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 semi-analytical model for the dust produced during self-stirring is developed and applied to the statistics for A stars, and the authors show that there is no significant statistical difference between fractional excesses of A-stars.50Myr old.
Abstract: This paper aims to consider the evidence that debris disks are self-stirred by the formation of Pluto-size objects. A semi-analytical model for the dust produced during self-stirring is developed and applied to the statistics for A stars. We show that there is no significant statistical difference between fractional excesses of A-stars .50Myr old, and therefore focus on reproducing the broad trends, the “rise and fall” of the fraction of stars with excesses that the pre-stirred model of Wyatt et al. (2007b) does not predict. Using a population model, we find that the statistics and trends can be reproduced with a self-stirring model of planetesimal belts with radius distribution N(r) / r 0.8 between 15–120AU, with width dr = r=2. Disks must have this 15AU minimum radius in order to show a peak in disk fraction, rather than a monotonic decline. However, the marginal significance of the peak in the observations means that models with smaller minimum radii also formally fit the data. Populations of extended disks with fixed inner and/or outer radii fail to fit the statistics, due mainly to the slow 70�m evolution as stirring moves further out in the disk. This conclusion, that debris disks are narrow belts rather than extended disks, is independent of the significance of 24�m trends for young A-stars. Although the rise and fall is naturally explained by self-stirring, we show that the statistics can also be reproduced with a model in which disks are stirred by secular perturbations from a nearby eccentric planet. Detailed imaging, which can reveal warps, sharp edges, and offsets in individual systems is the best way to characterise the stirring
117 citations
Cites background from "Predictions for a planet just insid..."
...This hypothesis is partly motivated by stars with debris disks known or predicted to harbour planets, such as Fomalhaut and β Pic (Mouillet et al. 1997; Quillen 2006; Kalas et al. 2008; Lagrange et al. 2009a)....
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TL;DR: In this paper, the authors used adaptive optics coronagraphy and polarimetry to image the dust in an annulus between 43 and 302 AU from the star, a region never seen before.
Abstract: The young star AB Aurigae is surrounded by a complex combination of gas-rich and dust-dominated structures. The inner disk, which has not been studied previously at sufficient resolution and imaging dynamic range, seems to contain very little gas inside a radius of least 130 AU from the star. Using adaptive optics coronagraphy and polarimetry, we have imaged the dust in an annulus between 43 and 302 AU from the star, a region never seen before. An azimuthal gap in an annulus of dust at a radius of 102 AU, along with a clearing at closer radii inside this annulus, suggests the formation of at least one small body at an orbital distance of ~100 AU. This structure seems consistent with crude models of mean motion resonances or accumulation of material at two of the Lagrange points relative to the putative object and the star. We also report a low significance detection of a point source in this outer annulus of dust. This source may be an overdensity in the disk due to dust accreting onto an unseen companion. An alternate interpretation suggests that the object's mass is between 5 and 37 times the mass of Jupiter. The results have implications for circumstellar disk dynamics and planet formation.
114 citations
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...For example, the star Fomalhaut has an offset ring of material, with some models claiming that this ring is due to a Saturn mass object at an orbital distance of ∼ 120 AU (Quillen 2006) with low eccentricity....
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TL;DR: In this paper, a point spread function subtraction technique based on angular differential imaging and Locally Optimized Combination of Images was used to improve the Spitzer contrast at small separations.
Abstract: The nearby A4-type star Fomalhaut hosts a debris belt in the form of an eccentric ring, which is thought to be caused by dynamical influence from a giant planet companion. In 2008, a detection of a point source inside the inner edge of the ring was reported and was interpreted as a direct image of the planet, named Fomalhaut b. The detection was made at ~600-800 nm, but no corresponding signatures were found in the near-infrared range, where the bulk emission of such a planet should be expected. Here, we present deep observations of Fomalhaut with Spitzer/IRAC at 4.5 μm, using a novel point-spread function subtraction technique based on angular differential imaging and Locally Optimized Combination of Images, in order to substantially improve the Spitzer contrast at small separations. The results provide more than an order of magnitude improvement in the upper flux limit of Fomalhaut b and exclude the possibility that any flux from a giant planet surface contributes to the observed flux at visible wavelengths. This renders any direct connection between the observed light source and the dynamically inferred giant planet highly unlikely. We discuss several possible interpretations of the total body of observations of the Fomalhaut system and find that the interpretation that best matches the available data for the observed source is scattered light from a transient or semi-transient dust cloud.
114 citations
University of Cambridge1, Harvard University2, University of California, Berkeley3, Search for extraterrestrial intelligence4, University of Grenoble5, Wesleyan University6, Massachusetts Institute of Technology7, Pennsylvania State University8, Goddard Space Flight Center9, University of California, Los Angeles10, UK Astronomy Technology Centre11, University of Leeds12, University of Arizona13
TL;DR: Matra et al. as discussed by the authors used spectrospatial filtering to detect CO J = 2-1 emission colocated with dust emission from the cometary belt in the 440 Myr old Fomalhaut system.
