We present new radial velocities from Keck Observatory and both Newtonian and Keplerian solutions for the triple-planet system orbiting HD 37124. The orbital solution for this system has improved ...dramatically since the third planet was first reported in Vogt et al. with an ambiguous orbital period. The period ambiguity is resolved, and the outer two planets have an apparent period commensurability of 2:1. A dynamical analysis finds both resonant and non-resonant configurations consistent with the radial velocity data and constrains the mutual inclinations of the planets to be <~30?. We discuss HD 37124 in the context of the other 19 exoplanetary systems with apparent period commensurabilities, which we summarize in a table. We show that roughly one in three well-characterized multiplanet systems has a apparent low-order period commensurability, which is more than would naively be expected if the periods of exoplanets in known multiplanet systems were drawn randomly from the observed distribution of planetary orbital periods.
ABSTRACT
A widely held assumption is that each single white dwarf containing observable rocky debris requires the presence of at least one terrestrial or giant planet to have gravitationally ...perturbed the progenitor of the debris into the star. However, these planets could have been previously engulfed by the star or escaped the system, leaving behind asteroids, boulders, cobbles, pebbles, sand, and dust. These remaining small bodies could then persist throughout the host star’s evolution into a white dwarf at ≈2–100 au scales, and then be radiatively dragged into the white dwarf without the help of a planet. Here, we identify the parameter space and cooling ages for which this one metal-pollution mechanism is feasible by, for the first time, coupling Poynting–Robertson drag, the Yarkovsky effect, and the YORP effect solely from rapidly dimming white dwarf radiation. We find that this no-planet pollution scenario is efficient for remnant 10−5 to 10−4 m dust up to about 80 au, 10−4 to 10−3 m sand up to about 25 au, and 10−3 to 10−2 m small pebbles up to about 8 au, and perhaps 10−1 to 100 m small boulders up to tens of au. Further, young white dwarf radiation can spin-up large strengthless boulders with radii of 102–103 m to destruction, breaking them down into smaller fragments that then can be dragged towards the white dwarf. Our work hence introduces a planetless metal-pollution mechanism that may be active in some fraction of white dwarf planetary systems.
ABSTRACT
The dynamical excitation of asteroids due to mean motion resonant interactions with planets is enhanced when their parent star leaves the main sequence. However, numerical investigation of ...resonant outcomes within post-main-sequence simulations is computationally expensive, limiting the extent to which detailed resonant analyses have been performed. Here, we combine the use of a high-performance computer cluster and the general semi-analytical libration width formulation of Gallardo, Beaugé & Giuppone in order to quantify resonant stability, strength, and variation instigated by stellar evolution for a single-planet system containing asteroids on both crossing and non-crossing orbits. We find that resonant instability can be accurately bound with only main-sequence values by computing a maximum libration width as a function of asteroid longitude of pericentre. We also quantify the relative efficiency of mean motion resonances of different orders to stabilize versus destabilize asteroid orbits during both the giant branch and white dwarf phases. The 4:1, 3:1, and 2:1 resonances represent efficient polluters of white dwarfs, and even when in the orbit-crossing regime, both the 4:3 and 3:2 resonances can retain small reservoirs of asteroids in stable orbits throughout giant branch and white dwarf evolution. This investigation represents a preliminary step in characterizing how simplified extrasolar Kirkwood gap structures evolve beyond the main sequence.
Context. Planetary debris is observed in the atmospheres of over 1000 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 ∼1010 yr; these long-running simulations restrict the amount of phase space that can be investigated. Aims. 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. Methods. 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. Results. 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. Conclusions. 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.
ABSTRACT
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 unstable and stable configurations of minor planets, we find that this critical lower bound equals approximately one Luna mass (1M☾ ≈ 10-1 M♂ ≈ 10-2 M⊕ ≈ 102 MCeres). Further, we find that as this mass limit is approached from above, the typical cooling age at which white dwarf pollution occurs increases. Consequently, there is a two order-of-magnitude range of perturber masses between Earth and its moon that has remained largely unexplored in white dwarf pollution studies, despite the potential formation of thousands of such Luna-sized objects in these systems.
We study the stability of systems of three giant planets orbiting 3-8 M 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 on to 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 circularized. 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 destabilized following instability in systems of multiple giant planets, although further work incorporating low-mass planets and planetesimals is needed.
Abstract
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 four-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 per cent 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.
ABSTRACT
White dwarfs that exhibit transit signatures of planetary debris and accreted planetary material provide exceptional opportunities to probe the material composition and dynamical structure ...of planetary systems. Although previous theoretical work investigating the role of minor body disruption around white dwarfs has focused on spherical bodies, Solar system asteroids can be more accurately modelled as triaxial ellipsoids. Here, we present an analytical framework to identify the type of disruption (tidal fragmentation, total sublimation, or direct impact) experienced by triaxial asteroids approaching white dwarfs on extremely eccentric (e ∼ 1) orbits. This framework is then used to identify the outcomes for simplified Main belt analogues of 100 bodies across five different white dwarf temperatures. We also present an empirical relationship between cooling age and effective temperature for both DA and DB white dwarfs to identify the age of the white dwarfs considered here. We find that using a purely spherical shape model can underestimate the physical size and radial distance at which an asteroid is subjected to complete sublimation, and these differences increase with greater elongation of the body. Contrastingly, fragmentation always occurs in the largest semi-axis of a body and so can be modelled by a sphere of that radius. Both fragmentation and sublimation are greatly affected by the body’s material composition, and hence by the composition of their progenitor asteroid belts. The white dwarf temperature, and hence cooling age, can affect the expected debris distribution: higher temperatures sublimate large elongated asteroids, and cooler temperatures accommodate more direct impacts.
Mounting discoveries of debris discs orbiting newly formed stars and white dwarfs (WDs) showcase the importance of modelling 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 periodic orbits can circumvent the guesswork. Here, we begin a comprehensive analysis directly linking periodic orbits with N-body integration outcomes with an extensive exploration of the planar circular restricted three-body problem (CRTBP) with an outer planet and inner asteroid near or inside of the 2:1 mean motion resonance. We run nearly 1000 focused simulations for the entire age of the Universe (14 Gyr) with initial conditions mapped to the phase space locations surrounding the unstable and stable periodic orbits for that commensurability. In none of our simulations did the planar CRTBP architecture yield a long-time-scale ( greater than or equal to 0.25 per cent of the age of the Universe) asteroid-star collision. The pericentre distance of asteroids which survived beyond this time-scale ( approximately 35 Myr) varied by at most about 60 per cent. These results help affirm that collisions occur too quickly to explain WD pollution in the planar CRTBP 2:1 regime, and highlight the need for further periodic orbit studies with the eccentric and inclined TBP architectures and other significant orbital period commensurabilities.
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