is the Anti-Correlation Real? 150

Figure 6.15. This plot is adapted from Fig. 3 of Carney et al. (2005). The black triangles are the points from the CL sample of proper motion stars with prograde Galactic tangential velocities. We overplot the binary fraction as a function of host metallicity for our close (d < 25 pc) F7-K3 sample (Fig. 6.4) with red circles and the green squares are from the volume limited GC sample (d < 40 pc) for F7-K3 stars (Fig. 6.12). The three samples contain diﬀerent average binary fractions because the period range and the levels of completeness of the stellar companions varies between the samples as discussed in the text. We normalise the distributions by scaling our sample and the GC sample so that they contain the same fraction of binary stars as the sample of Carney et al. (2005) at [Fe/H] = 0. The linear and non-linear best-ﬁts to the three samples combined are shown as dashed and solid lines respectively. 6-4. Is the Anti-Correlation Real? 151

Figure 6.16. We plot tangential Galactic velocity V as a function of metallicity [Fe/H] for the kinematically unbiased GC sample (d < 40 pc). We use a probabilistic method to assign the stars in the GC sample to the three Galactic populations (halo, thick and thin disks) as discussed in the Appendix. Red points are thin disk stars, green points are thick disk stars and a blue point is the single halo star in the sample at V < −500 km/s. Crosses represent FG spectral-type stars and circles K stars. The ratio of thick/thin disk stars is ∼ 3 times higher for K stars than for FG stars. 6-4. Is the Anti-Correlation Real? 152

Figure 6.17. Histogram of the stars in Fig. 6.16 suspected of belonging to the thick disk and the thin disk in the GC sample (d < 40 pc). Notice the diﬀerence by a factor ∼ 2 between the higher binary fraction thick disk stars and the lower binary fraction thin disk stars. The K star distribution contains a higher ratio of thick disk stars than the FG star distribution in the thick/thin disk overlap region. 6-4. Is the Anti-Correlation Real? 153

6-4.3 Probability of Galactic Population Membership

We use a similar method to that of Reddy et al. (2006) in assigning a probability to each star of being a member of the thin disk, thick disk or halo populations. We assume the GC sample is a mixture of the three populations. These populations are assumed to be represented by a Gaussian distribution for each of the 3 Galactic velocities U, V, W and for the metallicity [Fe/H]. The age dependence of the quantities for the thin disk are ignored. The equations establishing the probability that a star belongs to the thin disk (Pthin), the thick disk (Pthick) or the halo (Phalo) are

P P P P = f 1 ,P = f 2 ,P = f 3 (6.6) thin 1 P thick 2 P halo 3 P

where

P = fiPi (6.7) X U 2 (V − hV i)2 W 2 ([Fe/H] − h[Fe/H]i)2 P = C exp − − − − i i  2 2 2 2  2σUi 2σVi 2σWi 2σ[Fe/H]i 1  Ci = (i = 1, 2, 3) σUi σVi σWi σ[Fe/H]i

Using the data in Table 6.4 taken from Robin et al. (2003) we compute the prob- abilities for stars in the GC sample. For each star, we assign it to the population (thin disk, thick disk or halo) that has the highest probability. We plot the probable halo, thick and thin disk stars of the GC sample in Fig. 6.16.

Table 6.4. Properties of the Three Stellar Populations

Component σU hV i σV σW h[Fe/H]i σ[Fe/H] Fraction f Thin Disc 43 -15 28 17 -0.1 0.2 0.925 Thick Disc 67 -53 51 42 -0.8 0.3 0.070 Halo 131 -226 106 85 -1.8 0.5 0.005 6-4. Is the Anti-Correlation Real? 154

6-4.4 Discussion

We examine our results in terms of Galactic populations by determining the most likely population membership (halo, thick or thin disk) for each star in the GC sample using the method outlined in Section 6-4.3 and then plotting them in the Galactic tangential velocity V - metallicity [Fe/H] plane as in Fig. 6.16. We use red points for the thin disk stars, green points for the thick disk stars and a blue point for the single halo star. The kinematically unbiased GC sample contains mostly thin disk stars. Excluding the one halo star in the GC sample, stars with [Fe/H] ∼< − 0.9 belong to the thick disk and stars with [Fe/H] ∼> − 0.1 belong to the thin disk. The region −0.9 ∼> [Fe/H] ∼> − 0.1 contains a combination of both thick and thin disk stars.

We also plot these thick and thin disk stars as separate histograms in metallicity in Fig. 6.17. In the region [Fe/H] ∼< −0.9 that contains only thick disk stars, we ﬁnd that the binary fraction is approximately twice as large as for the region [Fe/H] ∼> − 0.1 that contains only thin disk stars. In both of these single population regions the binary fraction also appears to be approximately independent of metallicity. While our purely probabilistic method of assigning the stars in the GC sample to Galactic populations is useful for determining the general regions of parameter space that the individual populations occupy, it is not precise enough to show exactly which stars belong to which population. This is especially true for the regions of parameter space that have large overlaps such as that between the thick and thin disk stars in Fig. 6.16. Thus the thin and thick disk binary fractions in the interval

−0.9 ∼< [Fe/H] ∼< −0.1 are probably mixtures. We suspect that the thin and thick disk binary fractions in this overlap region will remain at the same levels as found for the non-overlapping regions. The anti-correlation between binarity and metallicity in the −0.9 ∼< [Fe/H] ∼< − 0.1 range may be due to this overlap between higher binarity thick disk stars and lower binarity thin disk stars.

We now partition the Galactic tangential velocity V - metallicity [Fe/H] parameter space into four quadrants. We split the V parameter space into those stars on 6-4. Is the Anti-Correlation Real? 155 prograde Galactic orbits (P) and those on retrograde Galactic orbits (R). We split the [Fe/H] parameter space into those stars that are metal rich (r) with [Fe/H] ∼> −0.9 and those that are metal poor (p) with [Fe/H] ∼< − 0.9. We then label these quadrants by the direction of Galactic orbital motion followed by the range in metallicity or Pp, Pr, Rr and Rp as shown in Fig. 6.16. We now assume that the Pp quadrant contains a mixture of halo and thick disk stars and that the Pr quadrant contains a mixture of thin and thick disk stars and that the Rp and Rr quadrants only contain halo stars.

The combined anti-correlation between binarity and metallicity in Fig. 6.15, that all three samples appear to have in common, is predominantly in the Pr quadrant of V − [Fe/H] parameter space that contains a mixture of thick and thin disk stars. As discussed above this anti-correlation may be due to the overlap of high binarity thick disk stars and lower binarity thin disk stars.

While Latham et al. (2002) suggest that the halo and disk populations have the same binary fraction, Carney et al. (2005) ﬁnd lower binarity in retrograde stars. As shown in Fig. 6.15 there is a clear diﬀerence of about a factor of 2 in the region

[Fe/H] ∼> − 0.9 between the binary fractions of prograde disk stars compared to retrograde halo stars (Pr and Rr respectively). All the retrograde halo stars appear to have the same binary fraction (quadrants Rr and Rp). The Pp quadrant contains prograde halo stars and has a ∼ 2 times higher binary fraction than the quadrants containing retrograde halo stars. However the Pp quadrant also contains thick disk stars in addition to prograde halo stars.

We propose that the Pp region, [Fe/H] ∼< − 0.9, for stars on prograde Galactic orbits contains a mixture of low binarity halo stars and high binarity thick disk stars. In Fig. 6.15 at [Fe/H] ∼ −0.9 our close sample (d < 25 pc) and the GC sample (d < 40 pc) start to diverge from the data points of the CL survey. This observed divergence may be due to the CL survey being comprised of high proper motion stars and consequently a higher fraction of prograde halo stars compared to thick disk stars than the kinematically unbiased GC sample and our relatively kinematically unbiased sample where thick disk stars probably numerically dominate over halo 6-4. Is the Anti-Correlation Real? 156 stars.

Using a kinemically unbiased sample, Chiba & Beers (2000) report that for the three regions −1.0 > [Fe/H] > −1.7, −1.7 > [Fe/H] > −2.2 and −2.2 > [Fe/H] that the fraction of stars that belong to the thick disk are 29%, 8% and 5% respectively, with the rest belonging to the halo. We restrict these thick disk fraction estimates to stars only on prograde orbits by assuming that all of the thick disk stars are on prograde orbits and that half of the halo stars are prograde and the other half are retrograde. Thus the fraction of prograde stars that are thick disk stars is 45%, 15% and 10% for the three metallicity regions respectively.

Using these three prograde restricted thick disk/halo ratios reported in Chiba & Beers (2000) combined with observed binary fraction for the thick disk (55%) and halo (12%) stars in Fig. 6.15 we can test the proposal in the Pp quadrant that the two lowest metallicity prograde points from Carney et al. (2005) contain a mixture of low binarity halo stars and high binarity thick disk stars. We plot the three estimated mixed thick disk/halo binary fraction points as grey triangles in Fig. 6.15. We note that they are consistent with the two prograde Carney et al. (2005) points thus supporting our proposal that the Pp quadrant contains a mixture of low binarity halo stars and high binarity thick disk stars. These mixed thick disk/halo points also show a correlation between the presence of stellar companions and metallicity for stars in the Pp region.

Our results suggest that thick disk stars have a higher binary fraction than thin disk stars which in turn have a higher binary fraction than halo stars. Thus for stars on prograde Galactic orbits we observe an anti-correlation between binarity and metallicity for the region of metallicity [Fe/H] ∼> − 0.9 that contains an overlap between the lower-binarity, higher-metallicity thin disk stars and the higher-binarity, lower-metallicity thick disk stars. We also ﬁnd for stars on prograde Galactic orbits, a correlation between binarity and metallicity for the range [Fe/H] ∼< − 0.9, that contains an overlap between the higher-binarity, higher-metallicity thick disk stars and the lower-binarity, lower-metallicity halo stars. 6-5. Summary 157

6-5 Summary

We examine the relationship between Sun-like (FGK dwarfs) host metallicity and the frequency of close companions (orbital period < 5 years). We find a correlation at the ∼ 4σ level between host metallicity and the presence of planetary companion and an anti-correlation at the ∼ 2σ level between host metallicity and the presence of a stellar companion. We find that the non-linear best-fit is α = 2.2 0.5 and α = −0.8 0.4 for planetary and stellar companions respectively (see Table 6.3).

Fischer & Valenti (2005) also quantify the planet metallicity correlation by fitting an exponential to a histogram in [Fe/H]. They find a best-fit of α = 2.0. Our result of α = 2.2 0.3 is a slightly more positive correlation and is consistent with theirs. Our estimate is based on the average of the best-fits to the metallicity data binned both as a function of [Fe/H] and Z/Z . Larger bins tend to smooth out the steep turn up at high [Fe/H] and may be responsible for their estimate being slightly lower.

We also analyse the sample of Nordströmet al. (2004) and again find an anti- correlation between metallicity and close stellar companions for this larger period range. We also find that K dwarf host stars have a stronger anti-correlation between host metallicity and binarity than FG dwarf stars.

We compare our analysis with that of Carney et al. (2005) and ﬁnd an alternative explanation for their reported binary frequency dichotomy between stars on prograde

Galactic orbits with [Fe/H] ∼< 0 compared to stars on retrograde Galactic orbits with

[Fe/H] ∼< 0. We propose that the region, [Fe/H] ∼< −0.9, for stars on prograde Galactic orbits contains a mixture of low binarity halo stars and high binarity thick disk stars. Thick disk stars appear to have a ∼ 2 higher binary fraction compared to thin disk stars, which in turn have a ∼ 2 higher binary fraction than halo stars.

