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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Princeton University1, Spanish National Research Council2, National Institutes of Natural Sciences, Japan3, University of Amsterdam4, College of Charleston5, Max Planck Society6, Ludwig Maximilian University of Munich7, University of Toronto8, Goddard Space Flight Center9, University of Hyogo10, Osaka University11, University of Notre Dame12, University of Nice Sophia Antipolis13, Graduate University for Advanced Studies14, Kyoto University15, Hiroshima University16, California Institute of Technology17, University of Tokyo18, Academia Sinica19, Institute for the Physics and Mathematics of the Universe20, Hokkaido University21, University of Oklahoma22, Tohoku University23
TL;DR: In this paper, the authors survey a population of debris-disk-hosting stars with gaps and cavities implied by their spectral energy distributions, in order to attempt to spatially resolve the disk as well as to detect any planets that may be responsible for the disk structure.
Abstract: Debris disks around young main-sequence stars often have gaps and cavities which for a long time have been interpreted as possibly being caused by planets. In recent years, several giant planet discoveries have been made in systems hosting disks of precisely this nature, further implying that interactions with planets could be a common cause of such disk structures. As part of the SEEDS high-contrast imaging survey, we are surveying a population of debris-disk-hosting stars with gaps and cavities implied by their spectral energy distributions, in order to attempt to spatially resolve the disk as well as to detect any planets that may be responsible for the disk structure. Here, we report on intermediate results from this survey. Five debris disks have been spatially resolved, and a number of faint point sources have been discovered, most of which have been tested for common proper motion, which in each case has excluded physical companionship with the target stars. From the detection limits of the 50 targets that have been observed, we find that β Pic b-like planets (~10 M jup planets around G-A-type stars) near the gap edges are less frequent than 15%-30%, implying that if giant planets are the dominant cause of these wide (27 AU on average) gaps, they are generally less massive than β Pic b.
84 citations
Cites background from "Predictions for a planet just insid..."
...…et al. 2011; Currie et al. 2012b; Quanz 2013), such as eccentric gaps with sharp inner boundaries or apparently resonant dust concentrations (e.g. Quillen & Thorndike 2002; Quillen 2006), although alternative mechanisms have been suggested (e.g. Jalali & Tremaine 2012; Lyra & Kuchner 2012)....
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TL;DR: In this paper, the Atacama Large Millimeter/submillimeter Array (ALMA) continuum observations at a wavelength of 1.25 mm of the debris disk surrounding the ~100 Myr old solar analog HD 107146 were analyzed.
Abstract: We present the Atacama Large Millimeter/submillimeter Array (ALMA) continuum observations at a wavelength of 1.25 mm of the debris disk surrounding the ~100 Myr old solar analog HD 107146. The continuum emission extends from about 30 to 150 AU from the central star with a decrease in the surface brightness at intermediate radii. We analyze the ALMA interferometric visibilities using debris disk models with radial profiles for the dust surface density parameterized as (1) a single power law, (2) a single power law with a gap, and (3) a double power law. We find that models with a gap of radial width ~8 AU at a distance of ~80 AU from the central star, as well as double power-law models with a dip in the dust surface density at ~70 AU provide significantly better fits to the ALMA data than single power-law models. We discuss possible scenarios for the origin of the HD 107146 debris disk using models of planetesimal belts in which the formation of Pluto-sized objects trigger disruptive collisions of large bodies, as well as models that consider the interaction of a planetary system with a planetesimal belt and spatial variation of the dust opacity across the disk. If future observations with higher angular resolution and sensitivity confirm the fully depleted gap structure discussed here, a planet with a mass of approximately a few Earth masses in a nearly circular orbit at ~80 AU from the central star would be a possible explanation for the presence of the gap.
81 citations
Cites background from "Predictions for a planet just insid..."
...At a given distance from the central star, a more massive planet carves a wider gap (Quillen 2006), which is set by the region of overlapping mean motion resonances on either side of the planet (Wisdom 1980)....
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TL;DR: In this paper, a multi-roll coronagraphic image of the HD 181327 debris disk obtained using the Space Telescope Imaging Spectrograph (STIS) on board the Hubble Space Telescope (HST) reveal the debris ring in its entirety at high S/N and unprecedented spatial resolution.
