The 1/1 resonance in extrasolar systems

Hadjidemetriou, John D.; Voyatzis, George

doi:10.1007/s10569-011-9341-7

Cited by 47 publications

(14 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the symbol • is the dot product. As it has been shown and already used in (Hadjidemetriou 1992;Hadjidemetriou 1999;Hadjidemetriou & Voyatzis 2000) or (Ferraz-Mello 1997) the generating function defines a mapping of the form:…”

Section: Define the Vector Of Modifiedmentioning

confidence: 99%

The orbit of 2010 TK7: possible regions of stability for other Earth Trojan asteroids

Dvořák

Lhotka

Zhou

2012

A&A

View full text Add to dashboard Cite

The first Earth Trojan has been observed and found to be on an interesting orbit close to the Lagrange point L4. In the present study, we therefore perform a detailed investigation of the stability of its orbit and moreover extend the study to give an idea of the probability of finding additional Earth Trojans. Our results are derived using three different approaches. In the first, we derive an analytical mapping in the spatial elliptic restricted three-body problem to find the phase space structure of the dynamical problem. We then explore the stability of the asteroid in the context of the phase space geometry, including the indirect influence of the additional planets of our Solar system. In the second approach, we use precise numerical methods to integrate the orbit forward and backward in time in different dynamical models. On the basis of a set of 400 clone orbits, we derive the probability of capture and escape of the Earth Trojan asteroid 2010 TK7. To this end, in the third approach we perform an extensive numerical investigation of the stability region of the Earth's Lagrangian points. We present a detailed parameter study of possible stable tadpole and horseshoe orbits of additional Earth Trojans, i.e. with respect to the semi-major axes and inclinations of thousands of fictitious Trojans. All three approaches lead to the conclusion that the Earth Trojan asteroid 2010 TK7 finds itself in an unstable region on the edge of a stable zone; additional Earth Trojan asteroids may be found in this regime of stability.

show abstract

Section: Define the Vector Of Modifiedmentioning

confidence: 99%

The orbit of 2010 TK7: possible regions of stability for other Earth Trojan asteroids

Dvořák

Lhotka

Zhou

2012

A&A

View full text Add to dashboard Cite

show abstract

“…An empirical relation exists for eccentricities below 0.6 (e.g. Giuppone et al 2010;Hadjidemetriou & Voyatzis 2011):…”

Section: Introductionmentioning

confidence: 99%

Origin and detectability of co-orbital planets from radial velocity data

Giuppone

Benítez-Llambay

Beaugé

2012

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

We analyse the possibilities of detection of hypothetical exoplanets in co‐orbital motion from synthetic radial velocity (RV) signals, taking into account different types of stable planar configurations, orbital eccentricities and mass ratios. For each nominal solution corresponding to small‐amplitude oscillations around the periodic solution, we generate a series of synthetic RV curves mimicking the stellar motion around the barycentre of the system. We then fit the data sets obtained assuming three possible different orbital architectures: (a) two planets in co‐orbital motion, (b) two planets in a 2/1 mean‐motion resonance (MMR) and (c) a single planet. We compare the resulting residuals and the estimated orbital parameters. For synthetic data sets covering only a few orbital periods, we find that the discrete RV signal generated by a co‐orbital configuration could be easily confused with other configurations/systems, and in many cases the best orbital fit corresponds to either a single planet or two bodies in a 2/1 resonance. However, most of the incorrect identifications are associated with dynamically unstable solutions. We also compare the orbital parameters obtained with two different fitting strategies: a simultaneous fit of two planets and a nested multi‐Keplerian model. We find that, even for data sets covering over 10 orbital periods, the nested models can yield incorrect orbital configurations (sometimes close to fictitious MMRs) that are nevertheless dynamically stable and with orbital eccentricities lower than the correct nominal solutions. Finally, we discuss plausible mechanisms for the formation of co‐orbital configurations, by the interaction between two giant planets and an inner cavity in the gas disc. For equal‐mass planets, both Lagrangian and anti‐Lagrangian configurations can be obtained from same initial condition depending on final time of integration.

show abstract

“…An application of LCN maps of dynamical stability to planetary dynamics is given inHadjidemetriou and Voyatzis (2011a).…”

mentioning

confidence: 99%

Multiplanet destabilization and escape in post-main-sequence systems

Voyatzis¹,

Hadjidemetriou²,

Veras³

et al. 2013

Monthly Notices of the Royal Astronomical Society

Self Cite

View full text Add to dashboard Cite

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 planetplanet 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.

show abstract

The 1/1 resonance in extrasolar systems

Cited by 47 publications

References 29 publications

The orbit of 2010 TK7: possible regions of stability for other Earth Trojan asteroids

The orbit of 2010 TK7: possible regions of stability for other Earth Trojan asteroids

Origin and detectability of co-orbital planets from radial velocity data

Multiplanet destabilization and escape in post-main-sequence systems

Contact Info

Product

Resources

About