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 semi-major axes to precess at different rates, and after some time t_cross initially non-intersecting orbits begin to cross. We show that t_cross is proportional to a_disc^(9/2)/(m_pl e_pl a_pl^3), where m_pl, e_pl and a_pl are the mass, eccentricity, and semi-major axis of the planet, and a_disc is the semi-major 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 amongst 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 epsilon Eridani, we find that the known RV planet can excite the planetesimal belt at 60 AU sufficiently to cause destructive collisions of bodies up to 100 km in size, on a time-scale of 40 Myr.
Debris discs consist of belts of bodies ranging in size from dust grains to planetesimals; these belts are visible markers of planetary systems around other stars that can reveal the influence of extrasolar planets through their shape and structure. Two key stirring mechanisms -- self-stirring by planetesimals and secular perturbation by an external giant planet -- have been identified to explain the dynamics of planetesimal belts; their relative importance has been studied independently, but are yet to be considered in combination. In this work we perform a suite of 286 N-body simulations exp…
The dust production in debris discs by grinding collisions of planetesimals requires their orbits to be stirred. However, stirring levels remain largely unconstrained, and consequently the stirring mechanisms as well. This work shows how the sharpness of the outer edge of discs can be used to constrain the stirring levels. Namely, the sharper the edge is the lower the eccentricity dispersion must be. For a Rayleigh distribution of eccentricities ($e$), I find that the disc surface density near the outer edge can be parametrised as $\tanh[(r_{\max}-r)/l_{\rm out}]$, where $r_{\max}$ approximate…
A significant fraction of main-sequence stars are encircled by dusty debris discs, where the short-lived dust particles are replenished through collisions between planetesimals. Most destructive collisions occur when the orbits of smaller bodies are dynamically stirred up, either by the gravitational effect of locally formed Pluto-sized planetesimals (self-stirring scenario), or via secular perturbation caused by an inner giant planet (planetary stirring). The relative importance of these scenarios in debris systems is unknown. Here we present new Herschel Space Observatory imagery of 11 discs…
When a protoplanetary disc loses gas, it leaves behind planets and one or more planetesimal belts. The belts get dynamically excited, either by planets ('planet stirring') or by embedded big planetesimals ('self-stirring'). Collisions between planetesimals become destructive and start to produce dust, creating an observable debris disc. Following Kenyon & Bromley (2008), it is often assumed that self-stirring starts to operate as soon as the first ~1000 km-sized embedded 'Plutos' have formed. However, state-of-the-art pebble concentration models robustly predict planetesimals between a few km …
We study the gravitational instability (GI) of small solids in a gas disk as a mechanism to form planetesimals. Dissipation from gas drag introduces secular GI, which proceeds even when standard GI criteria for a critical density or Toomre's $Q$ predict stability. We include the stabilizing effects of turbulent diffusion, which suppresses small scale GI. The radially wide rings that do collapse contain up to $\sim 0.1$ Earth masses of solids. Subsequent fragmentation of the ring (not modeled here) would produce a clan of chemically homogenous planetesimals. Particle radial drift time scales (a…
This paper considers the evidence that debris disks are self-stirred by the formation of Plutos. A model for the dust produced during self-stirring is applied to statistics for A stars. As there is no significant difference between excesses of A-stars <50Myr old, we focus on reproducing the broad trends, the "rise and fall" of the fraction of stars with excesses. Using a population model, we find that the statistics and trends can be reproduced with a self-stirring model of planetesimal belts with radii distributed between 15-120AU. Disks must have this 15AU minimum radius to show a peak in di…
Resolved images suggest that asymmetric structures are a common feature of cold debris disks. While planets close to these disks are rarely detected, their hidden presence and gravitational perturbations provide plausible explanations for some of these features. To put constraints on the properties of yet undetected planetary companions, we aim to predict what features such a planet imprints in debris disks undergoing continuous collisional evolution. We discuss the basic equations, analytic approximations and timescales governing collisions, radiation pressure and secular perturbations. In ad…
