arXiv subjects

Dimitri Veras

Publications and source records attributed to Dimitri Veras.

At least 145 records · Page 8Linked to original sources

arXiv2014

A simple bound for the variation at closest approach of a small body and star due to general relativity

As a comet, asteroid or planet approaches its parent star, the orbit changes shape due to the curvature of spacetime. For comets in particular, the deviation at the pericentre may noticeably change their ephemerides and affect the dynamics of outgassing, tidal disruption or other processes which act on orbital timescales and are assumed to follow Newtonian gravity. By obtaining and analysing the unaveraged equations of motion in orbital elements due to the dominant post-Newtonian contribution (1PN), I derive a simple analytic expression for the maximum deviation in terms of only the stellar mass and eccentricity of the orbit. This relation can be used to assess the potential importance of including short-period relativistic terms in models containing comets, asteroids or planets, and help determine the level of precision needed in numerical integrations. The magnitude of the deviation in systems with Solar-like stars is typically comparable to the size of comet nuclei, and the direction of the deviation is determined by the eccentricity. I show that for eccentricities above a critical value of approximately 0.359, the direction is away from the star.

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arXiv2014

Debris from giant impacts between planetary embryos at large orbital radii

We consider the observational signatures of giant impacts between planetary embryos. While the debris released in the impact remains in a clump for only a single orbit, there is a much longer lasting asymmetry caused by the fact that all debris must pass through the collision-point. The resulting asymmetry is stationary, it does not orbit the star. The debris is concentrated in a clump at the collision-point, with a more diffuse structure on the opposite side. The asymmetry lasts for typically around 1000 orbital periods of the progenitor, which can be several Myr at distances of ~50 AU. We describe how the appearance of the asymmetric disc depends on the mass and eccentricity of the progenitor, as well as viewing orientation. The wavelength of observation, which determines the grain sizes probed, is also important. Notably, the increased collision rate of the debris at the collision-point makes this the dominant production site for any secondary dust and gas created. For dust small enough to be removed by radiation pressure, and gas with a short lifetime, this causes their distribution to resemble a jet emanating from the (stationary) collision-point. We suggest that the asymmetries seen at large separations in some debris discs, like Beta Pictoris, could be the result of giant impacts. If so this would indicate that planetary embryos are present and continuing to grow at several tens of AU at ages of up to tens of Myr.

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arXiv2014

Explicit evolution relations with orbital elements for eccentric, inclined, elliptic and hyperbolic restricted few-body problems

Planetary, stellar and galactic physics often rely on the general restricted gravitational N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted problem entirely and specifically in terms of the commonly-used orbital elements of semimajor axis, eccentricity, inclination, longitude of ascending node, argument of pericentre, and true anomaly, without any assumptions about their magnitudes. I derive the equations of motion in the general, unaveraged case, as well as specific cases, with respect to both a bodycentric and barycentric origin. I then reduce the equations to three-body systems, and present compact singly- and doubly-averaged expressions which can be readily applied to systems of interest. This method recovers classic Lidov-Kozai and Laplace-Lagrange theory in the test particle limit to any order, but with fewer assumptions, and reveals a complete analytic solution for the averaged planetary pericentre precession in coplanar circular circumbinary systems to at least the first three nonzero orders in semimajor axis ratio. Finally, I show how the unaveraged equations may be used to express resonant angle evolution in an explicit manner that is not subject to expansions of eccentricity and inclination about small nor any other values.

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arXiv2013

The Long-Term Dynamical Evolution of Planetary Systems

This chapter concerns the long-term dynamical evolution of planetary systems from both theoretical and observational perspectives. We begin by discussing the planet-planet interactions that take place within our own Solar System. We then describe such interactions in more tightly-packed planetary systems. As planet-planet interactions build up, some systems become dynamically unstable, leading to strong encounters and ultimately either ejections or collisions of planets. After discussing the basic physical processes involved, we consider how these interactions apply to extrasolar planetary systems and explore the constraints provided by observed systems. The presence of a residual planetesimal disc can lead to planetary migration and hence cause instabilities induced by resonance crossing; however, such discs can also stabilise planetary systems. The crowded birth environment of a planetary system can have a significant impact: close encounters and binary companions can act to destabilise systems, or sculpt their properties. In the case of binaries, the Kozai mechanism can place planets on extremely eccentric orbits which may later circularise to produce hot Jupiters.

