Planetary debris is observed in the atmospheres of over 1,000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through scattering with major planets. However, the architectures that allow for this scattering to take place are time-consuming to explore with $N$-body simulations lasting $\sim 10^{10}$ yr; these long-running simulations restrict the amount of phase space that can be investigated. Here we use planar and three-dimensional (spatial) elliptic periodic orbits, as well as chaotic indicators through dynamical stability maps, as quick scale-free analytic alternatives to $N$-body simulations in order to locate and predict instability in white dwarf planetary systems that consist of one major and one minor planet on very long timescales. We then classify the instability according to ejection versus collisional events. We generalized our previous work by allowing eccentricity and inclination of the periodic orbits to increase, thereby adding more realism but also significantly more degrees of freedom to our architectures. We also carried out a suite of computationally expensive 10 Gyr $N$-body simulations to provide comparisons with chaotic indicators in a limited region of phase space. We compute dynamical stability maps that are specific to white dwarf planetary systems and that can be used as tools in future studies to quickly estimate pollution prospects and timescales for one-planet architectures. We find that these maps also agree well with the outcomes of our $N$-body simulations. As observations of metal-polluted white dwarfs mount exponentially, particularly in the era of Gaia, tools such as periodic orbits can help infer dynamical histories for ensembles of systems.
A significant fraction of white dwarfs show metal lines indicative of pollution with planetary material but the accretion process remains poorly understood. The main aim of this paper is to produce a road-map illustrating several potential routes for white dwarf pollution and to link these paths to observational outcomes. Our proposed main road begins with the tidal disruption of a scattered asteroid and the formation of a highly eccentric tidal disc with a wide range of fragment sizes. Accretion of these fragments by Poynting-Robertson (PR) drag alone is too slow to explain the observed rates…
A significant fraction of white dwarfs (WDs) are observed to be polluted with metals despite high surface gravities and short settling times. The current theoretical model for this pollution is accretion of rocky bodies delivered to the WD through perturbations by orbiting planets. Using N-body simulations, we examine the possibility of a single planet as the source of pollution. We determine the stability of test particles on circular orbits in systems with a single planet located at 4 au for a range of masses and eccentricities, comparing the fractions that are ejected and accreted. In parti…
Secular oscillations in multi-planet systems can drive chaotic evolution of a small inner body through non-linear resonant perturbations. This "secular chaos" readily pushes the inner body to an extreme eccentricity, triggering tidal interactions or collision with the central star. We present a numerical study of secular chaos in systems with two planets and test particles using the ring-averaging method, with emphasis on the relationship between the planets' properties and the time-scale and efficiency of chaotic diffusion. We find that secular chaos can excite extreme eccentricities on time-…
How a Close-in Planet Protects its White Dwarf Host from Pollution
School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory of Modern Astronomy and Astrophysics, Ministry of Education（教育部现代天文与天体物理重点实验室）；School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）
Previous investigations have revealed that eccentric super-Earths represent a class of planets which are particularly effective at transporting minor bodies towards white dwarfs and subsequently polluting their atmospheres with observable chemical signatures. However, the lack of discoveries of these planets beyond a few astronomical units from their host stars prompts a better understanding of their orbital architectures from their nascent birth cluster. Here, we perform stellar cluster simulations of 3-planet and 7-planet systems containing super-Earths on initially circular, coplanar orbits…
At least 25% of white dwarfs show atmospheric pollution by metals, sometimes accompanied by detectable circumstellar dust/gas discs or (in the case of WD 1145+017) transiting disintegrating asteroids. Delivery of planetesimals to the white dwarf by orbiting planets is a leading candidate to explain these phenomena. Here, we study systems of planets and planetesimals undergoing planet-planet scattering triggered by the star's post-main sequence mass loss, and test whether this can maintain high rates of delivery over the several Gyr that they are observed. We find that low-mass planets (Earth t…
Of the 21 known gaseous debris discs around white dwarfs, a large fraction of them display observational features that are well described by an eccentric distribution of gas. In the absence of embedded objects or additional forces, these discs should not remain eccentric for long timescales, and should instead circularise due to viscous spreading. The metal pollution and infrared excess we observe from these stars is consistent with the presence of tidally disrupted sub-stellar bodies. We demonstrate, using smoothed particle hydrodynamics, that a sublimating or partially disrupting planet on a…
