Institute for Computational Science at the University of Zurich Bachelor thesis A model for moon formation around giant planets formed by gravitational instability Supervisors Author Dr. Judit Szul´agyi Cassandra Inderbitzi Prof. Dr. Lucio Mayer August 28, 2018 Contents 1 Introduction 4 1.1 Planets and their satellites in our Solar System...................4 1.1.1 Jupiter.....................................5 1.1.2 Saturn......................................6 1.1.3 Uranus.....................................6 1.1.4 Neptune.....................................7 1.1.5 Moons of the terrestrial planets........................7 1.2 Star formation.....................................7 1.2.1 Jeans criterion.................................8 1.3 Terrestrial planet formation..............................8 1.3.1 Goldreich-Ward mechanism..........................9 1.3.2 Streaming instabilities............................. 10 1.4 Giant planet formation................................. 11 1.4.1 Core accretion................................. 11 1.4.2 Disk instability................................. 12 1.4.3 Comparison of CPDs formed by core accretion and disk instability.... 13 1.5 Satellite formation................................... 13 2 Semianalytic model 14 2.1 Disk........................................... 14 2.2 Disk evolution...................................... 15 2.2.1 Gas and dust densities............................. 15 2.2.2 Temperature.................................. 16 2.3 Satellite formation................................... 16 2.3.1 Formation model................................ 17 2.4 Migration........................................ 17 2.4.1 Type I migration................................ 17 2.4.2 Type II migration............................... 18 2.4.3 Migration model................................ 19 2.5 Accretion........................................ 20 2.5.1 Accretion model................................ 21 2.5.2 Depletion.................................... 21 2.5.3 Dust refilling.................................. 21 2.6 Resonance trapping................................... 21 2.7 Collisions........................................ 22 2.8 Population synthesis.................................. 22 3 Results 23 3.1 Number of satellites.................................. 23 3.2 Mass distribution.................................... 24 3.3 Positions......................................... 28 3.4 Survival timescales................................... 32 3.5 Formation temperature................................ 35 3.6 Formation timescales.................................. 36 4 Discussion 36 4.1 Comparison to a Jupiter-analog model........................ 36 4.1.1 Number of satellites.............................. 37 4.1.2 Masses...................................... 38 4.1.3 Survival timescale............................... 39 4.1.4 Formation temperature............................ 40 4.1.5 Formation timescale.............................. 41 1 4.1.6 Summary of the comparison between the Jupiter-analog model and my model...................................... 41 5 Conclusion 42 5.1 Outlook......................................... 42 Bibliography 43 2 To my best friend, without whom I wouldn't be who I am today. 3 1 Introduction In the second millenium BC, the ancient Babylonians identified the first 6 planets of our Solar System [1]. This shows the longstanding interest of humanity in the mysteries of outer space. With the advance in technology, the telescope allowed for a continued study of the bodies in our solar system. In the 17th century, for the first time moons around other planets were observed, first the 4 big Jupiter satellites by Galileo Galilei [2] and later the largest of Saturn's moons, Titan, by Christiaan Huygens [3]. It took another century for Frederick William Herschel to discover Uranus [4] and another 30 years for Giuseppe Piazzi to discover Neptune [5] and finally, in the beginning of the 20th century, Clyde William Tombaugh discovered the then 9th planet, which was later reclassified as a dwarf planet, Pluto [6]. And while we are still discovering new objects within our solar system, our focus has mostly shifted to objects that aren't within our Sun's sphere of influence. Since the first discovery of an exoplanet in 1992, orbiting around the pulsar PSR B1257+12 [8], and the discovery of the first planet orbiting a main sequence star, Pegasi 51 [9] , we have since steadily expanded that number and as of June 5th, 2018, there are 3786 planets [10] orbiting various types of stars. With technology becoming ever better, it is only a matter of time until we start detecting moons around such planets. In fact, there is already work being done on this, and preliminary results suggest that we might have discovered one already [11]. 