View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by University of Southern Queensland ePrints HORNER ET AL.: EXOPLANS ET HORNER ET AL.: EXOPLANS ET Testing proposed planetary systems – to destruction J Horner, R A Wittenmyer, J P Marshall, T C Hinse and P Robertson examine the dynamics of exoplanet systems and find that some of them don’t last long. The stability of planetary systems offers a check on the likelihood of proposed multiple-exoplanet systems. he detection of planets around other ical derivation of Kepler’s Laws of Planetary future (and past) behaviour. stars is, to many, the single most exciting Motion, which Kepler had proposed almost a In a coarse sense, two broad types of behav­ Tastronomical discovery of our times. For century earlier. The science of orbital mechan­ iour are observed for objects moving in systems millennia, people have asked whether we are ics studies the gravitational interaction between of three or more bodies. Stable orbits show very Downloaded from alone in the universe, and while we do not yet planets, stars and smaller bodies in planetary little modification on long timescales, such know the answer to that question, the detection systems (comets and asteroids). Once a system that the objects moving on those orbits would of these exoplanets surely brings that answer contains more than two bodies, it is no longer be expected to be moving on the same (or very within our grasp. Indeed, we are the first genera­ possible to exactly solve for the motion of all similar) orbits were the observer to return in tion to be able to gaze up at the night sky and those bodies as they interact under the influ­ a billion years, or ten billion years. Unstable know that planets orbit most of the stars we see. ence of gravity. This conundrum is known as the orbits, by contrast, exhibit dramatic variations http://astrogeo.oxfordjournals.org/ Since 1992, when the first planets or planet­ three ­body problem, and essentially means that as time goes by. esimals were found orbiting a pulsar, around it is impossible to predict, on long timescales, In reality, on long enough timescales, almost fifteen hundred exoplanets have been discov­ the motion of the planets around the Sun, or the all orbits become unstable; stability is actually a ered, using two principal techniques: periodic dynamical evolution of exoplanetary systems. sliding scale, from the very unstable to the very radial velocity variations in the motion of A simple example of the problems inherent stable. An example of a very stable orbit would their host stars determined by the mass of the in studies of orbital mechanics is to consider be that of the Earth around the Sun. Although unseen orbiting planet; and the slight drop in a simplified version of our solar system: the the orbit of the Earth is constantly nudged and light from the host star when a planet crosses Sun, the planet Jupiter, and a small object such tweaked by the gravitational influence of all its face. As time has passed, a handful of other as a comet. Consider two versions of the sys­ of the other objects in the solar system, it has by Jenni Thistlewood on January 5, 2015 techniques have begun to be used in the search tem, absolutely identical except for the initial remained essentially unchanged since the for­ for exoplanets. Aside from direct imaging, all location of the small object. In one system, the mation of the solar system, and it is highly likely of the techniques are indirect, detecting the small object is displaced from its location in the to remain so until the Sun becomes a red giant influence of the unseen planet on its host star other by a single atomic radius, with all other star. At the other extreme, the solar system’s or on light from background stars. At the same quantities (the velocities, masses and locations cometary bodies provide numerous examples time, an increasing number of multiple­planet of the objects considered) remaining identical. of highly unstable orbits, continually being systems have been discovered – a scenario that At that instant, the two particles in the two thrown on to new orbits as a result of chaotic provides for a new test to be applied to exam­ planetary systems will experience forces acting inter actions with the planets. Indeed, most com­ ine the veracity of the claimed planets. When on them that differ very slightly, as a result of ets are eventually ejected from the solar system more than one planet is identified in a given their minutely different distances from the Sun entirely as a result of a close encounter with the exoplanetary system, it is possible to examine and from Jupiter. As a result, they will expe­ giant planet Jupiter – our system’s biggest, bad­ the mutual gravitational interaction between rience slightly different accelerations, causing dest bully. the planets. If they are real, and the proposed their orbits to gradually drift apart. The further Typically in these systems, objects whose orbits a fair reflection of the true architecture apart the objects move, the more disparate the orbits are widely separated exhibit significantly of the system, it is reasonable to assume that forces they experience, and the more dramati­ greater dynamical stability than those whose the planetary orbits must be dynamically sta­ cally their orbits will diverge. orbits are closely packed. Furthermore, objects ble on timescales comparable to the age of the Because the initial location, mass and velocity moving on orbits with low eccentricity (i.e. planetary system. By contrast, if the proposed of every single object in a given planetary system circular, or near­circular orbits) are typically planets in a given system become unstable on cannot be precisely known, it is impossible to more dynamically stable than those moving on timescales far shorter than the age of the system, determine how those objects will evolve under eccentric orbits. The most extreme instability then it would be reasonable to conclude that the influence of their mutual gravitational pulls typically occurs when the orbits of two objects those planets are unlikely to exist – at least on on long timescales. But all is not lost. The gravi­ cross one another, or approach one another the proposed orbits. tational evolution of planetary systems (or test particularly closely. In those cases, there is the particles therein) can be modelled computation­ possibility that these objects will eventually Orbital dynamics and stability ally, allowing a wide range of initial conditions experience a close encounter, leading to signifi­ When Sir Isaac Newton published Philosophiæ to be tested. The more tightly packed the initial cant changes in their orbits. Naturalis Principia Mathematica in 1687, he conditions, the longer the different solutions The situation is complicated by orbital res­ laid out the mathematical tools that allow us to will take to diverge and so the better we can tie onances, such as the interaction between the understand fully the motion of objects orbiting down the initial motion of the objects in ques­ giant planet Neptune and the dwarf planet stars. In particular, they allowed the mathemat­ tion, and the better we can understand their Pluto. The orbit of Pluto crosses that of 4.30 A&G • August 2014 • Vol. 55 HORNER ET AL.: EXOPLANS ET Downloaded from http://astrogeo.oxfordjournals.org/ by Jenni Thistlewood on January 5, 2015 Neptune, such that the dwarf planet spends 1: Artist’s impression of the PLATO mission to covery process of the Anglo­Australian Planet approximately 20 years of each ~248­year orbit explore exoplanets. Announced in February Search programme, and have also tested a num­ interior to the orbit of Neptune, and the rest of by the European Space Agency and due to ber of the multiple­planet systems proposed over launch in 2024, PLATO will observe around the time exterior. Normally, one would expect a million stars to find and characterize new the past few years to see whether they stand such a situation to be untenable in the long term planets. (Mark A Garlick) up to dynamical scrutiny. For some systems, – eventually, the two objects would be expected dynamical simulations simply reveal that the to experience a close encounter and disruption proposed planets are dynamically stable across of their orbits, or even a collision. However, years old. As such, given that the planets orbit­ the whole range of orbital architectures allowed Pluto is actually protected from experiencing ing them can reasonably be expected to have by the observational data. More interestingly, close encounters with Neptune because they formed at around the same time as their host in several cases, we have found that dynami­ are trapped in mutual 3:2 mean motion reso­ star, it is reasonable to expect that their orbits cal studies can enable us to more effectively nance. In the time it takes Neptune to complete would be stable on timescales comparable to constrain the orbits of the proposed planets. three orbits of the Sun, Pluto completes two – a the age of their host system. Conversely, the Finally, in several cases, we have found that the commensurability between their orbital peri­ likelihood of discovering planets as they move proposed planetary systems are not dynamically ods that ensures that, whenever Pluto is cross­ towards destruction on dynamically unstable feasible, indicating either that the proposed ing the orbit of Neptune, that giant planet is orbits during the last few thousand years of their planets do not exist, or that they are moving on far away. Despite the fact their orbits cross, the life is very low.