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arXiv2013

Long-term evolution of three-planet systems to the post-Main Sequence and beyond

We study the stability of systems of three giant planets orbiting 3 - 8 M_Sol stars at orbital distances of >10 au as the host star ages through the Main Sequence (MS) and well into the White Dwarf (WD) stage. Systems are stable on the MS if the planets are separated by more than ~9 Hill radii. Most systems surviving the MS will remain stable until the WD phase, although planets scattered onto small pericentres in unstable systems can be swallowed by the expanding stellar envelope when the star ascends the giant branches. Mass loss at the end of the asymptotic giant branch triggers delayed instability in many systems, leading to instabilities typically occurring at WD cooling ages of a few 100 Myr. This instability occurs both in systems that survived the star's previous evolution unscathed, and in systems that previously underwent scattering instabilities. The outcome of such instability around WDs is overwhelmingly the ejection of one of the planets from the system, with several times more ejections occurring during the WD phase than during the MS. Furthermore, few planets are scattered close to the WD, just outside the Roche limit, where they can be tidally circularised. Hence, we predict that planets in WD systems rarely dynamically evolve to become "hot Jupiters". Nor does it appear that the observed frequency of metal pollution in WD atmospheres can be entirely explained by planetesimals being destabilised following instability in systems of multiple giant planets, although further work incorporating low-mass planets and planetesimals is needed.

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arXiv2013

The Great Escape III: Placing post-main-sequence evolution of planetary and binary systems in a Galactic context

Our improving understanding of the life cycle of planetary systems prompts investigations of the role of the Galactic environment before, during and after Asymptotic Giant Branch (AGB) stellar evolution. Here, we investigate the interplay between stellar mass loss, Galactic tidal perturbations, and stellar flybys for evolving stars which host one planet, smaller body or stellar binary companion and reside in the Milky Way's bulge or disc. We find that the potential evolutionary pathways from a main sequence (MS) to a white dwarf (WD) planetary system are a strong function of Galactocentric distance only with respect to the prevalence of stellar flybys. Planetary ejection and collision with the parent star should be more common towards the bulge. At a given location anywhere in the Galaxy, if the mass loss is adiabatic, then the secondary is likely to avoid close flybys during AGB evolution, and cannot eventually escape the resulting WD because of Galactic tides alone. Partly because AGB mass loss will shrink a planetary system's Hill ellipsoid axes by about 20 to 40 per cent, Oort clouds orbiting WDs are likely to be more depleted and dynamically excited than on the MS.

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arXiv2013

Main-sequence progenitor configurations of the NN Ser candidate circumbinary planetary system are dynamically unstable

Recent observations of the NN Serpentis post-common envelope binary system have revealed eclipse timing variations that have been attributed to the presence of two Jovian-mass exoplanets. Under the assumption that these planets are real and survived from the binary's Main Sequence state, we reconstruct initial binaries that give rise to the present NN Ser configuration and test the dynamical stability of the original system. Under standard assumptions about binary evolution, we find that survival of the planets through the entire Main Sequence life-time is very unlikely. Hence, we conclude that the planets are not survivors from before the Common Envelope phase, implying that either they formed recently out of material ejected from the primary, or that the observed signals are of non-planetary origin.

