Solar System analogues among exoplanetary systems Maria Lomaeva Lund Observatory Lund University ´´ 2016-EXA105 Degree project of 15 higher education credits June 2016 Supervisor: Piero Ranalli Lund Observatory Box 43 SE-221 00 Lund Sweden Populärvetenskaplig sammanfattning Människans intresse för rymden har alltid varit stort. Man har antagit att andra plan- etsystem, om de existerar, ser ut som vårt: med mindre stenplaneter i banor närmast stjärnan och gas- samt isjättar i de yttre banorna. Idag känner man till drygt 2 000 exoplaneter, d.v.s., planeter som kretsar kring andra stjärnor än solen. Man vet även att vissa av dem saknar motsvarighet i solsystemet, t. ex., heta jupitrar (gasjättar som har migrerat inåt och kretsar väldigt nära stjärnan) och superjordar (stenplaneter större än jorden). Därför blir frågan om hur unikt solsystemet är ännu mer intressant, vilket vi försöker ta reda på i det här projektet. Det finns olika sätt att detektera exoplaneter på men två av dem har gett flest resultat: transitmetoden och dopplerspektroskopin. Med transitmetoden mäter man minsknin- gen av en stjärnas ljus när en planet passerar framför den. Den metoden passar bäst för stora planeter med små omloppsbanor. Dopplerspektroskopin använder sig av Doppler effekten som innebär att ljuset utsänt från en stjärna verkar blåare respektive rödare när en stjärna förflyttar sig fram och tillbaka från observatören. Denna rörelse avslöjar att det finns en planet som kretsar kring stjärnan och påverkar den med sin gravita- tion. Dopplerspektroskopin är lämpligast för massiva planeter med små omloppsbanor. Under projektets gång har vi inte bara letat efter solsystemets motsvarigheter utan även studerat planetsystem som är annorlunda. Vi har hittat tecken på att vissa av heta jupitrar fortfarande kan hålla på och migrera inåt vilket kan leda till att mindre planeter i dessa system blir utkastade. En annan fråga som dyker upp i detta sammanhang är om det finns liv på andra planeter än jorden. Vi har funnit några kandidater som skulle kunna ha samma upp- byggnad som jorden har. Man kan även definiera gränserna för en så kallad beboelig zon, d.v.s., det avstånd från stjärnan på vilket en planet får lagom med stjärnljus och kan ha vatten i flytande form på sin yta. En planet inom denna zon skulle då, rent teoretiskt, kunna vara bebodd. Bland planeter som vi betraktat fanns det sju sådana. Uppkomsten av ett liv är dock väldigt komplex och beror inte enbart på avstånd från stjärnan. Därför kan man tyvärr inte garantera att det finns ett utomjordiskt liv på dessa planeter. Solsystemets motsvarigheter är fortfarande väldigt svåra att detektera med dagens teknologier. Därför förblir frågan om deras existens obesvarad. Man behöver uppfinna mer känsliga teleskop som kommer att kunna detektera små stenplaneter samt planeter med stora omloppsbanor. Det återstår att se vad morgondagens upptäckter kommer att visa. 1 Abstract Over the past two decades many discoveries of exoplanets have been made, which have drawn much attention to extrasolar planetary systems. In this work we study the com- position of these systems and search for analogues of the Solar System. We considered the planets in the database at exoplanet.eu. The search of solar-like systems required these planets to be classified. The classification was performed using k-means clustering algorithm and planets with measured masses and semi-major axes were divided into three clusters: hot Jupiters, gas giants and the third cluster with rocky and Neptunian planets. Our first attempt to separate rocky and Neptunian planets by their density was per- formed by using k-means algorithm for planets with three measured parameters: mass, radius and semi-major axis. The results, however, were not satisfactory and a simple mass limit was chosen instead. Our examination of the extrasolar systems showed that there are few Solar System analogues. This most probably depends on the selection effects of the present-day de- tection techniques. Two of them were studied more closely: the Doppler radial velocity and transit technique. The first one is more likely to detect massive planets in close orbits, while the latter is more preferable for planets that pass in front of their host stars and have large radii and short orbital periods. Low-mass Earth-like rocky planets are more likely to be detected by the transit technique. Overall, the distribution of planets in their classes has been shown to follow expectations and selection effects. The systems that contain hot Jupiters were studied closely and the results suggest that there is a number of hot Jupiters that might likely be caught in the act of migration. Also, the number of transiting extrasolar Neptunes and Earths was compared to the results presented by Petigura et al. (2013). It revealed a discrepancy, which arose due to the correction of the occurrence rate of these planets made by the article’s authors. Rocky planets that potentially can host life were another interesting subject in the search of Solar System analogues. According to our definition of the habitable zone, we found six super-Earths and one Earth-like planet that might be habitable. However, such conclusions need deeper examination of the planetary properties. 