While the ratio of thick/thin disk stars is ∼ 3 times higher for K stars than for FG stars we only observe a marginal diﬀerence in their distributions as a function of metallicity. In the region −0.9 ∼< [Fe/H] ∼< −0.1 that we suspect contains a mixture of thick and thin disk stars, the K star distribution contains a higher ratio of thick disk 6-5. Summary 158 stars compared to the FG star distribution at a given metallicity. This diﬀerence is marginal but can partially explain the kinematic and spectral-type (∼ mass) results.

Thus for stars on prograde Galactic orbits as we move from low metallicity to high metallicity we move through low binarity halo stars to high binarity thick disk stars to medium binarity thin disk stars. Since halo, thick disk and thin disk stars are not discrete populations in metallicity and contain considerable overlap, as we go from low metallicity to high metallicity for prograde stars, we ﬁrstly observe a correlation between binarity and metallicity for the overlapping halo and thick disk stars and then an anti-correlation between binarity and metallicity for the overlapping thick and thin disk stars. Chapter 7

Conclusions

We have found and analysed a number of empirical trends in a variety of extrasolar planet parameters detected using the Doppler technique. We compare these trends with those found for other close-orbiting companions to Sun-like stars. We also examine the relationship between host metallicity and the frequency of close companions to Sun-like stars.

The mass distribution of detected planets is strongly peaked towards the lowest detectable masses despite the fact that massive planets are easier to detect (Fig. 2.2). Similarly, the period distribution is strongly peaked towards the longest detectable periods despite the fact that short period planets are easier to detect (Fig. 2.4). We have identiﬁed a less-biased subsample of exoplanets which we use to quantify these trends as accurately as possible. Extrapolations of these trends into the area of parameter space occupied by Jupiter, indicates that Jupiter lies in the most densely occupied region. Since Jupiter is the dominant planet in our Solar System, these trends in the exoplanets detected thus far do not rule out the hypothesis that our Solar System is typical. They support it. Our results suggest that the detected exoplanets are the observable tail of the main concentration of massive planets of which Jupiter is likely to be a typical member rather than an outlier.

To determine what fraction of stars have planets we have analysed the results of eight Doppler surveys. The number of target stars and the number of detected 160 planet hosts are used to estimate the fraction of stars with planets. We show how the naive fraction of ∼ 5% increases to ∼ 11% when only long-duration targets are included (Fig. 3.2). This fraction increases to ∼ 25% when only longest duration targets with the lowest excess in radial velocity dispersion are considered (Fig. 3.4). Our results for the fraction of Sun-like stars with planets are consistent with but are, in general, larger than previous estimates. The hypothesis that ∼ 100% of stars have planets is consistent with both the observed exoplanet data which probes only the high-mass, close-orbitting exoplanets and with the observed frequency of circumstellar disks in both single and binary stars. The observed fractions f that we have derived from current exoplanet data are lower limits that are consistent with

< < a true fraction of stars with planets ft, in the range 0.25 ∼ ft ∼ 1.

We analyse the close-orbitting (P < 5 years) planetary, brown dwarf and stellar companions to Sun-like (∼ FGK) stars to help constrain their formation and migration scenarios. We deﬁne a less-biased sample of Sun-like stars from which to extract the stellar, brown dwarf and planetary companions (Fig. 4.1). We discuss the selection eﬀects and completeness of the detected close companions in this sample.

The period and eccentricitry distributions of close-orbitting companion stars is different from that of the planetary companions. Planets tend to be more abundant at longer periods and are less frequent at very low and very high eccentricities than stellar companions. The period and eccentricity distributions of close-orbiting companions may be more a result of post-formation migration and gravitational jostling than representive of the relative number of companions that are formed at a specific distance and with a specific eccentricity from their hosts.

We verify the existence of a very dry brown dwarf desert for close companions to Sun-like stars (Fig. 5.1) where both planetary and stellar companions reduce in number by more than an order of magnitude towards the brown dwarf mass range. We ﬁnd that approximately 16% of Sun-like stars have a close companion more massive than Jupiter. Of these 16%, 11% 3% are stellar, < 1% are brown dwarf and 5% 2% are planetary companions. Splitting our sample of companions into 161

those with hosts above and below 1M , we ﬁnd that lower mass hosts have more stellar companions and fewer giant planet companions while higher mass hosts have fewer stellar companions but more giant planet companions.

We find marginal evidence that the minimum of the companion mass desert is a function of host mass with lower mass hosts having a lower mass companion desert but we find no evidence for a direct correlation between host mass and companion mass (Fig. 5.5). A comparison with the initial mass function of individual stars and free-floating brown dwarfs (Fig. 5.6), suggests either a different spectrum of gravitational fragmentation in the formation environment or post-formation migratory processes disinclined to leave brown dwarfs in close orbits.

Finally we examine the relationship between Sun-like host metallicity and the frequency of companions in close companion systems. We confirm and quantify a ∼ 4σ positive correlation between host metallicity and planetary companions (Fig. 6.4). We find little or no dependence on spectral type or distance in this correlation. In contrast to the metallicity dependence of planetary companions, stellar companions tend to be more abundant around low metallicity hosts. At the ∼ 2σ level we find an anti-correlation between host metallicity and the presence of a stellar companion.

Upon dividing our sample into FG and K sub-samples, we ﬁnd a negligible anti- correlation in the FG sub-sample and a ∼ 3σ anti-correlation in the K sub-sample. A kinematic analysis suggests that this anti-correlation is produced by a combination of low metallicity high binarity thick disk stars and high metallicity lower binarity thin disk stars (Fig. 6.17).

For stars on prograde Galactic orbits as we move from low metallicity to high metallicity, we move from low binarity halo stars to high binarity thick disk stars to medium binarity thin disk stars. Since halo, thick disk and thin disk stars are not discrete populations in metallicity and contain considerable overlap, we thus ﬁrstly observe a correlation between binarity and metallicity for the overlapping halo and thick disk stars and then an anti-correlation between binarity and metallicity for the overlapping thick and thin disk stars. Appendix A

Extrasolar Planet Data

We tabulate all of the 206 known extrasolar planets as of November 2006 in this Appendix. We list the 180 known extrasolar planets detected with the radial velocity method (See Section 1-2) in Table A.1. The 14 planets ﬁrst detected using the transit method (See Section 1-3.1) are listed in Table A.2. The 4 planets detected using microlensing (See Section 1-3.2) are listed in Table A.3. The 4 directly imaged planets (See Section 1-3.3) are listed in Table A.4 and the 4 planets detected using pulsar timing (See Section 1-3.4) are listed in Table A.5.

Each of the Tables A.1-A.5 contains the planet name, orbital period P , mass M or minimum mass Msini, semimajor axis a, the date of detection and references. The date of detection refers to the ﬁrst public reference to the planet. Depending on the method used to detect the extrasolar planet some of the following properties may also be given, the eccentricity e, the radial velocity induced in the host star K, the orbital inclination i, the planetary radius R or the date of ﬁrst observation. For the planets detected using the transit method, where all the orbital periods are small, tidal circularisation of the orbit leads to e = 0. We also list the host mass

M∗, the distance to the host d and the host metallicity [Fe/H] when known.

Extrasolar planets are given the same name as their host star followed by a letter of the alphabet that represents the planetary component. The first planet found in each system is designated by the letter ‘b’. Each subsequent planet found in 163 a system is assigned the next available letter in the alphabet. We use the most common host names found in the literature to identify the planets. To ensure that we include all possible planets, some low mass brown dwarfs have also been included that could potentially be planets due to uncertainty in mass. Also, if a star already has a planetary companion then any other low mass brown dwarf companions are also included. The planets in Tables A.1-A.5 are sorted by detection date with the exception of systems containing multiple planets where all of the planets in the same system have been grouped together. The first reference shown is typically for the extrasolar planet discovery with the last reference the source of the current orbital solution. Additional references are given for planets that have multiple independent discoverers or updates of significance.

References for Table A.1. (Bon05) Bonﬁls et al. (2005), (Bou05) Bouchy et al. (2005b), (But96) Butler & Marcy (1996), (But97) Butler et al. (1997), (But98) Butler et al. (1998), (But99) Butler et al. (1999), (But00) Butler et al. (2000), (But01) Butler et al. (2001), (But02) Butler et al. (2002), (But03) Butler et al. (2003), (But04) Butler et al. (2004), (But06) Butler et al. (2006), (Car03) Carter et al. (2003), (Cha00) Charbonneau et al. (2000), (Cha06) Charbonneau et al. (2006), (Coc97) Cochran et al. (1997), (Coc04) Cochran et al. (2004), (Cor05) Correia et al. (2005), (DaS06) da Silva et al. (2006), (Del98) Delfosse et al. (1998), (Egg06) Eggenberger et al. (2006), (Fis99) Fischer et al. (1999), (Fis01) Fischer et al. (2001), (Fis02a) Fischer et al. (2002a), (Fis02b) Fischer et al. (2002b), (Fis03a) Fischer et al. (2003a), (Fis03b) Fischer et al. (2003b), (Fis05) Fischer et al. (2005), (Fis06) Fischer et al. (2006), (Fri02) Frink et al. (2002), (Gal05) Galland et al. (2005), (Ge06) Ge et al. (2006), (Hat00) Hatzes et al. (2000), (Hat03) Hatzes et al. (2003), (Hat05) Hatzes et al. (2005), (Hat06) Hatzes et al. (2006), (Hen00) Henry et al. (2000), (Joh06) Johnson et al. (2006b), (Jon02a) Jones et al. (2002a), (Jon02b) Jones et al. (2002b), (Jon03) Jones et al. (2003), (Jon06) Jones et al. (2006), (Kor00) Korzennik et al. (2000), (Kue00) K¨ursteret al. (2000), (Lat89) Latham et al. (1989), (Lee06) Lee et al. 164

(2006), (LoC06) Lo Curto et al. (2006), (Lov05) Lovis et al. (2005), (Lov06) Lovis et al. (2006), (Mar96) Marcy & Butler (1996), (Mar98) Marcy et al. (1998), (Mar99) Marcy et al. (1999), (Mar00) Marcy et al. (2000), (Mar01a) Marcy et al. (2001a), (Mar01b) Marcy et al. (2001b), (Mar02) Marcy et al. (2002), (Mar05) Marcy et al. (2005b), (May95) Mayor & Queloz (1995), (May04) Mayor et al. (2004), (McA04) McArthur et al. (2004), (McC04) McCarthy et al. (2004), (Mou05) Moutou et al. (2005), (Mou06) Moutou et al. (2006), (Nae01a) Naef et al. (2001a), (Nae01b) Naef et al. (2001b), (Nae03) Naef et al. (2003), (Nae04) Naef et al. (2004), (Noy97) Noyes et al. (1997b), (Pep02) Pepe et al. (2002), (Pep04) Pepe et al. (2004), (Pep06) Pepe et al. (2006), (Per03) Perrier et al. (2003), (Que00) Queloz et al. (2000), (Riv05) Rivera et al. (2005), (San00) Santos et al. (2000), (San01) Santos et al. (2001), (San04) Santos et al. (2004a), (Sat03) Sato et al. (2003), (Sat05) Sato et al. (2005), (Set03) Setiawan et al. (2003), (Set05) Setiawan et al. (2005), (Soz06) Sozzetti et al. (2006), (Tin01) Tinney et al. (2001), (Tin02) Tinney et al. (2002), (Tin03) Tinney et al. (2003), (Tin05) Tinney et al. (2005), (Tin06) Tinney et al. (2006), (Udr00) Udry et al. (2000), (Udr02) Udry et al. (2002), (Udr03a) Udry et al. (2003a), (Udr03b) Udry et al. (2003b), (Udr06) Udry et al. (2006), (Vog00) Vogt et al. (2000), (Vog02) Vogt et al. (2002), (Vog05) Vogt et al. (2005), (Wit04) Wittenmyer et al. (2004), (Wri06) Wright et al. (2006), (Zuc02) Zucker et al. (2002), (Zuc03) Zucker et al. (2003), (Zuc04) Zucker et al. (2004). 165 Fis02a But99, But06 But99, But06 Mar02, McA04 Mar02, McA04 McA04, McA04 [Fe/H] References d ) (pc) ∗