1.1 Planets and their satellites in our Solar System The International Astronomical Union divides the objects in a solar system broadly into 4 categories [12]: 1. \A 'planet' is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit. 2. \A 'dwarf planet' is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, (c) has not cleared the neighbourhood around its orbit, and (d) is not a satellite. 3. \All other objects, except satellites, orbiting the Sun shall be referred to collectively as 'Small Solar-System Bodies'." (The International Astronomical Union,[12]) 4. Satellites, which are objects whose orbit is around planets or asteroids. They are more colloquially called moons. This means that there are 8 planets, from Mercury to Neptune, a number of dwarf planets, such as Pluto and Ceres, and a host of small solar-system bodies, like in the asteroid belt between Mars and Jupiter, in the Kuiper-belt past Neptune, which Pluto is a part of, and in the spherical Oort-cloud, which is the source of comets. While this categorization is a good baseline, it still does not quite work in every case. Pluto in particular, as Charon is designated a satellite, even though the mass ratio is 8:1 and thus the two objects orbit a point that lies outside of either surface, which would make it more accurate to call it a twin system of two dwarf planets. The different types of planets in our Solar System are further subdivided into categories: 1. Terrestrial planets are planets whose mass is mostly compromised of solid material like silicates and metals. These are planets like Earth or Mars and at least in the solar system they all seem to be made up of three basic layers: a metallic core, a silicate inner mantel and a solid outer mantle. Many satellites also share this characteristic composition and in some cases even the sizes are comparable (for example, Mercury is slightly smaller than Jupiter moon Ganymede (see table1)) 2. Gas giants are planets whose mass is mostly made up of gaseous Hydrogen and Helium. Although we do not have a clear picture of their internal structure, the theory is that gas 4 giants have an outer layer made up of gas, which is kept in that state due to internal and external heating, a middle layer of metallic hydrogen, kept in that state by pressure and maybe some solid inner core. In our solar system Jupiter and Saturn are the gas giants. 3. Ice giants are planets whose mass is mostly made up by heavier elements (such as oxygen, hydrogen or carbon, as well as water ice) which is the main difference between them and gas giants. These planets are Neptune and Uranus. 1.1.1 Jupiter The largest planet in our solar system is Jupiter. It has so far 69 confirmed moons, although its four main moons (called the Galilean satellites, after their discoverer) make up the vast majority −4 of the combined satellite mass, which is around 2 · 10 MJupiter (as a comparison, the Moon is −2 about 10 MEarth. Name Diameter [km] Mass [Mjup] Orbital radius [Rjup] Io 3660 4:47 · 10−5 6 Europa 3121:6 2:4 · 10−5 9:6 Ganymede 5262:4 7:4 · 10−5 15:3 Callisto 4820:6 5:4 · 10−5 26:9 Table 1: Jupiter's moons [26] Io is the innermost of Jupiter's satellites and the second to lightest. Its density suggests that Io is 100% rocky, being mainly composed of silicates [27]. Models based on measurements taken by the Voyage and Galileo missions suggest that it is has a similar inner structure as Earth with a silicate/rocky crust, a mantle and an iron core [28]. Gravitational interactions with Jupiter and the outer Galilean satellites, called tidal heating, causes Io to be extremely geologically active, resulting in over 400 active volcanoes. Europa is the lightest Galilean satellite. It is in a 2:1 mean-motion resonance with Io, which means Europa completes one orbit in the same time that Io completes two. Europa's density suggests that it is about 90% rocky and 10% ice or water. The smooth surface, which is in fact the smoothest of any body in the Solar System, suggest not only that it has a crust of frozen water, but also a layer of liquid water beneath that. This is further supported by magnetic-field data from the Galileo mission, which shows that Jupiter induces a magnetic field in Europa. This could be explained by a conductive layer of salty water, which is kept liquid due to tidal heating, under the frozen surface [29]. This ocean is of great interest, as it could be a potentially