Predictions for a planet just inside Fomalhaut's eccentric ring
01 Oct 2006-Monthly Notices of the Royal Astronomical Society: Letters (Blackwell Publishing Ltd)-Vol. 372, Iss: 1
TL;DR: In this paper, the eccentricity and sharpness of the edge of Fomalhaut's disk are due to a planet just interior to the ring edge, which is likely to be located at the boundary of a chaotic zone in the corotation region of the planet.
Abstract: We propose that the eccentricity and sharpness of the edge of Fomalhaut’s disk are due to a planet just interior to the ring edge. The collision timescale consistent with the disk opacity is long enough that spiral density waves cannot be driven near the planet. The ring edge is likely to be located at the boundary of a chaotic zone in the corotation region of the planet. We find that this zone can open a gap in a particle disk as long as the collision timescale exceeds the removal or ejection timescale in the zone. We use the slope measured from the ring edge surface brightness profile to place an upper limit on the planet mass. The removal timescale in the chaotic zone is used to estimate a lower limit. The ring edge has eccentricity caused by secular perturbations from the planet. These arguments imply that the planet has a mass between that of Neptune and that of Saturn, a semi-major axis of approximately 119 AU and longitude of periastron and eccentricity, 0.1, the same as that of the ring edge.
Citations
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TL;DR: The applicability of the Bulirsh-Stoer algorithm for solving the planar restricted three-body problem is investigated in this article , where variations in the value of the Jacobi integral are considered as the main parameter.
13 Oct 2015
TL;DR: Fomalhaut b was long thought to shape the eccentric debris belt in the Fomalhauts system, but its orbit was found to be too eccentric for it to be the dominant belt-shaping perturber as discussed by the authors.
Abstract: Fomalhaut b was long thought to shape the eccentric debris belt in the Fomalhaut system, but its orbit was found to be too eccentric for it to be the dominant belt-shaping perturber. This indicates that Fomalhaut b is Earth-sized at most and that the belt-shaping perturber, hereafter named Fomalhaut c, remains to be discovered. In addition, since its orbit more or less crosses that of Fomalhaut b, it also indicates that the current configuration of the system is transient and was reached recently. In this talk, we show that this current configuration can be explained if Fomalhaut c is Saturn- to Neptune-sized, and Fomalhaut b originates from a mean-motion resonance with Fomalhaut c.
TL;DR: In this paper, the authors studied the role played by mean-motion resonances with Fom c, which could have brought Fom b sufficiently close to FOM c for it to be scattered on its current orbit, but also delay this scattering event.
Abstract: 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 with the putative Fom c.
Our goal is to give insights on the probability for Fom b to have been set on its highly eccentric orbit by a close-encounter with the putative Fom c. We aim to study in particular the part played by mean-motion resonances with Fom c, which could have brought Fom b sufficiently close to Fom c for it to be scattered on its current orbit, but also delay this scattering event.
Using N-body simulations, we found that the generation of orbits similar to that of Fom b, either in term of dimensions or orientation, is a robust process involving a scattering event and a further secular evolution of inner material with an eccentric massive body such as the putative Fom c. We found in particular that mean-motion resonances can delay scattering events, and thus the production of Fom b-like orbits, on timescales comparable to the age of the system, thus explaining the witnessing of an unstable configuration.
We conclude that Fom b probably originated from an inner resonance with Fom c, which is at least Neptune-Saturn size, and was set on its current orbit by a scattering event with Fom c. Since Fom b could not have formed from material in resonance, our scenario also hints at former migration processes in this planetary system.
Cites background or methods or result from "Predictions for a planet just insid..."
...These constraints are fully compatible with the shaping of the outer belt (Quillen 2006)....
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...This eccentric shape hinted at the presence of a massive body orbiting inside the belt on an eccentric orbit, dynamically shaping the belt (Quillen 2006; Deller & Maddison 2005)....
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...…Chiang et al. (2009) found an upper-mass limit of 3 MJup, a lower semi-major axis limit of ∼ 101.5 AU, and an orbital eccentricity of ∼ 0.11−0.13, while Quillen (2006) found that the belt-shaping planet should rather be Neptune or Saturn-mass, with a semi-major axis of ∼ 120 AU and an orbital…...
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...We followed the approach of Quillen (2006); Chiang et al. (2009) and Duncan et al. (1989), and considered that the belt inner edge, located at 133 AU, was created by the chaotic zone around Fom c, that is, the region where material is on a highly unstable orbit....
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...Finally, a 0.25 − 0.5 MJup Fom c is completely in accordance with the shaping the outer belt into the observed eccentric ring, as shown by Quillen (2006)....