M 0.89 40.57 -0.65 Lat89, But06 Detection Observation ) (AU) Date Start ( M i a Jup sin Planets Detected with the Radial Velocity Method Table A.1. P e K M c 2594.00 0.00 11.10 0.79 3.79 Jun 2001 c 241.23 0.26 55.60 1.98 0.83 Apr 1999 c 44.36 0.07 9.60 0.16 0.24 Jun 2002 e 2.80 0.09 5.80 0.04 0.04 Aug 2004 d 1290.10 0.26 63.40 3.95 2.54 Apr 1999 d 5552.00 0.09 47.50 3.90 5.97 Jun 2002 Name (days) (m/s) ( M Planet HD 114762 b 83.89 0.34 615.20 11.68 0.36 May 1989 continued on next page. . . 51 Peg70 Vir b47 Uma 4.23 b b 116.69 0.01 1089.00 0.40 55.94 0.06 316.30 49.30 0.47 7.49 2.63 0.05 0.48 Oct 2.13 1995 Jan 1996 Feb 1996 Sep 1994 Jan 1988 Jun 1987 1.09 1.11 15.36 1.08 18.11 0.20 14.08 -0.03 0.05 May95, Mar96, But06 But06 But96, Fis02a Ups And b 4.62 0.02 69.80 0.69 0.06 Aug 1996 Sep 1987 1.32 13.47 0.13 But97, But06 Tau Boo55 Cnc b 3.31 b 0.02 14.65 461.10 0.01 4.13 73.38 0.05 0.83 Aug 1996 0.11 Oct 1987 Aug 1996 1.35 Feb 1989 15.60 0.91 0.26 12.53 But97, But06 0.36 But97, McA04 16 Cyg BRho CrB bIot 798.50 Hor b 0.68 39.84 50.50 b 0.06 302.80 1.68 64.90 0.14 1.68 1.09 57.10 Nov 1996 0.23 2.08 Sep Apr 19871997 0.93 May Jun 1996 0.99 1998 21.41 1.00 Nov 1992 0.06 17.43 1.17 -0.23 Coc97, But06 17.24 Noy97, But06 0.19 Kue00, But06 166 , But06 e Riv05 Vog05 , But03, But06 a Mar01a, Riv05 Mar01b, Udr02 [Fe/H] References d ) (pc) ∗

M Detection Observation ) (AU) Date Start ( M Jup sin i a .continued Planets Detected with the Radial Velocity Method – Table. A.1 P e K M c 30.34 0.22 88.36 0.62 0.13 Dec 2000 c 3200.00 0.55 34.00c 2.21 1764.30 4.30 0.22 297.40 Jun 2005 18.10 2.92 Aug 2000 d 1.94 0.00 6.46 0.02 0.02 Jun 2005 Name (days) (m/s) ( M Planet 14 Her b 1773.08 0.38 88.75 4.89 2.85 Jul 1998 Sep 1994 1.00 18.15 0.46 Nae04 GJ 876 b 60.94 0.02 212.60 1.93 0.21 Jun 1998 Sep 1994 0.32 4.69 0.00 Del98, Mar98, Riv05 continued on next page. . . HD 187123 bHD 195019 3.10 bHD 217107 18.20 0.02 b 70.00 0.01 7.13GJ 271.50 86 0.53 0.13HD 3.69 168443 140.70 0.04 b b 0.14 1.41 Sep 1998 58.11 15.76 Oct 1998 0.07 0.53 Dec 0.04 1997 475.80 Oct Jul 376.70 1998 1998 1.08 8.01 3.91 Jul 1.07 1998 47.92 0.30 0.11 37.36 0.14 1.10 Dec Nov 1998 0.06 1998 19.72 Jul Jan 1996 1998 0.37 But98, But06 Fis99, 0.77 1.05 But06 10.91 38.50 Fis99, Vog05 -0.26 0.08 Que00, Mar99, But06 But06 HD 210277 bHD 75289 442.19HD b 130322 0.48 b 38.94HD 3.51 177830 10.71 bHD 0.03 1.29 134987 410.10 0.03 54.90 b 109.60 1.14 0.10 258.31 0.47 Dec 32.64 1.09 1998 0.24 0.05 50.03 1.53 0.09 Jul 1996 Feb 1999 Sep 1.62 1999 1.23 1.01 Nov Jan 1999 1998 0.82 Feb 1999 21.29 Nov 1999 Jul 0.21 1.21 1996 0.88 28.94 Jul 29.76 1996 1.46 0.26 0.03 Mar99, 59.03 But06 1.10 0.41 25.65 Udr00, But06 0.30 Udr00, But06 Vog00, But06 Vog00, But06 167 , But06 , But06 , Vog05 b f ESO , Lee06 , Lee06 ESO ESO ESO Vog05 Nae01b May04 But03, Udr03b [Fe/H] References d ) (pc) ∗

M Detection Observation 0.05 Nov 1999 Aug 1997 1.14 47.08 0.02 Cha00, Hen00, Wit04 ) (AU) Date Start ( M i 1 Jup sin i a .continued Planets Detected with the Radial Velocity Method – Table. A.1 P e K M c 843.60 0.14 15.40 0.62 1.64 Jun 2002 c 219.50 0.39 59.30 1.81 0.75 Apr 2001 d 2295.00 0.20 12.20 0.68 3.19 Jun 2005 Name (days) (m/s) ( M Planet HD 10697HD 37124 b 1076.40 b 0.10 154.46 115.00 0.05 6.38 27.50 2.16 0.64 Nov 1999 0.53 Oct 1996 Nov 1999HD 16141 1.16 Dec 1996HD 89744 32.56 b 0.83HD 0.16 46375 75.52 b 33.25HD 0.25256.80 52265 b -0.40 11.990.68 3.02 b Vog00, 267.30 But06 0.26 119.29 0.06 8.58 Vog00, 0.32 Vog05 0.36 33.65 0.93 42.10 Mar 2000 0.23 Mar 2000 1.09 Octcontinued 1996 on 0.04 next Dec page. 1996 . . 0.50 Mar 2000 1.12 Apr 1.64 2000 35.91 Sep 1998 38.99 Jan 0.17 1998 0.26 0.92 1.20 33.41 28.07 0.25 Mar00, But06 Kor00, 0.23 But06 But00, Nae01b Mar00, But06 HD 222582HD b 192263 572.38GJ b 3021 0.73 24.36 276.30 b 0.05 7.75 133.71 51.90 1.35 0.51 0.64 167.00 Nov 1999 0.15 3.37 Dec 1997 Nov 1999 0.50 0.99 JunJan 1998 2000 41.95 Nov 0.81 1998 0.01 19.89 0.90 0.00 17.62 Vog00, But06 0.15 Vog00, San00, But06 HD 83443 b 2.99 0.01 56.20 0.40 0.04 May 2000 Feb 1999 1.00 43.54 0.36 But02, May04 HD 209458 b 3.52 0.00 84.26 0.69 BD -10 3166 bHD 82943 3.49 b 0.02 439.20 60.90 0.02 41.70 0.46 1.74 0.05 Apr 1.19 2000 May 2000 Dec 1998 Dec 1998 1.01 120.01.18 27.46 0.35 0.28 But00, But06 May04 168 , But06 c c h c d , May04 ESO , Cor05 , But06 , But06 ESO ESO ESO ESO Cor05 May04 Fis03b, But06 Fis03b, But06 [Fe/H] References d ) (pc) ∗

M Detection Observation ) (AU) Date Start ( M Jup sin i a .continued Planets Detected with the Radial Velocity Method – Table. A.1 P e K M c 1383.40 0.27c 42.01 2165.00 0.35 2.40 170.30 2.52 13.20 Nov 2004 3.74 Jun 2002 c 2100.00 0.33 54.30 4.10 3.62 Jun 2003 c 1679.00 0.02 29.27 1.83 2.86 Jun 2002 Name (days) (m/s) ( M Planet HD 108147 b 10.90 0.53HD 168746 25.10 b 0.26 6.40HD 202206 0.10 0.11 b May 255.87 2000 28.60 0.44 Mar 1999 0.25 564.80 1.19 17.30 0.07 38.57 May 2000 0.82 0.17 May May 2000 1999 Aug Pep02 1999 0.93 43.12 1.12 -0.07 46.34HD 6434 0.34 Pep02 HD 19994 b Udr02 continued b on 22.00 next page. . . 535.70 0.17 0.30 34.20 36.20 0.40 1.69 0.14 1.43 Aug 2000 Aug 2000 Nov 1998 Nov 1998 0.79 1.35 40.32 22.38 -0.54 0.19 May04 May04 HD 169830 b 225.62 0.31HD 80.70 162020 b 2.90 8.43 0.82 0.28 May 2000 1813.00 15.00 Apr 1999 0.08 1.43 May 2000 36.32 Jun 0.18 1999 0.78 Nae01b 31.26 0.04 Udr02 HD 38529 b 14.31 0.25 56.80 0.85 0.13 Jul 2000 Dec 1996 1.47 42.43 0.41 Fis01, But06 HD 92788 b 325.81 0.33 106.00 3.67 0.96 Jul 2000 Jan 1998 1.13 32.32 0.32 Fis01, May04 HD 12661 b 262.53Eps Eri 0.36HD 190228 74.19 b b 2500.00 1146.00 2.34 0.25 0.50 18.60 0.83 91.00 Jul 2000 1.06 4.49 Aug 3.38 1998 2.25 Aug 2000 Aug 1.11 2000 37.16 Aug 1987 Jul 1997 0.36 0.82 1.16 3.22 62.11 Fis01, But06 -0.08 -0.23 Hat00, But06 Per03 169 , But06 , But06 c , But06 ESO ESO ESO ESO ESO , But06 , But06 , But06 ESO ESO ESO ESO Pep06 Pep06 May04 Nae04 Sant04, Pep06 [Fe/H] References d ) (pc) ∗

