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.
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TL;DR: In this article, the authors studied the influence of mean-motion resonance with Fomalhaut's companion on the formation of the debris disk, and concluded that Fomhaut probably originated from an inner resonance with a Neptune-Saturn mass, and was set on its current orbit by a scattering event with Fom c.
Abstract: Context. The eccentric shape of the debris disk observed around the star 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 ~ 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.Aims. 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.Methods. We assumed that Fom c is much more massive than Fom b, that is, Fom b behaves as a massless test particle compared to Fom c. This allowed us to use N -body numerical simulations and to study the influence of a fixed orbit Fom c on a population of massless test particles, that is, to study the generation of Fom b-like orbits by direct scattering events or via mean-motion resonance processes. We assumed that Fom b originated from an orbit inner to that of the putative Fom c.Results. We found that the generation of orbits similar to that of Fom b, either in terms 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.Conclusions. We conclude that Fom b probably originated from an inner resonance with a Neptune-Saturn mass Fom c, 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.
22 citations
TL;DR: In this paper, the authors explore an alternative scenario, where A and C form as a tighter binary from a single molecular cloud core (with semimajor axis ~1E4 au), and B is captured during cluster dispersal.
Abstract: Fomalhaut is a triple system, with all components widely separated (~1E5 au). Such widely separated binaries are thought to form during cluster dissolution, but that process is unlikely to form such a triple system. We explore an alternative scenario, where A and C form as a tighter binary from a single molecular cloud core (with semimajor axis ~1E4 au), and B is captured during cluster dispersal. We use N-body simulations augmented with the Galactic tidal forces to show that such a system naturally evolves into a Fomalhaut-like system in about half of cases, on a timescale compatible with the age of Fomalhaut. From initial non-interacting orbits, Galactic tides drive cycles in B's eccentricity that lead to a close encounter with C. After several close encounters, typically lasting tens of millions of years, one of the stars is ejected. The Fomalhaut-like case with both components at large separations is almost invariably a precursor to the ejection of one component, most commonly Fomalhaut C. By including circumstellar debris in a subset of the simulations, we also show that such an evolution usually does not disrupt the coherently eccentric debris disk around Fomalhaut A, and in some cases can even produce such a disk. We also find that the final eccentricity of the disk around A and the disk around C are correlated, which may indicate that the dynamics of the three stars stirred C's disk, explaining its unusual brightness.
21 citations
Cites background from "Predictions for a planet just insid..."
...In seven cases, the disk around Fomalhaut A is not significantly perturbed, and such cases would be compatible with the dynamics of A’s disk being set by an internal source (see e.g., Quillen 2006)....
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...It has been suggested it may result from the action of one or more shepherding planet(s) (Quillen 2006; Chiang et al. 2009; Boley et al. 2012), although other possible origins have been advanced (e.g., Lyra & Kuchner 2013)....
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Stockholm University1, National Institutes of Natural Sciences, Japan2, ETH Zurich3, Tokyo Institute of Technology4, University of Nice Sophia Antipolis5, Max Planck Society6, College of Charleston7, Ludwig Maximilian University of Munich8, Goddard Space Flight Center9, University of Hawaii10, Princeton University11, University of Tokyo12, Kyoto University13, Graduate University for Advanced Studies14, Hiroshima University15, Johns Hopkins University16, Space Telescope Science Institute17, Academia Sinica18, Hokkaido University19, University of Oklahoma20, Tohoku University21
TL;DR: In this article, high-contrast angular differential imaging (ADI) observations of the debris disk around HD32297 in H-band, as well as the first polarimetric images for this system in polarized differential imaging mode with Subaru/HICIAO were presented.