Many potential mechanisms for delivering planetary debris to within a few Roche radii of white dwarfs rely on gravitational scattering events that feature perturbers which are giant planets or terrestrial planets. However, the population of these planets orbiting white dwarfs is still unknown, and for a substantial fraction of white dwarfs the largest planetary survivors of stellar evolution may be sub-terrestrial mass minor planets. Here, we attempt to identify the smallest mass perturbers that could pollute white dwarfs. Through computationally expensive numerical simulations of both unstabl…
We study the orbital stability of a non-zero mass, close-in circular orbit planet around an eccentric orbit binary for various initial values of the binary eccentricity, binary mass fraction, planet mass, planet semi--major axis, and planet inclination by means of numerical simulations that cover $5 \times 10^4$ binary orbits. For small binary eccentricity, the stable orbits that extend closest to the binary (most stable orbits) are nearly retrograde and circulating. For high binary eccentricity, the most stable orbits are highly inclined and librate near the so-called generalised polar orbit …
25%-50% of all white dwarfs (WDs) host observable and dynamically active remnant planetary systems based on the presence of close-in circumstellar dust and gas and photospheric metal pollution. Currently-accepted theoretical explanations for the origin of this matter include asteroids that survive the star's giant branch evolution at au-scale distances and are subsequently perturbed onto WD-grazing orbits following stellar mass loss. In this work we investigate the tidal disruption of these highly-eccentric (e > 0.98) asteroids as they approach and tidally disrupt around the WD. We analyticall…
Several white dwarfs with atmospheric metal pollution have been found to host small planetary bodies (planetesimals) orbiting near the tidal disruption radius. We study the physical properties and dynamical origin of these bodies under the hypothesis that they underwent high-eccentricity migration from initial distances of several astronomical units. We examine two plausible mechanisms for orbital migration and circularization: tidal friction and ram-pressure drag in a compact disc. For each mechanism, we derive general analytic expressions for the evolution of the orbit that can be rescaled f…
Asteroid material is detected in white dwarfs (WDs) as atmospheric pollution by metals, in the form of gas/dust discs, or in photometric transits. Within the current paradigm, minor bodies need to be scattered, most likely by planets, into highly eccentric orbits where the material gets disrupted by tidal forces and then accreted onto the star. This can occur through a planet-planet scattering process triggered by the stellar mass loss during the post main-sequence evolution of planetary systems. So far, studies of the $N$-body dynamics of this process have used artificial planetary system arc…
In the past few decades, observations have revealed signatures of metals polluting the atmospheres of white dwarfs. The diffusion timescale for metals to sink from the atmosphere of a white dwarf is of the order of days for a hydrogen-dominated atmosphere. Thus, there must be a continuous supply of metal-rich material accreting onto these white dwarfs. We investigate the role of secular resonances that excite the eccentricity of asteroids allowing them to reach star-grazing orbits leading them to tidal disruption and the formation of a debris disc. Changes in the planetary system during the ev…
The discovery of over 400 extrasolar planets allows us to statistically test our understanding of formation and dynamics of planetary systems via numerical simulations. Traditional N-body simulations of multiple-planet systems without gas disks have successfully reproduced the eccentricity (e) distribution of the observed systems, by assuming that the planetary systems are relatively closely packed when the gas disk dissipates, so that they become dynamically unstable within the stellar lifetime. However, such studies cannot explain the small semi-major axes (a) of extrasolar planetary systems…
Applying the technique of dynamical maps we study the orbital stability of test particles in the Solar System in the space (a,e,i) defined by 0.1<a<38 au, 0<e<0.9 and 0<i<180 identifying the unstable and stable regions. We find stable niches where small bodies can survive even for very high eccentricities. Mean motion resonances play a fundamental role providing stability against the planetary perturbations specially for high inclination orbits. A stability stripe around i=150 is present all along the Solar System. We found that the population of objects with semimajor axes between 10 and 30 a…
