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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 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 around other ical derivation of Kepler’s Laws of Planetary future (and past) behaviour. 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 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 , 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 ­ 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 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 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 when a planet crosses Sun, the planet , 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, and locations cometary bodies provide numerous examples time, an increasing number of multiple-planet 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 near-circular 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

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Neptune, such that the dwarf planet spends 1: Artist’s impression of the PLATO mission to covery process of the Anglo-Australian Planet approximately 20 years of each ~248- 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 multiple-planet 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. The dynamical tools perfected orbits vastly different to those proposed in the two objects never approach one another more for study of our solar system can provide a san­ discovery work. closely than the distance between the Sun and ity check for newly announced exoplanetary Uranus – approximately 2 billion km. systems, to determine whether those planets, Simulating multiple planets Most of the multiple-planet systems that have as proposed, are dynamically feasible. In order to test the dynamical evolution of plan­ been proposed in recent years orbit stars that With this in mind, we have now incorporated etary systems on timescales comparable to the are hundreds of millions, if not billions, of dynamical testing as part of the exoplanet dis­ lifetime of their host stars, we use the Hybrid

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2: The stability of the integrator within the n-body dynamics package recently proposed planet Mercury (Chambers 1999), and follow a proce­ candidate HD 52265 c, as a dure we first used to study the dynamics of the function of its initial orbital directly imaged four-planet system HR 8799, semi-major axis (a) and back in 2010. We always follow the evolution of e eccentricity ( ). This figure a given planetary system for a period of 100 Myr shows the results of 11 025 individual simulations, within the software – this compromise allows each testing a different us to run a large number of simulations on a initial orbital solution for reasonable timescale, while still spanning a suf­ HD 52265 c. The lifetime ficiently long time period to allow us to assess shown at each location in the stability of the proposed system. this a–e plot is the mean When a planet is announced around a given lifetime of 25 unique trials that were performed for star, a best-fit orbital solution is given in the initial orbits featuring that particular combination of semi-major axis and eccentricity. The hollow discovery work. For multiple-planet systems, box shows the location of the best-fit solution for the orbit of HD 52265 c, while the solid lines that the orbital parameters of one planet are typi­ radiate from that box denote the ±1σ uncertainties on the semi-major axis and eccentricity of the cally better constrained than those of the others planet’s orbit. In this case, almost the entire allowed orbital element space for HD 52265 c was (usually, but not always, the better-constrained dynamically stable – adding weight to the hypothesis that the observed variations in the radial planet is the one with the shortest orbital velocity of HD 52265 are the result of perturbations by at least two massive companions. The only Downloaded from regions of instability lie far from the nominal best-fit orbit (at the top right and top left of the plot). period, such that the observational data span the greatest number of complete orbital periods for that planet). In our simulations, we place the better -constrained planet on its best-fit orbit, 3: The stability of three (a) and then vary the orbit of the other planet(s) to candidate multiple-planet sample the full ±3σ phase space about the best http://astrogeo.oxfordjournals.org/ systems resulting from the solution for that planet. This leads to the crea­ Anglo-Australian Planet tion of a large number of unique planetary sys­ Search programme. (a): The dynamical stability tems (in our earliest work, we studied samples of of the planet candidate ~10 000 test systems, while nowadays we typi­ HD 142 d, with 30 625 cally consider ~100 000 systems at a time). For scenarios tested. each of those test systems, we follow the evolu­ (b): HD 159868 c; 30 625 tion of the planets until they either collide with scenarios tested. (c): Planet candidate one another, are thrown into the central star, or HD 85390 c; 11 025 scenarios are ejected from the planetary system entirely by Jenni Thistlewood on January 5, 2015 tested. In each case, – all common results of dynamical instability. the full ±1σ uncertainty Every time a system falls apart in this way, the range in semi-major axis (b) time at which the ejection or collision occurred and eccentricity solely is recorded, which allows us to create dynami­ contains orbits that are dynamically stable, with cal maps of the system in question, showing any regions of instability those orbits that are most stable or unstable. located far from the best- An example of such a map is shown in figure 2. fit solution denoted by the hollow box. Dynamically stable systems – supporting discoveries In many cases, the second planet discovered in a given exoplanetary system moves on an orbit that is well separated from that of the first planet known in that system. As such, the gravitational interaction between the two (c) planets will typically be weak, and so it is to be expected that most such systems will be dynam­ ically stable on astronomically long timescales. Such has been the case for several of the systems we have studied, including the planet candidates proposed around HD 52265 (figure 2), and the three systems shown in figure 3. In each of these cases, the whole area within the ±1σ uncertain­ ties around the best-fit solution for the planet in question is highly dynamically stable, with all solutions tested in that region being stable for the full 100 million years of integration time. Any instability that might be present in these systems is found well away from the nominal best-fit orbits – either to higher orbital

