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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University of California, Los Angeles1, University of Grenoble2, University of California, Berkeley3, Foundation for Research & Technology – Hellas4, Search for extraterrestrial intelligence5, California Institute of Technology6, Space Telescope Science Institute7, PSL Research University8, Lawrence Livermore National Laboratory9, National Institutes of Natural Sciences, Japan10, University of Notre Dame11, University of Georgia12, European Southern Observatory13, Université de Montréal14, Amherst College15, University of Victoria16, National Research Council17, Durham University18, University of Michigan19, Arizona State University20, United States Geological Survey21, University of California, San Diego22, Stanford University23, Ames Research Center24, Stony Brook University25, University of Western Ontario26, American Museum of Natural History27, Cornell University28, Leiden University29
TL;DR: In this article, a forward-modeled geometric disk is used to extract geometric parameters, polarized fraction, and total intensity scattering phase functions for the resolved debris disk HR4796A taken in the polarimetric mode of the Gemini Planet Imager (GPI).
Abstract: HR4796A hosts a well-studied debris disk with a long history due to its high fractional luminosity and favorable inclination, which facilitate both unresolved and resolved observations. We present new J- and K 1-band images of the resolved debris disk HR4796A taken in the polarimetric mode of the Gemini Planet Imager (GPI). The polarized intensity features a strongly forward-scattered brightness distribution and is undetected at the far side of the disk. The total intensity is detected at all scattering angles and also exhibits a strong forward-scattering peak. We use a forward-modeled geometric disk in order to extract geometric parameters, polarized fraction, and total intensity scattering phase functions for these data as well as H-band data previously taken by GPI. We find the polarized phase function becomes increasingly more forward-scattering as wavelength increases. We fit Mie and distribution of hollow spheres (DHS) grain models to the extracted functions. We find that it is possible to generate a satisfactory model for the total intensity using a DHS model, but not with a Mie model. We find that no single grain population of DHS or Mie grains of arbitrary composition can simultaneously reproduce the polarized fraction and total intensity scattering phase functions, indicating the need for more sophisticated grain models.
17 citations
Cites background from "Predictions for a planet just insid..."
...Resolved images of disks show that features such as sharp radial profiles, warps, clumps, and spirals can be caused by unseen planets (Quillen 2006a; Nesvold & Kuchner 2015)....
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...Models of observable disk features have led to the discoveries of directly imaged planets around their host stars such as β-Pictoris b (Lagrange et al. 2010) and Fomalhaut b (Quillen 2006b)....
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TL;DR: In this paper, the relative distribution of abundances of refractory, intermediate, and volatile elements in stars with planets can be used for investigating the internal migration of a giant planet.
Abstract: The relative distribution of abundances of refractory, intermediate, and volatile elements in stars with planets can be an important tool for investigating the internal migration of a giant planet. This migration can lead to the accretion of planetesimals and the selective enrichment of the star with these elements. We report on a spectroscopic determination of the atmospheric parameters and chemical abundances of the parent stars in transiting planets CoRoT-2b and CoRoT-4b. Adding data for CoRoT-3 and CoRoT-5 from the literature, we find a flat distribution of the relative abundances as a function of their condensation temperatures. For CoRoT-2, the relatively high lithium abundance and intensity of its Li i resonance line permit us to propose an age of 120 Myr, making this star one of the youngest stars with planets to date. We introduce a new methodology to investigate a relation between the abundances of these stars and the internal migration of their planets. By simulating the internal migration of a planet in a disk formed only by planetesimals, we are able, for the first time, to separate the stellar fractions of refractory, intermediate, and volatile rich planetesimals accreting onto the central star. Intermediate and volatile element fractions enriching the star are similar and much larger than those of pure refractory ones. This result is opposite to what has been considered in the literature for the accreting self-enrichment processes of stars with planets. We also show that these results are highly dependent on the model adopted for the disk distribution regions in terms of refractory, intermediate, and also volatile elements and other parameters considered. We note however, that this self-enrichment mechanism is only efficient during the first 20–30 Myr or later in the lifetime of the disk when the surface convection layers of the central star for the first time attain its minimum size configuration.
16 citations
Additional excerpts
...According to Quillen (2006), a body is captured into the 2:1 resonance when its ini- tial eccentricity is below a certain limit given byelim ∼ 1.5µ1/3....
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TL;DR: In this paper, the authors present 1.3 millimeter observations of the debris disk surrounding the HR 8799 multi-planet system from the Submillimeter Array to complement archival ALMA observations that spatially filtered away the bulk of the emission.
Abstract: We present 1.3 millimeter observations of the debris disk surrounding the HR 8799 multi-planet system from the Submillimeter Array to complement archival ALMA observations that spatially filtered away the bulk of the emission. The image morphology at $3.8$ arcsecond (150 AU) resolution indicates an optically thin circumstellar belt, which we associate with a population of dust-producing planetesimals within the debris disk. The interferometric visibilities are fit well by an axisymmetric radial power-law model characterized by a broad width, $\Delta R/R\gtrsim 1$. The belt inclination and orientation parameters are consistent with the planet orbital parameters within the mutual uncertainties. The models constrain the radial location of the inner edge of the belt to $R_\text{in}= 104_{-12}^{+8}$ AU. In a simple scenario where the chaotic zone of the outermost planet b truncates the planetesimal distribution, this inner edge location translates into a constraint on the planet~b mass of $M_\text{pl} = 5.8_{-3.1}^{+7.9}$ M$_{\rm Jup}$. This mass estimate is consistent with infrared observations of the planet luminosity and standard hot-start evolutionary models, with the uncertainties allowing for a range of initial conditions. We also present new 9 millimeter observations of the debris disk from the Very Large Array and determine a millimeter spectral index of $2.41\pm0.17$. This value is typical of debris disks and indicates a power-law index of the grain size distribution $q=3.27\pm0.10$, close to predictions for a classical collisional cascade.