M Detection Observation ) (AU) Date Start ( M Jup sin i a .continued Planets Detected with the Radial Velocity Method – Table. A.1 P e K M c 9.64 0.17 3.06 0.03 0.09 Aug 2004 e 4205.80 0.10 21.79 1.81 5.24 Aug 2006 c 2025.00 0.58 104.00 6.00 3.35 Apr 2001 d 310.55 0.07 14.91 0.52 0.92 Aug 2006 Name (days) (m/s) ( M Planet HD 121504HD 179949 bHD 27442 63.33 bHD 0.03 160691 3.09 b 55.80 0.02428.10 b 1.22 112.60 643.25 0.06 32.200.13 0.92 0.33 37.78 Aug 2000 1.56 0.04 1.68 Oct Mar 2000 1.27 2000 1.50 Dec Nov 2000 1.18 1998 Dec 2000 44.37 Jan 1998 1.21 Apr 0.14 1998 27.05HD 8574 1.49 0.18 1.15 18.23 15.28 b 0.41 0.30 225.00HD Tin01, 80606 But06 0.37 64.10 But01, But06 b But01, Pep06 continued 1.96 on 111.45 next page. . . 0.93 0.76 481.90 Apr 2001 4.31 Jan 1998 0.47 Apr 1.15 2001 44.15 Apr 1999 0.02 1.10 58.38 Per03 0.33 Nae01a HD 106252 b 1516.00 0.59 152.00 7.10 2.60 Apr 2001 Mar 1997 1.02 37.44 -0.05 Fis02b, Per03 HD 178911 B b 71.51 0.14 346.90 7.35 0.34 Apr 2001 Jul 1998 1.06 46.73 0.28 Zuc02 HD 141937 b 653.22 0.41 234.50 9.70 1.52 Apr 2001 Mar 1999 1.08 33.46 0.12 Udr02 HD 213240 b 882.70 0.42 96.60 4.72 1.92 Apr 2001 Jul 1999 1.22 40.75 0.18 San01 HD 50554HD 74156 b 1224.00 b 0.44 51.64 91.50 0.64 4.46 112.00 2.28 1.80 Apr 2001 0.29 Nov Apr 1997 2001 1.05 Jan 1998 31.03 1.21 -0.01 64.56 Fis02b, Per03 0.15 Nae04 170 , But06 f f f ESO , Vog05 f Vog05 [Fe/H] References d ) (pc) ∗

M Detection Observation ) (AU) Date Start ( M Jup sin i a .continued Planets Detected with the Radial Velocity Method – Table. A.1 P e K M c 17.10 0.01 4.60 0.06 0.13 Jun 2005 Name (days) (m/s) ( M Planet HD 28185HD b 4208 383.00HD 68988 b 0.07HD 828.00 b 161.00 142 0.05HD 6.28 5.72 23079 19.06 bHD 0.12 b 1.03 33636 350.30 0.80 184.70 730.60 Apr 0.26 b 2001 0.10 1.86 2127.70 1.65 33.90 Oct 54.90 0.48 1999 Oct 2001 0.07 164.20 1.31 2.45 0.99 Oct 2001 Oct 9.28 1996 1.04 39.56 1.60 Apr Oct 1997 3.27 2001 0.87 0.23 Oct 2001 Oct 32.70 2001 1.18 Jan 1998 Jan -0.26 1998 58.82 Jan 1998 1.24 San01 0.34 1.01 25.64 1.02 Vog02, But06 34.60 0.12 28.69 -0.13 Vog02, But06 -0.11HD 114386 Vog02, Per03 Tin02, b But06 continued Tin02, on But06 next 938.00 page. . . 0.23 34.30 1.34 1.71 Jun 2002 Oct 1997 0.76 28.04 -0.03 May04 HD 114729 bHD 150706 1114.00 b 0.17 264.90 18.80 0.38 0.95 33.00 2.11 0.95 Jun 2002 0.80 Jan Jun 1997 2002 1.00 Jul 1997 35.00 0.98 -0.26 27.23 -0.01 But03, But06 Udr03b HD 114783 bHD 39091 496.90HD b 4203 0.09 2151.00 29.36Iot Dra 0.64 b 196.40HD 431.88 1.03 136118 b 10.27 0.52 bHD 1.17 190360 511.10 1193.10 60.30 3.38 b Oct 0.35 0.71 2001 2891.00 Oct 2001 212.80 2.07 307.60 0.36 Jun 1998 12.00 Nov 8.82 1.16 23.50 1998 2.37 0.86 Oct 2001 1.27 1.55 1.10 Feb 20.43 2002 Jan 20.55 2002 Jul 3.99 2000 0.13 Jan 0.08 1998 May Jun 2000 2002 1.13 1.23 1.05 77.82Sep Vog02, 1994 But06 Jon02b, But06 52.27 31.33 0.42 1.01 -0.05 0.13 15.89 Vog02, But06 0.23 Fis02b, But06 Fri02, But06 Nae03 171 , But06 , But06 f f f f f Tin06 Vog05 Vog05 Per03 May04 [Fe/H] References d ) (pc) ∗

M Detection Observation ) (AU) Date Start ( M Jup sin i a .continued Planets Detected with the Radial Velocity Method – Table. A.1 P e K M c 928.30 0.17 76.20 3.21 1.76 Jun 2005 c 1599.00 0.25 18.35 1.02 2.68 Jun 2005 c 376.88 0.40 67.40 2.26 1.04 Feb 2006 Name (days) (m/s) ( M Planet HD 20367HD b 72659 469.50HD b 23596 0.32 3630.00HD b 40979 0.27 29.00 1565.00 42.50HD b 128311 0.29 1.17 263.84 b 124.00 3.30 1.25 458.60 0.27 7.80 112.00 4.77 Jun 0.25 2002 2.83 Jun 66.80HD 3.83 2002 30177 Nov 1997 Jun 2002HD b 2.18 Jan 0.86 216437 1998 1.17 2770.00 b Jan Jun 1998 2002 1.10 0.19 27.13 1353.00 1.10 146.80 Jun 0.32 2002 Jan 1.23 51.36 0.13 1998 10.45 39.00 51.98 0.02 Jun 1998 1.19 3.95 2.26 0.27 33.33 Jun 0.84 2002 2.54 Udr03b 0.19 But03, 16.57 But06 Oct Jun 1998 2002 0.12 Nov 1.07 1998 Fis03b, But06 54.71continued 1.19 But03, on Vog05 next 0.38 page. . . 26.52 0.24 Jon02a, Tin03, May04 But06 HD 147513 b 528.40 0.26 29.30 1.18 1.31 Jun 2002 Jul 1998 1.07 12.87 0.08 HD 108874 b 395.27HD 49674 0.07 37.91HD b 2039 4.95 1.37 b 1120.00 0.09 1.05 0.71 12.04 Jun 2002 153.00 0.10 6.11 Jun 1999 0.06 2.23 1.00 Jun 2002 Jul 68.54 2002 Dec 0.21 2000 Oct 1998 1.06 1.17 40.73 But03, Vog05 89.85 0.32 0.32 But03, But06 Tin03, But06 HD 196050 bHD 73526 1378.00 0.23 b 49.70 187.50 0.39 2.90 76.10 2.54 2.04 Jun 2002 0.65 Nov 1998 Jun 2002 1.15 Feb 1999 46.93 1.05 0.23 94.61 Jon02a, May04 0.26 Tin03, Tin06 172 h h h h h ESO , Zuc04 g g h Zuc03 [Fe/H] References d 45.52 0.05 ) (pc) ∗

M Jan 2004 Jun 2000 Detection Observation ) (AU) Date Start ( M Jup sin i a 2.90 .continued Planets Detected with the Radial Velocity Method – Table. A.1 P e K M Name (days) (m/s) ( M Planet HD 76700Gam Cep bHD 216435 3.97 bHD b 905.00 47536 0.09 1311.00 0.12HD 3651 27.60 0.07 b 27.50HD 712.13 19.60 73256 0.23 b 0.20 1.77HD 10647 b 1.26 62.21 0.05 113.00HD 2.14 65216 0.62 2.55 b Jul 2.56 2002 5.20 Sep 1003.00HD 2002 142415 16.00 Sep 0.03 b 2002 0.16 Feb 1.61 1999 AugHD 613.00 269.00 b 1988 111232 Aug 17.90 0.23 Dec 1998 2002 386.30 0.41 1.13HD b 1.87 216770 1.59 0.30 0.50 0.93 Nov 1.30 59.70 1143.00 33.70 1999HD 13.79 b 41004 0.04 0.20 Jan B 33.29 51.30 2003 0.38 2.03 118.45 1.10 1.22 0.16 b Apr 159.30 2003 0.24 Jun Sep 0.37 1.69 121.4 2003 1987 Tin03, But06 1.37 1.33 6.84 Feb 2001 30.90 -0.54 Jon03, Aug But06 1.07 Jun 1998 0.89 2003 Hat03 0.08 1.97 1.05 Jun 6114.00 11.11 0.65 2003 1.10 Mar JunHD Set03 1999 2003 219449 36.52 18.40 0.14 Mar 17.35 0.46 1999continued b Mar 0.27 0.92 on 2000 0.02 next -0.06 Jun page. Fis03a, . 2003 . But06 182.00 1.09 35.59 Udr03a, Jun Udr03a 2003 0.78 34.57 Sep -0.12 2000 28.88 But06 Dec 2000 0.15 -0.36 0.90 May04 0.40 37.89 43.03 May04 0.24 May04 May04 HD 104985HD b 70642 198.20HD 59686 b 0.03 2068.00 161.00 b 0.03 303.00 6.33 30.40 0.00 0.78 149.00 1.97 Jun 2003 5.25 3.23 Mar 2001 Jul 0.91 2003 Jan 1.60 2004 Jan 1998 102.0 Jun 1999 1.05 -0.28 28.76 1.09 92.51 0.18 Sat03 0.28 Car03, But06 173 , But06 i i i ESO But04, But06 [Fe/H] References d ) (pc) ∗

M Detection Observation ) (AU) Date Start ( M i a Jup sin .continued Planets Detected with the Radial Velocity Method – Table. A.1 P e K M Name (days) (m/s) ( M Planet HD 330075HD 37605 bGJ 436 3.39 b 0.00 54.23 107.00 b 0.74 0.62 262.90 2.64 2.86 0.04 0.21 Jan 2004 0.26 18.30 Jul 2004 Jul 0.07 2003 Dec 0.03 2003 0.70 Aug 2004 50.20 0.80 Jan 0.08 42.88 2000 0.31 0.41 10.23 Pep04 Coc04 HD 93083continued on next page. . b . 143.58 0.14 18.30 0.37 0.48 Feb 2005 Jan 2004 0.70 28.90 0.15 Lov05 HD 117618HD 102117 b 25.83 b 0.42 20.81 12.80 0.12 11.98 0.18 0.17 0.18 Sep 2004 0.15 Sep 2004 Jan 1998 May 1998 1.09 38.02 1.11 42.00 0.03 0.31 Tin05, Tin05, Lov05 But06 HD 208487HD 154857 bHD 130.08 88133 b 0.24HD 398.50 41004 A 19.70 b 0.51HD 99492 b 52.00 3.42 0.52 963.00HD 117207 0.13 1.85 b 0.74 0.52HD 45350 36.10 b 99.00 17.04 Sep 2004 1.13 2597.00HD 188015 0.25 0.30 2.60 Sep 0.14 b Aug 2004 1998HD 183263 9.80 26.60 967.00 b 0.05 1.70 Apr 2002 1.13HD 461.20 0.80 142022 Sep Nov 1.88 b A 0.11 2004 2004 44.00 64.200.14 b 1.22 635.40 3.79 Dec 0.12 Jan 1928.00 37.60 0.04 2000 2004 68.54 0.36 1.96 0.53 Jan Jan 2005 2005 -0.23 87.30 1.50 0.70 1.20 92.00 1.96 Tin05, Jan 43.03 Jan But06 74.46 3.82 1997 1.20 1997 Jan 2005 4.50 0.16 0.34 Jan 2005 1.52 1.08 0.86 Dec McC04 2.93 1999 Jan 33.01 17.99 2005 Jul Feb 2000 2005 Zuc04, 1.06 Fis05, Zuc04 0.25 0.31 But06 Jul 2001 48.95 Jul 1.09 1999 0.29 52.63 1.17 Mar05, Mar05, But06 But06 0.90 0.30 52.83 35.87 Mar05, 0.32 But06 0.19 Mar05, But06 Mar05, But06 Egg06 174 i i i j j j i j Hat05 [Fe/H] References d ) (pc) ∗

