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, a review describes the theoretical framework within which debris disk evolution takes place and shows how that framework has been constrained by observations, including infrared photometry of large numbers of debris disks, providing snapshots of the dust present at different evolutionary phases.
Abstract: Circumstellar dust exists around several hundred main sequence stars. For the youngest stars, that dust could be a remnant of the protoplanetary disk. Mostly it is inferred to be continuously replenished through collisions between planetesimals in belts analogous to the Solar System’s asteroid and Kuiper belts, or in collisions between growing protoplanets. The evolution of a star’s debris disk is indicative of the evolution of its planetesimal belts and may be influenced by planet formation processes, which can continue throughout the first gigayear as the planetary system settles to a stable configuration and planets form at large radii. Evidence for that evolution comes from infrared photometry of large numbers of debris disks, providing snapshots of the dust present at different evolutionary phases, as well as from images of debris disk structure. This review describes the theoretical framework within which debris disk evolution takes place and shows how that framework has been constrained by observations.
985 citations
TL;DR: Optical observations of an exoplanet candidate, Fomalhaut b, show that the planet's mass is at most three times that of Jupiter; a higher mass would lead to gravitational disruption of the belt, matching predictions of its location.
Abstract: Fomalhaut is a bright star 7.7 parsecs (25 light years) from Earth that harbors a belt of cold dust with a structure consistent with gravitational sculpting by an orbiting planet. Here, we present optical observations of an exoplanet candidate, Fomalhaut b. In the plane of the belt, Fomalhaut b lies approximately 119 astronomical units (AU) from the star and 18 AU from the dust belt, matching predictions. We detect counterclockwise orbital motion using Hubble Space Telescope observations separated by 1.73 years. Dynamical models of the interaction between the planet and the belt indicate that the planet's mass is at most three times that of Jupiter for the belt to avoid gravitational disruption. The flux detected at 0.8 m is also consistent with that of a planet with mass no greater than a few times that of Jupiter. The brightness at 0.6 micron and the lack of detection at longer wavelengths suggest that the detected flux may include starlight reflected off a circumplanetary disk, with dimension comparable to the orbits of the Galilean satellites. We also observed variability of unknown origin at 0.6 micron.
964 citations
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01 May 2011TL;DR: In this paper, the authors present an overview of the solar system and its evolution, including the formation and evolution of stars, asteroids, and free-floating planets, as well as their internal and external structures.
Abstract: 1. Introduction 2. Radial velocities 3. Astrometry 4. Timing 5. Microlensing 6. Transits 7. Imaging 8. Host stars 9. Brown dwarfs and free-floating planets 10. Formation and evolution 11. Interiors and atmospheres 12. The Solar System Appendixes References Index.
527 citations
TL;DR: In this paper, a simple analytical model for the steady-state evolution of debris disks due to collisions is confronted with Spitzer observations of dust around main sequence A stars, and the detection statistics and trends seen at both 24 and 70 µm can be fitted well by the model.
Abstract: In this paper a simple analytical model for the steady-state evolution of debris disks due to collisions is confronted with Spitzer observations of dust around main sequence A stars. All stars are assumed to have planetesimal belts with a distribution of initial masses and radii. In the model disk mass is constant until the largest planetesimals reach collisional equilibrium whereupon the mass falls off ∝ t −1 age. Using parameters that are reasonable within the context of planet formation models and observations of proto-planetary disks, the detection statistics and trends seen at both 24 and 70 µm can be fitted well by the model. While there is no need to invoke stochastic evolution or delayed stirring to explain the detection statistics of dust around A stars, the model is also consistent with a moderate rate of stochastic events. Potentially anomalous systems are identified by their high ratio of observed dust luminosity to the maximum permissible in the model given their radii and ages, f/fmax; these are HD3003, HD38678, HD115892, and HD172555. It is not clear if their planetesimals have unusual properties (e.g., high strength or low eccentricity), or if their dust is a transient phenomenon. There are also well-studied examples from the literature where transient phenomena are favored (e.g., Vega, HD69830). However, the overall success of our model, which assumes planetesimals in all belts have the same strength, eccentricity and maximum size, suggests there is a large degree of uniformity in the outcome of planet formation. The distribution of the radii of the planetesimal belts, once corrected for detection bias, is found to follow N(r) ∝ r −0.8±0.3 in the range 3-120 AU. Since the inner edge of a belt is often attributed to an unseen planet, this provides a unique constraint on the planetary systems of A stars. It is also shown that the effect of P-R drag on the inner edge of A star disks may need to be considered for those close to the Spitzer detection threshold, such as HD2262, HD19356, HD106591, and HD115892. Predictions are made for the upcoming SCUBA-2 survey, including that at least 17 of the 100 A stars should be detectable above 2 mJy at 850 µm, illustrating how this model can be readily applied to the interpretation of future surveys. Subject headings: circumstellar matter – planetary systems: formation
289 citations
Cites background from "Predictions for a planet just insid..."