16 citations
Cites background from "Predictions for a planet just insid..."
...The separation of the planet from the disk is sensitive to the planet mass, as the planet clears a chaotic zone around itself due to resonance overlap (e.g. Quillen 2006; Chiang et al. 2009)....
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Stockholm University1, National Institutes of Natural Sciences, Japan2, ETH Zurich3, Tokyo Institute of Technology4, University of Nice Sophia Antipolis5, Max Planck Society6, College of Charleston7, Ludwig Maximilian University of Munich8, Goddard Space Flight Center9, University of Hawaii10, Princeton University11, University of Tokyo12, Kyoto University13, Graduate University for Advanced Studies14, Hiroshima University15, Johns Hopkins University16, Space Telescope Science Institute17, Academia Sinica18, Hokkaido University19, University of Oklahoma20, Tohoku University21
TL;DR: In this paper, high-contrast angular differential imaging (ADI) observations of the debris disk around HD 32297 in H-band, as well as the first polarimetric images for this system in polarized differential imaging mode with Subaru/HICIAO were presented.
Abstract: We present high-contrast angular differential imaging (ADI) observations of the debris disk around HD 32297 in H-band, as well as the first polarimetric images for this system in polarized differential imaging (PDI) mode with Subaru/HICIAO. In ADI, we detect the nearly edge-on disk at >5sigma levels from ~0.45 arcsec to ~1.7 arcsec (50-192 AU) from the star and recover the spine deviation from the midplane already found in previous works. We also find for the first time imaging and surface brightness (SB) indications for the presence of a gapped structure on both sides of the disk at distances of ~0.75 arcsec (NE side) and ~0.65 arcsec (SW side). Global forward-modelling work delivers a best-fit model disk and well-fitting parameter intervals that essentially match previous results, with high-forward scattering grains and a ring located at 110 AU. However, this single ring model cannot account for the gapped structure seen in our SB profiles. We create simple double ring models and achieve a satisfactory fit with two rings located at 60 and 95 AU, respectively, low-forward scattering grains and very sharp inner slopes. In polarized light we retrieve the disk extending from ~0.25-1.6 arcsec, although the central region is quite noisy and high S/N are only found in the range ~0.75-1.2 arcsec. The disk is polarized in the azimuthal direction, as expected, and the departure from the midplane is also clearly observed. Evidence for a gapped scenario is not found in the PDI data. We obtain a linear polarization degree of the grains that increases from ~10% at 0.55 arcsec to ~25% at 1.6 arcsec. The maximum is found at scattering angles of ~90degrees, either from the main components of the disk or from dust grains blown out to larger radii.
14 citations
University of Toronto1, University of California, Berkeley2, Search for extraterrestrial intelligence3, University of Grenoble4, Stanford University5, Space Telescope Science Institute6, Goddard Space Flight Center7, Stony Brook University8, University of Western Ontario9, Lawrence Livermore National Laboratory10, University of Arizona11, Subaru12, University of Georgia13, Université de Montréal14, University of Victoria15, National Research Council16, University of California, Los Angeles17, Johns Hopkins University18, European Southern Observatory19, University of Exeter20, University of California, San Diego21, Ames Research Center22, American Museum of Natural History23, Arizona State University24, Cornell University25, University of Toledo26, California Institute of Technology27, The Aerospace Corporation28
TL;DR: In this paper, the authors present near-infrared polarimetric imaging observations of the F5V star HD~157587 obtained with the Gemini Planet Imager (GPI) that reveal the debris disk as a bright ring structure at a separation of approximately 80-100 AU.
Abstract: We present $H$-band near-infrared polarimetric imaging observations of the F5V star HD~157587 obtained with the Gemini Planet Imager (GPI) that reveal the debris disk as a bright ring structure at a separation of $\sim$80$-$100~AU. The new GPI data complement recent HST/STIS observations that show the disk extending out to over 500~AU. The GPI image displays a strong asymmetry along the projected minor axis as well as a fainter asymmetry along the projected major axis. We associate the minor and major axis asymmetries with polarized forward scattering and a possible stellocentric offset, respectively. To constrain the disk geometry we fit two separate disk models to the polarized image, each using a different scattering phase function. Both models favor a disk inclination of $\sim 70\degr$ and a $1.5\pm0.6$ AU stellar offset in the plane of the sky along the projected major axis of the disk. We find that the stellar offset in the disk plane, perpendicular to the projected major axis is degenerate with the form of the scattering phase function and remains poorly constrained. The disk is not recovered in total intensity due in part to strong adaptive optics residuals, but we recover three point sources. Considering the system's proximity to the galactic plane and the point sources' positions relative to the disk, we consider it likely that they are background objects and unrelated to the disk's offset from the star.
14 citations
Cites background from "Predictions for a planet just insid..."
...Such an interaction can manifest as a warp (e.g., Beta Pic; Burrows et al. 1995; Mouillet et al. 1997), a stellocentric offset (e.g., HR 4796A; Wyatt et al. 1999; Telesco et al. 2000), or a sharp radial profile at the inner edge of a dust ring (e.g., Fomalhaut; Kalas et al. 2005; 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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