M Detection Observation 0.04 Jul 2005 Jul 2004 1.30 78.86 0.36 Sat05, Cha06 ) (AU) Date Start ( M i 2 Jup sin i a .continued Planets Detected with the Radial Velocity Method – Table. A.1 P e K M Name (days) (m/s) ( M Planet HD 11977HD b 50499 711.00HD b 149026 0.40 2480.00 b 105.00 0.14 2.88 22.90 6.54 0.00 1.75 1.94 43.20 May 2005 3.87 0.36 Jun Oct 2005 1999 Dec 1.91 1996 66.45 1.25 -0.21 47.26 0.34 Set05 Vog05 HD 101930 bHD 63454 70.46HD b 27894 0.11HD 2.82 b 2638 18.10 17.99HD 0.00 13189 b 0.30 64.30 0.05 b 3.44 0.30 58.10 471.60 0.38 Feb 0.00 2005 0.27 0.62 0.04 67.40 173.30 Feb 2004 0.12 Feb 2005 8.00 0.48 Feb 2005 0.74 Feb 2004 1.50 0.04 30.50 Sep 2004 Apr Feb 2005 2005 0.80 0.17 35.80 0.75GJ Aug 581 Oct 2001 2004 42.37 0.11 Lov05 HD 118203 2.01 0.93 0.30 b bHD 1851 212301 53.71 Mou05 5.37 6.13 bHD 0.16 33564 Mou05 0.00 0.31 2.25HD b 189733 217.00 13.20 Mou05 388.00 0.00 bcontinued on 2.14 next 0.05 0.34 59.50 page. . . 2.22 232.00 0.07 0.04 0.40 0.00 9.10 Aug Aug 2005 205.00 2005 0.03 1.12 May 1.15 2004 May Aug 2004 2005 Sep 2005 0.03 1.23 Feb 0.31 2005 Mar Oct 88.57 2004 2005 6.27 1.05 0.10 Aug 1.25 -0.25 2005 52.71 20.98 -0.18 0.82 DaS06 -0.12 Bon05 19.25 LoC06 -0.03 Gal05 Bou05 HD 149143 bHD 109749 4.07 bHD 4308 0.025.24 b 149.60 0.01 15.56 1.33 28.30 0.00 0.05 0.28 4.07 Aug 2005 0.06 0.05 Jul Aug 2004 2005 0.12 Feb 2005 1.20 Aug 2005 63.49 1.21 Sep 2003 0.26 59.03 Fis06, 0.90 DaS06 0.25 21.90 -0.31 Fis06 Udr06 175 k ESO ESO ESO Wri06 Hat06 Lov06 Lov06 [Fe/H] References d ) (pc) ∗

M 0.99 52.88 0.23 But06, Wri06 Detection Observation ) (AU) Date Start ( M Jup sin i a .continued Planets Detected with the Radial Velocity Method – Table. A.1 P e K M c 113.83 0.28 41.80 0.95 0.46 Jul 2006 c 31.56 0.13 2.70 0.04 0.19 May 2006 d 197.00 0.07 2.20 0.06 0.63 May 2006 Name (days) (m/s) ( M Planet HD 81040HD b 102195 1001.70 bHD 20782 0.53 4.11 168.00HD b 187085 0.06 585.86 b 6.86HD 33283 1147.00 64.00 0.93 1.94 0.75HD b 115.00 224693 0.48 Nov 26.00 b 2005 18.18HD 1.78 86081 26.73 0.05 May 0.48 0.98 1999HD b 1.36 69830 Jan 25.20 0.05 2006 2.26 Mar 0.96 2.14 b 2006 40.20 0.33 Mar 32.56 Jan 2006 2005 Aug 0.018.67 1998 0.71 -0.16 207.70 0.17 Nov 1998HD 0.93 0.10 62509 0.98 0.23 Apr 1.50 2006 28.98 3.60 1.16 36.02 b Soz06 Apr 2006 -0.09 Jan 0.04 44.98 589.64 -0.05 2004 0.03 Jul Apr 0.02 2004 2006 0.05 1.24 0.08 Ge06 41.00 Jon06 Nov 86.88 2005 1.33 May 2006 2.30 Jon06 94.07 0.37 1.21 Oct 2003 1.64 0.34 91.16continued on Jun 0.86 Joh06 next 2006 0.26 page. . . 12.58 Joh06 Oct 1980 -0.05 Joh06 1.86 Lov06 10.34 HIP 14810 b 6.67 0.15 420.70 3.84 0.07 Jul 2006 HD 164922 bHD 11964 1155.00 0.05HD b 89307 2110.00 7.30 b 0.06 2900.00 0.36 9.00 0.01 37.20 2.11 0.61 Jul 2.61 2006 3.34 3.90 Jul Jul 2006 1996 Jul 2006 Oct 0.94 1996 Jan 1998 21.93 1.12 0.17 1.00 33.98 30.88 0.12 But06 -0.16 But06 But06 176 Ge, k Udry, S. e Mou06 [Fe/H] References Sivan, J.-P. (2000), d d ) (pc) ∗

Mayor, M. & Queloz, D. (2005), M j Queloz, D. (2000), c Mayor, M. (2005), i Detection Observation Naef, D. (2000), b ) (AU) Date Start ( M Udry, S. (2003), h Jup sin i a .continued Planets Detected with the Radial Velocity Method – Mayor, M. (1998), a Mitchell, D.S. (2003), P e K M g Table. A.1 = 85.2 (deg). = 85.8 (deg). i i Name (days) (m/s) ( M Planet Udry, S. (2002), HD 107148 bHD 99109 48.06HD b 66428 0.05 439.30HD b 10.90 185269 0.09 1973.00 b 14.10 0.21 0.47 6.84 48.30 0.50 0.27 0.30 2.82 Jul 1.11 2006 91.00 3.18 Jul 2006 Jan 0.94 2000 Jul 2006 Dec 0.08 2000 1.12 Dec Aug 2000 2006 51.26 0.93 May 0.31 1.10 60.46 2004 55.04 0.31 1.28 But06 0.31 47.37 But06 But06 f First announced with an ESO Press Release. Inclination Inclination (2000), First announced at a conference by ESO i 1 i 2 J. (2006). 177 ), ), ), ( 2004 ( 2005 ( 2002c Butler et al. Konacki Pont et al. Sah06 Sah06 ODo06 McC06 Kon05b Bakos06 References Udalski et al. ), (But06) Alo04, But06 Uda02c, Pon04 Collier Cameron06 Collier Cameron06 ), (Kon05b) ), (Pon04) ( 2005a ( 2005 ( 2006 ), (Uda02b) [Fe/H] ( 2002a Bouchy et al. d Konacki et al. ) (pc) ∗

O’Donovan et al. M ), (Bou05) Udalski et al. ), (Kon05a) ( 2004 ), (ODo06) Oct 2006Oct 0.79 2006 1.15 Oct 2006 1.24 Oct 2006 1.10 ( 2004 Aug 2005 1.06 44.82 Detection ). ( 2004 ), (Uda02a) ( 2003 Bouchy et al. ) (deg) Date ( M ( 2004 jup Planets Detected with the Transit Method Konacki et al. Moutou et al. Udalski et al. ), (Bou04) Torres et al. ) (AU) ( R ), (Kon04) Table A.2. ( 2004 Jup ), (Mou04) ( 2003 ), (Uda03) ( 2006 ), (Tor04) P M a R i ( 2002b Alonso et al. ( 2006 b 3.94 0.90 0.05 1.30 87.7 May 2006 1.00 200 Konacki et al. - (Alo04) Udalski et al. McCullough et al. Name (days) ( M Sahu et al. Planet ), (Kon03) SWEEP-04 b 4.20 3.80 0.05 0.81 OGLE-TR-111 bOGLE-TR-10 4.02 bHD 188753A 0.53 3.10XO-1 b 0.05 0.66TrES-2 3.35 1.00 0.04HAT-P-1 1.14 86.5 1.54WASP-2 b 0.04 Aug 2004 b 89.2WASP-1 2.47 0.82 Dec 4.47 2004SWEEP-11 b 1500 1.28 1.22 2.15 0.53 b 0.12 b 0.04 1500 2.52 0.06 0.88 1.80 1.24 0.39 1.36 0.89 0.03 83.9 9.70 85.9 0.96 0.04 Uda02a, Sep Kon05a, 2006 Bou05 0.03 Sep 2006 1.93 1.08 1.13 1.12 230 139 0.13 OGLE-TR-56 bOGLE-TR-132 b 1.21OGLE-TR-113 1.69 b 1.18TrES-1 1.43 1.19 0.02 1.35 0.03 1.25 b 1.13 0.02 81.0 3.03 85.0 1.08 Jan 2003 0.76 Apr 2004 87.5 1.10 1.35Apr 0.04 2004 1500 1500 0.77 1.08 0.17 0.43 1500 88.2 Uda02b, Kon03, Tor04, Bou05 Aug 0.14 2004 Uda03, 0.89 Bou04, Mou04 Uda02c, 150 Kon04, Bou04 0.00 (Sah06) (Uda02c) (McC06) ( 2006 References 178 Gould et al. ), (Gou06) References ( 2004 d ) (kpc) Bond et al. ∗

M ), (Bon04) Detection ( 2006 2.6 Jan2.7 2006 Mar 0.22 2006 0.50 6.6 2.7 Bea06 Gou06 ) (AU) Date ( M a b Jup Bennett et al. P M a Planets Detected with the Microlensing Method (years) ( M ), (Ben06) ( 2006 ). Table A.3. ( 2005 Name Planet Beaulieu et al. . ⊕ Udalski et al. OGLE-2003-BLG-235L bOGLE-2005-BLG-071L 11.2 bOGLE-2005-BLG-390L b 6.7 2.6 8.9 4.30.9 0.017 Apr 2004 1.8 0.63 May 2005 5.8 0.13 Bon04, Ben06 2.0 Uda05 OGLE-2005-BLG-169L b 6.3 0.04 M 13 - (Bea06) b . ⊕ ), (Uda05) M 5.5 ( 2006 References a 179 Chauvin et al. ), (Cha05b) ( 2005a References d 59.0 Cha04, Cha05a Chauvin et al. ) (pc) a ∗

). M ), (Cha05a) Detection ( 2004 Chauvin et al. 2004 4.5 Mar 2006 0.07 3.85 Bil06 ). ) (AU) Date ( M Planets Detected by Direct Imaging b Jup Chauvin et al. P M a ). Table A.4. Biller et al. 2006 ), (Cha04) ( 2005 ( 2006 Name (years) ( M Planet AB PicGQ Lup bSCR b 1845 5300 b 1250 13.5 30 21.5 275 20.0 103 Apr 2005 Mar 2005 0.74 0.70 47.3 140.0 Cha05b Neu05 2M1207 b 1800 5.0 46 Sep 2004 0.03 Biller et al. Neuhäuseret al. - (Bil06) ), (Neu05) A brown dwarf host with a planetary mass companion ( Probably a brown dwarf companion ( ( 2005b References a b 180 ), (Tho99) ( 2003 Sigurdsson et al. Arz96, Tho99, Sig03 ). b ( 1992 ), (Sig03) ) but not confirmed as a planet until Jan 1996 ( 2003 Detection References Wolszczan & Frail Backer et al. 1993 ) (AU) (deg) Date i a i Konacki & Wolszczan Jup sin ), (Wol94) 2.5 23 55 Jan 1996 ( 1992 ), (Kon03) Planets Detected with the Pulsar Timing Method a ( 1996 P e M c 66.542 0.02 0.0135292 0.36 53 Sep 1991 Wol92, Wol94, Kon03 d 98.211 0.03 0.0122706 0.46 47 Sep 1991 Wol92, Wol94, Kon03 Table A.5. Wolszczan & Frail ). Name (days) ( M Planet Arzoumanian et al. ), (Wol92) A companion was first detected in Oct 1993 ( b PSR B1620-26 b 100 PSR B1257+12 b 25.262 0 0.0000629 0.19 Apr 1994 Wol94, Kon03 ( 1999 - (Arz96) Period in years. Thorsett et al. ( Arzoumanian et al. 1996 References a Appendix B

Close Sun-like Sample

We list our close sample (d < 25 pc) of Sun-like stars in Table B.1 that we construct from the Hipparcos catalog in Chapter 4. We use this sample in our analyses in Chapters 5 and 6. We list the Hipparcos number, colour B − V , absolute visual magnitude MV , distance, metallicity [Fe/H], metallicity source, exoplanet target status and the known stellar and planetary companions. We use the following ab- breviations for the metallicity source: EP - Extrasolar Planet Target Spectroscopy, CdS - Cayrel de Strobel et al. (2001) Spectroscopy, uvby - uvby Photometry, BB - Broad-Band Photometry and HR - HR Diagram K Dwarf.