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arXiv2013

An Exoplanet's Response to Anisotropic Stellar Mass-Loss During Birth and Death

The birth and death of planets may be affected by mass outflows from their parent stars during the T-Tauri or post-main-sequence phases of stellar evolution. These outflows are often modelled to be isotropic, but this assumption is not realistic for fast rotators, bipolar jets and supernovae. Here we derive the general equations of motion for the time evolution of a single planet, brown dwarf, comet or asteroid perturbed by anisotropic mass loss in terms of a complete set of planetary orbital elements, the ejecta velocity, and the parent star's co-latitude and longitude. We restrict our application of these equations to 1) rapidly rotating giant stars, and 2) arbitrarily-directed jet outflows. We conclude that the isotropic mass-loss assumption can safely be used to model planetary motion during giant branch phases of stellar evolution within distances of hundreds of au. In fact, latitudinal mass loss variations anisotropically affect planetary motion only if the mass loss is asymmetric about the stellar equator. Also, we demonstrate how constant-velocity, asymmetric bipolar outflows in young systems incite orbital inclination changes. Consequently, this phenomenon readily tilts exoplanetary orbits external to a nascent disc on the order of degrees.

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arXiv2013

A simple scaling for the minimum instability time-scale of two widely spaced planets

Long-term instability in multi-planet exosystems is a crucial consideration when confirming putative candidates, analyzing exoplanet populations, constraining the age of exosystems, and identifying the sources of white dwarf pollution. Two planets which are Hill stable are separated by a wide-enough distance to ensure that they will never collide. However, Hill stable planetary systems may eventually manifest Lagrange instability when the outer planet escapes or the inner planet collides with the star. We show empirically that for two nearly coplanar Hill stable planets with eccentricities less than about 0.3, instability can manifest itself only after a time corresponding to X initial orbits of the inner planet, where log_{10}(X) is of the order of 5.2 mu^{-0.18} and mu is the planet-star mass ratio measured in (Jupiter mass/Solar mass). This relation applies to any type of equal-mass secondaries, and suggests that two low-eccentricity Hill stable terrestrial-mass or smaller-mass planets should be Lagrange stable throughout the main sequence lifetime of any white dwarf progenitor. However, Hill stable giant planets are not guaranteed to be Lagrange stable, particularly within a few tens of percent beyond the critical Hill separation. Our scaling represents a useful "rule of thumb" for planetary population syntheses or individual systems for which performing detailed long-term integrations is unfeasible.

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arXiv2013

Simulations of two-planet systems through all phases of stellar evolution: implications for the instability boundary and white dwarf pollution

Exoplanets have been observed at many stages of their host star's life, including the main sequence (MS), subgiant and red giant branch stages. Also, polluted white dwarfs (WDs) likely represent dynamically active systems at late times. Here, we perform 3-body simulations which include realistic post-MS stellar mass loss and span the entire lifetime of exosystems with two massive planets, from the endpoint of formation to several Gyr into the WD phase of the host star. We find that both MS and WD systems experience ejections and star-planet collisions (Lagrange instability) even if the planet-planet separation well-exceeds the analytical orbit-crossing (Hill instability) boundary. Consequently, MS-stable planets do not need to be closely-packed to experience instability during the WD phase. This instability may pollute the WD directly through collisions, or, more likely, indirectly through increased scattering of smaller bodies such as asteroids or comets. Our simulations show that this instability occurs predominately between tens of Myr to a few Gyrs of WD cooling.

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arXiv2013

Multi-Planet Destabilisation and Escape in Post-Main Sequence Systems

Discoveries of exoplanets orbiting evolved stars motivate critical examinations of the dynamics of $N$-body systems with mass loss. Multi-planet evolved systems are particularly complex because of the mutual interactions between the planets. Here, we study the underlying dynamical mechanisms which can incite planetary escape in two-planet post-main sequence systems. Stellar mass loss alone is unlikely to be rapid and high enough to eject planets at typically-observed separations. However, the combination of mass loss and planet-planet interactions can prompt a shift from stable to chaotic regions of phase space. Consequently, when mass loss ceases, the unstable configuration may cause escape. By assuming a constant stellar mass loss rate, we utilize maps of dynamical stability to illustrate the distribution of regular and chaotic trajectories in phase space. We show that chaos can drive the planets to undergo close encounters, leading to the ejection of one planet. Stellar mass loss can trigger the transition of a planetary system from a stable to chaotic configuration, subsequently causing escape. We find that mass loss non-adiabatically affects planet-planet interaction for the most massive progenitor stars which avoid the supernova stage. For these cases, we present specific examples of planetary escape.