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TL;DR: In this article, a search for low mass companions within 10 AU of the star Fomalhaut, using narrow band observations at 4.05 microns obtained with the Apodizing Phase Plate (APP) coronagraph on the VLT/NaCo.
Abstract: We report on a search for low mass companions within 10 AU of the star Fomalhaut, using narrow band observations at 4.05 microns obtained with the Apodizing Phase Plate (APP) coronagraph on the VLT/NaCo. Our observations place a model dependent upper mass limit of 12-20 Jupiter masses from 4 to 10 AU, covering the semi-major axis search space between interferometric imaging measurements and other direct imaging non-detections. These observations rule out models where the large semi-major axis for the putative candidate companion Fomalhaut b is explained by dynamical scattering from a more massive companion in the inner stellar system, where such giant planets are thought to form.
01 May 2004
TL;DR: In this article, a simple and general description of the dynamics of a narrow-eccentric ring is presented, which can be seen as originating from a standing wave superposed on an axisymmetric background.
Abstract: Abstract A simple and general description of the dynamics of a narrow-eccentric ring is presented. We view an eccentric ring which precesses uniformly at a slow rate as exhibiting a global m = 1 mode, which can be seen as originating from a standing wave superposed on an axisymmetric background. We adopt a continuum description using the language of fluid dynamics which gives equivalent results for the secular dynamics of thin rings as the well-known description in terms of a set of discrete elliptical streamlines formulated by Goldreich and Tremaine (1979, Astron. J. 84, 1638–1641). We use this to discuss the nonlinear mode interactions that appear in the ring through the excitation of higher m modes because of the coupling of the m = 1 mode with an external satellite potential, showing that they that can lead to the excitation of the m = 1 mode through a feedback process. In addition to the external perturbations by neighboring satellites, our model includes effects due to inelastic inter-particle collisions. Two main conditions for the ring to be able to maintain a steady m = 1 normal mode are obtained. One can be expressed as an integral condition for the normal mode pattern to precess uniformly, which requires the correct balance between the differential precession induced by the oblateness of the central planet, self-gravity and collisional effects is the continuum form of that obtained from the N streamline model of Goldreich and Tremaine (1979, Astron. J. 84, 1638–1641). The other condition, not before examined in detail, is for the steady maintenance of the nonzero radial action that the ring contains because of its finite normal mode. This requires a balance between injection due to eccentric resonances arising from external satellites and additional collisional damping associated with the presence of the m = 1 mode. We estimate that such a balance can occur in the e-ring of Uranus, given its currently observed physical and orbital parameters.
References
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Book•
01 Jan 1999TL;DR: In this paper, the two-body problem and the restricted three body problem are considered. And the disturbing function is extended to include the spin-orbit coupling and the resonance perturbations.
Abstract: Preface 1 Structure of the solar system 2 The two-body problem 3 The restricted three-body problem 4 Tides, rotation and shape 5 Spin-orbit coupling 6 The disturbing function 7 Secular perturbations 8 Resonant perturbations 9 Chaos and long-term evolution 10 Planetary rings Appendix A Solar system data Appendix B Expansion of the disturbing function Index
2,383 citations
01 Jan 1999
TL;DR: In this paper, the two-body problem and the restricted three body problem are considered. But the disturbing function is defined as a special case of the two body problem and is not considered in this paper.
Abstract: Preface 1. Structure of the solar system 2. The two-body problem 3. The restricted three-body problem 4. Tides, rotation and shape 5. Spin-orbit coupling 6. The disturbing function 7. Secular perturbations 8. Resonant perturbations 9. Chaos and long-term evolution 10. Planetary rings Appendix A. Solar system data Appendix B. Expansion of the disturbing function Index.
2,132 citations
"Predictions for a planet just insid..." refers background in this paper
...2 T H E P E R I C E N T R E G L OW M O D E L A N D A N E C C E N T R I C E D G E I N F O M A L H AU T ’ S D I S C We follow the theory for secular perturbations induced by a planet (e.g. Murray & Dermott 1999; Wyatt et al. 1999)....
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...Secular perturbations in the plane can be described in terms of the complex eccentricity variable, z = e exp(i ), where e is the object’s eccentricity and is its longitude of periastron (e.g. Murray & Dermott 1999; Wyatt et al. 1999)....
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...The functions, b js (α), are Laplace coefficients (see Murray & Dermott 1999 for definitions and numerical expressions)....
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...The time variation of z is ż = zforced + zproper(t) (1) where zforced = b23/2(α) b13/2(α) ep exp(i p) (2) (Murray & Dermott 1999; Wyatt et al. 1999)....