Table B.1. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 171 0.69 5.33 12.40 -0.80 CdS Yes HIP 518 0.69 4.44 20.28 0.05 uvby No Star HIP 544 0.75 5.39 13.70 0.18 EP Yes HIP 1031 0.78 5.68 20.33 -0.16 uvby Yes HIP 1292 0.75 5.36 17.62 0.15 EP Yes Planet continued on next page. . . 182

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 1349 0.66 5.03 23.02 -0.59 uvby Yes Star HIP 1499 0.67 4.62 23.44 0.18 EP Yes HIP 1598 0.64 4.99 24.84 -0.43 uvby Yes HIP 1599 0.58 4.56 8.59 -0.14 EP Yes HIP 1768 0.89 6.55 22.44 -0.13 uvby No HIP 1803 0.66 4.84 20.39 0.25 EP Yes HIP 1936 0.94 6.64 18.01 -0.29 EP Yes HIP 2021 0.62 3.45 7.47 -0.08 EP Yes HIP 2762 0.57 3.58 21.05 0.03 uvby Yes Star HIP 2941 0.72 4.61 15.53 -0.09 uvby Yes HIP 3093 0.85 5.65 11.11 0.14 EP Yes HIP 3206 0.94 6.17 17.27 0.18 EP Yes HIP 3497 0.66 4.85 21.85 -0.31 EP Yes HIP 3535 0.98 6.32 22.01 0.34 EP Yes HIP 3583 0.64 4.93 14.94 -0.03 EP Yes HIP 3765 0.89 6.38 7.46 -0.27 EP Yes HIP 3810 0.50 3.18 23.92 0.00 uvby No Star HIP 3821 0.59 4.59 5.95 -0.25 EP Yes HIP 3850 0.77 5.78 18.84 -0.21 EP Yes HIP 3876 0.90 6.09 21.52 0.08 BB No HIP 3909 0.51 4.22 15.46 -0.15 CdS Yes HIP 3979 0.66 5.26 22.09 -0.19 EP Yes HIP 4148 0.94 6.41 14.08 -0.17 EP Yes HIP 4151 0.54 3.46 18.57 -0.01 CdS Yes HIP 5336 0.70 5.78 7.55 -0.85 CdS No HIP 5842 1.00 5.60 21.11 0.23 EP Yes HIP 5862 0.57 4.08 15.05 0.18 EP Yes StarJ continued on next page. . . 183

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 5944 0.59 4.72 23.64 -0.03 EP Yes HIP 6379 0.83 6.04 16.82 -0.15 EP No HIP 6917 0.97 5.92 23.17 -1.05 uvby No Star HIP 7235 0.77 5.52 19.50 -0.02 EP Yes HIP 7339 0.69 4.91 20.99 0.02 EP Yes HIP 7372 0.91 5.24 23.65 -0.76 uvby Yes HIP 7513 0.54 3.45 13.47 0.13 EP Yes Planet HIP 7576 0.80 5.79 23.61 0.06 uvby Yes HIP 7734 0.69 4.95 21.40 0.12 EP Yes HIP 7751 0.88 6.21 8.15 -0.23 EP Yes HIP 7918 0.62 4.45 12.64 -0.04 CdS No HIP 7978 0.55 4.32 17.35 -0.06 EP Yes Planet HIP 7981 0.84 5.87 7.47 -0.04 EP Yes HIP 8102 0.73 5.68 3.65 -0.52 EP Yes HIP 8362 0.80 5.64 9.98 0.03 EP Yes HIP 8486 0.65 4.91 23.00 -0.09 CdS Yes HIP 9269 0.77 5.19 24.55 0.26 EP Yes HIP 9829 0.66 5.06 23.18 -0.28 EP Yes HIP 10138 0.81 5.93 10.91 -0.26 EP Yes Planet HIP 10531 0.92 5.27 23.55 0.35 EP Yes HIP 10644 0.61 4.66 10.85 -0.47 uvby No Star HIP 10723 0.59 3.61 24.98 0.00 CdS No Star HIP 10798 0.72 5.81 12.68 -0.47 EP Yes HIP 11072 0.61 3.48 21.93 0.02 CdS Yes HIP 12114 0.92 6.50 7.21 -0.12 EP Yes HIP 12158 0.94 6.17 24.34 0.25 EP Yes HIP 12444 0.52 4.12 21.54 -0.01 CdS Yes continued on next page. . . 184

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 12530 0.51 4.05 21.63 -0.17 uvby Yes HIP 12623 0.58 2.95 24.68 0.19 uvby No Star HIP 12653 0.56 4.22 17.24 0.19 EP Yes Planet HIP 12777 0.51 3.85 11.23 0.06 EP Yes HIP 13081 0.82 5.81 22.37 0.21 CdS No HIP 13402 0.86 5.97 10.38 0.06 EP Yes HIP 13642 0.95 5.72 22.88 0.28 EP Yes HIP 13772 0.86 5.57 22.48 -0.11 uvby Yes HIP 13976 0.93 6.12 23.44 0.25 EP Yes HIP 14150 0.70 4.99 21.16 0.11 EP Yes HIP 14286 0.63 4.84 22.86 -0.28 CdS Yes HIP 14632 0.60 3.94 10.53 0.16 EP Yes HIP 14879 0.54 3.05 14.11 -0.19 EP Yes HIP 14954 0.58 3.32 22.38 0.19 EP Yes Planet HIP 15099 0.86 6.09 22.24 -0.03 EP Yes HIP 15131 0.59 4.82 24.36 -0.55 CdS Yes HIP 15330 0.64 5.11 12.12 -0.21 EP Yes HIP 15371 0.60 4.83 12.08 -0.23 EP Yes HIP 15442 0.66 5.09 24.68 -0.21 EP Yes HIP 15457 0.68 5.03 9.16 0.12 EP Yes HIP 15510 0.71 5.35 6.06 -0.38 EP Yes HIP 15673 0.99 7.27 22.71 -0.17 BB No HIP 15799 0.84 5.74 17.09 0.16 EP Yes HIP 16537 0.88 6.18 3.22 -0.08 EP Yes HIP 16852 0.58 3.60 13.72 -0.02 EP Yes HIP 17147 0.55 4.75 24.35 -0.91 EP Yes HIP 17420 0.93 6.36 14.05 -0.11 EP Yes continued on next page. . . 185

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 17439 0.87 5.94 16.23 0.06 EP Yes HIP 17666 0.80 5.72 24.49 -1.03 EP Yes Star HIP 18267 0.72 5.23 20.68 0.01 EP Yes HIP 18324 0.83 6.20 21.30 -0.51 EP Yes HIP 18413 0.70 4.88 21.40 -0.11 uvby No HIP 18859 0.52 3.96 19.23 -0.03 CdS Yes HIP 19076 0.62 4.78 16.73 0.10 EP Yes HIP 19233 0.64 4.54 23.19 -0.07 EP Yes StarJ HIP 19255 0.87 5.56 20.58 -0.40 uvby No HIP 19335 0.52 3.87 21.34 -0.11 CdS Yes HIP 19422 0.95 6.37 18.46 -0.03 EP Yes HIP 19849 0.82 5.92 5.04 -0.31 EP Yes HIP 19855 0.68 5.34 20.89 -0.13 CdS Yes HIP 19859 0.57 4.69 21.19 0.08 CdS Yes HIP 21988 0.91 6.25 22.35 -0.18 EP Yes HIP 22122 0.88 6.03 20.45 0.08 CdS Yes HIP 22263 0.63 4.87 13.32 0.02 EP Yes HIP 22451 0.90 6.21 17.99 -0.06 EP Yes HIP 23437 0.64 5.28 22.25 -0.56 EP Yes HIP 23693 0.53 4.38 11.65 -0.23 CdS Yes HIP 23786 0.80 5.84 23.98 -0.16 uvby No HIP 23835 0.66 3.91 15.87 -0.17 EP Yes HIP 24786 0.57 3.98 24.93 -0.07 EP Yes HIP 24813 0.63 4.18 12.65 0.12 EP Yes HIP 25110 0.51 3.47 20.98 -0.12 EP No HIP 25119 0.98 6.27 19.90 -0.64 uvby No HIP 25278 0.54 4.17 14.66 -0.04 CdS Yes continued on next page. . . 186

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 25421 0.95 6.43 17.93 -0.04 EP Yes HIP 25544 0.76 5.53 19.57 0.00 EP Yes HIP 25647 0.83 6.01 14.94 -0.69 uvby Yes HIP 26373 0.85 6.06 23.87 -0.43 uvby Yes HIP 26394 0.60 4.35 18.21 0.08 EP Yes HIP 26505 0.83 6.18 20.53 -0.49 EP No HIP 26779 0.84 5.77 12.24 0.19 EP Yes HIP 27207 0.83 5.77 20.58 -0.08 EP Yes HIP 27435 0.64 5.01 15.56 -0.23 EP Yes HIP 27887 0.94 6.63 12.83 -0.30 EP Yes HIP 27913 0.59 4.70 8.66 -0.01 EP Yes HIP 27922 0.70 5.72 22.80 -0.51 uvby Yes HIP 28267 0.72 5.16 23.20 -0.10 EP Yes HIP 28954 0.81 5.81 15.45 0.07 CdS Yes HIP 29271 0.71 5.05 10.15 0.10 EP Yes HIP 29432 0.64 5.03 23.12 -0.11 EP Yes HIP 29525 0.66 5.14 18.12 -0.11 uvby Yes HIP 29568 0.71 5.26 16.69 -0.01 EP Yes HIP 29860 0.61 4.27 19.32 -0.04 EP Yes HIP 30314 0.61 4.68 23.50 -0.10 uvby Yes HIP 30503 0.63 4.65 22.04 0.04 EP Yes HIP 30630 0.94 5.95 14.66 -1.16 uvby No Star HIP 31711 0.62 4.47 21.67 -0.17 uvby Yes HIP 32423 0.96 6.81 24.99 -0.20 BB No HIP 32439 0.52 4.18 17.85 -0.17 uvby No HIP 32480 0.58 4.15 16.51 0.12 EP Yes HIP 33277 0.57 4.55 17.27 -0.18 EP Yes continued on next page. . . 187