The vertical distribution of dust in debris disks is sensitive to the number and size of large planetesimals dynamically stirring the disk, and is therefore well-suited for constraining the prevalence of otherwise unobservable Uranus and Neptune analogs. Information regarding stirring bodies has previously been inferred from infrared and optical observations of debris disk vertical structure, but theoretical works predict that the small particles traced by short-wavelength observations will be `puffed up' by radiation pressure, yielding only upper limits. The large grains that dominate the dis…
We investigate the evolution on secular time-scales of a radially extended debris disc under the influence of a system of two coplanar planets interior to the disc, showing that the secular resonances of the system can produce a depleted region in the disc by exciting the eccentricities of planetesimals. Using Laplace-Lagrange theory, we consider how the two exterior secular resonance locations, time-scales and widths depend on the masses, semi-major axes and eccentricities of the planets. In particular, we find that unless the resonances are very close to each other, one of them is very narro…
The dynamics of small bodies around the Earth has gained a renewed interest, since the awareness of the problems that space debris can cause in the nearby future. A relevant role in space debris is played by lunisolar secular resonances, which might contribute to an increase of the orbital elements, typically of the eccentricity. We concentrate our attention on the lunisolar secular resonance described by the relation $2\dotω+\dotΩ=0$, where $ω$ and $Ω$ denote the argument of perigee and the longitude of the ascending node of the space debris. We introduce three different models with increasin…
Spatially resolved images of debris disks frequently reveal complex morphologies such as gaps, spirals, and warps. Most existing models for explaining such morphologies focus on the role of massive perturbers (i.e. planets, stellar companions), ignoring the gravitational effects of the disk itself. Here we investigate the secular interaction between an eccentric planet and a massive, external debris disk using a simple analytical model. Our framework accounts for both the gravitational coupling between the disk and the planet, as well as the disk self-gravity -- with the limitation that it ign…
Context. The interaction between low-mass companions and the debris discs they reside in is still not fully understood. A debris disc can evolve due to self-stirring, a process in which planetesimals can excite their neighbours to the point of destructive collisions. In addition, the presence of a companion could further stir the disc (companion-stirring). Additional information is necessary to understand this fundamental step in the formation and evolution of a planetary system, and at the moment of writing only a handful of systems are known where a companion and a debris disc have both been…
Extended gaps in the debris disks of both Vega and Fomalhaut have been observed. These structures have been attributed to tidal perturbations by multiple super-Jupiter gas giant planets. Within the current observational limits, however, no such massive planets have been detected. Here we propose a less stringent `lone-planet' scenario to account for the observed structure with a single eccentric gas giant and suggest that clearing of these wide gaps is induced by its sweeping secular resonance. During the depletion of the disk gas, the planet's secular resonance propagates inward and clears a …
We know little about the outermost exoplanets in planetary systems, because our detection methods are insensitive to moderate-mass planets on wide orbits. However, debris discs can probe the outer-planet population, because dynamical modelling of observed discs can reveal properties of perturbing planets. We use four sculpting and stirring arguments to infer planet properties in 178 debris-disc systems from the ISPY, LEECH and LIStEN planet-hunting surveys. Similar analyses are often conducted for individual discs, but we consider a large sample in a consistent manner. We aim to predict the po…
Using bifurcation theory, we study the secular resonances induced by the Sun and Moon on space debris orbits around the Earth. In particular, we concentrate on a special class of secular resonances, which depend only on the debris' orbital inclination. This class is typically subdivided into three distinct types of secular resonances: those occurring at the critical inclination, those corresponding to polar orbits, and a third type resulting from a linear combination of the rates of variation of the argument of perigee and the longitude of the ascending node. The model describing the dynamics …
