Exomoon habitability and tidal evolution in low-mass star systems

Current technology and theoretical methods are allowing for the detection of sub-Earth sized extrasolar planets. In addition, the detection of massive moons orbiting extrasolar planets ("exomoons") has become feasible and searches are currently underway. Several extrasolar planets have now been discovered in the habitable zone (HZ) of their parent star. This naturally leads to questions about the habitability of moons around planets in the HZ. Red dwarf stars present interesting targets for habitable planet detection. Compared to the Sun, red dwarfs are smaller, fainter, lower mass, and much more numerous. Due to their low luminosities, the HZ is much closer to the star than for Sun-like stars. For a planet-moon binary in the HZ, the close proximity of the star presents dynamical restrictions on the stability of the moon, forcing it to orbit close to the planet to remain gravitationally bound. Under these conditions the effects of tidal heating, distortion torques, and stellar perturbations become important considerations to the habitability of an exomoon. Utilizing an evolution model that considers both dynamical and tidal interactions, I performed a computational investigation into long-term evolution of exomoon systems. My study focused on satellite systems in the HZ of red dwarf stars and the dependence of exomoon habitability on the mass of the central star. Results show that dwarf stars with masses < 0.2 M© cannot host habitable exomoons within the stellar HZ due to extreme tidal heating in the moon. These results suggest that a host planet could be located outside the stellar HZ to where higher tidal heating rates could act to promote habitability for an otherwise uninhabitable moon. Perturbations from a central star may continue to have deleterious effects in the HZ up to « 0.5 MSun, depending on the host planet's mass and its location in the HZ. In cases with lower intensity tidal heating, stellar perturbations may have a positive influence on exomoon habitability by promoting long-term heating rates above a minimum for habitable terrestrial environments. In addition to heating concerns, torques due to tidal and spin distortion can lead to the relatively rapid inward spiraling of a moon. The effects of torque and stability constraints also make it unlikely that long-term resonances between two massive moons will develop in the HZs around red dwarf stars. My study showed that moons in the circumstellar HZ are not necessarily habitable by definition. In addition, the HZ for an exomoon may extend beyond the HZ for an exoplanet. Therefore, an extended model is required when considering exomoon habitability in comparison to exoplanet habitability.

EXOMOON HABITABILITY AND TIDAL EVOLUTION IN LOW-MASS STAR SYSTEMS by Rhett R. Zollinger A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Department of Physics and Astronomy The University of Utah December 2014 Copyright © Rhett R. Zollinger 2014 All Rights Reserved The University of Utah Graduate School STATEMENT OF DISSERTATION APPROVAL The dissertation of Rhett R. Zollinger has been approved by the following supervisory committee members: Benjamin C. Bromley Chair 07/08/2014 Date Approved John C. Armstrong Member 07/08/2014 Date Approved Bonnie K. Baxter Member 07/08/2014 Date Approved Jordan M. Gerton Member 07/08/2014 Date Approved Anil C. Seth Member 07/08/2014 Date Approved and by Carleton DeTar Chair/Dean of the Department/College/School o f _____________Physics and Astronomy and by David B. Kieda, Dean of The Graduate School. ABSTRACT Current technology and theoretical methods are allowing for the detection of sub-Earth sized extrasolar planets. In addition, the detection of massive moons orbiting extrasolar planets ("exomoons") has become feasible and searches are currently underway. Several extrasolar planets have now been discovered in the habitable zone (HZ) of their parent star. This naturally leads to questions about the habitability of moons around planets in the HZ. Red dwarf stars present interesting targets for habitable planet detection. Compared to the Sun, red dwarfs are smaller, fainter, lower mass, and much more numerous. Due to their low luminosities, the HZ is much closer to the star than for Sun-like stars. For a planet-moon binary in the HZ, the close proximity of the star presents dynamical restrictions on the stability of the moon, forcing it to orbit close to the planet to remain gravitationally bound. Under these conditions the effects of tidal heating, distortion torques, and stellar perturbations become important considerations to the habitability of an exomoon. Utilizing an evolution model that considers both dynamical and tidal interactions, I performed a computational investigation into long-term evolution of exomoon systems. My study focused on satellite systems in the HZ of red dwarf stars and the dependence of exomoon habitability on the mass of the central star. Results show that dwarf stars with masses < 0.2 M© cannot host habitable exomoons within the stellar HZ due to extreme tidal heating in the moon. These results suggest that a host planet could be located outside the stellar HZ to where higher tidal heating rates could act to promote habitability for an otherwise uninhabitable moon. Perturbations from a central star may continue to have deleterious effects in the HZ up to « 0.5 MSun, depending on the host planet's mass and its location in the HZ. In cases with lower intensity tidal heating, stellar perturbations may have a positive influence on exomoon habitability by promoting long-term heating rates above a minimum for habitable terrestrial environments. In addition to heating concerns, torques due to tidal and spin distortion can lead to the relatively rapid inward spiraling of a moon. The effects of torque and stability constraints also make it unlikely that long-term resonances between two massive moons will develop in the HZs around red dwarf stars. My study showed that moons in the circumstellar HZ are not necessarily habitable by definition. In addition, the HZ for an exomoon may extend beyond the HZ for an exoplanet. Therefore, an extended model is required when considering exomoon habitability in comparison to exoplanet habitability. iv To Stefanie, Missy, Bella, and Conner---- if I've learned one thing from this experience it's that your support is worth more than any success. CONTENTS A B S T R A C T .................................................................................................................................. iii LIST OF FIG U R E S .................................................................................................................. ix LIST OF T A B L E S .......................................................................................................................xiii A C K N O W L E D G M E N T S ...................................................................................................... xv C H A P T E R S 1......IN T R O D U C T IO N ............................................................................................................. 1 1.1 Exoplanet Detection Methods...................................................................................... 1 1.1.1 Historical Perspective.......................................................................................... 2 1.1.2 Radial V elocity...................................................................................................... 3 1.1.3 Transiting Planets................................................................................................. 5 1.1.4 Direct Im agin g...................................................................................................... 6 1.1.5 Additional Detection M ethods.......................................................................... 7 1.1.5.1 Gravitational Microlensing....................................................................... 7 1.1.5.2 A strom etry.................................................................................................... 8 1.1.5.3 Pulsar Timing............................................................................................... 8 1.2 Extrasolar Systems Overview ...................................................................................... 8 1.2.1 An Explosion of Discoveries.............................................................................. 9 1.2.2 Apparent Detection B ias...................................................................................... 10 1.2.3 Exoplanet Composition ........................................................................................ 12 1.2.4 Additional Orbital Properties ............................................................................ 14 1.2.5 Some Interesting Examples ................................................................................. 15 1.3 Habitability ....................................................................................................................... 16 1.3.1 The Habitable Zone ............................................................................................. 16 1.3.2 Additional Considerations for the Habitable Zone ...................................... 18 1.3.3 Detected Planets in the Habitable Zone ......................................................... 18 1.4 From Exoplanets to Exomoons ................................................................................... 19 1.5 Dissertation Outline ...................................................................................................... 22 2. EX T R A SO LA R M O O N S ............................................................................................... 24 2.1 Motivation ......................................................................................................................... 24 2.2 Formation ......................................................................................................................... 24 2.3 Predicted Properties of Exomoons ............................................................................ 25 2.3.1 Stability .................................................................................................................. 25 2.3.2 Evolution.................................................................................................................. 27 2.3.3 Composition ........................................................................................................... 28 2.4 Exomoon Detection Methods ...................................................................................... 28 2.4.1 Dynamical Effects on Transiting Exoplanets (TTV and TDV) .............. 29 2.4.2 Eclipse Features Induced by E xom oons......................................................... 30 2.4.3 Direct Detection of Exomoons .......................................................................... 30 2.4.4 Detection Outlook................................................................................................. 31 2.5 Exomoon H abitability.................................................................................................... 31 2.5.1 Mass Requirements............................................................................................... 31 2.5.2 Global Energy F lux............................................................................................... 32 3. IN T E R E S T IN LOW-MA SS S T A R S ....................................................................... 34 3.1 Red Dwarfs ....................................................................................................................... 34 3.1.1 Detected P lanets.................................................................................................... 35 3.2 Habitable Zones Around Red Dwarf S ta r s .............................................................. 36 3.2.1 Concerns for H abitability................................................................................... 39 3.3 So Why Bother with Exom oons................................................................................. 41 4. D Y N AM IC A L A N D TID A L EV O LU T IO N ....................................................... 42 4.1 Tidal Heating .................................................................................................................. 42 4.1.1 Examples of Tidally Heated M o o n s................................................................ 44 4.2 Surface Heat F lu x ........................................................................................................... 46 4.3 Coupling Tidal and Gravitational Effects................................................................ 47 4.4 A Self-Consistent Evolution Model for Planetary System s................................. 49 4.4.1 Equations of M otion............................................................................................. 49 4.4.2 The Simulation Code .......................................................................................... 53 5. SIM U LA T IN G EX OM O O N EV O LU TIO N : S E T U P ...................................... 55 5.1 System Architectures and Physical Properties ....................................................... 55 5.1.1 The Exomoon Model............................................................................................. 56 5.1.2 The Planet M odels............................................................................................... 58 5.1.3 The Star Models .................................................................................................... 60 5.2 Estimates for Eccentricity Damping Timescales .................................................... 60 5.3 2-body Orbital Evolution: Tides versus No-Tides.................................................. 60 6. 3-BODY S IM U L A T IO N S ............................................................................................... 71 6.1 3-body Stability Considerations ................................................................................. 71 6.2 Short-Term Orbital Variation ...................................................................................... 74 6.3 Results ............................................................................................................................... 76 6.4 Discussion ......................................................................................................................... 84 6.4.1 Simulation End Value Summary ....................................................................... 93 6.4.1.1 Satellites at the Center of the HZ (Tables 6.4 and 6.5) ................... 99 6.4.1.2 Earth-equivalent Satellite Distances (Table 6.6).................................102 7. 4-BO D Y S IM U L A T IO N S ...............................................................................................104 7.1 4-body Stability Considerations .................................................................................105 7.2 Results............................................................................................................................... 105 7.3 Discussion........................................................................................................................106 vii 8. D ISC U SSIO N A N D F U T U R E W O R K ...................................................................118 8.1 Summation of Key P o in ts.............................................................................................118 8.2 Constraints on Exomoon Habitability.......................................................................119 8.3 Future W o rk .................................................................................................................... 