Being the first of its kind, the white dwarf WD 1145+017 exhibits a complex system of disintegrating debris which offers a unique opportunity to study its disruption process in real time. Even with plenty of transit observations there are no clear constraints on the masses or eccentricities of such debris. Using $N$-body simulations we show that masses greater than approximately $10^{20}$ kg (a tenth of the mass of Ceres) or orbits that are not nearly circular ($\mathrm{eccentricity}>10^{-3}$) dramatically increase the chances of the system becoming unstable within two years, which would contr…
Eccentric Keplerian discs are believed to be unstable to three-dimensional hydrodynamical instabilities driven by the time-dependence of fluid properties around an orbit. These instabilities could lead to small-scale turbulence, and ultimately modify the global disc properties. We use a local model of an eccentric disc, derived in a companion paper, to compute the nonlinear vertical ("breathing mode") oscillations of the disc. We then analyse their linear stability to locally axisymmetric disturbances for any disc eccentricity and eccentricity gradient using a numerical Floquet method. In the …
A significant fraction of white dwarfs (WDs) exhibit signs of ongoing accretion of refractory elements at rates $\sim10^3$--$10^7$ kg s$^{-1}$, among which, 37 WDs were detected to harbor dusty debris disks. Such a concurrence requires not only fertile reservoirs of planetary material, but also a high duty cycle of metal delivery. It has been commonly suggested that this material could be supplied by Solar System analogs of Main Belt asteroids or Kuiper Belt objects. Here we consider the primary progenitors of WD pollutants as a population of residual high-eccentricity planetesimals, de-volati…
We formulate a local dynamical model of an eccentric disc in which the dominant motion consists of elliptical Keplerian orbits. The model is a generalization of the well known shearing sheet, and is suitable for both analytical and computational studies of the local dynamics of eccentric discs. It is spatially homogeneous in the horizontal dimensions but has a time-dependent geometry that oscillates at the orbital frequency. We show how certain averages of the stress tensor in the local model determine the large-scale evolution of the shape and mass distribution of the disc. The simplest solut…
Sub-Jupiter classed circumbinary planets discovered in close-in binary systems have orbits just beyond the dynamically unstable region, which is determined by the eccentricity and mass ratio of the host binary stars. These planets are assumed to have formed beyond the snow line and migrated to the current orbits rather than forming in situ. We propose a scenario in which a planet formed beyond the snow line and migrated to the inner edge of the circumbinary disk, which was within the unstable area, and then moved to the current orbit through outward transportation. This outward transportation …
Many observed giant planets lie on eccentric orbits. Such orbits could be the result of strong scatterings with other giant planets. The same dynamical instability that produces these scatterings may also cause habitable planets in interior orbits to become ejected, destroyed, or be transported out of the habitable zone. We say that a habitable planet has resilient habitability if it is able to avoid ejections and collisions and its orbit remains inside the habitable zone. Here we model the orbital evolution of rocky planets in planetary systems where giant planets become dynamically unstable.…
We study the final architecture of planetary systems that evolve under the combined effects of planet-planet and planetesimal scattering. Using N-body simulations we investigate the dynamics of marginally unstable systems of gas and ice giants both in isolation and when the planets form interior to a planetesimal belt. The unstable isolated systems evolve under planet-planet scattering to yield an eccentricity distribution that matches that observed for extrasolar planets. When planetesimals are included the outcome depends upon the total mass of the planets. For system masses exceeding about …
The stability of the Lagrangian point $L_4$ is investigated in the elliptic restricted three-body problem by using Floquet's theory. Stable and unstable domains are determined in the parameter plane of the mass parameter and the eccentricity by computing the characteristic exponents. Frequencies of motion around $L_4$ have been determined both in the stable and unstable domains and fitting functions for the frequencies are derived depending on the mass parameter and the eccentricity. Resonances between the frequencies are studied in the whole parameter plane. It is shown that the 1:1 resonance…
It is well known that asteroids and comets fall into the Sun. Metal pollution of white dwarfs and transient spectroscopic signatures of young stars like $β$-Pic provide growing evidence that extra solar planetesimals can attain extreme orbital eccentricities and fall onto their parent stars. We aim to develop a general, practically implementable, semi-analytical theory of secular eccentricity excitation of small bodies in mean motion resonances with an eccentric planet valid for arbitrary values of the eccentricities and including the short-range force due to General Relativity. Our semi-analy…