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TL;DR: In this article, the authors calculate the rate at which angular momentum and energy are transferred between a disk and a satellite which orbit the same central mass, and show that substantial changes in both the structure of the disk and the orbit of Jupiter must have taken place on a time scale of a few thousand years.
Abstract: We calculate the rate at which angular momentum and energy are transferred between a disk and a satellite which orbit the same central mass. A satellite which moves on a circular orbit exerts a torque on the disk only in the immediate vicinity of its Lindblad resonances. The direction of angular momentum transport is outward, from disk material inside the satellite's orbit to the
satellite and from the satellite to disk material outside its orbit. A satellite with an eccentric orbit exerts a torque on the disk at corotation resonances as well as at Lindblad resonances. The angular momentum and energy transfer at Lindblad resonances tends to increase the satellite's orbit eccentricity whereas the transfer at corotation resonances tends to decrease it. In a Keplerian disk, to lowest order in eccentricity and in the absence of nonlinear effects, the corotation resonances dominate by a slight margin and the eccentricity damps. However, if the strongest corotation resonances saturate due to particle trapping, then the eccentricity grows. We present an illustrative application of our results to the interaction between Jupiter and the protoplanetary disk. The angular momentum transfer is shown to be so rapid that substantial
changes in both the structure of the disk and the orbit of Jupiter must have taken place on a time scale of a few thousand years.
1,601 citations
"Predictions for a planet just insid..." refers background or methods in this paper
...(4) We have recovered the scaling with planet mass predicted by previous works (Goldreich & Tremaine 1980; Franklin et al. 1980; Lissauer & Espresate 1998) but have also included a dependence on distance from the planet....
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...Franklin et al. (1980), Goldreich & Tremaine (1980) and Lissauer & Espresate (1998) showed that spiral density waves were efficiently driven at a Lindblad resonance by a satellite when the collision time-scale was above a critical one, t crit, where t crit ∝ μ−2/3, and μ ≡ m p/M ∗ is the ratio of…...
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TL;DR: In this article, the resonance overlap criterion for the onset of stochastic behavior was applied to the planar circular-restricted three-body problem with small mass ratio (mu), and its predictions for mu = 0.001, 0.0001, and 0.00001 were compared to the transitions observed in the numerically determined Kolmogorov-Sinai entropy and found to be in remarkably good agreement.
Abstract: The resonance overlap criterion for the onset of stochastic behavior is applied to the planar circular-restricted three-body problem with small mass ratio (mu). Its predictions for mu = 0.001, 0.0001, and 0.00001 are compared to the transitions observed in the numerically determined Kolmogorov-Sinai entropy and found to be in remarkably good agreement. In addition, an approximate scaling law for the onset of stochastic behavior is derived.
488 citations
"Predictions for a planet just insid..." refers background in this paper
...The width of this zone has been measured numerically and predicted theoretically for a planet in a circular orbit by predicting the semi-major axis at which the first-order mean motion resonances overlap (Wisdom 1980; Duncan, Quinn & Tremaine 1989; Murray & Holman 1997; Mudryk & Wu 2006)....
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TL;DR: In this paper, the presence of the central cavity, approximately the size of Neptune's orbit, was detected in the emission from Fomalhaut, beta Pictoris and Vega, which may be the signature of Earth-like planets.
Abstract: Indirect detections of massive — presumably Jupiter-like — planets orbiting nearby Sun-like stars have recently been reported1,2. Rocky, Earth-like planets are much more difficult to detect, but clues to their possible existence can nevertheless be obtained from observations of the circumstellar debris disks of dust from which they form. The presence of such disks has been inferred3 from excess far-infrared emission but, with the exception of beta Pictoris4, it has proved difficult to image these structures directly as starlight dominates the faint light scattered by the dust5. A more promising approach is to attempt to image the thermal emission from the dust grains at submillimetre wavelengths6,7. Here we present images of such emission around Fomalhaut, beta Pictoris and Vega. For each star, dust emission is detected from regions comparable in size to the Sun's Kuiper belt of comets. The total dust mass surrounding each star is only a few lunar masses, so any Earth-like planets present must already have formed. The presence of the central cavity, approximately the size of Neptune's orbit, that we detect in the emission from Fomalhaut may indeed be the signature of such planets.
459 citations
"Predictions for a planet just insid..." refers background in this paper
...1 I N T RO D U C T I O N The nearby star Fomalhaut hosts a ring of circumstellar material (Aumann 1985; Gillett 1985) residing between 120 and 160 au from the star (Holland et al. 1998; Dent et al. 2000; Holland et al. 2003)....
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