122 B IB L IO G R A P H Y .......................................................................................................................124 viii LIST OF FIGURES 1.1 Cartoon illustrating the (exaggerated) reflex motion of a star in the inertial frame of the barycenter. The presence of the planet causes variations in the position (used for astrometry and pulsar timing) and the velocity (used for radial velocity) of the host star, which can be used to detect an exoplanet. . . . 4 1.2 Exoplanet detections per year after 1995. The very recent spike is primarily due to a large release of Kepler candidate confirmations......................................... 9 1.3 Relationship between mass and orbital distance (semimajor axis) for detected exoplanets. The colorscale indicates the detection date of the planet. Bluish-green colors represent the years when RV surveys dominated. Results from Kepler are included in the orange-red colors. The chosen axial limits result in the exclusion of a few higher mass or longer period planets. For comparison, 1 Earth mass = 0.0031 Jupiter masses. [Source: exoplanets.org] ........................ 11 1.4 Relationship between planet radius and orbital distance (semimajor axis) for detected exoplanets. The colorscale indicates the detection date of the planet. Green colors represent a time when RV surveys dominated. Results from Kepler are included in the orange-red colors. From the coloring, it is obvious that the most radius measurements were made only recently. For comparison, 1 Earth radius = 0.089 Jupiter radii. [Source: exoplanets.org]............................ 13 3.1 Illustrative comparison between low-mass stars and the Sun. Earth is also represented for contrast. The radius of Earth is less than 1% the radius of the Sun.......................................................................................................................................... 35 3.2 Habitable zones with planet mass. The dotted black line represents the upper red dwarf (low-mass) star boundary. The red dashed line represents the tidal locking radius. The colored circles represent the orbital distances of Mercury, Venus, Earth, and Mars. The size of each circle is scaled to the planet's size relative to Earth (but not to scale with the horizontal coordinates).................... 37 4.1 An illustration depicting distortion caused by tidal interactions. (a) The gravitational forces on a moon from a planet (assuming the planet was located to the right of the moon). (b) The differential gravitational force on a moon, relative to its center............................................................................................................ 43 4.2 A very simple depiction of the orbital effects that produce tidal heating........... 44 4.3 Two moons of Jupiter. (a) Io, the innermost Galilean moon. Tidal heating in Io has made it the most geologically active object in the Solar System. (b) Europa, the second innermost Galilean moon. A vast salt-water ocean is believed to exist underneath the icy surface of Europa as the result of tidal heating. .............................................................................................................................. 45 4.4 Hierarchical (Jacobi) coordinates. The symbol c12 denotes the center of mass of m 1 and m2, with a similar definition for c123......................................................... 50 5.1 Orbital evolution comparisons for shorter moon orbital distances. The systems included a Jupiter-like planet and a Mars-like moon (2-body system). The two curves in each plot represent two separate simulations, one with tidal interactions and one without............................................................................................ 62 5.2 A continuation of Figure 5.1 for wider moon orbital distances. The 2-body systems included a Jupiter-like planet........................................................................... 63 5.3 Orbital evolution comparisons for shorter moon orbital distances involving a Saturn-like planet and a Mars-like moon (2-body system). The two curves in each plot represent two separate simulations, one with tidal interactions and one without.......................................................................................................................... 64 5.4 A continuation of Figure 5.3 for wider moon orbital distances. The 2-body systems involved a Saturn-like planet............................................................................ 65 5.5 Spin evolution for Io-like orbits. (a) Two binary systems are represented. The blue lines comprise a system with a Jupiter-like host planet, the green lines involved a Saturn-like host. All bodies are represented, referring to both the planet and moon in each system. (b) Ratio of spin magnitude (Q) and mean motion (n) for the moons represented in plot a.......................................................... 68 5.6 Evolution for an Io-like moon orbit around a fast spinning Saturn-like host. (a) Spin evolution for the satellite and host planet. (b) Semimajor axis evolution for the satellite..................................................................................................................... 70 6.1 Comparison of satellite eccentricity for three different simulations. The top and middle plots represent 3-body simulations. The bottom plot represents an isolated planet-moon system (2-body simulation)................................................ 75 6.2 Satellite tidal evolution. Planet orbit in the center of the HZ. Io-like moon orbit. Jupiter-like host planet.......................................................................................... 77 6.3 Satellite tidal evolution. Planet orbit in the center of the HZ. Europa-like moon orbit. Jupiter-like host planet.............................................................................. 78 6.4 Satellite tidal evolution. Planet orbit in the center of the HZ. Ganymede-like moon orbit. Jupiter-like host planet.............................................................................. 79 6.5 Satellite tidal evolution. Planet orbit in the center of the HZ. Titan-like moon orbit. Jupiter-like host planet.......................................................................................... 80 6.6 Satellite tidal evolution. Planet orbit in the center of the HZ. Callisto-like moon orbit. Jupiter-like host planet.............................................................................. 80 6.7 Satellite tidal evolution. Planet orbit in the center of the HZ. Io-like moon orbit. Saturn-like host planet........................................................................................... 81 6.8 Satellite tidal evolution. Planet orbit in the center of the HZ. Europa-like moon orbit. Saturn-like host planet............................................................................... 82 6.9 Satellite tidal evolution. Planet orbit in the center of the HZ. Ganymede-like moon orbit. Saturn-like host planet............................................................................... 83 x 6.10 Satellite tidal evolution. Planet orbit in the center of the HZ. Ganymede-like moon orbit. Saturn-like host planet............................................................................... 83 6.11 Satellite tidal evolution. Earth-equivalent planetary distance. Io-like moon orbit. Jupiter-like host planet.......................................................................................... 85 6.12 Satellite tidal evolution. Earth-equivalent planetary distance. Europa-like moon orbit. Jupiter-like host planet.............................................................................. 86 6.13 Satellite tidal evolution. Earth-equivalent planetary distance. Ganymede-like moon orbit. Jupiter-like host planet.............................................................................. 87 6.14 Satellite tidal evolution. Earth-equivalent planetary distance. Titan-like moon orbit. Jupiter-like host planet.......................................................................................... 87 6.15 Satellite tidal evolution. Earth-equivalent planetary distance. Io-like moon orbit. Saturn-like host planet........................................................................................... 88 6.16 Satellite tidal evolution. Earth-equivalent planetary distance. Europa-like moon orbit. Saturn-like host planet............................................................................... 89 6.17 Satellite tidal evolution. Earth-equivalent planetary distance. Ganymede-like moon orbit. Saturn-like host planet............................................................................... 90 6.18 Estimated lifetimes from each 3-body simulation for the moon to completely spiral into the host planet................................................................................................. 98 6.19 Graphical representations of the surface heat fluxes listed in Tables 6.4, 6.5, and 6.6. The red shaded regions represent surface heating values above hmax = 2 W/m2 or below hmin = 0.04 W/m2 for exomoon habitability. The dashed vertical lines at 0.4 and 0.5 M© are where Ganymede-like orbits (wider orbits) begin to be gravitationally stable................................................................................... 100 7.1 Artistic representation of two Mars-like moons around a Jupiter-like giant planet.....................................................................................................................................104 7.2 Jupiter-like host planet with two moons and a 0.3 solar mass central star. The inner moon started with an Io-like orbit. Surface heating plots only show results for the inner moon. (a) Attempted 1:2 resonance. (b) Attempted 1:3 resonance...............................................................................................................................108 7.3 Jupiter-like host planet with two moons and a 0.4 solar mass central star. The inner moon started with an Io-like orbit. Surface heating plots only show results for the inner moon. (a) Attempted 1:2 resonance. (b) Attempted 1:3 resonance. (c) Attempted 1:4 resonance....................................................................... 109 7.4 Jupiter-like host planet with two moons and a 0.5 solar mass central star. The inner moon started with an Io-like orbit. Surface heating plots only show results for the inner moon. (a) Attempted 1:2 resonance. (b) Attempted 1:3 resonance. (c) Attempted 1:4 resonance....................................................................... 110 7.5 Jupiter-like host planet with two moons and a 0.5 solar mass central star. The inner moon started with a Europa-like orbit. Surface heating plots only show results for the inner moon. (a) Attempted 1:2 resonance. (b) Attempted 1:3 resonance...............................................................................................................................111 xi 7.6 Saturn-like host planet with two moons and a 0.5 solar mass central star. The inner moon started with an Io-like orbit. Surface heating plots only show results for the inner moon. Note that for these systems, the simulations terminated early when the inner moon spiraled into the host planet. A 1:2 resonance was not included due to early system instability which ejected the outer moon. (a) Attempted 1:3 resonance. (b) Attempted 1:4 resonance...........112 7.7 Illustration showing how relative orientation changes the minimum distance between two satellites. The large blue disk represents a planet; small red disks are moons. Both orbits have an eccentricity of 0.15. The semimajor axes are consistent with a 1:2 resonant configuration. The planet is located at a focus for each orbit. (a) Inline orbits with ! out - ! in = 0°. (b) The inner orbit is the same, the outer orbit was rotated 180 degrees so that - ! in = 180°. . 114 7.8 A typical example for the overall evolution of a 4-body system. This particular system is represented in Figure 7.2(a)...........................................................................116 xii LIST OF TABLES 1.1 Summary of confirmed exoplanet detections as of 06/22/2014. Source: exo-planets. org............................................................................................................................ 10 1.2 Empirical Mass-Radius and Density-Radius Relations calculated by Marcy et al. (2014) ....................................................................................................................... 14 1.3 Coefficients to calculate habitable stellar fluxes, and corresponding habitable zones, for stars with 2600 K < Teff < 7200 K (Kopparapu et al. 2013a)........... 17 1.4 Properties of HZ planet candidates. Parameter Source: exoplanets.org ......... 20 3.1 Properties of HZ planet candidates that orbit low-mass stars. Parameter Source: exoplanets.org .................................................................................................... 39 5.1 Physical properties for a hypothetical Mars-like exomoon. The parameters A, B and C are the principal moments of inertia....................................................... 56 5.2 Physical properties for hypothetical giant exoplanets. The planet shape is assumed spherical with principal moments of inertia A = B = C ......................... 58 5.3 Eccentricity damping timescale estimates for a Mars-like moon at different orbital distances. ............................................................................................................. 61 6.1 3-body stability summary. The J symbol means the moon was stable around a Jupiter-like planet, an S for a Saturn-like planet. The symbol "-" represents an unstable satellite system. ........................................................................................ 72 6.2 3-body stability summary for a Jupiter-like host planet. The moon semimajor axes are presented as fractions of Rum. Blue shaded cells represent stable moon orbits.......................................................................................................................... 73 6.3 3-body stability summary for a Saturn-like host planet. The moon semimajor axes are presented as fractions of Ruill. Blue shaded cells represent stable moon orbits.......................................................................................................................... 73 6.4 3-body moon evolution summary for systems in the center of the stellar HZaround a Jupiter-like host planet. Values represent the average at the end of each simulation. Shaded rows are 2-body planet/moon systems. Red text indicates steady state values above hmax. Values of ** indicates the moon spiraled into the planet.............................................................................................................................. 94 6.5 3-body moon evolution summary for systems in the center of the stellar HZaround a Saturn-like host planet. Values represent the average at the end of each simulation. Shaded rows are 2-body planet/moon systems. Red text indicates steady state values above hmax. Values of ** indicates the moon spiraled into the planet.............................................................................................................................. 95 6.6 3-body moon evolution summary for systems at Earth-equivalent distances. Values represent the average at the end of each simulation. Shaded rows are 2-body planet/moon systems. Red text highlights steady state values above hmax. Values of ** indicates the moon spiraled into the planet............................. 96 7.1 4-body Hill stability summary, as compared with Table 6.1. The shaded cells represent stable 3-body simulations. The J symbol means a second moon was stable around a Jupiter-like planet, an S for a Saturn-like planet. The symbol "-" represents an unstable satellite system...................................................................106 7.2 A more detailed 4-body stability summary. Included are all systems that had potential for multiple moons based on Hill stability alone (aouter . 