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 33537 0.62 5.02 24.24 -0.40 EP Yes HIP 33690 0.79 5.49 18.41 0.22 EP Yes HIP 33817 0.88 5.89 14.62 0.16 EP Yes HIP 33852 0.99 6.43 20.42 0.00 HR Yes HIP 34017 0.60 4.53 19.09 -0.10 EP Yes HIP 34065 0.62 4.51 16.25 -0.19 EP Yes HIP 34069 0.78 5.94 15.09 -0.26 EP Yes HIP 34414 0.91 6.58 22.26 -0.37 CdS No HIP 34567 0.70 5.14 24.58 -0.01 uvby No Star HIP 35136 0.58 4.41 16.86 -0.30 CdS Yes HIP 35296 0.98 5.85 14.77 -0.03 EP Yes HIP 36210 0.69 4.96 22.51 0.02 EP Yes HIP 36357 0.92 6.51 17.55 Yes HIP 36515 0.64 4.97 21.77 -0.24 uvby Yes HIP 36704 0.86 6.21 19.69 0.06 EP Yes HIP 36827 0.90 6.19 24.80 -0.17 EP Yes HIP 37349 0.89 6.42 14.20 0.01 EP Yes HIP 37853 0.59 4.45 15.20 -0.88 CdS Yes HIP 38228 0.68 5.21 21.82 0.07 EP Yes HIP 38382 0.60 4.05 16.67 -0.08 uvby Yes HIP 38657 0.95 6.26 19.98 0.07 EP Yes Star HIP 38784 0.72 5.39 17.04 -0.16 uvby Yes HIP 38908 0.57 4.54 16.19 -0.29 EP Yes HIP 39064 0.83 5.86 23.14 -0.12 EP Yes HIP 39157 0.72 5.84 16.80 -0.69 EP Yes HIP 39342 0.87 5.99 17.28 0.06 EP Yes HIP 39780 0.64 3.46 23.33 0.20 EP Yes continued on next page. . . 188

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 40118 0.68 5.10 21.72 -0.44 EP Yes HIP 40693 0.75 5.45 12.58 -0.03 EP Yes HIP 40774 0.90 6.51 23.32 -0.48 HR No HIP 41484 0.62 4.63 21.79 0.02 EP Yes HIP 41926 0.78 5.95 12.17 -0.37 EP Yes HIP 42074 0.79 5.63 21.76 0.12 EP Yes HIP 42173 0.71 5.40 23.41 0.24 CdS Yes HIP 42333 0.66 4.87 23.63 0.12 EP Yes HIP 42430 0.72 3.55 19.92 0.28 uvby Yes HIP 42438 0.62 4.86 14.27 -0.06 CdS Yes HIP 42499 0.83 6.27 18.53 -0.57 EP Yes HIP 42697 0.90 6.36 22.36 -0.18 uvby Yes HIP 42808 0.92 6.35 11.14 -0.03 EP Yes HIP 43557 0.64 4.66 24.14 -0.16 uvby No Star HIP 43587 0.87 5.47 12.53 0.36 EP Yes Planet HIP 43726 0.66 4.85 17.09 0.14 EP Yes HIP 44075 0.52 4.16 21.32 -0.92 CdS Yes HIP 44897 0.58 4.54 19.14 0.08 EP Yes HIP 45170 0.73 4.93 20.48 -0.27 uvby No Star HIP 45333 0.61 3.72 19.56 -0.06 CdS No Star HIP 45617 0.99 5.98 17.53 -0.22 uvby No HIP 45963 0.99 5.76 24.28 0.06 uvby No Star HIP 46626 0.99 6.88 19.34 -0.40 EP Yes HIP 46816 0.93 6.50 18.34 0.33 EP Yes HIP 46843 0.78 5.80 17.75 -0.33 HR No HIP 47080 0.77 5.16 11.18 0.19 uvby Yes HIP 47592 0.53 4.07 14.88 -0.03 EP Yes continued on next page. . . 189

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 48113 0.62 3.75 18.43 0.17 EP Yes HIP 49081 0.68 4.50 14.89 0.20 EP Yes HIP 49366 0.89 6.32 23.18 -0.07 EP Yes HIP 49699 0.97 6.28 18.06 0.07 EP Yes HIP 50075 0.59 4.60 22.74 -0.05 EP Yes HIP 50384 0.50 4.03 22.72 -0.37 CdS No HIP 50505 0.65 5.09 20.64 -0.20 EP Yes HIP 50921 0.66 5.20 22.09 -0.21 EP Yes HIP 51248 0.61 4.56 23.56 -0.33 CdS No HIP 51459 0.54 4.28 12.85 -0.07 EP Yes HIP 51523 0.50 3.19 21.87 -0.46 CdS Yes HIP 51819 0.82 5.68 21.03 0.05 HR Yes HIP 51933 0.53 3.76 24.59 -0.26 CdS Yes HIP 52369 0.62 4.94 23.40 -0.19 uvby Yes HIP 52462 0.87 6.05 21.57 0.13 EP Yes HIP 53486 0.92 6.15 17.55 0.15 EP Yes HIP 53721 0.62 4.29 14.08 0.05 EP Yes Planet HIP 54155 0.77 5.68 24.65 -0.12 uvby Yes HIP 54426 0.94 6.56 22.77 -0.35 HR No HIP 54704 0.76 5.37 21.64 -0.04 EP Yes HIP 54745 0.60 4.73 21.72 0.09 EP Yes HIP 54906 0.85 6.12 21.30 -0.26 EP Yes HIP 55210 0.73 5.58 21.99 -0.20 EP Yes HIP 55846 0.78 5.25 17.67 0.34 EP Yes HIP 56242 0.57 4.46 23.03 -0.01 EP Yes HIP 56452 0.81 6.06 9.54 -0.38 EP Yes HIP 56809 0.57 4.45 23.29 -0.19 EP Yes Star continued on next page. . . 190

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 56829 0.98 6.74 19.76 -0.32 BB Yes Star HIP 56997 0.72 5.41 9.54 -0.03 EP Yes HIP 57443 0.66 5.06 9.24 -0.27 EP Yes HIP 57507 0.68 5.23 17.77 -0.23 EP Yes HIP 57757 0.52 3.40 10.90 0.18 EP Yes HIP 58451 0.97 6.33 20.82 0.10 EP Yes HIP 58576 0.76 4.99 12.91 0.27 EP Yes HIP 59280 0.79 5.53 24.35 0.20 EP Yes HIP 60994 0.59 4.38 24.98 -0.10 CdS Yes HIP 61053 0.57 4.49 21.94 -0.12 CdS Yes HIP 61100 0.94 6.20 23.74 No Star HIP 61291 0.84 6.09 16.17 -0.24 EP Yes HIP 61317 0.59 4.63 8.37 -0.16 EP Yes HIP 61946 0.96 6.44 23.22 -0.15 HR No HIP 62145 0.94 6.12 15.06 -0.32 uvby Yes Star HIP 62207 0.56 4.75 17.37 -0.55 CdS No HIP 62229 0.94 6.30 20.12 0.07 EP Yes HIP 62505 0.95 6.30 21.19 Yes HIP 62523 0.70 5.12 17.17 0.13 EP No HIP 63366 0.77 5.93 21.01 -0.37 CdS Yes Star HIP 63406 0.94 6.68 24.18 -0.31 EP No Star HIP 63742 0.85 5.97 22.12 Yes HIP 64394 0.57 4.42 9.15 0.07 EP Yes HIP 64408 0.69 3.29 20.48 0.24 EP Yes HIP 64457 0.93 6.01 20.43 0.13 EP Yes Planet HIP 64550 0.64 4.99 24.47 -0.25 EP Yes HIP 64690 0.71 5.15 24.68 -0.09 uvby Yes continued on next page. . . 191

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 64792 0.58 3.92 17.95 0.28 EP Yes HIP 64797 0.93 6.24 11.23 -0.10 CdS Yes HIP 64924 0.71 5.09 8.53 0.01 EP Yes HIP 65352 0.78 6.04 16.02 -0.40 EP Yes HIP 65355 0.87 6.22 16.79 -0.38 EP Yes HIP 65515 0.80 5.59 21.85 -0.10 uvby No HIP 65530 0.74 4.85 21.34 0.04 uvby Yes HIP 65721 0.71 3.68 18.11 -0.03 EP Yes Planet HIP 66765 0.86 5.95 15.61 -0.01 EP Yes HIP 66781 0.83 5.89 23.74 -0.14 HR No HIP 67275 0.51 3.53 15.60 0.26 EP Yes Planet HIP 67620 0.70 4.93 19.92 0.05 EP Yes StarJ HIP 67742 0.89 6.29 16.43 -0.26 EP Yes HIP 68030 0.52 4.24 24.22 -0.42 EP Yes HIP 68682 0.73 5.17 16.60 0.01 EP Yes HIP 69357 0.87 6.11 23.07 -0.10 EP Yes HIP 69414 0.73 5.31 22.28 -0.08 EP Yes HIP 69671 0.60 4.69 21.05 -0.22 uvby Yes HIP 69701 0.51 2.42 21.40 -0.08 CdS Yes HIP 69965 0.52 4.62 17.78 -0.77 uvby Yes HIP 70016 0.87 5.99 20.78 -0.18 EP Yes HIP 70319 0.64 5.02 17.60 -0.35 EP Yes HIP 70857 0.77 5.42 19.59 -0.39 uvby No HIP 70873 0.70 4.50 23.57 0.27 EP Yes HIP 71181 1.00 6.60 13.42 0.00 EP Yes HIP 71395 0.97 6.38 16.57 0.12 EP Yes Planet HIP 71683 0.71 4.34 1.35 0.28 EP Yes continued on next page. . . 192

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 71743 0.71 5.38 23.57 0.05 CdS Yes HIP 71855 0.71 5.19 20.35 -0.12 uvby Yes HIP 72146 0.93 6.42 19.53 -0.23 HR No HIP 72312 0.89 6.29 19.67 -0.16 EP Yes HIP 72493 0.84 5.36 23.99 -0.19 uvby Yes HIP 72567 0.58 4.59 17.94 0.05 EP Yes HIP 72659 0.72 5.41 6.70 -0.04 EP Yes HIP 72848 0.84 5.69 11.54 0.17 EP Yes Star HIP 72875 0.93 6.85 22.90 -0.54 uvby No HIP 73005 0.79 5.88 23.91 -0.45 EP Yes HIP 73100 0.53 3.65 24.84 0.02 CdS Yes HIP 73241 0.71 4.39 24.52 0.11 EP Yes StarJ HIP 73695 0.65 4.30 12.76 -0.35 uvby No Star HIP 74273 0.62 4.38 24.15 0.09 EP Yes HIP 74537 0.76 5.39 17.30 -0.11 EP Yes HIP 74702 0.83 5.96 15.58 -0.05 EP Yes HIP 74975 0.54 3.08 24.72 -0.12 CdS Yes HIP 75181 0.64 4.83 14.56 -0.31 EP Yes HIP 75253 0.97 6.28 21.82 0.22 EP Yes HIP 75277 0.80 5.64 20.13 -0.07 EP Yes HIP 75312 0.58 3.64 18.62 -0.04 uvby Yes HIP 75718 0.79 5.40 19.86 0.04 uvby Yes Star HIP 75722 0.87 5.98 20.81 0.28 EP Yes HIP 75809 0.67 4.85 22.07 -0.30 uvby No HIP 75829 0.80 5.62 21.72 0.14 EP No HIP 76375 0.95 5.91 22.26 0.37 EP Yes HIP 76382 0.91 5.09 21.81 No continued on next page. . . 193

