The TROY project: Searching for co-orbital bodies to known planets. I. Project goals and first results from archival radial velocity

The TROY project: Searching for co-orbital bodies to known planets. I. Project goals and first results from archival radial velocity

Authors:

Lillo-Box et al

Abstract:

The detection of Earth-like planets, exocomets or Kuiper belts show that the different components found in the solar system should also be present in other planetary systems. Trojans are one of these components and can be considered fossils of the first stages in the life of planetary systems. Their detection in extrasolar systems would open a new scientific window to investigate formation and migration processes. In this context, the main goal of the TROY project is to detect exotrojans for the first time and to measure their occurrence rate (eta-Trojan). In this first paper, we describe the goals and methodology of the project. Additionally, we used archival radial velocity data of 46 planetary systems to place upper limits on the mass of possible trojans and investigate the presence of co-orbital planets down to several tens of Earth masses. We used archival radial velocity data of 46 close-in (P less than 5 days) transiting planets (without detected companions) with information from high-precision radial velocity instruments. We took advantage of the time of mid-transit and secondary eclipses (when available) to constrain the possible presence of additional objects co-orbiting the star along with the planet. This, together with a good phase coverage, breaks the degeneracy between a trojan planet signature and signals coming from additional planets or underestimated eccentricity. We identify nine systems for which the archival data provide 1-sigma evidence for a mass imbalance between L4 and L5. Two of these systems provide 2-sigma detection, but no significant detection is found among our sample. We also report upper limits to the masses at L4/L5 in all studied systems and discuss the results in the context of previous findings.

Transit Detection of a "Starshade" at the Inner Lagrange Point of an Exoplanet

Transit Detection of a "Starshade" at the Inner Lagrange Point of an Exoplanet 

Author:

Gaidos

Abstract: 

All water-covered rocky planets in the inner habitable zones of solar-type stars will inevitably experience a catastrophic runaway climate due to increasing stellar luminosity and limits to outgoing infrared radiation from wet greenhouse atmospheres. Reflectors or scatterers placed near Earth's inner Lagrange point (L1) have been proposed as a 'geo-engineering" solution to anthropogenic climate change and an advanced version of this could modulate incident irradiation over many Gyr or "rescue" a planet from the interior of the habitable zone. The distance of the starshade from the planet that minimizes its mass is 1.6 times the Earth-L1 distance. Such a starshade would have to be similar in size to the planet and the mutual occultations during planetary transits could produce a characteristic maximum at mid-transit in the light-curve. Because of a fortuitous ratio of densities, Earth-size planets around G dwarf stars present the best opportunity to detect such an artifact. The signal would be persistent and is potentially detectable by a future space photometry mission to characterize transiting planets. The signal could be distinguished from natural phenomenon, i.e. starspots or cometary dust clouds, by its shape, persistence, and transmission spectrum.

Did a Large Ringed Exoplanet With Trojans dim Tabby's Star?

KIC 8462852: Will the Trojans return in 2021?

Authors:

Ballesteros et al

Abstract:
KIC 8462852 stood out among more than 100,000 stars in the Kepler catalogue because of the strange features of its light curve: a wide and asymmetric dimming taking up to 15 per cent of the total light, together with a period of multiple, narrow dimmings happening approximately 700 days later. Several models have been proposed to account for this abnormal behaviour, most of which require either unlikely causes or a finely-tuned timing. We aim at offering a relatively natural solution, invoking only phenomena that have been previously observed, although perhaps in larger or more massive versions. We model the system using a large, ringed body whose transit produces the first dimming and a swarm of Trojan objects sharing its orbit that causes the second period of multiple dimmings. The resulting orbital period is T≈12 years, with a semi-major axis a≈6 au. Our model allows us to make two straightforward predictions: we expect the passage of a new swarm of Trojans in front of the star starting during the early months of 2021, and a new transit of the main object during the first half of 2023.

Binary Systems HD 41004 and HD 196885 Have Trojan Points Capable of Supporting a Habitable Exoplanet

On the possibility of habitable Trojan planets in binary star systems

Authors:

Schwarz et al

Abstract:

Approximately 60 percent of all stars in the solar neighbourhood (up to 80 percent in our Milky Way) are members of binary or multiple star systems. This fact led to the speculations that many more planets may exist in binary systems than are currently known. To estimate the habitability of exoplanetary systems, we have to define the so-called habitable zone (HZ). The HZ is defined as a region around a star where a planet would receive enough radiation to maintain liquid water on its surface and to be able to build a stable atmosphere. We search for new dynamical configurations - where planets may stay in stable orbits - to increase the probability to find a planet like the Earth. Therefore we investigated five candidates and found that two systems (HD 41004 and HD 196885) which have small stable regions.