0.4Rhui). The ‘Extended Stability' column represents instability caused by the mutual interaction of the two moons............................................................................................107 xiv ACKNOWLEDGMENTS I would first like to thank John Armstrong for nearly a decade of encouragement and support. I originally met John as an undeclared undergraduate student taking my first-ever physics course (PHYS 1010). If at that time I had not randomly picked his class to fulfill a general requirement, I would simply not be writing this dissertation today. His guidance has been invaluable and I immensely appreciate the many hours he has volunteered to the completion of this particular project. I express my sincere appreciation to Ben Bromley for agreeing to sponsor me in this work. Ben helped me find my way as a graduate student and his direction made this study a success. I also thank the faculty and staff in the Department of Physics and Astronomy at the University of Utah, as well as the Telescope Array group. While my dissertation work did not directly involve cosmic rays, my experiences with their group are irreplaceable. I offer special thanks to Rene Heller for his contribution to this study, specifically, for our many conversations and for his incredibly valuable suggestions. His impressive work concerning exomoons has in many ways inspired this dissertation. I want to thank the Utah Space Grant Consortium and recognize their support, which gave me the time needed to explore this research. I am also indebted to the Department of Physics at Weber State University for multiple reasons: first, for providing the best undergraduate experience in physics that I can imagine; second, for providing me the opportunity to explore my passion for teaching during my graduate studies; finally, for the generous and unlimited access to their high-performance computing cluster. I cannot imagine doing this research without it. This research has also made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org. I need to thank my mother and father, and not just for the obvious reasons. My father, Ronald Zollinger, volunteered many hours to the editing and proofreading of this document. Beyond that, I am who I am today because of my parent's love and immeasurable support. In the last, most important place, I thank my wife, Stefanie. There were dark times as a graduate student, but she never let me give up. Words can simply not express my gratitude for her. CHAPTER 1 INTRODUCTION Long ago, watchers of the night sky noticed that certain stars did not appear in the same part of the sky each night. The ancients called them the asteres planetai, or the "wandering stars." It was the irregular motions of the wandering stars that eventually distinguished them as planets. Today, as we also turn our gaze toward the vast ocean of space and time, we continue to wonder as to the existence of other worlds similar to our own. Extrasolar planets, or "exoplanets," are planets that orbit stars other than our sun. It is no exaggeration to say that a significant amount of motivation in the search for extrasolar planets is embodied in the age-old question: "Are we alone?." Earth is currently the only environment where life is known to reside. Searches for extrasolar life would naturally begin with environments similar to this sole example. Planets are considered to offer the best locations for life to begin. With this in mind, this study will start with an overview of the work currently being performed in the field of extrasolar planetary science. In our Solar System, the exploration of the moons of Jupiter and Saturn has also reaped immense understanding of otherworldly environments. For this reason, the primary motivation for this dissertation is an investigation into objects other than planets which may also provide environments suitable for life to begin. By this I refer to the moon's of large exoplanets, or "exomoons." 1.1 Exoplanet Detection Methods The first definitive exoplanet detection is credited to Wolszczan and Frail (1992),1 which involved a pulsar as the parent star. As planetary hosts, pulsars undoubtedly provide hellish environments due to their intense radiation. So it can be assumed that orbiting planets would not harbor life. Nevertheless, the first confirmed exoplanet detection was a major accomplishment that spurred on the exoplanet hunt towards the real prize of finding a planet 1Previous claims for detection had been made, but none were satisfactorily confirmed until after the announcement by Wolszczan and Frail (1992). 2 around a Sun-like star. Since this discovery, exoplanet searches have enjoyed significant success thanks to continual advancements in detection instrumentation and theory. In this section, only a brief introduction to modern detection techniques will be provided. 1.1.1 H isto ric a l P e rsp e c tiv e It was not until 1609 that the first incontrovertible evidence was provided for celestial bodies orbiting something other than Earth. This achievement was made by Galileo Galilei when he used his newly designed telescope to observe the four largest moons of Jupiter. It was Galileo's telescope design that paved the way for the first significant planetary discovery in centuries, the discovery of Uranus in 1781 (Herschel). In this detection and in all prior detections, the method utilized was the classical method of directly observing the reflected starlight from planets and moons. The transition between the classical method and methods later used to detected extraso­lar planets in many ways began with the discovery of Neptune. Bouvard (1821) was the first to hypothesize Neptune's existence when he noticed substantial deviations from predictions in the tabulated observations of the orbit of Uranus. The explanation he provided was that Uranus was being perturbed by an unknown outer planet. His idea was further advanced by Le Verrier (1845) and Adams (1846) when they calculated what the orbit of the perturbing body must be. Following their predictions, the detection was made soon after by Galle (1846). Neptune, then, represented a transitional stage between the classic technique to an indirect technique for detecting bodies based on the predictions of celestial mechanics. The practice of using an advanced understanding of celestial mechanics for detecting planets would later play a vital role in extrasolar planetary searches. The planetary picture of our Solar System became apparently complete with the detec­tion of Pluto2 in 1930 by Clyde Tombaugh. After that, many astronomers set their sights on more distant planets - those orbiting stars other than our Sun. One complication to this new challenge was that the light reflected from extrasolar planets is typically one million to one billion times fainter than the reflected starlight of solar system planets. To make matters worse, the light is extremely challenging to spatially resolve from the host star. Needless to say, when astronomers began the ambitious goal of detecting exoplanets, they understood that it would not be achievable through conventional techniques and that new indirect methods would need to be developed. 2Pluto has since been reclassified as a "dwarf planet." 3 1.1.2 R a d ia l V elo city Taking a lesson from basic classical mechanics, the motion of a single planet in orbit around a star causes the star to undergo a reflex motion about the star-planet barycenter (see Figure 1.1). This motion leads to variations in the line-of-sight (radial) component of the star's velocity in which the star moves towards and away from an external observer. Utilizing this motion, the radial velocity (RV) detection method measures the line-of-sight velocity of a star in order to indirectly test for the presence of a planet. Measuring the radial component of a star's velocity can be achieved by measuring Doppler shifts in the star's spectral lines. This requires a very stable spectrograph with highly sensitive calibration and a rich forest of lines to measure. For a two-body star/planet system in an inertial frame, the planetary motion must balance with the stellar motion about the system's center of mass. Because there is typically a large difference in mass between any star and planet, the star's orbit is much smaller than the planet's (i.e. the star's velocity will also be much slower). However, the more massive a planet is and the closer it orbits the star, the faster the resulting stellar motion will be. For this reason, the RV method is more sensitive to higher mass, shorter period planets. Consequently, the method presents a detection bias for these conditions. This bias has decreased in recent years as the result of modern technological advancements and refinements in procedures used for data analysis. For example, early RV surveys had sensitivities no less than 10 m/s. By the mid-1990s, this had increased to some 3-5 m/s (Butler et al. 1996). Today, RV surveys can detect velocity variations down to around 0.3-0.5 m/s (Pepe and Lovis 2008). The fact that the RV method is sensitive to the shape and orientation of a planet's orbit serves as both advantage and disadvantage. The advantage is that the eccentricity, the period, and the argument of periastron of the orbit can be measured directly. The disadvantage is that highly inclined orbits to the line of sight from Earth produce smaller steller "wobbles" and are thus more difficult to detect. In addition, this method can only estimate a planet's minimum mass (Mtrue x sini), where i is the inclination of the orbit. Hence, a planet's true mass cannot be determined unless the inclination of the planet's orbit is also found. Fortunately, there are ways around this obstacle. RV measurements can be used in combination with the transit method (see subsection 1.1.3) to determine the true mass of the planet. The first detection of an extrasolar planet using the RV method was also the first for a planet orbiting a Sun-like star (Mayor and Queloz 1995). At that time, a Swiss group based 4 F igure 1.1. Cartoon illustrating the (exaggerated) reflex motion of a star in the inertial frame of the barycenter. The presence of the planet causes variations in the position (used for astrometry and pulsar timing) and the velocity (used for radial velocity) of the host star, which can be used to detect an exoplanet. 5 in Geneva was looking at 142 bright K and G dwarfs for radial velocity variations with a sensitivity of ~13m/s. Their discovery centered around "51 Peg," a bright G2- to G4-type star relatively close at 15.6pc in the Pegasus constellation. The planet 51 Peg b was found at 0.05 AU from the star with a period of 4.2 days and a minimum mass of 0.5 M jupiter. With this mass, the planet is most likely a gas giant. 1.1.3 T ra n sitin g P la n e ts While the RV method provides important information about a planet's orbit, it also provides frustratingly little information about their actual bodies. If the ultimate goal of exoplanet detection is to find signs of life, then the RV method fails to provide the necessary information. Fortunately, there are other promising options. If a planet detected by the RV method also happens to transit in front of its host star, relative to Earth, then additional information can be inferred about the planet's size, composition, atmosphere, temperature, and albedo. The basic principle of the transit method is that the nominal flux (F ) from a host star is temporarily attenuated due to a planet blocking out a fraction of the projected stellar surface. This occurs as the planet passes across its disk with the effect repeating at the orbital period of the planet. Light curves from transiting planets are of particular interest because they allow for estimates of their radius and orbital inclination. If this information can be combined with mass measurements from RV surveys, then the bulk density can be determined, leading to first estimates of their composition. Further probing of the planet's structure and atmospheric properties are accessible from photometry and spectroscopy during the transit and during the secondary eclipse when the planet passes behind the star3 (Perryman 2011). The geometric depth of the transit (A F) for a circular orbit is given by the ratio of the sky-projected area of the planet and the sky-projected area of the star: A F = <L1> For a planet with RP ~ RJupiter transiting a Sun-like star (1R©), the drop in solar flux is (A F /F ) ' 1.1x10-2 , or about 1%. For an Earth-size planet transiting a Sun-like star, the change in brightness is only 84 parts per million, which is less than 1/100th of 1%. These examples illustrates the small effect being sought in this method. Ground-based surveys 3An eclipse is the (partial) obscuration of one celestial body by another. When of very different angular size, the term transit refers to the smaller (here the planet) moving in front of the larger (the star); an occultation, or secondary eclipse, refers to the planet passing behind the star. 6 will be limited by atmospheric seeing and scintillation, yet even modest current telescopes are capable of measuring transit depths up to about (A F /F ) ' 1%, in large part due to the development of CCDs. Photometric precision in this range is sufficient to reveal the presence of gas-giants. Spaced-based surveys, however, avoid atmospheric effects and are currently discovering planets with transit depths of a few times 10-4 , thereby extending detectable exoplanet radii down to sub-Earth sizes. Given the obvious need for a fortuitous geometric alignment, the key question becomes, how likely is it that a transit will occur? Assuming a nearly circular orbit, the probability for a randomly-oriented planet to be favorably aligned to transit, or secondary eclipse, is (Kane, Horner, and von Braun 2012) Pt = a , (1.2) where a is the semimajor axis of the planet's orbit. Note that the transit probability is independent of the star's distance; however, increasing distance does cause a decrease in photometric accuracy. Equation (1.2) indicates that the probability of detection is greater for larger planets that orbit close to their host stars. If a transit is observed, the frequency of transit is also proportional to the orbital distance as a-3/2. Thus, there is a natural bias for short orbits and large planets. Evaluation of inclination (i) and probability for realistic cases demonstrates that transits occur only for i ' 90° and that the probability is small. To increase the probability of detection, modern projects utilize a wide-field survey in which they can monitor a large number of stars at any given time. Charbonneau et al. (2000) and Henry et al. (2000) were the first to detect an exoplanet transit. The planet, HD 209458 b, is a Jupiter-mass planet orbiting close to its parent star. Charbonneau et al. (2000) observed two transits with a duration of 2.5 hrs and a transit depth of 1.5%. Their achievement is even more impressive knowing that it was done with the 4-inch STARE telescope, demonstrating the potential for inexpensive transit observations. 