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 76602 0.52 4.79 22.62 0.01 uvby Yes HIP 76603 0.51 4.47 24.88 -0.04 uvby Yes Star HIP 77052 0.68 5.03 14.67 0.08 EP Yes HIP 77257 0.60 4.07 11.75 0.05 EP Yes HIP 77358 0.72 5.09 15.24 0.13 EP Yes HIP 77408 0.80 5.79 21.35 -0.02 uvby Yes HIP 77760 0.56 3.60 15.85 -0.44 EP Yes HIP 77801 0.60 4.86 17.46 -0.43 EP Yes Star HIP 78459 0.61 4.18 17.43 -0.23 EP Yes Planet HIP 78527 0.53 2.41 20.92 0.22 CdS No Star HIP 78709 0.77 5.44 21.48 -0.14 uvby No HIP 78775 0.73 5.87 14.37 -0.69 EP Yes HIP 78913 0.96 6.73 23.49 -0.75 uvby No HIP 79190 0.86 6.32 14.36 -0.36 EP Yes HIP 79248 0.88 5.32 18.15 0.46 EP Yes Planet HIP 79492 0.76 4.75 24.36 -0.02 EP Yes HIP 79578 0.65 4.85 21.87 0.03 EP Yes StarJ HIP 79607 0.60 3.55 21.69 -0.22 uvby No Star HIP 79672 0.65 4.76 14.03 0.08 EP Yes HIP 80337 0.63 4.82 12.87 0.08 EP Yes Planet HIP 80366 0.95 6.73 21.53 -0.29 EP Yes HIP 80686 0.56 4.49 12.11 -0.19 CdS Yes Star HIP 80725 0.85 5.53 19.53 No HIP 80925 0.86 5.28 24.63 -0.56 uvby Yes Star HIP 81300 0.83 5.82 9.78 0.04 EP Yes HIP 81375 0.83 5.57 20.15 0.21 EP Yes HIP 81813 0.77 5.63 24.30 -0.19 EP Yes continued on next page. . . 194

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 82588 0.75 5.51 16.94 0.03 EP Yes HIP 83020 0.98 6.49 17.95 -0.33 uvby No HIP 83389 0.73 5.48 18.06 -0.10 EP Yes HIP 83541 0.81 5.30 18.08 0.33 EP Yes HIP 83601 0.58 4.45 20.38 0.04 EP Yes HIP 83990 0.89 6.70 13.69 -0.63 EP Yes HIP 84195 0.94 6.39 20.54 -0.15 HR No HIP 84405 0.86 5.44 5.99 -0.30 CdS Yes HIP 84720 0.76 5.75 8.79 -0.33 EP Yes StarJ HIP 84862 0.62 4.59 14.39 -0.36 EP Yes HIP 85042 0.68 4.83 19.46 0.03 EP Yes HIP 85235 0.76 5.90 12.80 -0.40 EP Yes HIP 85653 0.74 5.47 22.34 -0.51 uvby Yes HIP 85667 0.72 4.23 16.45 -0.05 CdS Yes HIP 85810 0.64 4.65 23.70 0.10 EP Yes HIP 86036 0.60 4.49 14.09 -0.17 uvby No HIP 86400 0.96 6.38 10.71 -0.09 uvby Yes Star HIP 86620 0.53 4.07 22.32 -0.07 CdS No HIP 86722 0.75 5.65 23.56 -0.39 uvby Yes HIP 86796 0.69 4.20 15.28 0.30 EP Yes Planet HIP 86974 0.75 3.80 8.40 0.30 EP Yes HIP 87579 0.94 6.52 24.86 -0.31 HR No HIP 88348 0.80 5.31 21.93 0.17 EP Yes HIP 88601 0.86 5.50 5.09 -0.25 CdS Yes HIP 88622 0.61 4.86 24.39 -0.42 CdS Yes HIP 88694 0.62 4.74 17.37 0.02 EP Yes HIP 88745 0.53 4.08 15.65 -0.57 CdS No continued on next page. . . 195

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 88972 0.88 6.15 11.10 -0.18 EP Yes HIP 89042 0.59 4.22 17.76 0.01 EP Yes HIP 89474 0.64 4.52 22.69 0.00 EP Yes HIP 89805 0.58 4.37 22.91 0.03 uvby Yes HIP 90790 0.86 6.21 13.21 -0.22 EP Yes HIP 91438 0.67 5.28 12.98 -0.21 EP Yes HIP 91605 0.87 6.65 23.88 -0.57 uvby No HIP 92858 0.86 6.09 23.90 -0.14 uvby Yes HIP 92919 0.91 6.50 21.44 -0.83 uvby No Star HIP 93017 0.59 4.32 14.98 -0.17 uvby Yes HIP 93185 0.61 4.95 23.43 -0.27 EP Yes HIP 93825 0.52 2.97 17.89 -0.15 uvby Yes HIP 93858 0.71 4.98 17.17 0.14 EP Yes HIP 93966 0.71 4.47 20.96 0.11 CdS No Star HIP 94336 0.67 3.87 24.90 -0.02 EP Yes HIP 94346 0.80 5.53 20.00 0.09 BB No HIP 95149 0.63 4.88 20.86 -0.23 uvby Yes HIP 95319 0.80 5.42 15.49 0.22 EP Yes HIP 95447 0.76 4.27 15.15 0.40 EP Yes HIP 95995 0.86 5.48 16.71 -0.33 uvby No Star HIP 96085 0.92 6.25 18.02 0.05 EP Yes HIP 96100 0.79 5.87 5.77 -0.19 EP Yes HIP 96183 0.75 5.37 20.16 0.15 EP Yes HIP 96395 0.64 4.81 24.25 -0.14 uvby Yes HIP 96895 0.64 4.32 21.62 0.10 EP Yes HIP 96901 0.66 4.60 21.41 0.06 EP Yes Planet HIP 97222 1.00 6.13 20.37 No continued on next page. . . 196

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 97675 0.56 3.68 19.39 0.16 EP Yes HIP 98416 0.60 3.92 24.54 -0.19 CdS Yes Star HIP 98505 0.93 6.25 19.25 -0.03 EP No HIP 98677 0.71 5.72 19.34 -0.37 EP Yes HIP 98767 0.75 4.72 15.89 0.23 EP Yes HIP 98792 0.82 6.32 15.58 -0.66 EP Yes HIP 98819 0.60 4.56 17.67 0.05 EP Yes HIP 98828 0.92 6.15 21.61 0.06 HR No HIP 98921 0.65 4.80 18.87 0.17 EP Yes HIP 98959 0.65 4.83 17.71 -0.23 EP Yes HIP 99137 0.53 4.43 23.21 -0.13 uvby Yes HIP 99240 0.75 4.62 6.11 0.36 EP Yes HIP 99316 0.81 5.63 24.35 No HIP 99452 0.83 5.78 20.48 -0.15 EP Yes HIP 99461 0.87 6.41 6.05 -0.55 EP Yes HIP 99711 0.94 6.30 19.89 0.00 EP Yes HIP 99825 0.88 6.00 8.82 -0.01 EP Yes HIP 100017 0.60 4.69 17.57 -0.09 EP Yes HIP 100925 0.72 5.17 19.42 -0.03 EP Yes HIP 101345 0.69 3.74 24.24 0.10 EP Yes HIP 101382 0.80 5.35 22.23 -0.66 CdS No Star HIP 101983 0.54 3.19 24.20 -0.34 EP Yes HIP 101997 0.72 5.53 14.65 -0.29 EP Yes HIP 102040 0.61 4.82 20.99 -0.09 EP Yes HIP 102264 0.67 5.20 22.44 -0.44 uvby Yes HIP 102766 0.94 6.38 23.68 No HIP 103389 0.51 4.09 21.00 -0.13 uvby Yes continued on next page. . . 197

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 103458 0.59 4.85 21.62 -0.63 EP Yes HIP 103859 0.97 6.26 19.36 -0.49 uvby No HIP 104239 0.90 5.89 17.65 0.11 EP Yes HIP 104436 0.62 5.06 24.22 -0.31 EP Yes HIP 104440 0.59 4.31 18.73 -0.04 uvby Yes HIP 104858 0.53 3.14 18.48 -0.05 uvby No HIP 105152 0.99 6.73 19.22 -0.10 EP Yes HIP 105184 0.64 4.87 23.79 -0.01 EP Yes HIP 105312 0.74 5.20 18.73 -0.38 CdS Yes Star HIP 105712 0.72 5.42 20.47 -0.21 CdS Yes HIP 105905 0.92 6.82 23.19 -0.90 uvby Yes HIP 105911 0.88 5.63 23.52 Yes HIP 106696 0.88 6.30 14.74 -0.17 EP Yes HIP 107022 0.76 5.34 22.14 -0.03 EP Yes HIP 107310 0.51 2.74 22.40 -0.22 CdS No HIP 107350 0.59 4.64 18.39 -0.02 EP Yes HIP 107625 0.96 6.74 23.74 -0.18 BB Yes HIP 107649 0.60 4.60 15.64 0.00 EP Yes HIP 108028 0.94 6.28 23.98 -0.04 HR No HIP 108156 0.91 6.19 20.32 -0.04 EP Yes HIP 109378 0.77 4.90 21.29 0.21 EP Yes Planet HIP 109527 0.81 5.48 22.44 0.23 EP Yes HIP 109821 0.65 4.51 22.13 -0.11 EP Yes StarJ HIP 109926 0.81 5.84 21.45 0.10 uvby Yes HIP 110109 0.61 4.69 13.61 -0.17 EP Yes HIP 110649 0.67 3.75 20.49 0.05 EP Yes HIP 110712 0.60 4.31 23.05 -0.01 EP Yes continued on next page. . . 198

Table. B.1 – continued. Sun-like 25 pc Sample

Hipparcos B − VMV Distance [Fe/H] [Fe/H] Exoplanet Companion Number (pc) Source Target (P < 5 years)

(M > MJup) HIP 110778 0.62 4.04 20.08 0.00 CdS Yes HIP 111888 0.94 6.70 22.68 -0.54 HR No HIP 112117 0.58 4.13 23.55 0.03 EP Yes HIP 112190 0.97 6.45 21.52 -0.11 HR Yes HIP 112447 0.50 3.15 16.25 -0.22 EP Yes HIP 112527 0.87 6.03 19.94 -0.11 HR No HIP 113357 0.67 4.52 15.36 0.20 EP Yes HIP 113421 0.74 4.70 19.72 0.37 EP Yes Planet HIP 113718 0.94 6.34 16.94 Yes Star HIP 113829 0.62 4.72 24.28 0.07 EP Yes HIP 114456 0.75 5.13 23.45 0.21 EP Yes HIP 114622 1.00 6.50 6.53 0.12 EP Yes HIP 114886 0.87 6.15 24.20 -0.04 EP Yes HIP 114924 0.56 4.04 20.28 0.00 CdS Yes HIP 114948 0.52 4.07 20.58 -0.17 uvby Yes HIP 115147 0.89 6.05 19.74 -0.63 uvby No HIP 115331 0.80 5.66 21.92 0.06 uvby Yes HIP 115445 0.88 6.35 19.47 -0.31 EP Yes HIP 116085 0.84 5.63 16.86 0.01 EP Yes HIP 116416 0.85 6.05 23.46 -0.10 uvby No HIP 116613 0.67 4.76 23.12 0.15 EP Yes HIP 116745 0.99 6.81 11.40 -0.31 EP Yes HIP 116763 0.80 5.82 18.68 -0.16 EP Yes HIP 116771 0.51 3.43 13.79 -0.09 EP Yes HIP 117712 0.98 6.19 10.79 -1.20 uvby No Star HIP 118008 0.97 6.52 22.08 -0.17 HR Yes HIP 118162 0.69 4.80 24.18 0.01 uvby No J Stellar companion is from Jones et al. (2002a) and assumed to have P < 5 years. References

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