Mounting discoveries of debris discs orbiting newly-formed stars and white dwarfs (WDs) showcase the importance of modeling the long-term evolution of small bodies in exosystems. WD debris discs are in particular thought to form from very long-term (0.1-5.0 Gyr) instability between planets and asteroids. However, the time-consuming nature of $N$-body integrators which accurately simulate motion over Gyrs necessitates a judicious choice of initial conditions. The analytical tools known as \textit{periodic orbits} can circumvent the guesswork. Here, we begin a comprehensive analysis directly lin…
The orbit of a planet is surrounded by a chaotic zone wherein nearby particles' orbits are chaotic and unstable. Wisdom (1980) showed that the chaos is driven by the overlap of mean motion resonances which occurs within a distance (da/a)_chaos = 1.3 mu^2/7 of the planet's orbit. However, the width of mean motion resonances grows with the particles' eccentricity, which will increase the width of the chaotic zone at higher eccentricities. Here we investigate the width of the chaotic zone using the iterated encounter map and N-body integrations. We find that the classical prescription works well …
High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations---large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect is modified by incorporating perturbations from the planetary oblateness. Tremaine et al. (2009) found that, for planets with obliquities > 68.875 degrees, orbits in the equilibrium local Laplace plane are unstable to eccentricity perturbations over a finite radial range, and execute large-amplitude chaotic oscillations in eccentricity and inclination. In th…
With $n$-body simulations we investigate the stability of tilted circumbinary planetary systems consisting of two nonzero mass planets. The planets are initially in circular orbits that are coplanar to each other, as would be expected if they form in a flat but tilted circumbinary gas disc and decouple from the disc within a time difference that is much less than the disc nodal precession period. We constrain the parameters of stable multiple planet circumbinary systems. Both planet-planet and planet-binary interactions can cause complex planet tilt oscillations which can destabilise the orbit…
Increasing observations of white dwarf atmospheric pollution and disrupting planetesimals is driving increased studies into the fate of exo-asteroids around post-main-sequence stars. Planetesimal populations in the Solar System which are most likely to survive the violent post-main-sequence evolution, such as the Kuiper Belt, display a large binary fraction with a propensity for near equal-mass components and provide a previously unexplored population of planetesimals which are likely to exist around white dwarfs. Here we simulate the dynamical evolution of equal-mass binary asteroid systems a…
We study the disruption process of hierarchical 3-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with 3-body numerical integrations, we show that the evolution and disruption of such systems can be statistically described as a simple random-walk process in the outer-orbit's energy, where the energy-exchange per pericenter passage (step-size) is calculated from the initial conditions. In our derivation of the step-size, we use previous analytic results for parabolic encounters,…
We explore planetary migration scenarios for formation of high inclination Neptune Trojans (NTs) and how they are affected by the planetary migration of Neptune and Uranus. If Neptune and Uranus's eccentricity and inclination were damped during planetary migration, then their eccentricities and inclinations were higher prior and during migration than their current values. Using test particle integrations we study the stability of primordial NTs, objects that were initially Trojans with Neptune prior to migration. We also study Trans-Neptunian objects captured into resonance with Neptune and be…
Eccentric gaseous discs are unstable to a parametric instability involving the resonant interaction between inertial-gravity waves and the eccentric mode in the disc. We present 3D global hydrodynamical simulations of inviscid circumbinary discs that form an inner cavity and become eccentric through interaction with the central binary. The parametric instability grows and generates turbulence that transports angular momentum with stress parameter $α\sim 5 \times 10^{-3}$ at distances $\lesssim 7 \;a_{bin} $, where $a_{bin}$ is the binary semi-major axis. Vertical turbulent diffusion occurs at …
We find that, under certain conditions, protoplanetary disks may spontaneously generate multiple, concentric gas rings without an embedded planet through an eccentric cooling instability. Using both linear theory and non-linear hydrodynamics simulations, we show that a variety of background states may trap a slowly precessing, one-armed spiral mode that becomes unstable when a gravitationally-stable disk rapidly cools. The angular momentum required to excite this spiral comes at the expense of non-uniform mass transport that generically results in multiple rings. For example, one long-term hyd…
Pollution of white dwarf atmospheres may be caused by asteroids that originate from the locations of secular and mean-motion resonances in planetary systems. Asteroids in these locations experience increased eccentricity, leading to tidal disruption by the white dwarf. We examine how the $ν_6$ secular resonance shifts outwards into a previously stable region of the asteroid belt, as the star evolves to a white dwarf. Analytic secular models require a planet to be engulfed in order to shift the resonance. We show with numerical simulations that as a planet gets engulfed by the evolving star, th…