1.1.4 D ire c t Im ag in g Direct imaging seeks to either spatially or spectrally resolve the light of the planet from that of the star. The light from the planet may be either reflected starlight (in the visible) or through its own thermal emission (in the infrared). Consequently, this method favors hot planets at wide separations. One obvious challenge to this method is the overwhelming comparative brightness of the host star. For most systems, the planet/star flux ratio for reflected light will be very low. The challenge of actually resolving the light will exacerbate matters further. The star and 7 planet have an angular separation of aP/d, where aP is the planet's semimajor axis about the star and d is the distance to the star from the observer. Telescopes typically have their angular resolution constrained by the diffraction limit, given by 1.22A/D, where A is the wavelength of the light and D is the diameter of the telescope. Therefore, direct imaging requires the use of large telescopes with short wavelengths to look around nearby stars with planets at wide separation. For ground-based telescopes, atmospheric effects provide additional complications. However, recent advancements in adaptive optics can be used to significantly lessen their impact. The first image of an extrasolar planet is 2M1207b by Chauvin et al. (2004). The primary of this system is actually a brown dwarf, so the contrast ratio between the planet and "star" is quite favorable. Also, the planet orbits at ~50 AU and is hot, being in the range 1000-2000 K. Since that time, several additional planets have been directly imaged. Marois et al. (2010) were the first to directly image a system of planets. Their image is in the infrared and shows four hot planets orbiting at 14, 27, 42, and 67 AU. Such an image is possible because of the wide orbits and youth (<100Myr) of the planets which are still hot and bright as they radiate away gravitational energy acquired during their formation. The star, named HR 8799, is an A-type star. Such a high luminosity star would normally be less than favorable due to the low planet-to-star contrast. However, in this case, its higher mass allowed it to retain a more extended disk which is believed to have formed the widely separated massive planets. 1.1.5 A d d itio n a l D e te c tio n M e th o d s In addition to the RV, transit, and direct imaging methods, other techniques have been proposed and have had success detecting exoplanets. However, their combined contribution to the total number of detected exoplanets is very low and they hold little interest to the study of exomoons. A few statements concerning the remaining detection methods will be provided in the interest of completeness. 1.1.5.1 G ra v ita tio n a l M icro len sin g Gravitational microlensing draws upon the theory of general relativity in which matter (energy density) distorts spacetime and the path of electromagnetic radiation is deflected as a result. Put more simply, massive bodies bend the apparent path of light, which in essence, acts as a lens. Under the right conditions, if a star passes in front of a more distant and luminous background object (the source), the star (the lens) will cause the brightness of the background object to dramatically increase for a few days or weeks, depending on the 8 configuration. The same is true if the lensing star hosts a planet except that an observer will see two (or more) increases in brightness; one large increase due to the massive star and one smaller increase due to the planet. This method would naturally be more sensitive to massive planets with wide separations. One major downside is that microlensing events are inherently transient and after the event is over, there is no additional opportunity for follow-up. 1.1.5.2 A stro m e try Astrometry is complimentary to the theory behind the RV method in that it concerns the reflex motion of the host star as it orbits the system's center-of-mass (refer to Figure 1.1) . In this case, it is variations in the star's position that can betray the presence of an extrasolar planet (whereas the RV method measures variations in the star's velocity). In particular, this method aims to determine the transverse component of the displacement relative to the line-of-sight. The accuracy required to detect planets astrometrically is typically sub-mas (milli-arc-seconds) with most modern instrumentation only reaching accuracies around 1 mas. However, the recently launched "Gaia" spacecraft is expected to achieve accuracies of ~20 - 25 ^as (Perryman 2011). 1.1.5.3 P u ls a r T im in g Similar to the discussion of RV and astrometry theory, if a pulsar has an orbiting planet, its reflex motion about the center-of-mass will cause periodic deviations in the times of arrival of the pulsar signal. Measurements of such timing deviations can provide an alternative route to the dynamical detection of orbiting planets. Interestingly, it is the pulsar timing method that is credited with the first unambiguous detection of an extrasolar planet (Wolszczan and Frail 1992). 1.2 Extrasolar Systems Overview As mentioned in subsection 1.1.2, 51 Peg b was the first extrasolar planet detected around a Sun-like star, which is a roughly Jupiter mass planet with an orbital period of only a few days. The detection of such a large body that close to its host star was previously unanticipated. Planetary formation models of the Solar System (Pollack et al. 1996) suggest that gas giants formed beyond the frost-line. This line is the distance from a star where it is cold enough for hydrogen compounds to condense into solid ice grains, typically estimated to be about 150 K. For the 51 Peg system, this distance should be at least a few AU. While inward migration had been considered before the detection of 51 Peg b, inspections of the 9 Solar System gas giants alluded that this mechanism was not very effective. Consequently, this discovery presented a serious challenge to planet formation theories of the time and spurred new investigations into formation theory. Planets such as 51 Peg b have since been described as "hot-Jupiters" where hot-Jupiters are defined as planets with an orbital period less than 10 days and a minimum mass equal to about 0.5 M jupiter. 1.2.1 A n E x p lo sio n o f D iscoveries Just six days after the 51 Peg b discovery, Geoff Marcy and Paul Butler of San Fran­cisco State University independently confirmed the signal, then shortly after achieved two new discoveries (Marcy and Butler 1996; Butler and Marcy 1996). So began the age of exoplanetary science with new discoveries being reported on an increasingly regular basis (see Figure 1.2). Today, over a thousand exoplanets are known to exist4 (Wright et al. 2011) and hundreds 4According to the exoplanet database at "exoplanets.org." I make use of this database throughout this document. 0 _________________ ' »------'I___u___u___u___u___u___u___u___u__ 1995 2000 2005 2010 Detection Year Figure 1.2. Exoplanet detections per year after 1995. The very recent spike is primarily due to a large release of Kepler candidate confirmations. 10 of these are found in multiplanet systems (two or more planets around a star). A detailed summary of the current number of confirmed detections is given in Table 1.1. Until the last couple of years, the large majority of detections resulted from RV surveys. However, that changed with the launch of NASA's Kepler space telescope in 2009 which utilized the transit method for planet detection. The Kepler spacecraft is essentially a photometer designed to continually monitor the brightness of over 145,000 main sequence stars in a fixed field of view (Borucki et al. 2008). Today, the combined efforts of RV and transit surveys have resulting in about 95% of all confirmed detections. In addition to the confirmed planets, there is another 3000+ unconfirmed Kepler "candidates" that await confirmation from additional observations or alternative detection techniques (other than transits). 1.2.2 A p p a re n t D e te c tio n B ias Extrasolar planets span a wide range of physical and orbital properties. Due to the bias of RV surveys to high mass, short-period planets, many initial detections included the previously unanticipated hot-Jupiters (Period < 10 days, Mass & 0.5 M jupiter). However, with increasingly longer observational baselines and improvements to instrument precision, detections began to emerge for lower mass planets and for multiyear orbital period planets. More recent RV surveys have found that planet counts increase toward smaller masses, at least within the range of 1000 M® down to ~5M® (Howard et al. 2010; Mayor et al. 2011), where M® is the mass of the Earth. Also, technique improvements have lead to discoveries down to minimum masses ' 1.1 M® (Dumusque et al. 2012). An illustration of the relationship between mass and orbital distance for the detected exoplanets is shown in Figure 1.3, which shows that the majority of lowest-mass planets were detected only recently. Table 1.1. Summary of confirmed exoplanet detections as of 06/22/2014. Source: exoplanets.org. T otal num ber of detections 1518 Planets in multiplanet systems 989 Systems with 2 planets 266 Systems with 3 planets 85 Systems with 4 planets 32 Systems with 5 planets 11 Systems with 6 planets 2 Systems with 7 planets 1 11 Figure 1.3. Relationship between mass and orbital distance (semimajor axis) for detected exoplanets. The colorscale indicates the detection date of the planet. Bluish-green colors represent the years when RV surveys dominated. Results from Kepler are included in the orange-red colors. The chosen axial limits result in the exclusion of a few higher mass or longer period planets. For comparison, 1 Earth mass = 0.0031 Jupiter masses. [Source: exoplanets.org] Measurements of planetary radii received a major boost with the recent success of the Kepler program, in particular, measurements for Earth-sized planets. Kepler was specifically designed to search for Earth-like planets in or near the so called "habitable zone" (see subsection 1.3.1) of Sun-like stars. Today, Earth-like planet detections (in terms of size and mass) are becoming more common. The Kepler program independently found that 85% of its transiting planet "candidates" have radii less than 4 R® (Batalha et al. 2013), and it is believed that more than 80% of these small candidates are actually planets (Morton and Johnson 2011; Fressin et al. 2013). For comparison, the radius of Neptune is 3.9 R®. Therefore, it seems that planets between the size of Earth and Neptune are common in our galaxy. It is worth pointing out that since the transit method favors close-in orbits, many of these detections are for short-period planets (<50 days). Consequently, a true 12 Earth analog has yet to be discovered. Still, these discoveries are impressive with the current record holder for smallest detection belongs to a Mercury-sized planet (~0.3 R®) (Batalha et al. 2013). 1.2.3 E x o p la n e t C o m p o sitio n The first detection of a transiting planet was that of a now fairly typical hot-Jupiter (Charbonneau et al. 2000; Henry et al. 2000). However, that detection provided the first confirmation that Jupiter-mass planets in close orbits about their host stars have radii and densities comparable to the gas-giants of our own Solar System. Interest in low-mass planets naturally stems from the separation between gas planets (higher mass) and rocky, terrestrial planets (lower mass). Traditionally, the accepted stan­dard for the critical mass that separates rocky planets from gas planets was approximately 10 M® (Valencia et al. 2006). However, this estimate was made during a time when very few radii were known for planets less than the mass of Jupiter (see Figure 1.4). Now that the sample size for planetary radii has significantly increased, the critical mass estimate is being reevaluated (see explanation below). With so many new examples of planets in the range 1-4 R®, it is interesting to consider that we have no Solar System analogs for planets with 2-3 R®. This makes it difficult to understand their chemical compositions, interior structures, and formation processes; although, much discussion can be found in the literature (Fortney et al. 2007; Seager et al. 2007; Zeng and Seager 2008; Rogers et al. 2011; Lissauer et al. 2012; Fabrycky et al. 2012; Zeng and Sasselov 2013). Determining the chemical composition is one step toward a deeper understanding, but at this planet-size scale, the relative amounts of rock, water, and H and He gas remain poorly known. Most likely, the mixture of those three ingredients changes as a function of planet mass, but differs among planets at a given mass as well (Marcy et al. 2014). One way to constrain the internal chemical composition for 1-4 R® planets is to measure the masses (which can be done with RV or TTV measurements), and thus, determine a bulk density. However, the gravitational acceleration that these planets induce on their host star is small and therefore challenging to detect with current telescopes and instruments. As a result, only a comparative handful of small planets have mass measurements. Weiss and Marcy (2014) studied the masses and radii of 65 exoplanets smaller than 4 R® with orbital periods shorter than 100 days.5 They showed that on average, planets with radii up to 5Of the 65 exoplanets considered, only 19 have vetted mass values listed on exoplanets.org. The rest have 13 - i ----------------------------- 1-----------------1- i- i- i i i i exoplanets.org | 6/22/2014 1 ■ ' ■ ' ■ .................................................................^ ' .......................................................................... ■ 1 1 0.01 0.1 1 10 Semi-Major Axis [Astronomical Units (All)] Figure 1.4. Relationship between planet radius and orbital distance (semimajor axis) for detected exoplanets. The colorscale indicates the detection date of the planet. Green colors represent a time when RV surveys dominated. Results from Kepler are included in the orange-red colors. From the coloring, it is obvious that the most radius measurements were made only recently. For comparison, 1 Earth radius = 0.089 Jupiter radii. [Source: exoplanets.org] Rp = 1.5R® increase in density with increasing radius. The densities in this range are consistent with rocky-type bodies with a maximum at 7.6 g cm-3 (Earth's density is 5.5 g cm-3). However, above 1.5 R®, the average planet density rapidly decreases with increasing radius, indicating that these planets have a large fraction of volatiles by volume overlying a rocky core. Weiss and Marcy (2014) also derived an empirical density-radius relation and mass-radius relation for the range Rp < 4R®. Their results are summarized in Table 1.2. Other studies have suggested that planets with a radius between 1.4 and 2.0 R® will have either homogeneous composition of water ice, silicates, and iron, or some differential composition of these compounds (Seager et al. 2007; Rogers et al. 2011; Lopez et al. 2012). mass values that have not yet been added to the online database. 14 Table 1.2. Empirical Mass-Radius and Density-Radius Relations calculated by Marcy et al. (2014) _________________________________________________ In addition to the study by Weiss and Marcy (2014), the authors took part in other similar empirical analyses (Weiss et al. 2013; Marcy et al. 2014). These studies suggest that a transition from planets containing significant light material to rocky planets occurs at ~2 R®, which would correspond to a mass of ~5 M® according to the mass-radius relation in Table 1.2. The authors acknowledge that these estimates are based on a small statistical sample and that the results may change for planets with larger orbital distances (longer periods). These values show a significant change from the classical estimate of 10 M® for the critical mass. There are currently 425 confirmed planets with a radius below 2 R® or mass less than 5 M®. However, of those potentially rocky planets, only 27 have vetted values for both mass and radius.6 Exceptions to the proposed transition radius of ~2 R® have already been found. Dumusque et al. (2014) recently reported the discovery of Kepler-10c, which is a 17 ± 1.9 M® planet with a radius of 2.35+0'09 R®. With a density of 7.1 ± 1.0 g cm-3 Kepler-10c suggests that medium-sized planets can stay rocky rather than always becoming gaseous and bloated. Needless to say, continued effort to obtain mass measurements for roughly Earth-sized planets is important. Another interesting difference between detected exoplanets and our Solar System is the shape of the orbits (not to be confused with the "size," which is represented by the semimajor axis). Most exoplanets have substantial orbital eccentricities with an average around 0.16. This is in contrast to the Solar System which has an average for the planets of about 0.07. Combining this observation with the much broader range of orbital distances seen in exoplanets suggests a violent and vigorous formation history. For example, studies of gravitational scattering have been successful in reproducing the broad distribution of orbital eccentricities (Chatterjee et al. 2008) while studies of interactions between a planet Planet Size Equation Rp < 1.5R® 1.5 < Rp/R® < 4 1.2.4 A d d itio n a l O rb ita l P ro p e rtie s 6 Several more masses are known, but are still awaiting final confirmation before their values will be added to the exoplanet.org database. 