Dynamical Instability And Hot Jupiters Formation In Multi-planet Systems

The number of current exoplanet systems has reached more than 570.Interest-ingly,the characteristics of some exoplanets and configurations of exoplanet system have distinct differences with our solar system.There are compact space super-earth systems,and planets in mean motion resonance chain.Hot Jupiter located extrem close to host star,and is difficult to form in suit in classical core planet formation theory。Hot Juiters are almost observed alone,at least without massive neighbor。However,com-panions far away aren’t found due to observation limit.Inward migration of planets due to the interaction between planets and planetary disk may be a routine to Hot Jupiters formation.Without considering migration of planets,the dyamical mechanisms have requirement on initial eccentricity and inclination.However,during the runawag stage of embroys,gas acceration of giants,dissipation of gas disk,multi-planet(embroys)systems are likely to be dynamical instability.The eccentricities and inclinations of planets after planet planet scattering are widely distributed,and may influence planet growth and trigger various dynamical mechanisms.So the procedure of dynamical in-stability may contribute to the final state of exoplanets and configurations of exoplanet systems.This thesis mostly focus on the instability of multi-planet(embroy)systems and the effeciencies of Hot Jupiters formed through different mechanisms.In Chapter 1,made a summing up of some issues in core acceration planetary formation model。Detailedly described universal model of gas disk and solid disk,the velocity of gas,gas drag adding on the solid bodies,the collision outcomes between planetesimals or embroys,as well as migration of planets.In Chapter 2,summarized several dynamical mechanisms maybe occur in plane-tary systems.Begin with the Hamiltonian of a hierarchical triple system,applying Leg-endre polynomials,expand the Hamiltonian to quadrupole and octupole terms.Based on Delauney canonical variables,adopt von Ziepel transformation to average the mean motion of inner and outer orbits and get the equations of motion.Then in some re-stricted conditions,we explain the inner restricted three body system(Kozai-Lidov mechanism,outer restricted three body system,coplanar high-eccentricity migration.At last,introduce the secular chaos and AMD in N body system.In Chapter 3,adopted a simplied N body model "EMS" systems to simulate the process of dynamical instability in multi-planet or planetesimals swarm.We give the critical space seperation between planets of dynamical stable within 1Gyr in the system consist of 2-5 planets with mass μ= 10-2～10-9.Then,find the influence of initial inclination on the instability time scale of systems and empirical formula.Finally,considering the acceration between planetesimals,recalculate the growth rate of aver-age inclination,and the relation between average eccentricity and average inclination during equilibrium state.In Chapter 4,focused on the formation of Hot Jupiters.Without considering the migration of planet in gas disk,Hot Jupiters usually form through high eccentricity mi-gration,which restrict on initial eccentricity,inclination,companion star or debris disk,etc.However,the conditions can be easily obtained during planet planet scattering.So,we classify the outcomes of multi-giant systems after dynamical instability,and get the efficiency of Hot Jupiters formation through each mechanism as well as the corre-sponding characteristics.By vast simulations,we make statistics about the efficiency with different space separation between planets.In Chapter 5,studied an interesting and controversial binary system "99Her",which was detected the third companion twice。The key project of Herschel,DEBRIS discovered a debris disk around the binary.According to stability analysis,the debris disk is likely in polar orbit.Suppose the existence of polar ring,we put into 30000 planetesimals,calculate the outcomes of each impact.And compare with the cases in coplaner disk aroud the same binary system and planetary disk around single star.We find the acceration ratio in polar disk is as high as 70%,while 67%in coplaner disk of binary system and 68%in disk of single star.So,if there are enough materials,planets can form in polar disk of binary star.In Chapter 6,we concluded the previous studies and make expectations.