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arXiv2012

Exoplanets Beyond the Solar Neighbourhood: Galactic Tidal Perturbations

The majority of Milky Way extrasolar planets likely reside within a few kpc of the Galactic centre. The Galactic tidal forces acting on planets scale inversely with radius in the Galaxy and so are much greater in the inner Galaxy than in the Solar neighbourhood. Within a range of 3.5 to 10 kpc, the vertical tide from the Galactic disc is predominant. Interior to 3.5 kpc, the effects of the Galactic bulge cannot be neglected and the in-plane tidal components are as important as the vertical ones. Here, we quantify the orbital changes induced by these tides. We find that the greatest perturbations occur when the planetary orbit is severely misaligned to the parent star's orbit. When both planes are perpendicular, the eccentricity of the planet is driven to unity, although the semimajor axis is secularly unaffected. When both planes are coincident, the effect from Galactic tides is minimized, but remains non-zero. In these cases, we provide estimates for the survival times, as well as the minimum baseline eccentricity variation for all Milky Way exoplanets as a function of Galactic parameters. Inclinations similar to the Solar System's (about 60 degrees) can easily cause eccentric Neptunes (at about 30 AU) around host stars deep within the Galactic bulge (within 50 pc) to experience eccentricity variations of several tenths, and cause the exoplanets with the widest-known separations (at about 1000 AU) to experience similar variations in the Galactic disc. These variations occur on timescales of a few Gyr, a fraction of a typical main sequence lifetime.

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arXiv2012

Planetary Orbital Equations in Externally-Perturbed Systems: Position and Velocity-Dependent Forces

The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the equations of motion of the unaveraged perturbed two-body problem in terms of planetary orbital elements by using a generalized form of Gauss' equations. We consider a varied set of position and velocity-dependent perturbations, and also derive relevant specific cases of the equations: when they are averaged over fast variables (the "adiabatic" approximation), and in the prograde and retrograde planar cases. In each instance, we delineate the properties of the equations. As brief demonstrations of potential applications, we consider the effect of Galactic tides. We measure the effect on the widest-known exoplanet orbit, Sedna-like objects, and distant scattered disk objects, particularly with regard to where the adiabatic approximation breaks down. The Mathematica code which can help derive the equations is freely available upon request.

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arXiv2012

Traditional formation scenarios fail to explain 4:3 mean motion resonances

At least two multi-planetary systems in a 4:3 mean motion resonance have been found by radial velocity surveys. These planets are gas giants and the systems are only stable when protected by a resonance. Additionally the Kepler mission has detected at least 4 strong candidate planetary systems with a period ratio close to 4:3. This paper investigates traditional dynamical scenarios for the formation of these systems. We systematically study migration scenarios with both N-body and hydro-dynamic simulations. We investigate scenarios involving the in-situ formation of two planets in resonance. We look at the results from finely tuned planet-planet scattering simulations with gas disk damping. Finally, we investigate a formation scenario involving isolation-mass embryos. Although the combined planet-planet scattering and damping scenario seems promising, none of the above scenarios is successful in forming enough systems in 4:3 resonance with planetary masses similar to the observed ones. This is a negative result but it has important implications for planet formation. Previous studies were successful in forming 2:1 and 3:2 resonances. This is generally believed to be evidence of planet migration. We highlight the main differences between those studies and our failure in forming a 4:3 resonance. We also speculate on more exotic and complicated ideas. These results will guide future investigators toward exploring the above scenarios and alternative mechanisms in a more general framework.

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arXiv2012

Disrupting Primordial Planet Signatures: The Close Encounter of Two Single-Planet Exosystems in the Galactic Disc

During their main sequence lifetimes, the majority of all Galactic Disc field stars must endure at least one stellar intruder passing within a few hundred AU. Mounting observations of planet-star separations near or beyond this distance suggest that these close encounters may fundamentally shape currently-observed orbital architectures and hence obscure primordial orbital features. We consider the commonly-occurring fast close encounters of two single-planet systems in the Galactic Disc, and investigate the resulting change in the planetary eccentricity and semimajor axis. We derive explicit 4-body analytical limits for these variations and present numerical cross-sections which can be applied to localized regions of the Galaxy. We find that each wide-orbit planet has a few percent chance of escape and an eccentricity that will typically change by at least 0.1 due to these encounters. The orbital properties established at formation of millions of tight-orbit Milky Way exoplanets are likely to be disrupted.