15 and a protoplanetary gas disk may explain the presence of planets with orbital semimajor axes of only a few hundredths of an AU (Lin et al. 1996). 1.2.5 S om e In te re s tin g E x am p les Before the first exoplanet detections, any speculation as to the existence and architecture of extrasolar systems had to be based solely on the example of our solar environment. With that limitation, it was only natural to assume the Solar System offered a typical example for other systems. Now that hundreds of extrasolar systems are known, it is safe to say that so far, our system appears to be anything but typical. The following are a few specific examples of interesting systems that are very different than our own. The Kepler-11 system provides a very unique and unexpected example of a multiplanet system, containing six planets around a K-type star. Of those planets, three have masses of ~ 2M®, two have ~ 8M®, and the last is a massive giant planet. To find a system with such low mass is interesting. However, the picture becomes even more intriguing with the knowledge that all six of these planets are packed tightly together with the largest orbit at 0.5 AU. For reference, this is much less than the orbit of Venus around the Sun (at 0.7 Au). In addition, these planets have low densities, none of which are dense enough to be composed entirely of rock. In fact, the Kepler-11 planets are less massive for a given radius than most other planets with both mass and radius measurements (Lissauer et al. 2013). Consequently, this system has been a major source of interest for both dynamical considerations and formation models. Other interesting examples are less about multiple planets than about multiple suns. It is estimated that binary stars are quite common in the galaxy. Yet, during the first decade and a half of planet detections, no planets were found in multiple star systems. Planets with two suns have long existed in the realm of science fiction. In 2011, that fantasy became one step closer to reality with the first unambiguous detection of a circumbinary planet (Doyle et al. 2011). Unlike the planets of our imagination, this planet (known as Kepler-16b) is cold, gaseous, and not thought to harbor life. Nevertheless, its discovery demonstrates the diversity of planets in our galaxy. Since that time, several more circumbinary planets have been detected and there has even been the discovery a circumbinary multiplanet system (Orosz et al. 2012). The system, Kepler-47, has two confirmed planets. Both planets are gas giants and one is believed to orbit in the habitable zone of the stars (see subsection 1.3.1). There is also recent evidence for the existence of a third planet; however, its detection has yet to be verified (Welsh et al. 2013). 16 1.3 Habitability An attempt to define ‘life' could require a completely independent study (Benner 2010) and one may expect to obtain different results depending on the context and motivation for the study. For this study, a definition of life used within the field of Biology is appropriate. This dissertation focuses environmental conditions (i.e. habitability) that are suitable for life, or at least, life as is understand on planet Earth. The sustained presence of liquid water on the surface of the Earth has played a crucial role in the development of life. Therefore, my working definition for planet habitability will be the requirement that physical conditions allow for the continued presence of liquid water on the surface of a terrestrial planet. 1.3.1 T h e H a b ita b le Z one Assuming that a planet has water on its surface, the primary consideration for habitabil­ity is the surface temperature. The major energy contribution is the radiation the planet receives from its parent star. Considerations of stellar radiation and climate have led to the definition of a "habitable zone" (hereafter referred to as "HZ") as the region around a star in which a terrestrial-mass planet with a CO2-H2O-N2 atmosphere and a sufficiently large water content can sustain liquid water on its surface (Kopparapu et al. 2013b). If a planet is too close to a star, the surface temperature will be too hot for liquid water; whereas too far from the star will be too cold. The zone between the two extremes is a range of orbits where surface liquid water should be stable (Kasting et al. 1993). The position of HZs around stars depends on the stellar type, luminosity class, and details of the planetary atmosphere. The concept of the HZ was proposed for the first time by Huang (1959). Since that time, it has been calculated by several other authors (Hart 1978; Kasting et al. 1993; Underwood et al. 2003; von Bloh et al. 2007; Selsis et al. 2007; Kaltenegger and Sasselov 2011). The main differences are in the climatic constraints imposed on the limits of the HZ by these studies. For the research presented in this dissertation, I have chosen to utilize an updated model proposed by Kopparapu et al. (2013b) which provides generalized expressions to calculate HZ boundaries around F, G, K, and M stellar spectral types. They used a one-dimensional, radiative-convective, cloud-free climate model, and assumed an Earth-mass planet with an H2O (inner edge) or CO2 (outer edge)-dominated atmosphere as their base model. Their calculations of the HZ boundaries relied on the so-called inverse climate modeling, where they specify a surface temperature and then use the model to calculate the corresponding stellar flux needed to sustain that temperature. The work by Kopparapu et al. (2013b) produced a variety of limits for the inner and 17 outer edges of the HZ. This study utilizes their most conservative boundary estimates. These estimates are based on derived relationships between HZ stellar fluxes (Sef f ) reaching the top of the atmosphere of an Earth-like planet and stellar effective temperatures (Tef f ) in the range 2600 K < Teff < 7200 K: Sef f = Sef f Q + aT? + bT? + cT?3 + dT?4, (1.3) where T* = Teff - 5780 K. The values of the coefficients are provided in Table 1.3. For these boundaries, the inner edge is based on the "moist-greenhouse" (or water-loss) limit. At this limit, the proximity to the star causes the water vapor content in the atmosphere to increase dramatically and become saturated. Once the stratosphere becomes wet, water molecules break down via photolysis and hydrogen is released. The hydrogen can then escape to space by the diffusion-limited escape rate, resulting in the eventual desiccation of the planet. With the HZ stellar flux, the corresponding HZ distances can be calculated using the relation d = ( f f a v - (L4) where L/L© is the luminosity of the star compared to the Sun. Moving away from the star, the stellar flux received by the planet will decrease and the planet's temperature will drop. The outer edge of the HZ is based on the working hypothesis that as a planet cools, its atmospheric CO2 will accumulate due to the negative feedback provided by the carbonate-silicate cycle. The additional CO2 compensates for the decreased stellar flux through a greenhouse effect which backscatters infrared emissions from the surface. Below a certain temperature and pressure, the CO2 will begin to condense out of the atmosphere and the greenhouse effect will no longer compensate for the low solar flux. For that reason, the outer orbital boundary is referred to as the "maximum greenhouse" limit. Table 1.3. Coefficients to calculate habitable stellar fluxes, and corresponding habitable zones, for stars with 2600 K < Teff < 7200 K (Kopparapu et al. 2013a). Constants Moist Greenhouse Maximum Greenhouse (Inner Limit) (Outer Limit) Seff © 1.0146 0.3507 a 8.1884 x 10-5 5.9578 x 10-5 b 1.9394 x 10-9 1.6707 x 10-9 c -4.3618 x 10-12 -3.0058 x 10-12 d -6.8260 x 10-16 -5.1925 x 10-16 18 Using the conservative limits represented by Equation (1.3), Equation (1.4), and Table 1.3, one can estimate the HZ for our Sun. The somewhat surprising result is an inner HZ boundary at 0.99 AU and an outer boundary at 1.67 AU. According to this estimate, the Earth (at 1 AU) is very near the hot edge of the Sun's habitable space, with Mars (at 1.52 AU) also located well within the estimate. 1.3.2 A d d itio n a l C o n sid e ra tio n s fo r th e H a b ita b le Z one A star's luminosity increases with age which causes the stellar HZ to migrate outward with time. As such, planets in the HZ at the current epoch may not have been habitable in the past. The idea of a continuously habitable zone has been introduced to deal with the luminosity evolution of the star and related studies have been performed (Underwood et al. 2003). As the name suggests, a continuously habitable zone is the region around a star in which a terrestrial planet can sustain liquid water on its surface for a specified period of time. With this extra condition, the requirement could be added that a circumstellar region receive sufficient flux for a planet to remain habitable long enough for life to emerge. Because my current study focuses only on the presence of liquid water, I do not introduce this extra condition. As such, my working definition of a HZ could be considered as the instantaneous habitable zone. The definition of the habitable zone can be further complemented by the dynamical requirement that other planets in the system do not gravitationally perturb the terrestrial planets outside the zone. In such a case, a planet's orbital eccentricity about the star can cause it to spend a fraction of its year outside the HZ, which could result in large variations in temperature and atmospheric pressure. Previous studies have considered this effect (Williams and Pollard 2002; Menou and Tabachnik 2003; Pilat-Lohinger et al. 2008; Dvorak et al. 2010; Dressing et al. 2010). In addition to eccentricity considerations, Armstrong et al. (2014) explored the impact of obliquity variations on planetary habitability and found that such oscillations further expand habitable orbits. The result is that terrestrial planets near the outer edge of the HZ may be more likely to support life in systems that induce rapid obliquity oscillations as opposed to fixed-spin planets. For reasons explained in Chapter 5, the planetary systems considered in this dissertation do not necessitate either of these additional dynamical consideration. 1.3.3 D e te c te d P la n e ts in th e H a b ita b le Z one Out of the many confirmed exoplanets, several HZ candidates have already been identi­fied (Udry et al. 2007; Pepe et al. 2011; Borucki et al. 2011, 2012; Vogt et al. 2012; Tuomi 19 et al. 2013) and the number of HZ planet detections is expected to significantly increase with time (Batalha et al. 2013). I performed my own analysis of potential HZ planets using the conservative limits provided with Equations (1.3) and (1.4), and Table 1.3. In order to make a HZ estimation, measurements must be known for the radius (R*) and effective temperature of the host star. From these, the stellar luminosity can be calculated using the well-known relationship: L = 4 ^ R * Teff, (1.5) where a is the Stefan-Boltzmann constant. For extrasolar systems that lack necessary measurements, I can estimate the star's radius using an empirical relation derived from observations of eclipsing binaries (Gorda and Svechnikov 1999): logioKt1 = 1-03 Kq logiomMq* + 0-1, (L6) where Rq and Mq are the radius and mass of the Sun, respectively. However, Equation (1.6) is valid only when M* < Mq . If a star's effective temperature is unknown, but the stellar mass has been measured, the luminosity can be determined by, A = 4.101^3 + 8.162^2 + 7.108^ + 0.065, (1.7) where A = logi0(L /LQ) and ^ = logi0(M*/MQ) (Scalo et al. 2007). From the stellar luminosity and radius, the effective temperature can be found using Equation (1.5). To compare orbital distances with Equation (1.4), I use the planet's semimajor axis as the average distance between the planet and host star. While this definition is not entirely accurate due to effects of orbital eccentricity, its use is sufficient for this simple analysis. From my estimations, the number of HZ planet candidates represents just 4.5% of the total number of confirmed exoplanets (68 out of 1518). Of these candidates, 93% have masses similar to or greater than Neptune (17 M®), and are therefore most likely gas planets. Only 3 meet the latest estimates for a potentially terrestrial planet (radius < 2 R® or mass < 5 M®, see subsection 1.2.3). A complete list of the HZ candidates and their properties is included in Table 1.4. 1.4 From Exoplanets to Exomoons It has been almost 20 years since the first exoplanet orbiting a Sun-like star was detected. Since that time, the rate of planet detections each year has continued to increase and with it, the overall interest of the scientific community. The impressive achievements in exoplanet detection have revolutionized our understanding of the formation and evolution 20 Table 1.4: P ro p erties of HZ planet candidates. P a ram eter Source: exoplanets.org N am e M ass (M®) R adius R® Sem im ajor Axis (AU) S tar Mass (MSun) T Ef f (K ) Kepler-186 f - 1.1 0.4 0.5 3788 Kepler-62 f - 1.4 0.7 0.7 4925 Kepler-283 c - 1.8 0.4 - 4351 Kepler-174 d - 2.2 0.8 - 4880 GJ 581 d 6.1 - 0.2 0.3 3498 HD 10180 g 21.4 - 1.4 1.1 5911 HD 192310 c 23.4 - 1.2 0.8 5166 HD 218566 b 67.6 - 0.7 0.8 4820 HD 137388 b 72.4 - 0.9 0.9 5240 HD 7199 b 93.7 - 1.4 0.9 5386 HIP 57050 b 94.6 - 0.2 0.3 3190 HD 215497 c 104.1 - 1.3 0.9 5113 HD 181720 b 118.2 - 1.8 0.9 5781 HD 99109 b 160.2 - 1.1 0.9 5272 HIP 14810 d 184.5 - 1.9 1.0 5485 GJ 876 c 194.5 - 0.1 0.3 - HD 63765 b 204.6 - 0.9 0.9 5432 HD 34445 b 251.2 - 2.1 1.1 5836 HD 187085 b 255.4 - 2.0 1.1 6075 Kepler-68 d 257.3 - 1.4 1.1 5793 HD 10647 b 293.9 - 2.0 1.1 6105 HD 114729 b 300.2 - 2.1 1.0 5821 HD 73534 b 339.4 - 3.0 1.2 4884 HD 114783 b 351.1 - 1.2 0.9 5135 HD 28254 b 369.0 - 2.1 1.1 5664 HD 100777 b 370.2 - 1.0 1.0 5582 HD 147513 b 374.8 - 1.3 1.1 5930 tau Gru b 386.0 - 2.5 1.2 5999 HD 65216 b 386.5 - 1.4 0.9 5666 HD 210277 b 404.4 - 1.1 1.0 5555 HD 30562 b 423.4 - 2.3 1.3 5936 HD 23127 b 446.4 - 2.3 1.1 5752 HIP 5158 b 453.2 - 0.9 0.8 4962 HD 188015 b 467.0 - 1.2 1.1 5746 BD +14 4559 b 482.8 - 0.8 0.9 4814 16 Cyg B b 521.1 - 1.7 1.0 5674 HD 4113 b 523.7 - 1.3 1.0 5688 HD 82943 b 535.5 - 1.2 1.1 5997 mu Ara b 554.6 - 1.5 1.1 5784 HD 20782 b 603.7 - 1.4 1.0 5758 HD 190647 b 604.7 - 2.1 1.1 5628 GJ 876 b 618.6 - 0.2 0.3 - 21 Table 1.4 - Continued N am e M ass (M®) R adius R® Sem im ajor Axis (AU) S tar Mass (MSun) T Eff (K) HD 5388 b 624.4 - 1.8 1.2 6297 HD 20868 b 638.4 - 0.9 0.8 4795 HD 4203 b 661.6 - 1.2 1.1 5702 HIP 79431 b 671.4 - 0.4 0.5 3191 HD 159868 b 699.1 - 2.3 1.2 5558 HD 163607 c 728.4 - 2.4 1.1 5543 HD 4732 c 751.5 - 4.6 1.7 4959 7 CMa b 772.9 - 1.8 1.3 4761 HD 23079 b 776.4 - 1.6 1.0 5927 HD 153950 b 871.3 - 1.3 1.1 6076 HD 125612 b 974.9 - 1.4 1.1 5897 HD 92788 b 1132.4 - 1.0 1.1 5836 HD 183263 b 1135.8 - 1.5 1.1 5936 upsilon And d 1307.8 - 2.5 1.3 6213 HD 16175 b 1391.6 - 2.1 1.3 6080 HD 213240 b 1440.2 - 1.9 1.1 5968 HD 13908 c 1630.1 - 2.0 1.3 6255 HD 28185 b 1842.1 - 1.0 1.0 5656 HD 190228 b 1888.1 - 2.6 1.8 5348 HD 10697 b 1981.2 - 2.1 1.1 5680 HD 86264 b 2105.9 - 2.8 1.4 6326 HD 222582 b 2424.5 - 1.3 1.0 5727 HD 23596 b 2460.3 - 2.8 1.2 5904 HD 141937 b 3010.8 - 1.5 1.0 5847 HD 136118 b 3711.6 - 2.3 1.2 6097 HD 16760 b 4223.6 - 1.1 0.8 5620 22 of planetary systems. With over a thousand confirmed detections and several thousand additional candidates, the focus of exoplanet research has begun to shift from detection to characterization. Through the characterization of extrasolar systems, scientists take the first step towards detecting habitats outside the Solar System. An examination of life on Earth suggests that ecosystems require at a minimum: liquid water, a stable energy source, and a supply of nutrients. At present, no other planet in our Solar System shows an environment that combines all three basic requirements.7 Yet, Earth is not the only object in our Solar System to contain liquids, heat, and nutrients. We know of at least three moons that possess those properties. They are the Jovian companion Europa, and the Saturnian satellites - Enceladus and Titan. From the study of our local habitat, it also appears that plate tectonics are essential for maintaining habitability on Earth. Only three bodies in the Solar System, other than Earth, are known to show tectonic activity. Remarkably, these three objects are not planets, but moons: Jupiter's Io, Saturn's Enceladus, and Neptune's Triton. From these local examples, it would seem that satellite systems represent mini-solar systems with a richness and diversity all their own. As extrasolar planets are explored with increasing detail, a new class of objects may soon become accessible to observation by which I refer to extrasolar moons (or "exomoons"). These moons are the naturally occurring satellites of extrasolar planets and based on the structure of our Solar System, they may be even more abundant than planets. 