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 presented new optical coronagraphic data of Fomalhaut b obtained with HST/STIS in 2010 and 2012, and the two epochs of Space Telescope Imaging Spectrograph (STIS) photometry exclude optical variability greater than 35%.
Abstract: We present new optical coronagraphic data of Fomalhaut obtained with HST/STIS in 2010 and 2012. Fomalhaut b is recovered at both epochs to high significance. The observations include the discoveries of tenuous nebulosity beyond the main dust belt detected to at least 209AU projected radius, and a approx. 50AU wide azimuthal gap in the belt northward of Fomalhaut b. The two epochs of Space Telescope Imaging Spectrograph (STIS) photometry exclude optical variability greater than 35%. A Markov chain Monte Carlo analysis demonstrates that the orbit of Fomalhaut b is highly eccentric, with e = 0.8 +/- 0.1, a = 177 +/- 68AU, and q = 32 +/- 24AU. Fomalhaut b is apsidally aligned with the belt and 90% of allowed orbits have mutual inclination <=36 deg. Fomalhaut b's orbit is belt crossing in the sky plane projection, but only 12% of possible orbits have ascending or descending nodes within a 25AU wide belt annulus. The high eccentricity invokes a dynamical history where Fomalhaut b may have experienced a significant dynamical interaction with a hypothetical planet Fomalhaut c, and the current orbital configuration may be relatively short-lived. The Tisserand parameter with respect to a hypothetical Fomalhaut planet at 30AU or 120AU lies in the range 2-3, similar to highly eccentric dwarf planets in our solar system. We argue that Fomalhaut b's minimum mass is that of a dwarf planet in order for a circumplanetary satellite system to remain bound to a sufficient radius from the planet to be consistent with the dust scattered light hypothesis. In the coplanar case, Fomalhaut b will collide with the main belt around 2032, and the subsequent emergent phenomena may help determine its physical nature.
175 citations
Cites result from "Predictions for a planet just insid..."
...This upper limit to the mass was also consistent with dynamical theory that showed the inner edge of the dust belt could not reside as close as 18 AU from a planet unless the planet mass is below a few Jupiter masses (Quillen 2006; Chiang et al. 2009)....
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TL;DR: In this paper, the authors present Spitzer 10-35 micrometers spectroscopic data centered at both stars and identify warm, unresolved excess emission in the close vicinity of Vega for the first time.
Abstract: Vega and Fomalhaut are similar in terms of mass, ages, and global debris disk properties; therefore, they are often referred to as debris disk twins. We present Spitzer 10-35 micrometers spectroscopic data centered at both stars and identify warm, unresolved excess emission in the close vicinity of Vega for the first time. The properties of the warm excess in Vega are further characterized with ancillary photometry in the mid-infrared and resolved images in the far-infrared and submillimeter wavelengths. The Vega warm excess shares many similar properties with the one found around Fomalhaut. The emission shortward of approximately 30 micrometers from both warm components is well described as a blackbody emission of approximately 170 K. Interestingly, two other systems, Eri and HR 8799, also show such an unresolved warm dust using the same approach. These warm components may be analogous to the solar system s zodiacal dust cloud, but of far greater mass (fractional luminosity of approximately 10(exp-5) to 10(exp-6) compared to 10(exp-8) to 10(exp-7). The dust temperature and tentative detections in the submillimeter suggest that the warm excess arises from dust associated with a planetesimal ring located near the water-frost line and presumably created by processes occurring at similar locations in other debris systems as well. We also review the properties of the 2 micrometers hot excess around Vega and Fomalhaut, showing that the dust responsible for the hot excess is not spatially associated with the dust we detected in the warm belt.We suggest it may arise from hot nano grains trapped in the magnetic field of the star. Finally, the separation between the warm and cold belt is rather large with an orbital ratio greater than or approximately 10 in all four systems. In light of the current upper limits on the masses of planetary objects and the large gap, we discuss the possible implications for their underlying planetary architecture and suggest that multiple, low-mass planets likely reside between the two belts in Vega and Fomalhaut.
174 citations
Cites background from "Predictions for a planet just insid..."