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eccentricities (as is the case for HD 142d, figure 4: The stability of four two- (a) 3a) or to smaller separations between the orbits planet systems for which of the two planets (as for HD 85390c, figure the dynamical simulations 3c). In such cases, while the dynamics does not yield significant additional tell us a huge amount of additional information constraints on the orbital on the system in question, it does reveal that parameters of the newly discovered planet. planets moving on the proposed orbits would be (a): HD 204313 c (Robertson dynamically feasible, an outcome that is clearly et al. 2012a); 52 855 necessary for the presence of the planets to be simulations. The newly taken seriously. discovered planet is only dynamically stable if it is Dynamically interesting systems – trapped in 3:2 MMR with constraining exoplanets HD 204313 b. (b): 24 Sextantis c A more interesting situation occurs when the (discovered by Johnson (b) candidate planets move on orbits that are suf­ et al. 2011); 126 075 ficiently tightly packed that the simulations. Here, the of the outermost is less than twice that of the newly discovered planet is trapped in 2:1 MMR with innermost. With such tightly packed systems, 24 Sex b. Downloaded from significant dynamical interaction between the (c): HD 200964 c (also two planets is likely, unless their masses are very discovered by Johnson small (as is the case for the terrestrial planets et al. 2011); 126 075 in our solar system). The precise details of the simulations. Here, the orbit proposed for the second planet in such sys­ planets are only stable if

they are trapped in the 4:3 http://astrogeo.oxfordjournals.org/ tems are clearly therefore critical in determining MMR. whether the planets are stable or unstable on (d): HD 155358 c (Robertson long timescales. In such cases, a detailed study et al. 2012b); as with of the dynamics of the system can actually help 24 Sex c, the best-fit orbit (c) to provide significant additional constraints on here lies in 2:1 MMR with HD 155358 b. the orbits of the planets contained therein, over and above those that can be placed solely on the basis of the observational data. Four examples of such systems are shown in figure 4.

In the four systems shown in figure 4, the by Jenni Thistlewood on January 5, 2015 newly discovered planets move on orbits whose uncertainties span regions of both significant dynamical stability and strong instability. In each case, however, the best-fit solution falls in the region of maximal dynamical stability, a result that once again strengthens the case for the observed radial velocity variations being (d) the result of massive unseen companions (i.e. planets). In each case, the best stability for the system is found when the planets involved are trapped in mutual mean motion resonance. In the case of HD 204313 (figure 4a), the plan­ etary system is only dynamically stable when the outermost planet completes two orbits in the time it takes the innermost to complete three – therefore, we say the planets are trapped in mutual 3:2 mean motion resonance (MMR). The sculpting of the stable region reveals the range of orbital solutions for HD 204313c for which the 3:2 MMR acts to stabilize the sys­ tem. Beyond that region, the orbits are unsta­ with the first planets discovered in those sys­ tem must be trapped in their mutual 2:1 MMR, ble on timescales of hundreds or thousands of tems. In the case of 24 Sex b, the only stable solu­ it seems by far the most likely solution – and we years. Beyond simply showing that the planets tions within ±1σ of the best fit orbit are those can rule out non-resonant solutions that place are dynamically feasible, our simulations here that are resonant – again, this allows us to more the newly discovered planet on more eccentric add a significant extra constraint on the orbit tightly constrain the orbit of that planet than orbits. Finally, in the case of HD 200964c (fig­ of the newly discovered planet. Simply, it must is possible on the basis of observations alone. ure 4c), the only stable solutions are those in be trapped in the 3:2 MMR. In the case of HD 155358, a large number of which the planets are trapped in 4:3 MMR. The newly discovered planets around 24 Sex­ orbital solutions outside the 2:1 MMR offer the Once again, studying the dynamics of the newly tantis (figure 4b) and HD 155358 (figure 4d) are possibility of stability. While this means we can­ discovered system has allowed us to better con­ both located in the vicinity of the 2:1 MMR not definitively state that the planets in that sys­ strain the orbits of the planets therein.