Abstract: Author(s): Matra, L; MacGregor, MA; Kalas, P; Wyatt, MC; Kennedy, GM; Wilner, DJ; Duchene, G; Hughes, AM; Pan, M; Shannon, A; Clampin, M; Fitzgerald, MP; Graham, JR; Holland, WS; Panic, O; Su, KYL | Abstract: Recent Atacama Large Millimeter/submillimeter Array observations present mounting evidence for the presence of exocometary gas released within Kuiper Belt analogs around nearby main-sequence stars. This represents a unique opportunity to study their ice reservoir at the younger ages when volatile delivery to planets is most likely to occur. We here present the detection of CO J = 2-1 emission colocated with dust emission from the cometary belt in the 440 Myr old Fomalhaut system. Through spectrospatial filtering, we achieve a 5.4σ detection and determine that the ring's sky-projected rotation axis matches that of the star. The CO mass derived ((0.65-42) × 10-7 M⊕) is the lowest of any circumstellar disk detected to date and must be of exocometary origin. Using a steady-state model, we estimate the CO+CO2 mass fraction of exocomets around Fomalhaut to be between 4.6% and 76%, consistent with solar system comets and the two other belts known to host exocometary gas. This is the first indication of a similarity in cometary compositions across planetary systems that may be linked to their formation scenario and is consistent with direct interstellar medium inheritance. In addition, we find tentative evidence that (49 ± 27)% of the detected flux originates from a region near the eccentric belt's pericenter. If confirmed, the latter may be explained through a recent impact event or CO pericenter glow due to exocometary release within a steady-state collisional cascade. In the latter scenario, we show how the azimuthal dependence of the CO release rate leads to asymmetries in gas observations of eccentric exocometary belts.
112 citations
Cites background from "Predictions for a planet just insid..."
...…of the very low mass companion Fomalhaut b (Kalas et al. 2008) appeared consistent with the hypothesis that a planet could sculpt the inner edge (Quillen 2006; Chiang et al. 2009), until further observations showed that Fomalhaut b’s orbit is highly eccentric (Kalas et al. 2013; Beust et al.…...
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University of Cambridge1, UK Astronomy Technology Centre2, Spanish National Research Council3, Herzberg Institute of Astrophysics4, University of Geneva5, University of St Andrews6, University of California, Berkeley7, Search for extraterrestrial intelligence8, University of British Columbia9, University of Arizona10, University of Victoria11, California Institute of Technology12, University of New South Wales13, Harvard University14
TL;DR: In this article, Herschel observations of the nearby (8.5pc) G5V multi-exoplanet host star 61Vir at 70, 100, 160, 250, 350 and 500m were carried out as part of the DEBRIS survey.
Abstract: This paper describes Herschel observations of the nearby (8.5pc) G5V multi-exoplanet host star 61Vir at 70, 100, 160, 250, 350 and 500m carried out as part of the DEBRIS survey. These observations reveal emission that is significantly extended out to a distance of >15arcsec with a morphology that can be fitted by a nearly edge-on (77° inclination) radially broad (from 30au out to at least 100au) debris disc of fractional luminosity 2.7 × 10 -5, with two additional (presumably unrelated) sources nearby that become more prominent at longer wavelengths. Chance alignment with a background object seen at 1.4GHz provides potential for confusion, however, the star's 1.4arcsecyr -1 proper motion allows archival Spitzer 70m images to confirm that what we are interpreting as disc emission really is circumstellar. Although the exact shape of the disc's inner edge is not well constrained, the region inside 30au must be significantly depleted in planetesimals. This is readily explained if there are additional planets outside those already known (i.e. in the 0.5-30au region), but is also consistent with collisional erosion. We also find tentative evidence that the presence of detectable debris around nearby stars correlates with the presence of the lowest mass planets that are detectable in current radial velocity surveys. Out of an unbiased sample of the nearest 60G stars, 11 are known to have planets, of which six (including 61Vir) have planets that are all less massive than Saturn, and four of these have evidence for debris. The debris towards one of these planet hosts (HD20794) is reported here for the first time. This fraction (4/6) is higher than that expected for nearby field stars (15per cent), and implies that systems that form low-mass planets are also able to retain bright debris discs. We suggest that this correlation could arise because such planetary systems are dynamically stable and include regions that are populated with planetesimals in the formation process where the planetesimals can remain unperturbed over Gyr time-scales.
108 citations
Cites background from "Predictions for a planet just insid..."
...It is not possible to set hard constraints on more distant planets, except for generalities such as that the planets cannot reside too close to the inner edge of the disk (Quillen 2006; Mustill & Wyatt 2012)....
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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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