...The inner hole in these belts has been inferred in other studies to be caused by the presence of inner planets (e.g., Roques et al. 1994; Wyatt et al. 1999; Wilner et al. 2002; Wyatt 2003; Quillen 2006)....
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TL;DR: In this article, the authors describe the formation of icy planets and debris disks at 30-150 AU around 1-3 M☉ stars and show that collisional cascades produce debris disks with maximum luminosity 2 × 10−3 times the stellar luminosity.
Abstract: We describe calculations for the formation of icy planets and debris disks at 30-150 AU around 1-3 M☉ stars. Debris disk formation coincides with the formation of planetary systems. As protoplanets grow, they stir leftover planetesimals to large velocities. A cascade of collisions then grinds the leftovers to dust, forming an observable debris disk. Stellar lifetimes and the collisional cascade limit the growth of protoplanets. The maximum radius of icy planets, -->rmax ≈ 1750 km, is remarkably independent of initial disk mass, stellar mass, and stellar age. These objects contain 3%-4% of the initial mass in solid material. Collisional cascades produce debris disks with maximum luminosity ~ -->2 × 10−3 times the stellar luminosity. The peak 24 μm excess varies from ~1% times the stellar photospheric flux for 1 M☉ stars to ~50 times the stellar photospheric flux for 3 M☉ stars. The peak 70-850 μm excesses are ~30-100 times the stellar photospheric flux. For all stars, the 24-160 μm excesses rise at stellar ages of 5-20 Myr, peak at 10-50 Myr, and then decline. The decline is roughly a power law, -->f t−n with -->n ≈ 0.6–1.0. This predicted evolution agrees with published observations of A-type and solar-type stars. The observed far-IR color evolution of A-type stars also matches model predictions.
271 citations
References
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TL;DR: The sharp inner edge and offset demonstrate the presence of planetary-mass objects orbiting Fomalhaut, demonstrating the structure of a dusty disk modified by the gravitational influence of planets.
Abstract: In 1983 the IRAS orbiting satellite detected excess infrared radiation from the direction of Fomalhaut, a first magnitude star in the otherwise dim constellation Piscis Austrinus. It was radiation from a huge dusty disk around the star, about four times the size of our Solar System. The Advanced Camera for Surveys onboard the Hubble Space Telescope has now detected Fomalhaut's dust complex at high resolution at optical wavelengths. The disk is offset from the star in a way that suggests the presence of several planets. The debris disks around Beta Pictoris and AU Microscopii are both edge-on, and the disk around HR 4796A has a small radius. So the Fomalhaut disk, seen on a slope rather like the ring around Saturn, older than the others and closer to us, may become the disk of choice for the study of planet formation. The Sun and >15 per cent of nearby stars are surrounded by dusty disks that must be collisionally replenished by asteroids and comets, as the dust would otherwise be depleted on timescales <107 years (ref. 1). Theoretical studies show that the structure of a dusty disk can be modified by the gravitational influence of planets2,3,4, but the observational evidence is incomplete, at least in part because maps of the thermal infrared emission from the disks have low linear resolution (35 au in the best case5). Optical images provide higher resolution, but the closest examples (AU Mic and β Pic) are edge-on6,7, preventing the direct measurement of the azimuthal and radial disk structure that is required for fitting theoretical models of planetary perturbations. Here we report the detection of optical light reflected from the dust grains orbiting Fomalhaut (HD 216956). The system is inclined 24° away from edge-on, enabling the measurement of disk structure around its entire circumference, at a linear resolution of 0.5 au. The dust is distributed in a belt 25 au wide, with a very sharp inner edge at a radial distance of 133 au, and we measure an offset of 15 au between the belt's geometric centre and Fomalhaut. Taken together, the sharp inner edge and offset demonstrate the presence of planetary-mass objects orbiting Fomalhaut.