Io Sized Trojans Around hot Jupiters in WASP-12 and HD 189733 Systems

On the ultraviolet anomalies of the WASP-12 and HD 189733 systems: Trojan satellites as a plasma source

Authors:

Kislyakova et al

Abstract:

We suggest an additional possible plasma source to explain part of the phenomena observed for the transiting hot Jupiters WASP-12b and HD 189733b in their ultraviolet (UV) light curves. In the proposed scenario, material outgasses from the molten surface of Trojan satellites on tadpole orbits near the Lagrange points L4 and L5. We show that the temperature at the orbital location of WASP-12b is high enough to melt the surface of rocky bodies and to form shallow lava oceans on them. In case of WASP-12b, this leads to the release of elements such as Mg and Ca, which are expected to surround the system. The predicted Mg and Ca outgassing rates from two Io-sized WASP-12b Trojans are ≈2.2×1027 s−1 and ≈2.2×1026 s−1, respectively. Trojan outgassing can lead to the apparent lack of emission in Mg{\sc ii}\,h\&k and Ca{\sc ii}\,H\&K line cores of WASP-12. For HD 189733b, the mechanism is only marginally possible due to the lower temperature. This may be one of the reasons that couldn't explain the early ingress of HD 189733b observed in the far-UV (FUV) C{\sc ii} doublet due to absence of carbon within elements outgassed by molten lava. We investigate the long-term stability region of WASP-12b and HD 189733b in case of planar and inclined motion of these satellites and show that unlike the classical exomoons orbiting the planet, Io-sized Trojans can be stable for the whole systems life time.

The effect of orbital damping during planet migration on the Inclination and Eccentricity Distributions of Neptune Trojans

The effect of orbital damping during planet migration on the Inclination and Eccentricity Distributions of Neptune Trojans

Authors:

Chen et al

Abstract:

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 becoming NTs during planet migration. We find that most primordial NTs were unstable and lost if eccentricity and inclination damping took place during planetary migration. With damping, secular resonances with Neptune can increase a low eccentricity and inclination population of Trans-Neptunian objects increasing the probability that they are captured into 1:1 resonance with Neptune, becoming high inclination NTs. We suggest that the resonant trapping scenario is a promising and more effective mechanism explaining the origin of NTs that is particularly effective if Uranus and Neptune experienced eccentricity and inclination damping during planetary migration.

Updated: Analysing hot Jupiter Kepler-91b's System

Analysis of the exoplanet containing system Kepler 91

Authors:

Budding et al

Abstract:

We have applied the graphical user interfaced close binary system analysis program WinFitter to an intensive study of Kepler 91 using all the available photometry from the NASA Exoplanet Archive (NEA) at the Caltech website: this http URL . Our fitting function for the tidal distortion derives from the relevant Radau equation and includes terms up to the fifth power of the fractional radius. This results in a systematic improvement in the mass ratio estimation over that of Lillo Box et al (2014a) and our derived value for the mass ratio is in close agreement with that inferred from recent high-resolution spectroscopic data. It is clear that the data analysis in terms of simply an eclipsing binary system is compromised by the presence of significant other causes of light variation, in particular non-radial pulsations. We apply a low-frequency filtering procedure to separate out some of this additional light variation. Whilst the derived eccentricity appears then reduced, an eccentric effect remains in the light curve. We consider how this may be maintained in spite of likely frictional effects operating over a long time. There are also indications of the possible effects of Trojan or other period-resonant mass concentrations. Suggestions of a possible secular period variation are briefly discussed.

Something Large, Long Lived and Interesting Near the Trojan L5 Point in Binary SDSS J1021+1744

A large, long-lived structure near the trojan L5 point in the post common-envelope binary SDSS J1021+1744

Authors:

Irawati et al

Abstract:

SDSS J1021+1744 is a detached, eclipsing white dwarf / M dwarf binary discovered in the Sloan Digital Sky Survey. Outside the primary eclipse, the light curves of such systems are usually smooth and characterised by low-level variations caused by tidal distortion and heating of the M star component. Early data on SDSS J1021+1744 obtained in June 2012 was unusual in showing a dip in flux of uncertain origin shortly after the white dwarf's eclipse. Here we present high-time resolution, multi-wavelength observations of 35 more eclipses over 1.3 years, showing that the dip has a lifetime extending over many orbits. Moreover the "dip" is in fact a series of dips that vary in depth, number and position, although they are always placed in the phase interval 1.06 to 1.26 after the white dwarf's eclipse, near the L5 point in this system. Since SDSS J1021+1744 is a detached binary, it follows that the dips are caused by the transit of the white dwarf by material around the Lagrangian L5 point. A possible interpretation is that they are the signatures of prominences, a phenomenon already known from H-alpha observations of rapidly rotating single stars as well as binaries. What makes SDSS J1021+1744 peculiar is that the material is dense enough to block continuum light. The dips appear to have finally faded out around 2015 May after the first detection by Parsons et al. in 2012, suggesting a lifetime of years.

Kepler-91b *MAY* Have a Trojan Companion

Characterization of Kepler-91b and the Investigation of a Potential Trojan Companion Using EXONEST

Authors:

Placek et al

Abstract:

Presented here is an independent re-analysis of the Kepler light curve of Kepler-91 (KIC 8219268). Using the EXONEST software package, which provides both Bayesian parameter estimation and Bayesian model testing, we were able to re-confirm the planetary nature of Kepler-91b. In addition to the primary and secondary eclipses of Kepler-91b, a third dimming event appears to occur approximately 60o away (in phase) from the secondary eclipse, leading to the hypothesis that a Trojan planet may be located at the L4 or L5 Lagrange points. Here, we present a comprehensive investigation of four possibilities to explain the observed dimming event using all available photometric data from the Kepler Space Telescope, recently obtained radial velocity measurements, and N-body simulations. We find that the photometric model describing Kepler-91b and a Trojan planet is highly favored over the model involving Kepler-91b alone. However, it predicts an unphysically high temperature for the Trojan companion, leading to the conclusion that the extra dimming event is likely a false-postive.

How Many Kepler Exoplanets are Expected to Have Trojan Asteroids?

A statistical search for a population of Exo-Trojans in the Kepler dataset

Authors:

Hippke et al

Abstract:

Trojans are small bodies in planetary Lagrangian points. In our solar system, Jupiter has the largest number of such companions. Their existence is assumed for exoplanetary systems as well, but none has been found so far. We present an analysis by super-stacking ∼4×104 Kepler planets with a total of ∼9×105 transits, searching for an average trojan transit dip. Our result gives an upper limit to the average Trojan transiting area (per planet) corresponding to one body of radius less than 460km at 2σ confidence. We find a significant Trojan-like signal in a sub-sample for planets with more (or larger) Trojans for periods greater than 60 days. Our tentative results can and should be checked with improved data from future missions like PLATO2.0, and can guide planetary formation theories.

How to Detect Trojan Configured Exoplanets in Binary Star Systems

Eclipse timing variations to detect possible Trojan planets in binary systems

Authors:

Schwarz et al

Abstract:

This paper is devoted to study the circumstances favourable to detect Trojan planets in close binary star systems by the help of eclipse timing variations (ETVs). To determine the probability of the detection of such variations with ground-based telescopes and space telescopes (like former missions CoRoT and Kepler and future space missions like PLATO, TESS and CHEOPS), we investigated the dynamics of binary star systems with a planet in tadpole motion. We did numerical simulations by using the full three-body problem as a dynamical model. The stability and the ETVs are investigated by computing stability/ETV maps for different masses of the secondary star and the Trojan planet. In addition, we changed the eccentricity of the possible Trojan planet. By the help of the libration amplitude σ, we could show whether or not all stable objects are moving in tadpole orbits. We can conclude that many amplitudes of ETVs are large enough to detect Earth-like Trojan planets in binary star systems. As an application, we prepared a list of possible candidates.

Inflated Hot Jupiter Kepler-91b may Have Trojan Asteroids

Analysis of the exoplanet containing system Kepler 91

Authors:

Budding et al

Abstract:

We have applied the graphical user interfaced close binary system analysis program WinFitter to an intensive study of Kepler 91 using all the available photometry from the NASA Exoplanet Archive (NEA) at the Caltech website. fitting function for the tidal distortion derives from the relevant Radau equation and includes terms up to the fifth power of the fractional radius. This results in a systematic improvement in the mass ratio estimation over that of Lillo Box et al (2014a) and our derived value for the mass ratio is in close agreement with that inferred from recent high-resolution spectroscopic data. It is clear that the data analysis in terms of simply an eclipsing binary system is compromised by the presence of significant other causes of light variation, in particular non-radial pulsations. We apply a low-frequency filtering procedure to separate out some of this additional light variation. Whilst the derived eccentricity appears then reduced, an eccentric effect remains in the light curve. We consider how this may be maintained in spite of likely frictional effects operating over a long time. There are also indications of the possible effects of Trojan or other period-resonant mass concentrations. Suggestions of a possible secular period variation are briefly discussed.