Planet--planet scattering is a major dynamical mechanism able to significantly alter the architecture of a planetary system. In addition to that, it may also affect the formation and retention of a debris disk by the system. A violent chaotic evolution of the planets can easily clear leftover planetesimal belts preventing the ignition of a substantial collisional cascade that can give origin to a debris disk. On the other end, a mild evolution with limited steps in eccentricity and semimajor axis can trigger the formation of a debris disk by stirring an initially quiet planetesimal belt. The v…
We have explored the evolution of a cold debris disk under the gravitational influence of dwarf planet sized objects (DPs), both in the presence and absence of an interior giant planet. Through detailed long-term numerical simulations, we demonstrate that, when the giant planet is not present, DPs can stir the eccentricities and inclinations of disk particles, in linear proportion to the total mass of the DPs; on the other hand, when the giant planet is included in the simulations, the stirring is approximately proportional to the mass squared. This creates two regimes: below a disk mass thres…
Cold debris disks trace the limits of planet formation or migration in the outer regions of planetary systems, and thus have the potential to answer many of the outstanding questions in wide-orbit planet formation and evolution. We characterized the infrared excess spectral energy distributions of 174 cold debris disks around 546 main-sequence stars observed by both Spitzer IRS and MIPS. We found a trend between the temperature of the inner edges of cold debris disks and the stellar type of the stars they orbit. This argues against the importance of strictly temperature-dependent processes (e.…
We investigate the interaction between an eccentric planet and a less massive external debris disc. This scenario could occur after planet-planet scattering or merging events. We characterise the evolution over a wide range of initial conditions, using a suite of n-body integrations combined with theory. Planets near the disc mid-plane remove the inner debris region, and surviving particles form an eccentric disc apsidally aligned with the planet. The inner disc edge is elliptical and lies just beyond the planet's orbit. Moderately inclined planets ($i_{\rm plt} \gtrsim 20^\circ$ for $e_{\rm p…
A "minimum model" for debris disks consists of a narrow ring of parent bodies, secularly forced by a single planet on a possibly eccentric orbit, colliding to produce dust grains that are perturbed by stellar radiation pressure. We demonstrate how this minimum model can reproduce a wide variety of disk morphologies imaged in scattered starlight. Five broad categories of disk shape can be captured: "rings," "needles," "ships-and-wakes," "bars," and "moths (a.k.a. fans)," depending on the viewing geometry. Moths can also sport "double wings." We explain the origin of morphological features from …
The surface energy constraint puts a limit on the smallest fragment $s_{surf}$ that can be produced after a collision. Based on analytical considerations, this mechanism has been recently identified as been potentially able to prevent the production of small dust grains in debris discs and cut off their size distribution at sizes larger than the blow-out size. We numerically investigate the importance of this effect to find under which conditions it can leave a signature in the small-size end of a disc's particle size distribution (PSD). An important part of this work is to map out, in a disc …
We have bandmerged candidate transiting planetary systems (from the Kepler satellite) and confirmed transiting planetary systems (from the literature) with the recent Wide-field Infrared Survey Explorer (WISE) preliminary release catalog. We have found 13 stars showing infrared excesses at either 12 and/or 22 microns. Without longer wavelength observations it is not possible to conclusively determine the nature of the excesses, although we argue that they are likely due to debris disks around the stars. If confirmed, our sample ~ doubles the number of currently known warm excess disks around o…
Numerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We…
Models of debris disk morphology are often focused on the effects of a planet orbiting interior to or within the disk. Nonetheless, an exterior planetary-mass perturber can also excite eccentricities in a debris disk, via Laplace-Lagrange secular perturbations in the coplanar case or Kozai-Lidov perturbations for mutually inclined companions and disks. HD 106906 is an ideal example of such a system, as it harbors a confirmed exterior 11 M_Jup companion at a projected separation of 650 au outside a resolved, asymmetric disk. We use collisional and dynamical simulations to investigate the intera…