Abstract: New multi-roll coronagraphic images of the HD 181327 debris disk obtained using the Space Telescope Imaging Spectrograph (STIS) on board the Hubble Space Telescope (HST) reveal the debris ring in its entirety at high S/N and unprecedented spatial resolution. We present and apply a new multi-roll image processing routine to identify and further remove quasi-static PSF-subtraction residuals and quantify systematic uncertainties. We also use a new iterative image deprojection technique to constrain the true disk geometry and aggressively remove any surface brightness asymmetries that can be explained without invoking dust density enhancements/deficits. The measured empirical scattering phase function for the disk is more forward scattering than previously thought and is not well-fit by a Henyey-Greenstein function. The empirical scattering phase function varies with stellocentric distance, consistent with the expected radiation pressured-induced size segregation exterior to the belt. Within the belt, the empirical scattering phase function contradicts unperturbed debris ring models, suggesting the presence of an unseen planet. The radial profile of the flux density is degenerate with a radially-varying scattering phase function; therefore estimates of the ring's true width and edge slope may be highly uncertain. We detect large scale asymmetries in the disk, consistent with either the recent catastrophic disruption of a body with mass >1% the mass of Pluto, or disk warping due to strong interactions with the interstellar medium (ISM).
80 citations
TL;DR: In this paper, the authors detect the signature of hot dust around the nearby A4V star Fomalhaut, which has already been suggested to harbor a warm dust population in addition to a cold dust ring located at about 140AU.
Abstract: The innermost parts of dusty debris disks around main sequence stars are currently poorly known due to the high contrast and small angular separation with their parent stars. Using near-infrared interferometry, we aim to detect the signature of hot dust around the nearby A4V star Fomalhaut, which has already been suggested to harbor a warm dust population in addition to a cold dust ring located at about 140AU. Archival data obtained with the VINCI instrument at the VLTI are used to study the fringe visibility of the Fomalhaut system at projected baseline lengths ranging from 4m to 140m in the K band. A signiflcant visibility deflcit is observed at short baselines with respect to the expected visibility of the sole stellar photosphere. This is interpreted as the signature of resolved circumstellar emission, producing a relative ∞ux of 0:88%§0:12% with respect to the stellar photosphere. While our interferometric data cannot directly constrain the morphology of the excess emission source, complementary data from the literature allow us to discard an ofi-axis point-like object as the source of circumstellar emission. We argue that the thermal emission from hot dusty grains located within 6AU from Fomalhaut is the most plausible explanation for the detected excess. Our study also provides a revised limb-darkened diameter for Fomalhaut (µLD = 2:223 § 0:022mas), taking into account the efiect of the resolved circumstellar emission. Subject headings: Circumstellar matter | techniques: interferometric | stars: individual (Fomalhaut)
80 citations
Cites background from "Predictions for a planet just insid..."
...1 FNRS Postdoctoral Researcher terpreted as the result of the gravitational influence of a massive planet located just inside the dust ring (Quillen 2006)....
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TL;DR: In this article, the authors used a dedicated MCMC code to derive the statistical distributions of the orbital elements of Fomalhaut's common proper motion companion (Fom b), and then they used symplectic N-body integration to investigate the dynamics of the dust belt, as perturbed by a single planet.
Abstract: The nearby star Fomalhaut harbours a cold, moderately eccentric dust belt with a sharp inner edge near 133 au. A low-mass, common proper motion companion (Fom b), was discovered near the inner edge and was identified as a planet candidate that could account for the belt morphology. However, the most recent orbit determination based on four epochs of astrometry over eight years reveals a highly eccentric orbit that appears to cross the belt in the sky plane projection. We perform here a full orbital determination based on the available astrometric data to independently validate the orbit estimates previously presented. Adopting our values for the orbital elements and their associated uncertainties, we then study the dynamical interaction between the planet and the dust ring, to check whether the proposed disk sculpting scenario by Fom b is plausible. We used a dedicated MCMC code to derive the statistical distributions of the orbital elements of Fom b. Then we used symplectic N-body integration to investigate the dynamics of the dust belt, as perturbed by a single planet. Different attempts were made assuming different masses for Fom b. We also performed a semi-analytical study to explain our results. Our results are in good agreement with others regarding the orbit of Fom b. We find that the orbit is highly eccentric, is close to apsidally aligned with the belt, and has a moderate mutual inclination relative to the belt plane of. If coplanar, this orbit crosses the disk. Our dynamical study then reveals that the observed planet could sculpt a transient belt configuration with a similar eccentricity to what is observed, but it would not be simultaneously apsidally aligned with the planet. This transient configuration only occurs a short time after the planet is placed on such an orbit (assuming an initially circular disk), a time that is inversely proportional to the planet's mass, and that is in any case much less than the 440 Myr age of the star. We constrain how long the observed dust belt could have survived with Fom b on its current orbit, as a function of its possible mass. This analysis leads us to conclude that Fom b is likely to have low mass, that it is unlikely to be responsible for the sculpting of the belt, and that it supports the hypothesis of a more massive, less eccentric planet companion Fom c.
78 citations
Cites background from "Predictions for a planet just insid..."
...The investigators suggest that an undetected planet could account for these features, as supported by numerical (Deller & Maddison 2005) and semi-analytic studies (Quillen 2006)....
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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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