1.5 Dissertation Outline In this dissertation, I undertake a computational exploration into specific characteristics of theoretical exomoon systems. The habitability of the moons will be considered and the study will serve as an early attempt at exomoon characterization. Chapter 2 will provide additional interest in exomoon systems. This chapter will also include an overview of exomoon theory and current predictions for their detectability. The information presented will be used in Chapter 5 as a basis for constructing a hypothetical exomoon model. In Chapter 3, I explain why M spectral type stars are receiving new interest as targets for extrasolar planets. Stars of this spectral type are often referred to as ‘low-mass' or ‘red dwarf' stars and they present certain advantages for detecting exoplanets in the HZ. The chapter ends with an explanation of how moons around giant planets in the HZ of 7However, there is evidence that Mars did have liquid water on its surface billions of years ago. 23 red dwarf stars do not face the same challenges to habitability as do the planets in these systems. However, potentially habitable exomoons around giant planets in the HZ of red dwarf stars do face challenges of long-term gravitational stability and tidal heating. These particular challenges represent the primary focus of this dissertation. A brief introduction to tidal theory and the impact of tidal heating on habitability is provided in Chapter 4. As part of this introduction, I explain the limitations of popular tidal models for evaluating long-term tidal evolution in strongly interacting, many-bodied systems. For systems such as these, a unique method for calculating self-consistently the tidal, spin, and dynamical evolution is described. At the end of Chapter 4, I explain how this method is utilized to create a computational program for simulating the long-term tidal and dynamical evolution of hypothetical exomoons in red dwarf star systems. The parameters used to model low-mass stars, exoplanets, and exomoons are described in Chapter 5. My primary investigation into exomoon habitability involved 3-body systems comprised of a giant planet, a Mars-like massive moon, and a M-dwarf central star. Using this newly created program, repeated simulations were performed to explore the tidal evolution of the moons in these systems. An explanation of the 3-body model and a discussion of the results is contained in Chapter 6. An extension to the 3-body simulations is described in Chapter 7. This extension involves a 4-body model where a second moon was added to the system and the effects of orbital resonance were explored. The implications on exomoon habitability in low-mass star systems is examined in Chapter 8. I then conclude with a look at related future work. CHAPTER 2 EXTRASOLAR MOONS 2.1 Motivation With so much attention being given to extrasolar planet detection and theory, it is interesting to note that the exploration of moons in the Solar System actually broadened our understanding of planet formation in our own system. Moons have been proposed as tracers of planet formation (Sasaki et al. 2010). Given the diversity and quantity of Solar System moons, it seems reasonable to envision a likewise abundant population of natural satellites around extrasolar planets. Therefore, an increased population sample through the detection of many extrasolar satellite systems could fundamentally reshape our understanding of formation processes. At the time of this writing, no moon outside the Solar System has been detected. However, extrasolar moons continue to excite the imagination as to other possible habitats for extrasolar life (Reynolds et al. 1987; Williams et al. 1997; Heller and Barnes 2013). Now that current technology and theoretical methods are allowing for the detection of sub-Earth sized extrasolar planets, the first detection of an extrasolar moon appears to be on the horizon (Kipping et al. 2009; Kipping et al. 2012). With that in mind, it is useful to consider the expected properties and characteristics of exomoons, the results of which can be used to inform those that are currently working to achieve the first detection. 2.2 Formation Two mechanisms have been proposed for the formation of satellites: (1) Formation from the disk material surrounding a planet. In this scenario, the objects will be "regular satellites" (always prograde) (Canup and Ward 2002). Examples in the Solar System are the Galilean satellites of Jupiter. (2) Formation by gravitational capture, impacts, or exchange interactions. These objects will be "irregular satellites" (either prograde or retrograde) (Jewitt and Haghighipour 2007). Only two examples of large irregular satellites are known, those being the Moon and Triton. While Triton is likely to have been gravitationally 25 captured by Neptune (Agnor and Hamilton 2006), the Moon's formation is more unique. The Moon is thought to have resulted from the collision between a Mars-sized planet, dubbed "Theia," and the primordial Earth (Taylor 1992). The two satellite formation mechanisms are based on observations of our Solar System and are quite distinct from planet formation models. Previous studies have applied these mechanism to the formation of satellites in potential extrasolar systems (Canup and Ward 2006; Porter and Grundy 2011; Williams 2013). Their predictions for the maximum possible satellite mass varied depending on the formation model and the planetary system being considered. However, the studies do show the potential for massive satellites around extrasolar gas giants. In-situ formation in the circumplanetary disk was shown to scale with planet mass, suggesting that the formation of a Mars-like1 moon would be possible if it was around a super-Jovian mass planet. One the other hand, formation by capture is the mechanism believed to give the best chance for massive terrestrial satellites. In some cases, moons the size of Earth are feasible (Williams 2013). However, Heller et al. (2014) performed a detailed formation analysis and concluded that a more reasonable result is that of moons with roughly the mass of Mars. Captured moons would be classified as irregular satellites, which is beneficial since this does not constrain the expected properties in many ways. 2.3 Predicted Properties of Exomoons Extrasolar moons are predicted to be abundant; however, as long as no such world is found, the science on extrasolar moons will remain theoretical. Regardless, predictions can be made as to their orbital evolution, physical properties, habitability, and ultimately, their detection. 2.3.1 S ta b ility After a moon has formed, its lasting survival can still be in question. Small gravitational perturbations from multiple satellites, the star, or from other planets can lead to chaos, ejections, and planet-satellite mergers. For a system of three bodies consisting of a star, planet, and moon, the region in which the planet dominates the attraction of the moon2 is known as the Hill sphere.3 The radius 1Mars has a mass of 0.11 M® and a radius of 0.53 R®. 2In the calculation, the moon is treated as a test particle (i.e. the mass of the moon is not important). 3Named after George William Hill who provided the definition. 26 of the sphere (RH) is found by solving the restricted circular three-body problem and is equal to the distance of the L1/L2 Lagrange points: ✓ Mp \ 1/3 , , R h = ap { u T . ) ' (2'1) where aP is the semimajor axis of the planet's orbit around the star, MP and M. are the masses of the planet and star, respectively. In realistic scenarios, this simple picture does not accurately represent the complete stable region of an extrasolar moon. The critical semi-axis (aps) for a satellite to remain bound to its host planet is merely a fraction (f) of the Hill radius, i.e. aps < f R H (Holman and Wiegert 1999). A conservative choice for prograde satellites is f = 1/3 (Barnes and O'Brien 2002). Domingos et al. (2006) extended this consideration and showed that the actual stability region depends upon the eccentricity and orientation of the orbit. For prograde and retrograde moons, respectively, the stable regions are: (C O m d = 0.4895Rh(1.0000 - 1.0305ep - 0.2738esat) (2.2) a r e te s = 0.9309Rh(1.0000 - 1.0764ep - 0.9812esat + 0.9446epesat), (2.3) where ep and esat are the orbital eccentricities of the planet and satellite, respectively. These results suggest that retrograde moons can be found at significantly greater distances than their prograde counterparts. It can also be seen that planets on eccentric orbits offer severely reduced regions of stability for potential moons. More recently, Donnison (2010) showed that moons on inclined orbits also yield con­tracted regions of orbital stability. As a result, moons are expected to be roughly coplanar with the planetary orbit. This conclusion is supported by the examples of massive satellites in our own Solar System. Recent investigations on the dynamic stability of exomoon systems have expanded to include the effects of planet-planet scattering. Gong et al. (2013) found that when the architecture of a planetary system is the result of planet-planet scattering and mergers, planets will have most likely lost their initial satellites. This result includes the most massive giant planets if these planets were the product of former planet-planet mergers. In a complimentary study, Payne et al. (2013) considered giant planet systems that were tightly-packed, but initially stable. They found that giant exoplanets in closely-packed systems can very well harbor exomoon systems if the planet architecture avoids planet-planet mergers or ejections. 27 2.3.2 E v o lu tio n Even for gravitationally stable systems, the moon's orbit will continue to evolve. The inclusion of tidal interaction between the planet and satellite can give rise to phenomena such as spin-orbit resonance and can even challenge a moon's long-term survival. Therefore, it is worthwhile to consider the effects of tides on the orbital evolution of a single planet-moon pair.4 Tidal bulges raised in both the planet and satellite will dissipate energy and apply torques between the two bodies. The rate of dissipation strongly depends on the distance between the two objects (see section 4.1 for a more detailed discussion of tidal theory). As a result of the tidal drag from the planet, a massive satellite orbiting a giant planet will have its rotation frequency braked and ultimately synchronized with its orbital motion around the planet (Dole 1964; Gonzalez 2005; Henning et al. 2009; Kaltenegger 2010; Kipping 2010). This effect is commonly known as tidal locking. Any initial obliquity will also be quickly eroded, causing the moon's rotation axis to be perpendicular to its orbit about the planet. In addition, a moon will inevitably orbit in the equatorial plane of the planet due to both the Kozai mechanism and tidal evolution (Porter and Grundy 2011). The combination of all these effects will result in the satellite having the same obliquity as the planet with respect to the circumstellar orbit. As for the host planet, massive planets are more likely to maintain their primordial spin-orbit misalignment than small planets (Heller et al. 2011). Therefore, satellites of giant planets are more likely to maintain an orbital tilt relative to the star than even a single terrestrial planet at the same distance from a star. Tidal torques can also cause a moon to either spiral in or out, as a consequence of the conservation of angular momentum. The direction of the spiral actually depends on the tidal bulge raised in the planet (caused by the moon). If the planet's rotation period is shorter than the orbital period of the satellite, the bulge will lead (assuming prograde orbits) and the moon will slowly spiral outward. This action could eventually destabilize the moon's orbit, leading to its ejection. On the other hand, if the planet's rotation period is longer, the bulge will lag and the moon will slowly spiral inward. As this happens, the tidal forces on the moon become increasingly greater. If the inward migration continues past the Roche limit, the satellite can be disintegrated. For planets with short orbital periods, the stability regions in which moons can reside will be tighter. As a consequence, the planet-moon tides will be greater, leading to a more rapid loss. For this reason, hot-Jupiters are generally considered to be unfavorable hosts. In 4Multiple moons are more complex due to the dynamical interactions that occur between the moons. 28 subsection 2.3.1, I indicated that retrograde satellites can be stable at far larger distances than prograde satellites. Therefore, retrograde moons have a larger distance over which to tidally spin-out or spin-in, which would ultimately allow for longer lifetimes. Barnes and O'Brien (2002) provided analytical approximations for the maximum time an Earth-mass moon can survive when subject to stellar radiation similar to the solar flux received by Earth (i.e. when the moon is located in the HZ at an Earth-equivalent distance). They encouragingly predicted moons to be stable around Jupiter-like planets for habitable-zone periods if the host star's mass is greater than 0.15 M©, where M© is one solar mass. Cassidy et al. (2009) claimed that an Earth-sized moon could maintain a stable orbit around a hot-Jupiter if the planet is rotationally synchronized to its orbit around the star.A nother dominant effect believed to cause the loss of moons is inward, disk-driven planetary migration. This type of migration for the planet occurs on a much faster time scale than tidal dissipation, causing the Hill radius of the planet to shrink very quickly. As a result, an initially stable moon can find itself outside the Hill sphere, and thus, be ejected. Namouni (2010) showed that a moon is unlikely to survive once a migrating gas giant crosses ~0.1 AU. This is another reason why hot-Jupiters are unfavorable as satellite hosts. 