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5: The stability of the four (a) (b) recently proposed two- planet systems for which the dynamical simulations show that the planets are simply not dynamically feasible. (a): HU Aquarii; 50 625 simulations. (b): HW Virginis; 91 125 simulations. (c): NSVS 14256825; 126 075 simulations. (d): QS Virginis; 126 075 simulations. In each case, the candidate (c) (d) planets lie on orbits that cross one another – a sure-fire recipe for instability without the protective influence of resonant motion. In the case of (c), there is a narrow strip of moderate stability that

is the result of the 2:1 MMR Downloaded from between the two planets. Even then, however, at the high eccentricities proposed in the discovery work, the resonant orbits still decay on timescales

of order a million years. http://astrogeo.oxfordjournals.org/

Not every wobble needs a planet proposed planets do not exist. If the observed Our results fall into three broad categories. In recent years, a number of planetary systems variations in the timings of eclipses between In the simplest cases, the planets are suffi­ have been proposed to orbit highly evolved, the stars in these binaries are the result of per­ ciently well separated that they do not undergo interacting binary-star systems – post-common- turbations from massive unseen companions, strong mutual interactions, and the systems envelope binaries. The candidate planets, which then those companions must move on orbits are dynamically stable across the full range of are inferred on the basis of variations in the tim­ dramatically different to those proposed in the potential orbital architectures. ing of eclipses between the two components of discovery works. In light of the dynamical evi­ More interesting are the systems in which the the binary-star system, are often found to move dence, however, it seems much more likely that planets are more tightly packed. In these sys­ by Jenni Thistlewood on January 5, 2015 on highly eccentric orbits. For those systems the observed variations must have some addi­ tems, it is often the case that the great majority in which two planets are proposed, the orbits tional cause. Indeed, recent work that has built of permitted orbital solutions are dynamically are so extreme that they cross one another in on our dynamical results has suggested that unstable on very short timescales. In those much the same way that the orbits of comets there might be a systematic under-estimation of systems, narrow islands of stability are often and near-Earth asteroids cross the orbits of the the uncertainty with which the eclipses in these found, resulting from the stabilizing influence of planets in our solar system. In our solar sys­ systems can be timed. Simply increasing the mean motion resonances between the proposed tem, it is well known that such orbits are highly uncertainty on the measurements of the eclipse planets. In the case of such resonant systems, dynamically unstable, unless the objects mov­ timings for the NSVS 14256825 system to ±5 s dynamical studies allow the orbits of the pro­ ing on them are protected from mutual close is enough to make all evidence for orbiting bod­ posed planets to be constrained far more tightly encounters by the protective influence of a ies disappear. Given that the eclipses in these than is possible on the basis of the observations mean motion resonance – an observation that systems are far from simple processes (a dis­ alone – and can be used to direct future obser­ immediately suggests that the orbital evolution torted secondary with significant temperature vations that will help to confirm the existence of these extreme planets should be examined variations across its surface, orbiting a white of the planets in question. They also allow us in some detail. dwarf star with a period of just a few hours; to examine planetary systems featuring gravi­ The dynamical stability of four of the pro­ significant mass loss and accretion occurring tational interactions that are very different to posed multiple-planet systems orbiting evolved between the two stars), such uncertainty is those that are occurring between the planets binary stars are shown in figure 5. In each case, perfectly reasonable, and might well prove to in our own solar system. These observations the systems prove incredibly unstable – often be the simplest explanation for the observed can not only help us to better understand these featuring collisions between the proposed plan­ eclipse timing variations. newly discovered exoplanetary systems, but will ets on timescales of months or years! The sys­ also yield exciting insights into the early evolu­ tems are clearly dynamically unfeasible. Even Conclusions tion of our youthful planetary system, where it the case of NSVS 14256825 (figure 7c), which As the search for planets around other stars has been proposed that the giant planets formed features a narrow strip of moderate stability advances, an ever-increasing number of multi­ in dramatically different orbits to those they that coincides with the 2:1 MMR between the ple planet systems are being discovered. But the occupy at the current . two proposed planets, is sufficiently unstable great majority of planets discovered are found Finally, a small number of systems are found that it seems unlikely that the planets exist. indirectly, and the orbits proposed often feature to fall down under dynamical scrutiny – par­ Even those relatively stable resonant solutions relatively large uncertainties. We have therefore ticularly those proposed orbiting highly evolved fall apart on timescales far shorter than the age undertaken a programme of dynamical investi­ binary -star systems. In these cases, the results of the host system. Dynamical investigation of gations in order to determine whether the candi­ of our dynamical simulations are such that the these systems has therefore revealed that the date planetary systems are dynamically feasible. observational data must be considered in a