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arXiv2012

The Great Escape II: Exoplanet Ejection from Dying Multiple Star Systems

Extrasolar planets and belts of debris orbiting post-main-sequence single stars may become unbound as the evolving star loses mass. In multiple star systems, the presence or co-evolution of the additional stars can significantly complicate the prospects for orbital excitation and escape. Here, we investigate the dynamical consequences of multi-phasic, nonlinear mass loss and establish a criterion for a system of any stellar multiplicity to retain a planet whose orbit surrounds all of the parent stars. For single stars which become white dwarfs, this criterion can be combined with the Chandrasekhar Limit to establish the maximum allowable mass loss rate for planet retention. We then apply the criterion to circumbinary planets in evolving binary systems over the entire stellar mass phase space. Through about 10^5 stellar evolutionary track realizations, we characterize planetary ejection prospects as a function of binary separation, stellar mass and metallicity. This investigation reveals that planets residing at just a few tens of AU from a central concentration of stars are susceptible to escape in a wide variety of multiple systems. Further, planets are significantly more susceptible to ejection from multiple star systems than from single star systems for a given system mass. For system masses greater than about 2 Solar masses, multiple star systems represent the greater source of free-floating planets.

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arXiv2012

Exoplanets Bouncing Between Binary Stars

Exoplanetary systems are found not only among single stars, but also binaries of widely varying parameters. Binaries with separations of 100--1000 au are prevalent in the Solar neighborhood; at these separations planet formation around a binary member may largely proceed as if around a single star. During the early dynamical evolution of a planetary system, planet--planet scattering can eject planets from a star's grasp. In a binary, the motion of a planet ejected from one star has effectively entered a restricted three-body system consisting of itself and the two stars, and the equations of motion of the three body problem will apply as long as the ejected planet remains far from the remaining planets. Depending on its energy, escape from the binary as a whole may be impossible or delayed until the three-body approximation breaks down, and further close interactions with its planetary siblings boost its energy when it passes close to its parent star. Until then this planet may be able to transition from the space around one star to the other, and chaotically `bounce' back and forth. In this paper we directly simulate scattering planetary systems that are around one member of a circular binary, and quantify the frequency of bouncing in scattered planets. We find that a great majority (70 to 85 per cent) of ejected planets will pass at least once through the space of it's host's binary companion, and depending on the binary parameters about 45 to 75 per cent will begin bouncing. The time spent bouncing is roughly log-normally distributed with a peak at about $10^4$ years, with only a small percentage bouncing for more than a Myr. This process may perturb and possibly incite instability among existing planets around the companion star. In rare cases, the presence of multiple planets orbiting both stars may cause post-bouncing capture or planetary swapping.

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arXiv2012

The Solar System's Post-Main Sequence Escape Boundary

The Sun will eventually lose about half of its current mass nonlinearly over several phases of post-main sequence evolution. This mass loss will cause any surviving orbiting body to increase its semimajor axis and perhaps vary its eccentricity. Here, we use a range of Solar models spanning plausible evolutionary sequences and assume isotropic mass loss to assess the possibility of escape from the Solar System. We find that the critical semimajor axis in the Solar System within which an orbiting body is guaranteed to remain bound to the dying Sun due to perturbations from stellar mass loss alone is approximately 1,000 AU - 10,000 AU. The fate of objects near or beyond this critical semimajor axis, such as the Oort Cloud, outer scattered disc and specific bodies such as Sedna, will significantly depend on their locations along their orbits when the Sun turns off of the main sequence. These results are applicable to any exoplanetary system containing a single star with a mass, metallicity and age which are approximately equal to the Sun's, and suggest that few extrasolar Oort Clouds could survive post-main sequence evolution intact.

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