Abstract: We present high-contrast angular differential imaging (ADI) observations of the debris disk around HD32297 in H-band, as well as the first polarimetric images for this system in polarized differential imaging (PDI) mode with Subaru/HICIAO. In ADI, we detect the nearly edge-on disk at > 5 sigma levels from similar to 0.45 '' to similar to 1.7 '' (50-192AU) from the star and recover the spine deviation from the midplane already found in previous works. We also find for the first time imaging and surface brightness (SB) indications for the presence of a gapped structure on both sides of the disk at distances of similar to 0.75 '' (NE side) and similar to 0.65 '' (SW side). Global forward-modelling work delivers a best-fit model disk and well-fitting parameter intervals that essentially match previous results, with high-forward scattering grains and a ring located at 110AU. However, this single ring model cannot account for the gapped structure seen in our SB profiles. We create simple double ring models and achieve a satisfactory fit with two rings located at 60 and 95AU, respectively, low-forward scattering grains and very sharp inner slopes. In polarized light we retrieve the disk extending from similar to 0.25-1.6 '', although the central region is quite noisy and high S/N are only found in the range similar to 0.75-1.2 ''. The disk is polarized in the azimuthal direction, as expected, and the departure from the midplane is also clearly observed. Evidence for a gapped scenario is not found in the PDI data. We obtain a linear polarization degree of the grains that increases from similar to 10% at 0.55 '' to similar to 25% at 1.6 ''. The maximum is found at scattering angles of similar to 90 degrees, either from the main components of the disk or from dust grains blown out to larger radii.
20 citations
Cites background from "Predictions for a planet just insid..."
...…and disk structures, such as warps, spiral arms, or gaps (e.g. Janson et al. 2016; Akiyama et al. 2015; Boccaletti et al. 2015; Muto et al. 2012; Kalas et al. 2007), and to provide indirect evidence of the presence of unseen planets (Dong et al. 2015; Nesvold & Kuchner 2015; Quillen 2006)....
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TL;DR: In this article, the authors present observations of the debris disk around the F1V star Doradus from the Herschel Key Programme DEBRIS (Disc Emission via Bias-free Reconnaissance in the Infrared/Submillimetre).
Abstract: We present observations of the debris disk around {gamma} Doradus, an F1V star, from the Herschel Key Programme DEBRIS (Disc Emission via Bias-free Reconnaissance in the Infrared/Submillimetre). The disk is well resolved at 70, 100, and 160 {mu}m, resolved along its major axis at 250 {mu}m, detected but not resolved at 350 {mu}m, and confused with a background source at 500 {mu}m. It is one of our best resolved targets and we find it to have a radially broad dust distribution. The modeling of the resolved images cannot distinguish between two configurations: an arrangement of a warm inner ring at several AU (best fit 4 AU) and a cool outer belt extending from {approx}55 to 400 AU or an arrangement of two cool, narrow rings at {approx}70 AU and {approx}190 AU. This suggests that any configuration between these two is also possible. Both models have a total fractional luminosity of {approx}10{sup -5} and are consistent with the disk being aligned with the stellar equator. The inner edge of either possible configuration suggests that the most likely region to find planets in this system would be within {approx}55 AU of the star. A transient event is not needed to explain themore » warm dust's fractional luminosity.« less
20 citations
TL;DR: In this article, the authors investigate whether varying the dust composition (described by the optical constants) can solve a persistent problem in debris disk modeling, the inability to fit the thermal emission without over-predicting the scattered light.
Abstract: We investigate whether varying the dust composition (described by the optical constants) can solve a persistent problem in debris disk modeling--the inability to fit the thermal emission without over-predicting the scattered light. We model five images of the beta Pictoris disk: two in scattered light from HST/STIS at 0.58 microns and HST/WFC3 at 1.16 microns, and three in thermal emission from Spitzer/MIPS at 24 microns, Herschel/PACS at 70 microns, and ALMA at 870 microns. The WFC3 and MIPS data are published here for the first time. We focus our modeling on the outer part of this disk, consisting of a parent body ring and a halo of small grains. First, we confirm that a model using astronomical silicates cannot simultaneously fit the thermal and scattered light data. Next, we use a simple, generic function for the optical constants to show that varying the dust composition can improve the fit substantially. Finally, we model the dust as a mixture of the most plausible debris constituents: astronomical silicates, water ice, organic refractory material, and vacuum. We achieve a good fit to all datasets with grains composed predominantly of silicates and organics, while ice and vacuum are, at most, present in small amounts. This composition is similar to one derived from previous work on the HR 4796A disk. Our model also fits the thermal SED, scattered light colors, and high-resolution mid-IR data from T-ReCS for this disk. Additionally, we show that sub-blowout grains are a necessary component of the halo.
19 citations
Cites background from "Predictions for a planet just insid..."
...The locations of debris disks reveal the architectures of planetary systems, as planets sculpt and clear the debris material (e.g. Wyatt et al. 1999; Moro-Mart́ın & Malhotra 2005; Quillen 2006; Rodigas et al. 2014a)....
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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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