458 citations
"Predictions for a planet just insid..." refers background in this paper
...Here the value of 0.013 is half the scaleheight measured by Kalas et al. (2005) (see discussion at the end of Section 2)....
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...3 by Kalas et al. 2005)....
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...◦6, and a semi-major axis a edge = 133 au (Kalas et al. 2005)....
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...A power-law size distribution with an upper cut-off of 500 km leads to an estimate of 50–100 Earth masses in the ring (Kalas et al. 2005)....
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...◦5 (Kalas et al. 2005)....
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TL;DR: In this paper, the authors show how the gravitational influence of a second body in the system with an eccentric orbit would cause a brightness asymmetry in a disk by imposing a forced eccentricity on the orbits of the constituent dust particles, thus shifting the center of symmetry of the disk away from the star and causing the dust near the forced pericenter of the perturbed disk to glow.
Abstract: Recent images of the disks of dust around the young stars HR 4796A and Fomalhaut show, in each case, a double-lobed feature that may be asymmetric (one lobe may be brighter than the other). A symmetric double-lobed structure is that expected from a disk of dust with a central hole that is observed nearly edge-on (i.e., close to the plane of the disk). This paper shows how the gravitational influence of a second body in the system with an eccentric orbit would cause a brightness asymmetry in such a disk by imposing a forced eccentricity on the orbits of the constituent dust particles, thus shifting the center of symmetry of the disk away from the star and causing the dust near the forced pericenter of the perturbed disk to glow. Dynamic modeling of the HR 4796 disk shows that its ~5% brightness asymmetry could be the result of a forced eccentricity as small as 0.02 imposed on the disk by either the binary companion HR 4796B or by an unseen planet close to the inner edge of the disk. Since it is likely that a forced eccentricity of 0.01 or higher would be imposed on a disk in a system in which there are planets but no binary companion, the corresponding asymmetry in the disk's structure could serve as a sensitive indicator of these planets that might otherwise remain undetected.
417 citations
"Predictions for a planet just insid..." refers background or methods in this paper
...These are the pericentre glow model (Wyatt et al. 1999) and the selfgravitating eccentric ring models (e.g. Goldreich & Tremaine 1979; Tremaine 2001; Papaloizou & Melita 2005)....
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...Previous studies have not placed constraints on the location of the planet that is causing the forced eccentricity in Fomalhaut’s disc, consequently constraints on the planet’s mass and eccentricity are lacking (Wyatt et al. 1999; Marsh et al. 2005)....
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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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...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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TL;DR: In this paper, the authors present a model for the outcome of collisions between planetesimals in a debris disc, and assesses the impact of collisional processes on the structure and size distribution of the disc.
Abstract: This paper presents a model for the outcome of collisions between planetesimals in a debris disc, and assesses the impact of collisional processes on the structure and size distribution of the disc. The model is presented by its application to Fomalhaut’s collisionally replenished dust disc; a recent 450-µm image of this disc shows a clump embedded within it with a flux ∼5 per cent of the total. The following conclusions are drawn. (i) Spectral energy distribution modelling is consistent with Fomalhaut’s disc having a collisional cascade size distribution extending from bodies 0.2 m in diameter (the largest that contribute to the 850-µm flux) down to 7-µm-sized dust (smaller grains are blown out of the system by radiation pressure). (ii) Collisional lifetime arguments imply that the collisional cascade starts with planetesimals 1.5‐4 km in diameter, and so has a mass of 20‐30 M⊕. Any larger bodies must be predominantly primordial. (iii) Constraints on the time-scale for the ignition of the collisional cascade from planet formation models are consistent with these primordial planetesimals having the same distribution as the cascade extending up to 1000 km, resulting in a disc mass of 5‐10 times the minimum solar nebula mass. (iv) The debris disc is expected to be intrinsically clumpy, as planetesimal collisions result in dust clumps that can last up to 700 orbital periods. The intrinsic clumpiness of Fomalhaut’s disc is below current detection limits, but it could be detectable by future observatories such as ALMA, and could provide the only way of determining this primordial planetesimal population. Also, we note that such intrinsic clumpiness in an exozodiacal cloudlike disc could present a confusion limit when trying to detect terrestrial planets. (v) The observed clump could have originated in a collision between two runaway planetesimals, both larger than 1400 km in diameter. It appears unlikely that we should witness such an event unless both the formation of these runaways and the ignition of the collisional cascade occurred relatively recently (within the last ∼10 Myr), however this is a topic which would benefit from further exploration using planet formation and collisional models. (vi) Another explanation for Fomalhaut’s clump is that ∼5 per cent of the planetesimals in the ring were trapped in 1:2 resonance with a planet orbiting at 80 au when it migrated out as a result of the clearing of a residual planetesimal disc. The motion on the sky of such a clump would be 0.2 arcsec yr −1 ,
251 citations
"Predictions for a planet just insid..." refers background in this paper
...The low scaleheight implied by the sharp edge suggests that fewer collisions are destructive than previously estimated (e.g. by Wyatt & Dent 2002)....