Many exoplanets in close-in orbits are observed to have relatively high eccentricities and large stellar obliquities. We explore the possibility that these result from planet-planet scattering by studying the dynamical outcomes from a large number of orbit integrations in systems with two and three gas-giant planets in close-in orbits (0.05 AU < a < 0.15 AU). We find that at these orbital separations, unstable systems starting with low eccentricities and mutual inclinations ($e\lesssim0.1$, $i\lesssim0.1$) generally lead to planet-planet collisions in which the collision product is a planet on…
The search for planets around White Dwarf stars, and evidence for dynamical instability around them in the form of atmospheric pollution and circumstellar discs, raises questions about the nature of planetary systems that can survive the vicissitudes of the Asymptotic Giant Branch (AGB). We study the competing effects, on planets at several AU from the star, of strong tidal forces arising from the star's large convective envelope, and of the planets' orbital expansion due to stellar mass loss. We, for the first time, study the evolution of planets while following each thermal pulse on the AGB.…
A significant fraction of unstable multiple planet systems likely scatter during the transitional disc phase as gas damping becomes ineffectual. Using an ensemble of FARGO hydrodynamic simulations and MERCURY n-body integrations, we directly follow planet-disc and planet-planet interactions through the clearing phase and on through 50 Myr of dynamical evolution. Disc clearing occurs via X-ray driven photoevaporation. The hydrodynamic evolution of individual scattering systems is complex, and involves phases in which massive planets orbit within eccentric gaps, or accrete directly from the disc…
We study how close-in systems such as those detected by Kepler are affected by the dynamics of bodies in the outer system. We consider two scenarios: outer systems of giant planets potentially unstable to planet--planet scattering, and wide binaries that may be capable of driving Kozai or other secular variations of outer planets' eccentricities. Dynamical excitation of planets in the outer system reduces the multiplicity of Kepler-detectable planets in the inner system in $\sim20-25\%$ of our systems. Accounting for the occurrence rates of wide-orbit planets and binary stars, $\approx18\%$ of…
The rectilinear elliptic restricted Three Body Problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity $e'=1$, but the collision of the primaries is assumed to be a non-singular point. The rectilinear model has been proposed as a starting model for studying the dynamics of motion around highly eccentric binary systems. Broucke (1969) explored the rectilinear problem and obtained isolated periodic orbits for mass parameter $μ=0.5$ (equal masses of the primaries). We found that all orbits obtained by…
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model have been extensively studied in the literature, only few results about the dynamics of the elliptic model were known up to now, namely the equations of motion and few unstable families of periodic orbits. In the present study we extend these results by computing a large set of families of periodic orbits and their linear stability and classify them according…
Robust evidence of an ice giant planet shedding its atmosphere around the white dwarf WD J0914+1914 represents a milestone in exoplanetary science, allowing us to finally supplement our knowledge of white dwarf metal pollution, debris discs and minor planets with the presence of a major planet. Here, we discuss the possible dynamical origins of this planet, WD J0914+1914 b. The very young cooling age of the host white dwarf (13 Myr) combined with the currently estimated planet-star separation of about 0.07 au imposes particularly intriguing and restrictive coupled constraints on its current or…
The star Fomalhaut hosts a narrow, eccentric debris disc, plus a highly eccentric companion Fomalhaut b. It is often argued that Fomalhaut b cannot have significant mass, otherwise it would quickly perturb the disc. We show that material in internal mean-motion resonances with a massive, coplanar Fomalhaut b would actually be long-term stable, and occupy orbits similar to the observed debris. Furthermore, millimetre dust released in collisions between resonant bodies could reproduce the width, shape and orientation of the observed disc. We first re-examine the possible orbits of Fomalhaut b, a…
A gas giant planet which survives the giant branch stages of evolution at a distance of many au and then is subsequently perturbed sufficiently close to a white dwarf will experience orbital shrinkage and circularization due to star-planet tides. The circularization timescale, when combined with a known white dwarf cooling age, can place coupled constraints on the scattering epoch as well as the active tidal mechanisms. Here, we explore this coupling across the entire plausible parameter phase space by computing orbit shrinkage and potential self-disruption due to chaotic f-mode excitation and…