...…young giant planet, a problem originally acknowledged in Kalas et al. (2008) and further demonstrated bySpitzer nondetections (Marengo et al. 2009; Janson et al. 2012), a perturbing planet is required to account for the observed disk asymmetry (Kalas et al. 2005; Quillen 2006; Chiang et al. 2009)....
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University of Victoria1, National Research Council2, University of Cambridge3, University of California, Berkeley4, Centre national de la recherche scientifique5, University of Chile6, University of St Andrews7, University of California, Los Angeles8, University of Arizona9, Spanish National Research Council10, Search for extraterrestrial intelligence11
TL;DR: In this article, the DEBRIS survey data was used to investigate the disc radii by tting narrow ring models to images at 70, 100 and 160 m and by comparing the resolved and blackbody radii to full spectral energy distributions.
Abstract: The majority of debris discs discovered so far have only been detected through infrared excess emission above stellar photospheres. While disc properties can be inferred from unresolved photometry alone under various assumptions for the physical properties of dust grains, there is a degeneracy between disc radius and dust temperature that depends on the grain size distribution and optical properties. By resolving the disc we can measure the actual location of the dust. The launch of Herschel, with an angular resolution superior to previous far-infrared telescopes, allows us to spatially resolve more discs and locate the dust directly. Here we present the nine resolved discs around A stars between 20 and 40 pc observed by the DEBRIS survey. We use these data to investigate the disc radii by tting narrow ring models to images at 70, 100 and 160 m and by tting blackbodies to full spectral energy distributions. We do this with the aim of nding an improved way of estimating disc radii for unresolved systems. The ratio between the resolved and blackbody radii varies between 1 and 2.5. This ratio is inversely correlated with luminosity and any remaining discrepancies are most likely explained by dierences to the minimum size of grain in the size distribution or dierences in composition. We nd that three of the systems are well t by a narrow ring, two systems are borderline cases and the other four likely require wider or multiple rings to fully explain the observations, reecting the diversity of planetary systems.
173 citations
Cites methods from "Predictions for a planet just insid..."
...…azimuthal structure (e.g. Greaves et al. 2005) and inner edges (e.g. Boley et al. 2012), which in turn can be used to infer the existence of planets in the system, as was successfully done with β Pic (Mouillet et al. 1997; Lagrange et al. 2010) and Fomalhaut (Kalas et al. 2005; Quillen 2006)....
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TL;DR: In this paper, the authors investigate the effects of the perturbations of a planet, which may lie at a significant distance from the planetesimal disc, to see if these perturbation can stir the disc, and if so over what time-scale.
Abstract: Detectable debris discs are thought to require dynamical excitation (`stirring'), so that planetesimal collisions release large quantities of dust. We investigate the effects of the secular perturbations of a planet, which may lie at a significant distance from the planetesimal disc, to see if these perturbations can stir the disc, and if so over what time-scale. The secular perturbations cause orbits at different semimajor axes to precess at different rates, and after some time tcross initially non-intersecting orbits begin to cross. We show that tcross ~ a_disc^9/2 /(m_pl e_pl a_pl^3), where mpl, epl and apl are the mass, eccentricity and semimajor axis of the planet, and adisc is the semimajor axis of the disc. This time-scale can be faster than that for the growth of planetesimals to Pluto's size within the outer disc. We also calculate the magnitude of the relative velocities induced among planetesimals and infer that a planet's perturbations can typically cause destructive collisions out to 100 s of au. Recently formed planets can thus have a significant impact on planet formation in the outer disc which may be curtailed by the formation of giant planets much closer to the star. The presence of an observed debris disc does not require the presence of Pluto-sized objects within it, since it can also have been stirred by a planet not in the disc. For the star ∊ Eridani, we find that the known radial velocity planet can excite the planetesimal belt at 60au sufficiently to cause destructive collisions of bodies up to 100km in size, on a time-scale of 40Myr. (Less)
171 citations
Cites background from "Predictions for a planet just insid..."
...Secondly, we note that, althoughef ≈ 0.1, the material in the Fomalhaut disc appears to have very low proper eccentricities (Quillen 2006; Chiang et al. 2009), as evidenced by the sharpinner edge to the disc....
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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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