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Exoplanets that never were

Before the confirmed discovery of planets about their common centre of mass, the star detected orbiting the pulsar PSR B1829-10 orbiting other stars, several other exoplanet wobbled back and forth around the centre of was made in the journal Nature in 1991. The findings had been claimed, but close scrutiny mass of the system as it moved across the sky. authors proposed that observed variations in revealed that they were not real objects. Two Such observations were not unprec­ the timing of pulses arriving from the pulsar examples are particularly illustrative – the edented – the same technique had been used were the result of a planet-mass companion planets proposed to orbit one of our nearest a century earlier to reveal the present of to the rotating neutron star. The proposed neighbours, Barnard’s star, and the planet Sirius B, the white dwarf companion to the planet would have had an orbital period of claimed orbiting the pulsar PSR B1829-10. brightest star in the night sky. However, van half a year, and a mass ten times that of the Barnard’s star is the fourth closest star to de Kamp’s observations were the first time Earth. In the discovery work, the authors the Sun, after the three stars that make up such variations had been used to propose the mentioned that an alternative explanation for the Alpha Centauri system (Alpha Centauri existence of planetary, rather than stellar, the observed signal would be that it was an A + B, and Proxima Centauri). Less than companions. Unfortunately for him, obser­ artefact resulting from the orbit of the Earth 6 light years away, it is a tiny red dwarf star vations from other observatories failed to around the Sun, but concluded that, since no far too faint to see with the unaided eye. find any evidence for his proposed wobbles such artefact could be found in the observa­ It is noteworthy because its and further investigation revealed a different tional data they had for 300 other pulsars, the Downloaded from isgreater than that of any other star. That is cause: the objective lens of the refracting tel­ most likely conclusion was that the variations the result of both the star’s proximity and escope had been removed and cleaned, then were the result of the proposed planet. Upon its high speed relative to the Sun – of order replaced, several times during the period of further analysis, however, the authors found 140 km/s. Barnard’s star has been a popular his observations. More recently, observations that the variation could be explained as being target for observers over the century since using the Hubble Space Telescope have put the result of the Earth’s elliptical orbit around E E Barnard first measured its proper motion the final nail in the coffin of van de Kamp’s the Sun. In their initial analysis, the authors http://astrogeo.oxfordjournals.org/ in 1916. proposal, definitively ruling out such massive had assumed the Earth’s orbit to be circular The Dutch astronomer Piet van de Kamp planets orbiting the tiny star. His technique when correcting for its motion around our star observed the motion of many nearby stars, may well see a renaissance in coming years, – and once the small but non-zero eccentricity including Barnard’s star, during his time as however: the GAIA space observatory, of the Earth’s orbit was taken into account, all director of Sproul Observatory (from 1938 launched on 19 December 2013, will make evidence for a planet around PSR B1829-10 to 1972). As he gathered data, van de Kamp incredibly precise measurements of the disappeared. The retraction of the discovery of claimed to have detected Barnard’s star wob­ proper motions of approximately 1 bil­ the planet appeared in Nature, one week after bling back and forth as it tracked across the lion stars. GAIA is expected to discover a the announcement of the discovery of planets