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...The total mass required to replenish the dust in the disc was estimated by Wyatt & Dent (2002) to be 20–30 M ⊕, however a larger mass is probably required as the velocity dispersion assumed by this study corresponded to h/r ∼ 0.1 and this value exceeds by a factor of 8 that consistent with the edge…...
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TL;DR: In this paper, the authors present a model for the outcome of collisions between planetesimals in a debris disk and assesses the impact of collisional processes on the structure and size distribution of the disk.
Abstract: This paper presents a model for the outcome of collisions between planetesimals in a debris disk and assesses the impact of collisional processes on the structure and size distribution of the disk. The model is presented by its application to Fomalhaut's collisionally replenished dust disk; a recent 450 micron image of this disk shows a clump embedded within it with a flux ~5 per cent of the total. The following conclusions are drawn: (i) SED modelling is consistent with Fomalhaut's disk having a collisional cascade size distribution extending from bodies 0.2 m in diameter down to 7 micron-sized dust. (ii) Collisional lifetime arguments imply that the cascade starts with planetesimals 1.5-4 km in diameter. Any larger bodies must be predominantly primordial. (iii) Constraints on the timescale for the ignition of the cascade are consistent with these primordial planetesimals having a distribution that extends up to 1000km, resulting in a disk mass of 5-10 times the minimum mass solar nebula. (iv) The debris disk is expected to be intrinsically clumpy, since planetesimal collisions result in dust clumps. The intrinsic clumpiness of Fomalhaut's disk is below current detection limits, but could be detectable by future observatories such as the ALMA, and could provide the only way of determining the primordial planetesimal population. (v) The observed clump could have originated in a collision between two runaway planetesimals, both larger than 1400 km diameter. It is unlikely that we should witness such an event unless both the formation of these runaways and the ignition of the collisional cascade occurred within the last ~10 Myr. (vi) Another explanation for Fomalhaut's clump is that ~5 per cent of the planetesimals in the ring are trapped in 1:2 resonance with a planet orbiting at 80 AU.
247 citations
TL;DR: In this paper, the authors considered a simple model in which dust produced in a planetesimal belt migrates in toward the star due to P-R drag suffering destructive collisions with other dust grains on the way.
Abstract: This paper considers a simple model in which dust produced in a planetesimal belt migrates in toward the star due to P-R drag suffering destructive collisions with other dust grains on the way Assuming the dust is all of the same size, the resulting surface density distribution can be derived analytically and depends only on the parameter η0 = 5000τeff (r0) √ M� /r0/β; this parameter can be determined observationally with the hypothesis that β = 05 For massive belts in which η0 � 1 dust is confined to the planetesimal belt, while the surface density of more tenuous belts, in which η0 � 1, is constant with distance from the star The emission spectrum of dust from planetesimal belts at different distances from different mass stars shows that the dust belts which have been detected to date should have η0 � 1; dust belts with η0 � 1 are hard to detect as they are much fainter than the stellar photosphere This is confirmed for a sample of 37 debris disk candidates for which η0 was determined to be >10 This means that these disks are so massive that mutual collisions prevent dust from reaching the inner regions of these systems and P-R drag can be ignored when studying their dynamics Models for the formation of structure in debris disks by the trapping of particles into planetary resonances by P-R drag should be reconsidered However, since collisions do not halt 100% of the dust, this means that in the absence of planetary companions debris disk systems should be populated by small quantities of hot dust which may be detectable in the mid-IR Even in disks with η0 � 1 the temperature of dust emission is shown to be a reliable tracer of the planetesimal distribution meaning that inner holes in the dust distribution imply a lack of colliding planetesimals in the inner regions
224 citations
"Predictions for a planet just insid..." refers methods in this paper
...As this time-scale is short, we can exclude Poynting–Robertson driven resonance capture models for the dust, as argued in detail by Wyatt (2005)....
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