Planetesimal belts are invoked to explain the prolonged existence of debris disks. Important parameters to model their collisional evolution and to compute the dust production rate are the intrinsic probability of collision $P_i$ and the mean impact velocity $U_c$. If a planet orbits close to the belt, the values of both these parameters are affected by its secular perturbations yielding a strong correlation between eccentricity $e$ and pericentre longitude $\varpi$. We adopt a new algorithm to compute both $P_i$ and $U_c$ in presence of various levels of secular correlation due to different r…
Two basic routes for planetesimal formation have been proposed over the last few decades. One is a classical "slow-growth" scenario. Another one is particle concentration models, in which small pebbles are concentrated locally and then collapse gravitationally to form planetesimals. Both types of models make certain predictions for the size spectrum and internal structure of newly-born planetesimals. We use these predictions as input to simulate collisional evolution of debris discs left after the gas dispersal. The debris disc emission as a function of a system's age computed in these simulat…
The protoplanetary disks of Herbig Ae stars eventually dissipate leaving a tenuous debris disk comprised of planetesimals and dust, as well as possibly gas and planets. This paper uses the properties of 10-20Myr A star debris disks to consider the protoplanetary to debris disk transition. The physical distinction between these two classes is argued to rest on the presence of primordial gas in sufficient quantities to dominate the motion of small dust grains (not the secondary nature of the dust or its level of stirring). This motivates an observational classification based on the dust spectrum…
We present a new model of the $β$ Pictoris disk-and-planet system that simulates both the planetesimal collisions and the dynamics of the resulting dust grains, allowing us to model features and asymmetries in both thermal and scattered light images of the disk. Our two-part model first simulates the collisional and dynamical evolution of the planetesimals with the Superparticle-Method Algorithm for Collisions in Kuiper belts (SMACK) and then simulates the dynamical evolution of the resulting dust grains with a standard Bulirsch-Stoer N-body integrator. Given the observed inclination and eccen…
The increasing threat raised by space debris led to the development of different mathematical models and approaches to investigate the dynamics of small particles orbiting around the Earth. Such models and methods strongly depend on the altitude of the objects above Earth's surface, since the strength of the different forces acting on an Earth orbiting object (geopotential, atmospheric drag, lunar and solar attractions, solar radiation pressure, etc.) varies with the altitude of the debris. In this review, our focus is on presenting different analytical and numerical approaches employed in mod…
To date, studies of $\textit{Laplace Surface}$ dynamics have concerned themselves with test particle orbits of fixed shape and orientation in the combined field of an oblate central body (to which the particle is bound) and a distant, inclined, companion which is captured to quadrupolar order. While amply sufficient for satellites around planets on near-circular orbits, the quadrupolar approximation fails to capture essential dynamical features induced by a wide binary companion (be it a star, a planet or a black hole) on a fairly eccentric orbit. With similar such astronomical settings in min…
Viscously Stirring Particle Disks into Lorentzians and Gaussians to Infer Dynamical and Collisional Masses (ARKS XIII)
University of California, Berkeley（加州大学伯克利分校）；University of Warwick（华威大学）；Institute of Physics Belgrade, University of Belgrade（贝尔格莱德物理研究所，贝尔格莱德大学）；California Institute of Technology（加州理工学院）；Wesleyan University（卫斯理安大学）
We have obtained a full suite of Spitzer observations to characterize the debris disk around HR 8799 and to explore how its properties are related to the recently discovered set of three massive planets orbiting the star. We distinguish three components to the debris system: (1) warm dust (T ~150 K) orbiting within the innermost planet; (2) a broad zone of cold dust (T ~45 K) with a sharp inner edge, orbiting just outside the outermost planet and presumably sculpted by it; and (3) a dramatic halo of small grains originating in the cold dust component. The high level of dynamical activity impli…