sky – evidence, he claimed, of the presence plethora of planets orbiting nearby stars. Van orbiting another pulsar, PSR B1257+12, which by Jenni Thistlewood on January 5, 2015 of at least two Jupiter-mass planets in orbit. de Kamp would be proud! were then acknowledged as the first confirmed As the planets and the low-mass star orbited The announcement that a planet had been planets orbiting another star.

whole new light. Most likely, the planets pro­ allow us to confirm that any exo-Earths discov­ Pennsylvania State University, USA. posed in those systems simply do not exist, and ered are dynamically stable on timescales long Acknowledgments. The work was supported by the claimed variability in the timing of eclipses enough that life could develop on their surfaces, iVEC through the use of advanced computing between the binary stars is simply the result of they will also allow us to draw conclusions on resources located at the Murdoch University in the underestimation of the uncertainty in the the variability of the climates of those worlds Western Australia, and has also made use of the eclipse timings themselves. (by examining the influence of distant perturb­ University of New South Wales’s supercomputing Most importantly, however, our results high­ ers driving small-scale variations in their orbital cluster, Katana. This research made use of NASA’s light the importance of dynamical studies parameters), as well as enabling us to investigate Astrophysics Data System (ADS). as a key component of the search for planets the impact regimes that they might experience References around other stars. As a result of our work, the (by studying the influence of the planets in the Chambers J 1999 MNRAS 304 793. Anglo-Australian Planet Search now routinely system on the small object reservoirs therein). Johnson J A et al. 2011 ApJS 197 26. carries out detailed dynamical mapping of all The future of exoplanet dynamics is definitely Robertson P et al. 2012a ApJ 754 50. Robertson P et al. 2012b ApJ 749 39. new multiple-planet systems discovered as a an exciting one! ● central part of the discovery process. While Further reading such simulations are time consuming (a typical J Horner, Computational Engineering and 24 Sex and HD 200964 dynamics: Wittenmyer R A, system will require more than 100 000 hours of Science Research Centre, University of Southern Horner J and Tinney C G 2012 ApJ 761 165. HD 142 and HD 159868: Wittenmyer R A et al. 2012 ApJ run time on a supercomputing cluster to create Queensland, Australia. R A Wittenmyer, School of 753 169. a dynamical map like those presented in this Physics and Australian Centre for Astrobiology, HD 52265 and HD 85390: Wittenmyer R A et al. 2013 work), the benefits of such work far outweigh University of New South Wales, Australia. J P ApJS 208 2. the extra time required to perform such simula­ Marshall, Departamento de Física Teórica, HR 8799: Marshall J, Horner J and Carter A 2010 IJA 9 259. tions prior to the announcement of a new plan­ Facultad de Ciencias, Universidad Autónoma de HU Aquarii I: Horner J et al. 2011 MNRAS 416 11. etary system. Madrid, Spain. T C Hinse, Korea Astronomy and HU Aquarii II: Wittenmyer R A et al. 2012 MNRAS 419 In future years, as the search for exoplanets Space Science Institute, Daejeon, South Korea. P 3258. HW Virginis: Horner J 2012 427 2812. continues to push towards the discovery of truly Robertson, Dept of Astronomy and McDonald et al. MNRAS NSVS 14256825: Wittenmyer R A, Horner J and Earth -like planets, such dynamical studies will Observatory, University of Texas at Austin, USA, Marshall J P 2013 MNRAS 431 2150. only grow in importance. Not only will they and Dept of Astronomy and Astrophysics, The QS Virginis: Horner J et al. 2013 MNRAS tmp. 2063.

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