The Implications of Neptune's Trojan Orbit Distribution for Exoplanet Migration

The Intrinsic Neptune Trojan Orbit Distribution: Implications for the Primordial Disk and Planet Migration

Author:

Parker

Abstract:

The present-day orbit distribution of the Neptune Trojans is a powerful probe of the dynamical environment of the outer solar system during the late stages of planet migration. In this work, I conservatively debias the inclination, eccentricity, and libration amplitude distributions of the Neptune Trojans by reducing a priori unknown discovery and follow-up survey properties to nuisance parameters and using a likelihood-free Bayesian rejection sampler for parameter estimation. Using this survey-agnostic approach, I confirm that the Neptune Trojans are a dynamically excited population: at greater than 95% confidence, the Neptune Trojans' inclination width must be σi greater than 11∘. For comparison and motivation purposes, I also model the Jupiter Trojan orbit distributions in the same basis and produce new estimates of their parameters (Jupiter Trojan σi=14.4∘±0.5∘, σL11=11.8∘±0.5∘, and σe=0.061±0.002). The debiased inclination, libration amplitude, and eccentricity distributions of the Neptune Trojans are nominally very similar to those of the Jupiter Trojans. I use these new constraints to inform a suite of simulations of Neptune Trojan capture by an eccentric, rapidly-migrating Neptune from an initially dynamically-hot disk. These simulations demonstrate that if migration and eccentricity-damping timescales were short (τa≲10 Myr, τe≲1 Myr), the disk that Neptune migrated into must have been pre-heated (prior to Neptune's appearance) to a width comparable to the Neptune Trojans' extant width to produce a captured population with an inclination distribution width consistent with that of the observed population.

Examining the Formation of Exoplanets in Trojan Points

Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systems

Authors:

Páez et al

Abstract:

We investigate the dynamics of small trojan exoplanets in domains of secondary resonances within the tadpole domain of motion. We consider the limit of a massless trojan companion of a giant planet. Without other planets, this is a case of the elliptic restricted three body problem (ERTBP). The presence of more planets (the restricted multi-planet problem, RMPP) induces new direct and indirect secular effects on the trojan's dynamics. In the theoretical part of this paper, we develop a Hamiltonian formalism in action-angle variables, which allows to treat in a unified way resonant dynamics and secular effects on the trojan body in both the ERTBP or the RMPP. Our formalism leads to a decomposition of the Hamiltonian in two parts, H=Hb+Hsec. Hb, called the basic model, describes resonant dynamics in the short-period (epicyclic) and synodic (libration) degrees of freedom. Hsec contains only terms depending on slow (secular) angles. Hb is formally identical in the ERTBP and the RMPP, apart from a re-definition of angular variables. An important physical consequence is that the slow chaotic diffusion proceeds in both the ERTBP and the RMPP by a qualitatively similar dynamical mechanism better approximated by the paradigm of `modulational diffusion'. In the numerical part, we focus on the ERTBP for making a numerical demonstration of the chaotic diffusion process along resonances. Using color stability maps, we provide a survey of the resonant web for characteristic mass parameters of the primary, in which the secondary resonances from 1:5 to 1:12 (ratio of the short over the synodic period) and their resonant multiplets appear. We give numerical examples of diffusion of weakly chaotic orbits in the resonant web. We make a statistics of the escaping times in the resonant domain, and find power-law tails of the distribution of escaping times for slowly diffusing chaotic orbits.

Modeling the Trojan Points in Exoplanetary Systems

Modeling resonant trojan motion in planetary systems

Authors:

Efthymiopoulos et al

Abstract:

We consider the dynamics of a small trojan companion of a hypothetical giant exoplanet under the secular perturbations of additional planets. By a suitable choice of action-angle variables, the problem is amenable to the study of the slow modulation, induced by secular perturbations, to the dynamics of an otherwise called `basic' Hamiltonian model of two degrees of freedom (planar case). We present this Hamiltonian decomposition, which implies that the slow chaotic diffusion at resonances is best described by the paradigm of modulational diffusion.