2 Contents 1 Introduction 4 1.1 Planetary Formation . 4 1.1.1 Formation of Terrestrial Planets . 5 1.1.2 Formation of Gaseous Planets . 6 1.2 Planetary Migration . 8 1.2.1 Type I and Type II Migration Regimes . 8 1.2.2 Alternative Migration Models . 9 1.3 Habitable Zone . 9 1.4 Database . 10 1.5 Detection Techniques . 11 2 Method 15 2.1 K-means Clustering . 15 2.2 Data Classification . 16 2.3 Database Reliability . 22 2.4 Application of the Classification . 23 3 Results and Discussion 25 3.1 Planetary Systems . 25 3.2 Solar Sys. Analogues . 32 4 Summary and Conclusions 36 5 Appendix 41 3 Chapter 1 Introduction 1.1 Planetary Formation A better understanding of the formation of our Solar System can shed some light onto the formation of other planetary systems by assuming that planet formation occurs in a similar way for all systems. Many theories have been proposed but the solar nebula theory is the most considered today. According to it, a molecular cloud which collapses due to gravitational instability in some of its regions possesses an angular momentum, which prevents it from collapsing directly onto the star. Instead it forms a flat symmet- ric rotating disk with a centre that coincides with the centre of mass of the system and is located in the plane, perpendicular to the direction of the total angular momentum. It is thought that frictional forces are responsible for this redistribution of material in a cloud: they allow an inward migration of the mass. This leads to a significant loss of angular momentum and enlargement of the radius of the accreting cloud (Perryman 2014). Massive accretion disks usually appear around stars that are younger than 1 Myr. During this period, gravitational potential energy stored in the gas is converted into thermal radiation due to inward flow of the gas and its accretion onto the star (Pringle 1981, Frank et al. 2002). It evolves further to low mass accretion disks which are typical for stars with ages between 1-10 Myr. At late evolutionary stages, i.e. stars aged older than 10 Myr, secondary disks, or debris disks, are generated by collisions of planetesimals. During this period, accretion has ceased and most of the gas has dissipated from the cloud. The transition between the protostellar and protoplanetary disk is rather arbitrary and ambiguous. However, the protoplanetary phase can be referred to as the final stage of the evolution of the protostar, i.e., when accretion rate is low and most of the mass in the disk has been used for accretion, the gas is dispersed and formation of planets takes place. Planetary formation processes strongly depend on the lifetime of the pro- 4 1.1. PLANETARY FORMATION CHAPTER 1. INTRODUCTION toplanetary disk: the longer the lifetime, the more material that is present to create planets (Perryman 2014). 1.1.1 Formation of Terrestrial Planets The formation of terrestrial planets begins in the mid-plane of the debris disk where most of the dust grains concentrate in the absence of turbulence. Dust grains are con- sidered to be condensed particles in the interstellar medium with sizes of about 1 µm. Electrostatic forces and collisions between them make them stick together and even- tually grow in size and form larger bodies and rocks with sizes up to ∼10 m (Kusaka et al. 1970). As they increase in size, their relative velocities will also increase to tens of m/s, which most probably will lead to bouncing and fragmentation of the bodies rather than their growth (Chambers 2014). Today there are two models that consider turbulence effects and explain how this bar- rier, also called “metre-size-barrier”, can be overcome, which allows planetesimals to form directly from smaller particles. The “streaming instability” states that if there is a sufficient amount of cm-to-m-sized particles in a cloud, a rapid drift and accumulation of these bodies will occur in the nearest local pressure maximum of turbulent regions (Chambers 2014, Righter & O’brien 2011). The “turbulent concentration” model im- plies that mm-sized particles will experience a drag caused by turbulent eddies and gather in the stagnant regions between them. This will result in formation of gravita- tionally bound clumps and eventually planetesimals. Planetesimals are generally defined as solid objects of size &1 km which are created in connection with planet formation. Their orbital dynamics are almost independent of the gas drag and they are held together mostly due to self-gravity.