In a previous paper, we have presented a global view of the stability of Neptune Trojan (NT hereafter) on inclined orbit. We discuss in this paper the dependence of stability of NT orbits on the eccentricity. High-resolution dynamical maps are constructed using the results of extensive numerical integrations of orbits initialized on the fine grids of initial semimajor axis (a0) versus eccentricity (e0). The extensions of regions of stable orbits on the (a0, e0) plane at different inclinations are shown. The maximum eccentricities of stable orbits in three most stable regions at low (0, 12deg.)…
Nearly all known white dwarf planetary systems contain detectable rocky debris in the stellar photosphere. A glaring exception is the young and still evolving white dwarf WD J0914+1914, which instead harbours a giant planet and a disc of pure gas. The stability boundaries of this disc and the future prospects for this white dwarf to be polluted with rocks depend upon the mass and orbit of the planet, which are only weakly constrained. Here we combine an ensemble of plausible planet orbits and masses to determine where observers should currently expect to find the outer boundary of the gas disc…
Most of the observed extrasolar planets are found on tight and often eccentric orbits. The high eccentricities are not easily explained by planet-formation models, which predict that planets should be on rather circular orbits. Here we explore whether fly-bys involving planetary systems with properties similar to those of the gas giants in the solar system, can produce planets with properties similar to the observed planets. Using numerical simulations, we show that fly-bys can cause the immediate ejection of planets, and sometimes also lead to the capture of one or more planets by the intrude…
The observed wide eccentricity distribution of extrasolar giant planets is thought to be the result of dynamical instabilities and gravitational scattering among planets. Previously, it has been assumed that the orbits in giant planet systems become gravitationally unstable after the gas nebula dispersal. It was not well understood, however, how these unstable conditions were established in the first place. In this work we numerically simulate the evolution of systems of three planets as the planets sequentially grow to Jupiter's mass, and dynamically interact among themselves and with the gas…
The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into account the frequency-dependent quality factors and Love numbers. The torque equations are integrated numerically with a small step in time, includng the oscillating triaxial torque components but neglecting the layered structure of the planet and assuming a zero obliquity. We find that a Mercury-like planet with its current value of orbital eccentricity (0.2056) is always captured in the 3:2 resonance…
The eccentric shape of the debris disk observed around Fomalhaut was first attributed to Fom b, a companion detected near the belt inner-edge, but new constraints on its orbit revealed that it is belt-crossing, highly eccentric $(e \sim 0.6-0.9)$, and can hardly account for the shape of the belt. The best scenario to explain this paradox is that there is another massive body in this system, Fom c, which drives the debris disk shape. The resulting planetary system is highly unstable, which hints at a dynamical scenario involving a recent scattering of Fom b on its current orbit, potentially wit…
The post-main sequence eclipsing binary NN Serpentis was recently announced as the potential host of at least two massive planetary companions. In that work, the authors put forward two potential architectures that fit the observations of the eclipsing binary with almost identical precision. In this work, we present the results of a dynamical investigation of the orbital stability of both proposed system architectures, finding that they are only stable for scenarios in which the planets are locked in mutual mean motion resonance. In the discovery work, the authors artificially fixed the orbita…
In this work we propose a new orbital architecture for the two proposed circumbinary planets around the polar eclipsing binary HU Aquarii. We base the new two-planet, light-travel time model on the result of a Monte Carlo simulation driving a least-squares Levenberg-Marquardt minimisation algorithm on the observed eclipse egress times. Our best-fitting model with $χ_{r}^2=1.43$ resulted in high final eccentricities for the two companions leading to an unstable orbital configuration. From a large ensemble of initial guesses we examined the distribution of final eccentricities and semi-major axe…
Using numerical methods we investigate the dynamical stability of the Gliese 581 exoplanetary system. The system is known to harbour four planets (b-e). The existence of another planet (g) in the liquid water habitable zone of the star is debated after the latest analyses of the radial velocity (RV) measurements. We integrated the 4 and 5-planet model of Vogt et al. (AN 333, 561-575, 2012) with initial circular orbits. To characterize stability, the maximum eccentricity was used that the planets reached over the time of the integrations and the LCI and RLI to identify chaotic motion. Since cir…
