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 paper, the authors 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).
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 micron, resolved along its major axis at 250 micron, detected but not resolved at 350 micron, and confused with a background source at 500 micron. It is one of our best resolved targets and we find it to have a radially broad dust distribution. The modelling 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 ~55 to 400 AU or an arrangement of two cool, narrow rings at ~70 AU and ~190 AU. This suggests that any configuration between these two is also possible. Both models have a total fractional luminosity of ~10^{-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 ~55 AU of the star. A transient event is not needed to explain the warm dust's fractional luminosity.
25 citations
Cites background from "Predictions for a planet just insid..."
...Resonance overlap studies have shown how a planet can sculpt the inner edge of a disk (e.g., Quillen 2006, Mustill & Wyatt 2012)....
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TL;DR: In this article, the linear perturbations of collisionless near-Keplerian disks were studied and it was shown that these disks can support large-scale "slow" modes, in which the frequency is proportional to the disc mass.
Abstract: We study the linear perturbations of collisionless near-Keplerian discs. Such systems are models for debris discs around stars and the stellar discs surrounding supermassive black holes at the centres of galaxies. Using a nite-element method, we solve the linearized collisionless Boltzmann equation and Poisson’s equation for a wide range of disc masses and rms orbital eccentricities to obtain the eigenfrequencies and shapes of normal modes. We nd that these discs can support large-scale ‘slow’ modes, in which the frequency is proportional to the disc mass. Slow modes are present for arbitrarily small disc mass so long as the self-gravity of the disc is the dominant source of apsidal precession. We nd that slow modes are of two general types: parent modes and hybrid child modes, the latter arising from resonant interactions between parent modes and singular van Kampen modes. The most prominent slow modes have azimuthal wavenumbers m = 1 and m = 2. We illustrate how slow modes in debris discs are excited during a y-by of a neighbouring star. Many of the non-axisymmetric features seen in debris discs (clumps, eccentricity, spiral waves) that are commonly attributed to planets could instead arise from slow modes; the two hypotheses can be distinguished by long-term measurements of the pattern speed of the features.
24 citations
01 Oct 2013
TL;DR: The Superparticle Model/Algorithm for Collisions in Kuiper belts and debris disks (SMACK) as discussed by the authors is a new method for simultaneously modeling, in 3D, the collisional and dynamical evolution of planetesimals in a debris disk with planets.
Abstract: We present the Superparticle Model/Algorithm for Collisions in Kuiper belts and debris disks (SMACK), a new method for simultaneously modeling, in 3-D, the collisional and dynamical evolution of planetesimals in a debris disk with planets. SMACK can simulate azimuthal asymmetries and how these asymmetries evolve over time. We show that SMACK is stable to numerical viscosity and numerical heating over 10(exp 7) yr, and that it can reproduce analytic models of disk evolution. We use SMACK to model the evolution of a debris ring containing a planet on an eccentric orbit. Differential precession creates a spiral structure as the ring evolves, but collisions subsequently break up the spiral, leaving a narrower eccentric ring.
24 citations
Cites background from "Predictions for a planet just insid..."
...Some authors have assumed that planetesimals in a debris disk have had their free eccentricities completely damped by collisions (Quillen 2006; Chiang et al. 2009) resulting in a ring of planetesimals on orbits with eccentricity equal to the forced eccentricity from the planet....
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...…of a planet on an eccentric orbit interacting with a debris disk have assumed either no particular collisional evolution of the planetesimal orbits (Wyatt 1999; Wilner et al. 2002; Quillen & Thorndike 2002; Moran et al. 2004), or complete collisional damping (Quillen 2006; Chiang et al. 2009)....
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...Then — in stark contrast to Wyatt (1999), which did not incorporate collisions — collisions break up the spiral before it can wrap once more around the star, leaving an apsealigned ring shown in the lower right, as described by Quillen (2006)....
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...Many authors have analyzed resolved images of debris disks to predict the presence of exoplanets and constrain their locations, orbits, and physical properties (e.g. Wyatt et al. 1999; Greaves et al. 2005; Quillen 2006; Stark & Kuchner 2008)....
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University of Toronto1, University of California, Berkeley2, Search for extraterrestrial intelligence3, University of Grenoble4, Stanford University5, Space Telescope Science Institute6, Goddard Space Flight Center7, Stony Brook University8, University of Western Ontario9, Lawrence Livermore National Laboratory10, University of Arizona11, Subaru12, University of Georgia13, Université de Montréal14, University of Victoria15, National Research Council16, University of California, Los Angeles17, Johns Hopkins University18, European Southern Observatory19, University of Exeter20, University of California, San Diego21, Ames Research Center22, American Museum of Natural History23, Arizona State University24, Cornell University25, University of Toledo26, California Institute of Technology27, The Aerospace Corporation28
TL;DR: The NEXSS program as mentioned in this paper is a NASA program that uses a set of experiments to evaluate the performance of the NEXS system on a series of NASA-funded satellites.
Abstract: NASA's NEXSS program [NNX15AD95G]; U.S. Department of Energy by Lawrence Livermore National Laboratory [DE-AC52-07NA27344]; NSF [AST-1413718, AST-1518332]; NASA [NNX15AC89G]; Office of Science of the U.S. Department of Energy [DE-AC02-05CH11231]
23 citations
TL;DR: In this article, collisional probability simulations of the Fomalhaut debris disk based on the structure of our Kuiper belt are performed, finding that the catastrophic disruption rate of d ~ 100 km bodies in the high-eccentricity scattering component is several per decade.
Abstract: The planet candidate Fomalhaut b is bright in optical light but undetected in longer wavelengths, requiring a large, reflective dust cloud. The most recent observations find an extremely eccentric orbit (e ~ 0.8), indicating that Fomalhaut b cannot be the planet that is constraining the system's eccentric debris ring. An irregular satellite swarm around a super-Earth has been proposed, however, explaining the well-constrained debris ring requires an additional planet on an orbit that crosses that of the putative super-Earth. This paper expands upon a second theory: Fomalhaut b is a transient dust cloud produced by a catastrophic collision between planetesimals in the disk. We perform collisional probability simulations of the Fomalhaut debris disk based on the structure of our Kuiper belt, finding that the catastrophic disruption rate of d ~ 100 km bodies in the high-eccentricity scattering component is several per decade. This model paints a picture of the Fomalhaut system as having recently (within ~10-100 Myr) experienced a dynamical instability within its planetary system, which scattered a massive number of planetesimals onto large, high eccentricity orbits similar to that of Fom b. If Fomalhaut b is indeed a dust cloud produced by such a collision, we should soon see another appear, while Fomalhaut b will expand until it is either resolved or becomes too faint to be seen.
22 citations
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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