2.3.3 C o m p o sitio n Section 2.2 indicated that gas giant planets have the greatest potential for massive satellites. The composition of regular satellites around gas giants in the Solar System tend to be ice-rich with the rest being silicates and iron (Consolmagno 1983). The accepted explanation is that gas giants formed beyond the snow line where ice does not sublimate. Therefore, moons that form in situ (i.e. regular moons) have plenty of ice to accumulate in their formation (Pollack et al. 1996). One the other hand, the solar system satellites are also relatively low in mass and certainly less than ideal for considerations of habitability. Since formation by capture provides the greatest potential for the most massive satellites, the composition of higher mass irregular moons is more likely to resemble Mercury, Venus, Earth, and Mars. 2.4 Exomoon Detection Methods The first technique ever proposed for the detection of an exomoon was made by Sartoretti and Schneider (1999). However, exomoon detection did not receive substantial interest until the more recent launch of NASA's Kepler space telescope (Kipping et al. 2009). The most 29 promising detection method relates to the transit of extrasolar planets. For a transiting planet, there are two categories of observational effects that can betray the presence of an exomoon (Kipping et al. 2012): (1) dynamical variations of the host planet, and (2) eclipse features induced by the moon. Dynamical effects primarily reveal information about the exomoon mass, whereas eclipsing features reveal information about the radius. Therefore, the detection of both effects allows for a measurement of the bulk density which can then be used to distinguish between different compositions (e.g. an icy moon versus a rocky moon). The following subsections provide a short review of these two categories. 2.4.1 D y n am ic a l E ffects on T ra n sitin g E x o p la n e ts (T T V a n d T D V ) Dynamical effects are measured as perturbations in the motion of the host planet away from a simple Keplerian orbit. Let us consider a three-body planet-moon-star system. The planet and moon will orbit a common barycenter. In turn, the barycenter of the two bodies will orbit the star on a Keplerian orbit. It follows that the planet itself will not orbit the star on a truly Keplerian orbit. During transit, the planet's perturbed motion will be indicated by variations in the timing of the transit, as well as variations in the duration of the transit. Transit timing variations (TTV) and transit duration variations (TDV) are thought to be the most observable dynamical effects (Sartoretti and Schneider 1999; Szabo et al. 2006; Kipping 2009a, 2009b). TTV is more sensitive to wide-orbit moons (sensitivity scales as / asat) and deviations caused by terrestrial moons can range from a few seconds to a few hours. TDV is more sensitive to close-orbit moons (sensitivity scales as / as_a1t '/ 2) and deviations can vary from a few seconds to tens of minutes in amplitude (Heller et al. 2014). One disadvantage to the detection of these effects is that similar variations can also be induced by a multitude of other phenomenon. These include: general relativistic procession of the orbit; gravitational influences from other planets in the system or from a binary companion star; torques due to a spin-induced quadrupole moment of the star; tidal deformation in the planet or star;, and parallax effects. By itself, a single variational measurement is not particular useful. However, Kipping (2009a) predicted that TDV will lead TTV by a ^/2 phase shift in amplitude, which offers a unique signature for exomoons. For this reason, both types of transit variations must be measured to have confidence of an actual exomoon detection. Also, with the combination of both measurements, the mass ratio between the planet and moon can be revealed. 30 2.4.2 E clip se F e a tu re s In d u c e d by E x om o o n s The second class of observational effect involves the transit of the moon itself. For this we can consider two types of eclipsing events. The first type is when the moon transits the star and causes a familiar transit shape on the stellar light curve. This type is referred to as "auxiliary transits" and is more likely to be detected for moons on wide orbits. The second eclipse effect is when the moon passes behind or in front of the planet during the planet-star transit. This latter type is often known as "mutual events" and is geometrically more probable for moons on close-in orbits. Unlike the dynamical effects, eclipses are sensitive to the size of the exomoon (and not the mass) and reveal information about the radius ratio between the satellite and the star. When considering the direct eclipsing effects of exomoons, one major source of false-positives are starspot crossings (Rabus et al. 2009) as these will appear to be almost identical. Fortunately, starspots do not follow Keplerian motion, so their overall behavior should be distinguishable. 2.4.3 D ire c t D e te c tio n o f E x om o o n s As discussed in subsection 1.1.4, the direct imaging of exoplanets is extremely difficult. The difficulty is enhanced for planets in the stellar HZ due to very small angular separation and high contrast ratio between a star and planet. All current exoplanet images have involved well-separated systems that are still hot from formation rather than being heated by stellar irradiation. These young planets have effective temperatures around 1000 K (Heller et al. 2014). Intuition suggests that exomoons would be even more difficult to directly image. However, a moon that is hot from intense tidal heating could provide a sufficient target. Peters and Turner (2013) recently proposed the direct imaging of tidally heated exo­moons (THEMs). From an observational point of view, directly imaging exomoons has several advantages over the direct imaging of exoplanets. Unlike exoplanets, THEMs retain their internal heat and can remain hot and luminous for significantly longer timescales, allowing them to be visible around both young and old stars. Additionally, THEMs do not require substantial amounts of stellar irradiation to remain hot. Therefore, they may be luminous at large separations from the central star. Assuming THEMs exist and are common, Peters and Turner (2013) showed that Spitzer's IRAC could detect an exomoon the size of Earth with a surface temperature of 850 K and at a distance of five parsecs (pc) from Earth. Future instruments such as JWSTs Mid-Infrared Instrument (MIRI) have even more potential for directly imaging exomoons. 31 2.4.4 D e te c tio n O u tlo o k Some additional constraints to the detection of moons around transiting exoplanets include photometric noise, instrumental noise, and natural stellar variability. Kipping et al. (2009) considered these constraints and performed a detailed analysis of TTV and TDV detection with Kepler-class photometry and obtained a lower detection limit of about 0.2 M® for moons orbiting in the stellar HZ of M, K, and later-G type stars. Lewis (2011) investigated the effects of noise filtering and found that exomoons hidden in the Kepler data will need to have radii & 0.75 R® to be detectable by direct eclipse effects. While exomoon detection is certainly challenging from a theoretical and experimental standpoint, these predictions offer hope that the first detection is on the horizon. Besides the transit method, other traditional planet detection techniques have been considered for exomoon detection (Lewis et al. 2008; Morais and Correia 2008; Liebig and Wambsganss 2010; Peters and Turner 2013) including direct imaging, microlensing, pulsar timing, astrometry, and radial velocity. Unfortunately, their estimated potential for success appears to be unlikely at best. For this reason, I will forego any further discussion concerning these methods. 2.5 Exomoon Habitability In section 2.2, I discussed predictions for exomoons the size of Mars orbiting gas giants. I also detailed the expectation for near-future detection of exomoons with roughly that same size in subsection 2.4.4. These statements naturally lead to questions about the habitability of these worlds. In this section, I consider some of the properties that factor into this determination. 2.5.1 M ass R e q u irem e n ts Lower boundary mass constraints start with the need to sustain a magnetic shield on a billion year timescale, which is necessary to protect life on the surface from high-energy stellar and interstellar radiation. For this, Tachinami et al. (2011) argued that a terrestrial world needs a mass & 0.1 M®. Another condition is that a moon must hold a substantial and long-lived atmosphere. Previous studies suggest that this would require satellite masses Msat & 0.12 M® (Williams et al. 1997; Kaltenegger 2000). Finally, sufficient mass is needed to drive tectonic activity over billions of years. Williams et al. (1997) proposed that Msat & 0.23 M® is mandatory to entertain plate tectonics and to promote the carbon-silicate cycle. Combining these constraints for habitability with formation theory and modern 32 technology points toward a preferred mass regime between 0.1 and 0.2 M® for habitable exomoons that can be detected in the near future. These mass limits for habitable worlds were all derived by assuming a cooling, terrestrial body such as Mars. However, there is an alternative internal heat source for exomoons that is typically less important for planets located in the HZ. This energy source is tidal heating and its effects can retard the cooling of the moon and thus maintain the aforementioned processes over longer epochs than in planets. Several studies have addressed the importance of tidal heating and its effects on the habitability of exomoons (Reynolds et al. 1987; Scharf 2006; Henning et al. 2009; Heller 2012; Heller and Barnes 2013; Heller and Zuluaga 2013). Reynolds et al. (1987) was the first to suggest the remarkable possibility that tidal heating, rather than stellar illumination, could maintain habitability in water-rich extrasolar moons beyond the stellar HZ. Support for their claim was given by findings of plankton in Antartica lakes which require an amount of solar illumination corresponding to the flux received at the orbit of Neptune. The theory of tidal heating and a personal investigation into its effects on exomoons is presented in Chapter 4. 2.5.2 G lo b al E n e rg y F lu x When considering exoplanet habitability, primary energy concerns involve the average stellar flux received by a parent star. Investigations of exomoon habitability can be dis­tinguished from studies on exoplanet habitability by other various astrophysical effects. For example, a moon's climate can be affected by the planet's stellar reflected light and its thermal emission. Moons also experience eclipses of the star by the planet, and tidal heating can provide an additional energy source that is typically less substantial for planets. Heller and Barnes (2013) considered these effects individually, and then combined them to compute the orbit-averaged global flux Fglob received by a satellite. More specifically, this computation summed the averaged stellar, reflected, thermal, and tidal heat flux for a satellite. In their study, they provided a convenient definition for the global flux as F L*(1 - A , k r 2pap! Fglob = ------------, 1 + 7T^2--- ++- --R--p--a--s-B-2(--T-p--q-)-4-- -1- ---A ------++ . > (24) 16ma2*p^ j1 - e*p \ 2aPs ) aps 4 where L* is the luminosity of the star, a*p is the semimajor axis of the planet about the star and aps is the satellite's semimajor axis about the planet, a is the bond albedo, e is eccentricity, osb is the Stefan-Boltzmann constant, and hs is the tidal heat flux in the satellite (refer to section 4.2). The planet's thermal equilibrium temperature Tpq is defined as 33 rTpPeq _ Te//,*(1 ap)R^ 4r*2 p 1/4 (2.5) where Te// * is the effective temperature of the star, and r*p is the distance between the planet and the star. As an analogy with the circumstellar HZ for planets, there is a minimum orbital separa­tion between a planet and moon that will allow the satellite to be habitable. Moons inside this minimum distance are in danger of runaway greenhouse effects by stellar and planetary illumination and/or tidal heating. There is not a corresponding maximum separation distance (other than stability limits) because satellites with host planets in the stellar HZ are habitable by definition. The benefit of Equation (2.4) is that it can be used to explore the minimum distance. This is accomplished by comparing the global flux to estimates of the critical flux for a runaway greenhouse (FRG). Pierrehumbert (2010) used a semi-analytical approach to calculate FRG as V l ( Frg _ o JSB R ln ( p 0/ q 2Poasz Rs)) (2.6) / with P ' _ Pref exp { r t J ' (2.7) where Pref _ 610.616Pa, l is the latent heat capacity of water, R is the universal gas constant, Tref _ 273.13K, o _ 0.7344 is a constant designed to match radiative transfer simulations, Po = 104Pa is the pressure at which the absorption line strengths of water vapor are evaluated, gs _ GMs/ R ‘2 is the gravitational acceleration at the satellite's surface, and k0 _ 0.055 is the grey absorption coefficient at standard temperature and pressure. Applying Equation (2.6) to an Earth-mass exomoon gives a critical flux of 295 W /m 2 for a water-rich world with an Earth-like atmosphere to enter a runaway greenhouse state. CHAPTER 3 INTEREST IN LOW-MASS STARS 3.1 Red Dwarfs Compared to the Sun, red dwarf stars are smaller, cooler, fainter, and lower-mass (refer to Figure 3.1). Nonetheless, they are the predominant stellar population of our Galaxy (e.g. Chabrier and Baraffe 2000). Stars in this category are mostly of M spectral type, with typical surface temperatures less than 4,000 K. Red dwarfs range in mass from ~0.075 M© to about 0.5 M©. The lower limit represents the hydrogen burning mass limit (Burrows et al. 1997) which is conversely the upper limit for a brown dwarf. It is estimated that 75% of the stars within 10 pc of Earth are M dwarfs (Henry et al. 2006). These stars are intrinsically fainter than solar-type stars. While they may dominate the stellar mass budget in galaxies, they contribute only a few percent of the total light (Conroy and van Dokkum 2012). This fact is made clear considering there are no M dwarf stars visible to the naked eye. Due to their large numbers, low-mass stars may be the most abundant planet hosts in our Galaxy and for this reason, they have received added attention in recent years. Also cause for attention, low-mass stars present certain advantages for detection. The radial velocity signal is proportional to M*- 2/3. Hence, a lower stellar mass will produce a larger RV signal for a given planet mass and orbit. This makes sense considering a higher planet/star mass ratio will move the system's center of mass away from the star, resulting in greater reflex motion. Another detection advantage comes from their smaller radius. The transit depth for a star's light curve is proportional to R-2 (see Equation (1.1)). As such, the transit signal for a given planet radius should be readily distinguishable. For example, an Earth-size planet orbiting a 3800 K dwarf star has a transit signal that is 3.3 times deeper than the signal for an Earth-size planet across a G star. This is due to the dwarf star being only 55% the size of the Sun. While the advantages are worth pointing out, there is also a down side to the low mass and small size. The geometric probability for transit is directly proportional to the stellar 35 Figure 3.1. Illustrative comparison between low-mass stars and the Sun. Earth is also represented for contrast. The radius of Earth is less than 1% the radius of the Sun. radius (see Equation (1.2)). Therefore, transits can also be less probable for a given orbital distance. Additionally, M dwarfs are much fainter than massive stars so there can be fewer visible stars in any given field of view. The faintness also leads to smaller signal-to-noise ratios. To overcome these obstacles, large surveys require the use of bigger telescopes and better spectrographs with more sensitive calibration. 