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 demonstrate that the cosmography, radial velocity, and photometric data for LP 876-10 are consistent with the star being a third bound stellar component to the Fomalhaut multiple system.
Abstract: LP 876-10 is a nearby active M4 dwarf in Aquarius at a distance of 7.6 pc. The star is a new addition to the 10 pc census, with a parallax measured via the REsearch Consortium On Nearby Stars (RECONS) astrometric survey on the Small and Moderate Aperture Research Telescope System’s 0.9 m telescope. We demonstrate that the astrometry, radial velocity, and photometric data for LP 876-10 are consistent with the star being a third bound stellar component to the Fomalhaut multiple system, despite the star lying nearly 6 ◦ away from Fomalhaut A in the sky. The three-dimensional separation of LP 876-10 from Fomalhaut is only 0.77 ± 0.01 pc, and 0.987 ± 0.006 pc from TW PsA (Fomalhaut B), well within the estimated tidal radius of the Fomalhaut system (1.9 pc). LP 87610 shares the motion of Fomalhaut within ∼ 1k m s −1 , and we estimate an interloper probability of ∼10 −5 . Neither our echelle spectroscopy nor astrometry are able to confirm the close companion to LP 876-10 reported in the Washington Double Star Catalog (WSI 138). We argue that the Castor Moving Group to which the Fomalhaut system purportedly belongs, is likely to be a dynamical stream, and hence membership to the group does not provide useful age constraints for group members. LP 876-10 (Fomalhaut C) has now risen from obscurity to become a rare example of a field M dwarf with well-constrained age (440 ± 40 Myr) and metallicity. Besides harboring a debris disk system and candidate planet, Fomalhaut now has two of the widest known stellar companions.
105 citations
TL;DR: In this article, the authors describe the formation of icy planets and debris disks at 30-150 AU around 1-3 M {sub sun} stars, and they suggest several critical observations that can test key features of their calculations.
Abstract: We describe comprehensive calculations of the formation of icy planets and debris disks at 30-150 AU around 1-3 M {sub sun} stars. Disks composed of large, strong planetesimals produce more massive planets than disks composed of small, weak planetesimals. The maximum radius of icy planets ranges from {approx}1500 km to 11,500 km. The formation rate of 1000 km objects-{sup P}lutos{sup -}is a useful proxy for the efficiency of icy planet formation. Plutos form more efficiently in massive disks, in disks with small planetesimals, and in disks with a range of planetesimal sizes. Although Plutos form throughout massive disks, Pluto production is usually concentrated in the inner disk. Despite the large number of Plutos produced in many calculations, icy planet formation is inefficient. At the end of the main sequence lifetime of the central star, Plutos contain less than 10% of the initial mass in solid material. This conclusion is independent of the initial mass in the disk or the properties of the planetesimals. Debris disk formation coincides with the formation of planetary systems containing Plutos. As Plutos form, they stir leftover planetesimals to large velocities. A cascade of collisions then grinds the leftovers to dust, forming an observable debris disk.more » In disks with small ({approx}<1-10 km) planetesimals, collisional cascades produce luminous debris disks with maximum luminosity {approx}10{sup -2} times the stellar luminosity. Disks with larger planetesimals produce debris disks with maximum luminosity {approx}5 x 10{sup -4} (10 km) to 5 x 10{sup -5} (100 km) times the stellar luminosity. Following peak luminosity, the evolution of the debris disk emission is roughly a power law, f {proportional_to} t {sup -n} with n{approx} 0.6-0.8. Observations of debris disks around A-type and G-type stars strongly favor models with small planetesimals. In these models, our predictions for the time evolution and detection frequency of debris disks agree with published observations. We suggest several critical observations that can test key features of our calculations.« less
101 citations
Cites background from "Predictions for a planet just insid..."
...These perturbations modify the evolution of the collisional cascade and impose structure in the radial distribution of small objects (e.g., Wilner et al. 2002; Moro-Mart́ın & Malhotra 2005; Quillen 2006; Booth et al. 2009)....
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...…al. 2008; Marois et al. 2008; Chen et al. 2009; Su et al. 2009) suggests similar processes occur in other planetary systems (see also Wilner et al. 2002; Moran et al. 2004; Deller & Maddison 2005; Moro-Mart́ın & Malhotra 2005; Quillen 2006; Wyatt 2006; Faber & Quillen 2007, and references therein)....