With the use of long-term numerical simulations, we study the evolution and orbital behavior of cometary nuclei in cold Kuiper belt-like debris disks under the gravitational influence of dwarf planets (DPs); we carry out these simulations with and without the presence of a Neptune-like giant planet. This exploratory study shows that in the absence of a giant planet, 10 DPs are enough to induce strong radial and vertical heating on the orbits of belt particles. On the other hand, the presence of a giant planet close to the debris disk, acts as a stability agent reducing the radial and vertical …
The first indication of the presence of a circumstellar debris disk is usually the detection of excess infrared emission from the population of small dust grains orbiting the star. This dust is short-lived, requiring continual replenishment, and indicating that the disk must be excited by an unseen perturber. Previous theoretical studies have demonstrated that an eccentric planet orbiting interior to the disk will stir the larger bodies in the belt and produce dust via interparticle collisions. However, motivated by recent observations, we explore another possible mechanism for heating a debri…
Debris disks have been found primarily around intermediate and solar mass stars (spectral types A-K) but rarely around low mass M-type stars. We have spatially resolved a debris disk around the remarkable M3-type star GJ581 hosting multiple planets using deep PACS images at 70, 100 and 160 microns as part of the DEBRIS Program on the Herschel Space Observatory. This is the second spatially resolved debris disk found around an M-type star, after the one surrounding the young star AU Mic (12 Myr). However, GJ 581 is much older (2-8 Gyr), and is X-ray quiet in the ROSAT data. We fit an axisymmetr…
Dynamics of the TWA 7 planetary system and possibility of an additional planet
Univ. Grenoble Alpes, CNRS, IPAG（格勒诺布尔阿尔卑斯大学）；Department of Astronomy, University of California, Berkeley（加州大学伯克利天文学系）；LIRA, CNRS, Observatoire de Paris, Université PSL（巴黎天文台）
TWA 7行星系统通过结合N体模拟和摄动理论，探讨未检测到的内行星对尘埃盘形态和共轨道动态的影响，揭示系统在参数空间中的窄区域配置。
We investigate the general interaction between an eccentric planet and a coplanar debris disc of the same mass, using analytical theory and n-body simulations. Such an interaction could result from a planet-planet scattering or merging event. We show that when the planet mass is comparable to that of the disc, the former is often circularised with little change to its semimajor axis. The secular effect of such a planet can cause debris to apsidally anti-align with the planet's orbit (the opposite of what may be naively expected), leading to the counter-intuitive result that a low-mass planet m…
We present a numerical simulation of the dynamical interaction between the proposed Planet Nine and a debris disk around the Sun for $4{\rm Gyr}$, accounting for the secular perturbation of the four giant planets in two scenarios: (a) an initially thin circular disk around the Sun (b) inclined and eccentric disk. We show, in both scenarios, that Planet Nine governs the dynamics in between $1000{\rm -5000{\rm AU}}$ and forms spherical structure in the inner part ($\sim1000{\rm AU}$) and inclined disk. This structure is the outcome of mean motion resonances and secular interaction with Planet Ni…
The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) IX: Gas-driven origin for the continuum arc in the debris disc of HD 121617
Millennium Nucleus on Young Exoplanets and their Moons (YEMS)（年轻系外行星及其卫星千年核）；Center for Interdisciplinary Research in Astrophysics Space Exploration (CIRAS), Universidad de Santiago（圣地亚哥大学天体物理空间探索跨学科研究中心）；Department of Astronomy, Graduate School of Science, The University of Tokyo（东京大学理学研究科天文学系）；Departamento de Astrofísica, Universidad de La Laguna（拉帕鲁纳大学天体物理学系）；Institute of Physics and Astronomy, ELTE Eötvös Loránd University（罗兰·厄特沃什大学物理与天文学研究所）；Max-Planck-Insitut für Astronomie（马克斯·普朗克天文学研究所）
This paper presents a study of circumstellar debris around Sun-like stars using data from the Herschel DEBRIS Key Programme. DEBRIS is an unbiased survey comprising the nearest ~90 stars of each spectral type A-M. Analysis of the 275 F-K stars shows that excess emission from a debris disc was detected around 47 stars, giving a detection rate of 17.1+2.6-2.3 per cent, with lower rates for later spectral types. For each target a blackbody spectrum was fitted to the dust emission to determine its fractional luminosity and temperature. The derived under- lying distribution of fractional luminosity…
Debris disc architecture presents [exo-]planetary scientists with precious clues for processes of planet formation and evolution, including constraints on planetary mass perturbers. This is particularly true of the disc in HD 106906, which in early HST, then follow up polarimetric observations, presented asymmetries and needle-like features that have been attributed to perturbations by a massive, and unusually distant external planetary companion. Here, we revisit the long-term secular dynamical evolution of the HD 106906 disc allowing for the combined gravitational action of the planetary com…
