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 com- panion. 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. Statement of Originality I hereby declare that this submission is my own work and to the best of my knowl- edge 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 ...................