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TL;DR: In this paper, a debris ring around the star HD 207129 (G0V; d = 16.0 pc) has been imaged in scattered visible light with the ACS coronagraph on the Hubble Space Telescope (HST) and in thermal emission using MIPS on the Spitzer Space Telescope at λ = 70 μm and 160 μm (unresolved).
Abstract: A debris ring around the star HD 207129 (G0V; d = 16.0 pc) has been imaged in scattered visible light with the ACS coronagraph on the Hubble Space Telescope (HST) and in thermal emission using MIPS on the Spitzer Space Telescope at λ = 70 μm (resolved) and 160 μm (unresolved). Spitzer IRS (λ = 7-35 μm) and MIPS (λ = 55-90 μm) spectrographs measured disk emission at λ> 28 μm. In the HST image the disk appears as a ~30 AU wide ring with a mean radius of ~163 AU and is inclined by 60° from pole-on. At 70 μm, it appears partially resolved and is elongated in the same direction and with nearly the same size as seen with HST in scattered light. At 0.6 μm, the ring shows no significant brightness asymmetry, implying little or no forward scattering by its constituent dust. With a mean surface brightness of V = 23.7 mag arcsec^(–2), it is the faintest disk imaged to date in scattered light. We model the ring's infrared spectral energy distribution (SED) using a dust population fixed at the location where HST detects the scattered light. The observed SED is well fit by this model, with no requirement for additional unseen debris zones. The firm constraint on the dust radial distance breaks the usual grain size-distance degeneracy that exists in modeling of spatially unresolved disks, and allows us to infer a minimum grain size of ~2.8 μm and a dust size distribution power-law spectral index of –3.9. An albedo of ~5% is inferred from the integrated brightness of the ring in scattered light. The low-albedo and isotropic scattering properties are inconsistent with Mie theory for astronomical silicates with the inferred grain size and show the need for further modeling using more complex grain shapes or compositions. Brightness limits are also presented for six other main-sequence stars with strong Spitzer excess around which HST detects no circumstellar nebulosity (HD 10472, HD 21997, HD 38206, HD 82943, HD 113556, and HD 138965).
96 citations
TL;DR: In this paper, a collisional grooming algorithm is proposed to model images of debris disks where the collision time is less than the Poynting Robertson time for the dominant grain size.
Abstract: We present a new "collisional grooming" algorithm that enables us to model images of debris disks where the collision time is less than the Poynting Robertson time for the dominant grain size. Our algorithm uses the output of a collisionless disk simulation to iteratively solve the mass flux equation for the density distribution of a collisional disk containing planets in 3 dimensions. The algorithm can be run on a single processor in ~1 hour. Our preliminary models of disks with resonant ring structures caused by terrestrial mass planets show that the collision rate for background particles in a ring structure is enhanced by a factor of a few compared to the rest of the disk, and that dust grains in or near resonance have even higher collision rates. We show how collisions can alter the morphology of a resonant ring structure by reducing the sharpness of a resonant ring's inner edge and by smearing out azimuthal structure. We implement a simple prescription for particle fragmentation and show how Poynting-Robertson drag and fragmentation sort particles by size, producing smaller dust grains at smaller circumstellar distances. This mechanism could cause a disk to look different at different wavelengths, and may explain the warm component of dust interior to Fomalhaut's outer dust ring seen in the resolved 24 micron Spitzer image of this system.
95 citations
Cites background from "Predictions for a planet just insid..."
...Some of these structures are likely the result of planetary companions that gravitationally perturb the disk (e.g. Quillen 2006; Chiang et al. 2009)....
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TL;DR: In this paper, the Fomalhaut debris ring was analyzed using ALMA 350 GHz observations and it was shown that the parent body population is 13-19 AU wide with a sharp inner and outer boundary.
Abstract: The dynamical evolution of planetary systems leaves observable signatures in debris disks. Optical images trace micron-sized grains, which are strongly affected by stellar radiation and need not coincide with their parent body population. Observations of mm-size grains accurately trace parent bodies, but previous images lack the resolution and sensitivity needed to characterize the ring's morphology. Here we present ALMA 350 GHz observations of the Fomalhaut debris ring. These observations demonstrate that the parent body population is 13-19 AU wide with a sharp inner and outer boundary. We discuss three possible origins for the ring, and suggest that debris confined by shepherd planets is the most consistent with the ring's morphology.
95 citations
References
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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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