3 .1.1 D e t e c t e d P lan e ts The RV technique was the first to unveil a candidate planet orbiting an M dwarf star (Delfosse et al. 1998; Marcy et al. 1998). The detected planet was a gas-giant with a minimum mass double that of Jupiter and an orbital distance only 20% of Earth's distance from the Sun. At this point in time, the detection of such a planet was not particularly revolutionary. The discovery was significant in that it proved planets could indeed form around low-mass stars. Of the 1518 total confirmed exoplanet detections, only 79 involve low-mass (red dwarf) star systems. While this number represents a small fraction of the total, the majority of these detections occurred only recently and the number is expected to grow. To a certain extent, the lack of known planets around M dwarfs is due to early observational biases. Until recently, the strong majority of exoplanets detections came from RV surveys 36 and early surveys did not target these faint stars because of the difficulties in obtaining sufficiently high signal-to-noise observations. Dwarf stars are particularly faint at optical wavelengths where the most high-precision spectrometers operate, with the bulk of their spectral energy emitted at wavelengths in the near infrared. The activity of the stars themselves also complicate detection with the presence of apparent RV and photometric variations by co-rotating features (star spots) and temporal variations of the stellar surface (Reiners et al. 2010). The fact that the first detected exoplanet around an M dwarf was a giant planet gave the early impression that such planets could be common around late-type stars. Today, 17 of the 79 exoplanets found around low-mass stars have masses equal to or greater than Saturn (~ 95 M®). This suggests that the ratio of giant planets to lower mass planets in these systems is not as high as once thought. In comparison to other host stars, there is continuing evidence that the occurrence rate for giant planets is lower in red dwarf systems than it is for Sun-like stars (Butler et al. 2004; Endl et al. 2006; Johnson et al. 2007; Cumming et al. 2008). Bonfils et al. (2013) conducted a radial velocity survey of M-dwarfs and concluded that giants planets (m sini = 100 - 1000 M®) have a low frequency whereas super-Earths (m sini = 1 - 1 0 M®) are likely very abundant. Their results are in agreement with similar studies of small planets around small stars (Dressing and Charbonneau 2013; Morton and Swift 2013; Tuomi et al. 2014). Note that these studies typically only involved planets with short orbital periods (less than 100 days) due to the limited sample of known orbits. Studies also show several high-multiplicity systems around M dwarfs consisting of only super-Earths or Neptune-like planets (Udry et al. 2007; Bonfils et al. 2013; Bonfils et al. 2013). Examples include the highly studied GJ 581 system of four confirmed1 planets, which include a 6 M® planet located on the outer edge of the estimated habitable zone (HZ) for the system (Forveille et al. 2011). 3.2 Habitable Zones Around Red Dwarf Stars As a consequence of their low mass, the rate of thermonuclear fusion is significantly less than even Sun-like stars. Red dwarfs therefore develop very slowly and once they reach the main sequence are capable of maintaining a constant luminosity and spectral type for some trillions of years (Laughlin et al. 1997). Because they have negligible brightening 1Two additional planet detections have been reported for this system. However, their existence is heavily disputed. 37 while on the main sequence, the liquid water HZ undergoes no radial expansion during this time. However, the lower core temperatures and decreased energy output result in a HZ that is much closer to the star. An illustration of the change in HZ boundaries with stellar mass is provide in Figure 3.2. The represented limits are the conservative limits defined in subsection 1.3.1. The proximity of the HZ around low-mass stars has an advantageous effect on the detectability of planets in this region. A radial velocity signal is proportional to a-1/2, where a is the semimajor axis of the planet's orbit. This inverse dependency is again (see section 3.1) due to the shift in the center-of-mass away from the star leading to a higher amplitude RV signal for close-in planets. For example, the RV signal induced by a 1 M® planet in the middle of the HZ of a 3800 K, 0.55 M© dwarf is 23 cm s-1 , while a signal for 0.01 0.10 1.00 Orbital Distance (AU) Figure 3.2. Habitable zones with planet mass. The dotted black line represents the upper red dwarf (low-mass) star boundary. The red dashed line represents the tidal locking radius. The colored circles represent the orbital distances of Mercury, Venus, Earth, and Mars. The size of each circle is scaled to the planet's size relative to Earth (but not to scale with the horizontal coordinates). 38 the same planet in the HZ of a G star is 9 cm s-1 (Dressing and Charbonneau 2013). The prospects are even better for planets around mid-to-late M dwarfs where a similar setup around a 3200 K dwarf would produce an RV signal of 1 m s-1 which is achievable with the current precision of modern spectrographs (Dumusque et al. 2012). Transit surveys also benefit from shorter orbital distances in the HZ. The geometric probability of transit is inversely proportional to the semimajor axis and therefore increases with smaller values. This probability increase would more than compensate for the decrease due to the direct dependency on stellar radius (refer to section 3.1). In addition, shorter distances result in shorter orbital periods for planets. This is a benefit to both the RV and transit techniques as it allows for more orbital phases to be sampled in data covering a fixed length of time. As an example of these advantages, the transit of a planet in the HZ of a G star happens only once per year, while a transit occurs five times per year for a planet in the HZ (~0.3 AU) of a 3800 K dwarf star. In addition, the geometric probability that a transit will actually occur relative to our line of site is 1.8 times greater. Bonfils et al. (2013) used their RV survey to calculate the frequency of habitable planets2 orbiting M dwarfs and estimated a value of 0.41+013. Kopparapu (2013) performed an independent study of the occurrence rate of terrestrial planets in the HZ3 of M-dwarfs using Kepler (transit) data and determined a frequency of 0.51-q ^ per star as a conservative estimate. Within the uncertainties, the estimates agree for the two studies. Considering that M dwarfs dominate the stellar count, these estimates suggest a significantly high frequency of habitable planets in our galaxy. Subsection 1.3.3 contains my own analysis of HZ exoplanets using an online database4 of confirmed exoplanets. Of the 68 candidates, only 6 were found around dwarf stars. Table 3.1 provides a list of these planets and their parameters. It is interesting to note that 4 of the 6 candidates have planet masses near that of Saturn (~95 M®) or greater. While giant planets in the HZ of dwarf stars are predicted to be much less frequent than Earth-like planets, the current confirmed5 detections have not yet caught up with this prediction. 2They define a habitable planet as one with m sini between 1 M® and 10 M®, which also orbits in the HZ of the star. Their HZ boundaries were defined by Selsis et al. (2007). 3He defined a terrestrial planet as having a radius between 0.5 R ® and 2 R ® and used the conservative HZ boundaries defined in Kopparapu et al. (2013a). 4exoplanets.org. 5However, there are also more than three thousand unconfirmed Kepler candidates, many of which are believed to have radii between 0.5 and 4 R®. 39 Table 3.1. Properties of HZ planet candidates that orbit low-mass stars. Parameter Source: exoplanets.org Name Mass (M®) Radius R® Semi-Major Axis (AU) Star Mass (MSun) T Eff (K ) Kepler-186 f - 1.1 0.4 0.5 3788 GJ 581 d 6.1 - 0.2 0.3 3498 HIP 57050 b 94.6 - 0.2 0.3 3190 GJ 876 c 194.5 - 0.1 0.3 - GJ 876 b 618.6 - 0.2 0.3 - HIP 79431 b 671.4 - 0.4 0.5 3191 Fortunately, upcoming facilities such as the James Webb Space Telescope and the Giant Magellan Telescope will be capable of detecting Earth-sized planets in the HZs of M dwarfs. It is even expected that they will be able to take spectra of these planets. As mentioned above, dwarf stars on the main sequence evolve slowly, which can be seen as a benefit for the development of life in the HZ. However, the close proximity to the star also introduces unique concerns for potentially habitable environments. 3 .2 .1 C o n c e rn s fo r H a b ita b i l ity The habitability of red dwarf systems is a subject of some debate. One of the main arguments against the potential for habitable planets is the issue of tidal locking. Because the HZ is so close to the star, tidal interactions will most likely cause the rotation of the planet to synchronize with its orbital period around the star. The result being that the same side of the planet will always face the star. The distance at which tidal locking is most likely to occur (in relation to stellar mass) is known as the tidal locking radius. This distance is included in Figure 3.2. Early studies have suggested that a hypothetical planet in the HZ of an M dwarf star would be inhospitable due to tidal locking (Dole 1964; Kasting et al. 1993) mainly because the atmosphere would freeze out on the dark side of the planet. Later work on the topic was actually more optimistic. Haberle et al. (1996) and Joshi et al. (1997) demonstrated that sufficient quantities of carbon dioxide could sustain circulation between the light and dark side and prevent the atmosphere from freezing. More recent models even allowed for ocean-covered water worlds (Joshi 2003). Tarter et al. (2007) similarly studied the ability of a very dense atmosphere to thermally distribute solar radiation and agreed that tidally locked synchronous rotation in the HZ does not necessarily lead to atmospheric collapse. Moreover, not all planets inside the tidal locking radius will become spin-synchronized. 40 Another option is to become trapped in a spin-orbit resonance, as is the case for Mercury in our own Solar System. Mercury orbits inside the tidal locking radius, yet maintains a 3:2 resonance rotating three times for every two orbits around the Sun. Tidal locking is also a concern in that it may inhibit the generation of convection in a liquid metal core and dimish magnetic field strength to nonhabitable levels. Besides the dynamical concern of tidal locking, the low-mass stars themselves cause reason for concern. While M dwarfs on the main sequence are capable of maintaining very stable luminosities for extremely long timescales, the situation is much different for the pre-main sequence phase. The luminosity of M dwarf protostars is much more variable than in later years. The lowest mass M stars take 0.3 - 1 Gyrs to reach the main sequence, during which time the luminosity decreases by roughly two orders of magnitude (Laughlin et al. 1997; Scalo et al. 2007). Considering that planets in the HZ of dwarf stars are expected to form more quickly than around Sun-like stars (Lissauer 2007), this behavior is problematic for future habitability. Planets that formed early and near the HZ are forced to endure a period of high energy flux and high temperatures which would likely deplete any existing atmosphere of useful volatiles. As a result, an early origin for life may be delayed or even permanently disabled. Of course, an alternative to this is if the planet forms further out and then migrates in at a later time. Another area for concern is that M stars exhibit extreme and intermittent variability due to their strong magnetic activity. However, these events occur on very small timescales of hours up to years. The activity manifests itself as intense flares similar to solar flares, but scaled up in frequency and relative energy output. Even in their quiescent state, low-mass stars have high UV emission compared to Sun-like stars (France et al. 2013). The flares would be most harmful to planets without a strong magnetic field requiring several years to rebuild an ozone layer after experiencing a strong flare, although the presence of a thick atmosphere should effectively screen out most of the UV flux keeping the majority from ever reaching the surface of a planet. For this reason, flares are not considered an insurmountable obstacle to habitability in these systems (Tarter et al. 2007; Segura et al. 2010). A very different kind of short-term variability for M dwarfs is due to large-amplitude star spots. Most spots reduce the stellar flux by less than a few percent (Messina et al. 2003). However, Joshi et al. (1997) found extreme spot cases that reduce the flux of the star by up to 40% for a few months. Such a decrease would significantly effect the surface temperature of a HZ planet, potentially causing some regions to occasionally suffer a severe freeze. However, Joshi et al. (1997) reported that the atmosphere itself did not freeze out. 41 Fortunately, most M stars do not experience such extreme spot variations. 3.3 So Why Bother with Exomoons Heller and Barnes (2012) recently considered the question as to why we should bother with the habitability of exomoons when it is yet so hard to characterize even planets. Their reasons include: (1) If they exist, then the first detected exomoons will be roughly Earth-sized (i.e. have masses & 0.2 M®) (Kipping et al. 2009). (2) Moons are expected to become tidally locked to their host planet. As a result, exomoons in the HZ have days much shorter than the stellar year. This is an advantage for their habitability compared to terrestrial planets in this zone which become tidally locked to the star. (3) Massive host planets of satellites are more likely to maintain their primordial spin-orbit misalignment than small planets (Heller et al. 2011). An extrasolar moon in the stellar HZ will likely orbit a massive planet in its equatorial plane (Porter and Grundy 2011). Thus, it is much more likely to experience seasons than a single terrestrial planet at the same distance from the star. (4) Extrasolar habitable moons could be much more numerous than planets. Subsection 1.3.3 documents that most of the detected HZ candidate planets have masses similar to or greater than Neptune. In addition, subsection 1.2.2 explains that Neptune-like planets appear to be common in our galaxy. Based on the number of moons around gas planets in our Solar System, it seems feasible for extrasolar gas planet to also have an abundance of moons. Beyond the reasons listed above, there is also the concept of tidal heating as an additional energy source for habitability which can be more prominent in moons than in planets. A discussion of exomoon tidal heating is even more relevant for low-mass star systems due to the close proximity of the HZ and the corresponding increase in gravitational influence from the star. This influence may act to perturb a satellite's orbit in such a way as to increase the tidal heating rate. For this reason, an exploration into the tidal evolution of exomoons in low-mass star systems will be the primary topic for the remainder of this dissertation. CHAPTER 4 DYNAMICAL AND TIDAL EVOLUTION Scientific studies of tides extend back to at least the early 1600s with Johannes Kepler's work on celestial motion (Caspar 1962). However, at that time, there were only six planets and five satellites (our Moon and the four Galilean satellites) known to study. The modern day discovery of thousands of extrasolar bodies has motivated more recent interest in the effect of tides as an important orbital and physical property of extrasolar planets. While red dwarf stars provide attractive candidates for HZ planet detections, tidal influ­ences between a planet and star present concerns for habitability that are somewhat unique to this class of star (see subsection 3.2.1). Chapter 3 presented reason for investigation into the habitability of moons around massive planets in