Context: High-resolution images of circumstellar debris discs reveal off-centred rings that indicate past or ongoing perturbation, possibly caused by secular gravitational interaction with unseen stellar or substellar companions. The purely dynamical aspects of this departure from radial symmetry are well understood. However, the observed dust is subject to additional forces and effects, most notably collisions and drag. Aims: To complement the studies of dynamics, we therefore aim to understand how new asymmetries are created by the addition of collisional evolution and drag forces, and exist…
This paper shows that the eccentric debris rings seen around the stars Fomalhaut and HD 202628 are narrower than expected in the standard eccentric planet perturbation scenario (sometimes referred to as "pericenter glow"). The standard scenario posits an initially circular and narrow belt of planetesimals at semi-major axis $a$, whose eccentricity is increased to $e_f$ after the gas disc has dispersed by secular perturbations from an eccentric planet, resulting in a belt of width $2ae_f$. In a minor modification of this scenario, narrower belts can arise if the planetesimals are initially ecce…
A key discovery of the Kepler mission is of the circumbinary planets known as "Tatooines", which appear to be well aligned with their host stars' orbits. Whether this alignment is due to initially coplanar circumbinary planet-forming discs (i.e. nature), or subsequent alignment of initially misaligned discs by warping the inner disc or torquing the binary (i.e. nurture), is not known. Tests of which scenario dominates may be possible by observing circumbinary Kuiper belt analogues ("debris discs"), which trace the plane of the primordial disc. Here, the 140 au diameter circumbinary debris disc…
The long-term dynamics of the geostationary Earth orbits (GEO) is revisited through the application of canonical perturbation theory. We consider a Hamiltonian model accounting for all major perturbations: geopotential at order and degree two, lunisolar perturbations with a realistic model for the Sun and Moon orbits, and solar radiation pressure. The long-term dynamics of the GEO region has been studied both numerically and analytically, in view of the relevance of such studies to the issue of space debris or to the disposal of GEO satellites. Past studies focused on the orbital evolution of …
In many ways, the HR 8799 planetary system strongly resembles our own. It features four giant planets and two debris belts, analogues to the Asteroid and Edgeworth-Kuiper belts. Here, we present the results of dynamical simulations of HR 8799's inner debris belt, to study its structure and collisional environment. Our results suggest that HR 8799's inner belt is highly structured, with gaps between regions of dynamical stability. The belt is likely constrained between sharp inner and outer edges, located at ~6 and ~8 au, respectively. Its inner edge coincides with a broad gap cleared by the 4:…
The HD 61005 debris disk ("The Moth") stands out from the growing collection of spatially resolved circumstellar disks by virtue of its unusual swept-back morphology, brightness asymmetries, and dust ring offset. Despite several suggestions for the physical mechanisms creating these features, no definitive answer has been found. In this work, we demonstrate the plausibility of a scenario in which the disk material is shaped dynamically by an eccentric, inclined planet. We present new Keck NIRC2 scattered-light angular differential imaging of the disk at 1.2-2.3 microns that further constrains …
Recent results suggest that the two planets in the HD 82943 system are inclined to the sky plane by 20 +/- 4deg. Here, we show that the debris disk in this system is inclined by 27 +/- 4deg, thus adding strength to the derived planet inclinations and suggesting that the planets and debris disk are consistent with being aligned at a level similar to the Solar System. Further, the stellar equator is inferred to be inclined by 28 +/- 4deg, suggesting that the entire star - planet - disk system is aligned, the first time such alignment has been tested for radial velocity discovered planets on ~AU …
The large scale structure of the Solar System has been shaped by a transient dynamical instability that may have been triggered by the interaction of the giants planets with a massive primordial disk of icy debris. In this work, we investigate the conditions under which this primordial disk could have coalesced into planets using analytic and numerical calculations. In particular, we perform numerical simulations of the Solar System's early dynamical evolution that account for the viscous stirring and collisional damping within the disk. We demonstrate that if collisional damping would have be…
