Planetesimal Belts Research Articles

Using debris disk observations to infer substellar companions orbiting within or outside a parent planetesimal belt (Corrigendum)

Using debris disk observations to infer substellar companions orbiting within or outside a parent planetesimal belt (Corrigendum)

Deep Search for a Scattered Light Dust Halo Around Vega with the Hubble Space Telescope

We present a provisory scattered-light detection of the Vega debris disk using deep Hubble Space Telescope (HST) coronagraphy (PID 16666). At only 7.7 pc, Vega is immensely important in debris disk studies both for its prominence and also because it allows the highest physical resolution among all debris systems relative to temperature zones around the star. We employ the STIS coronagraph’s widest wedge position and classical reference differential imaging to achieve among the lowest surface-brightness sensitivities to date ( ∼4μJyarcsec−2 ) at wide separations using 32 orbits in Cycle 29. We detect a halo extending from the inner edge of our effective inner working angle at 10.″5 out to the photon noise floor at 30″ (80–230 au). The face-on orientation of the system and the lack of a perfectly color-matched point-spread function star have posed significant challenges to the reductions, particularly regarding artifacts from the imperfect color matching. However, we find that a halo of small dust grains provides the best explanation for the observed signal. Unlike Fomalhaut (a close twin to Vega in luminosity, distance, and age), there is no clear distinction in scattered light between the parent planetesimal belt observed with the Atacama Large Millimeter/submillimeter Array and the extended dust halo. These HST observations complement JWST GTO Cycle 1 observations of the system with NIRCam and MIRI.

REsolved ALMA and SMA Observations of Nearby Stars. REASONS: A population of 74 resolved planetesimal belts at millimetre wavelengths

Planetesimal belts are ubiquitous around nearby stars, and their spatial properties hold crucial information for planetesimal and planet formation models. We present resolved dust observations of 74 planetary systems as part of the REsolved ALMA and SMA Observations of Nearby Stars (REASONS) survey and archival reanalysis. We uniformly modelled interferometric visibilities for the entire sample to obtain the basic spatial properties of each belt, and combined these with constraints from multi-wavelength photometry. We report key findings from a first exploration of this legacy dataset: (1) Belt dust masses are depleted over time in a radially dependent way, with dust being depleted faster in smaller belts, as predicted by collisional evolution. (2) Most belts are broad discs rather than narrow rings, with much broader fractional widths than rings in protoplanetary discs. We link broad belts to either unresolved substructure or broad planetesimal discs produced if protoplanetary rings migrate. (3) The vertical aspect ratios ($h=H/R$) of 24 belts indicate orbital inclinations of sim 1-20$^ circ $, implying relative particle velocities of sim 0.1-4 km/s, and no clear evolution of heights with system age. This could be explained by early stirring within the belt by large bodies (with sizes of at least sim 140 km to the size of the Moon), by inheritance of inclinations from the protoplanetary disc stage, or by a diversity in evolutionary pathways and gravitational stirring mechanisms. We release the REASONS legacy multidimensional sample of millimetre-resolved belts to the community as a valuable tool for follow-up multi-wavelength observations and population modelling studies.

The Solar System could have formed in a low-viscosity disc: A dynamical study from giant planet migration to the Nice model

Context. In the context of low-viscosity protoplanetary discs (PPDs), the formation scenarios of the Solar System should be revisited. In particular, the Jupiter-Saturn pair has been shown to lock in the 2:1 mean motion resonance while migrating generally inwards, making the Grand Tack scenario impossible. Aims. We explore what resonant chains of multiple giant planets can form in a low-viscosity disc, and whether these configurations can evolve into forming the Solar System in the post gas disc phase. Methods. We used hydrodynamical simulations with the code FARGOCA to study the migration of the giant planets in a disc with viscosity parameter of α = 10−4. After a transition phase to a gas-less configuration, we studied the stability of the obtained resonant chains through their interactions with a disc of leftover planetesimals by performing N-body simulations using rebound. Results. The gaps opened by giant planets are wider and deeper for lower viscosity, reducing the damping effect of the disc. Thus, when planets enter a resonance, the resonant angle remains closer to circulation, making the chain weaker. Exploring numerous configurations, we found five stable resonant chains of four or five planets. In a thin (cold) PPD, the four giant planets revert their migration and migrate outwards. After disc dispersal, under the influence of a belt of planetesimals, some resonant chains undergo an instability phase while others migrate smoothly over a billion years. For three of our resonant chains, about ~1% of the final configurations pass the four criteria to fit the Solar System. The most successful runs are obtained for systems formed in a cold PPD with a massive planetesimal disc. Conclusions. This work provides a fully consistent study of the dynamical history of the Solar System’s giant planets, from the protoplanetary disc phase up to the giant planet instability. Although building resonant configurations is difficult in low-viscosity discs, we find it possible to reproduce the Solar System from a cold, low-viscosity protoplanetary disc.

Atacama Large Aperture Submillimeter Telescope (AtLAST) science: Our Galaxy.

As we learn more about the multi-scale interstellar medium (ISM) of our Galaxy, we develop a greater understanding for the complex relationships between the large-scale diffuse gas and dust in Giant Molecular Clouds (GMCs), how it moves, how it is affected by the nearby massive stars, and which portions of those GMCs eventually collapse into star forming regions. The complex interactions of those gas, dust and stellar populations form what has come to be known as the ecology of our Galaxy. Because we are deeply embedded in the plane of our Galaxy, it takes up a significant fraction of the sky, with complex dust lanes scattered throughout the optically recognizable bands of the Milky Way. These bands become bright at (sub-)millimetre wavelengths, where we can study dust thermal emission and the chemical and kinematic signatures of the gas. To properly study such large-scale environments, requires deep, large area surveys that are not possible with current facilities. Moreover, where stars form, so too do planetary systems, growing from the dust and gas in circumstellar discs, to planets and planetesimal belts. Understanding the evolution of these belts requires deep imaging capable of studying belts around young stellar objects to Kuiper belt analogues around the nearest stars. Here we present a plan for observing the Galactic Plane and circumstellar environments to quantify the physical structure, the magnetic fields, the dynamics, chemistry, star formation, and planetary system evolution of the galaxy in which we live with AtLAST; a concept for a new, 50m single-dish sub-mm telescope with a large field of view which is the only type of facility that will allow us to observe our Galaxy deeply and widely enough to make a leap forward in our understanding of our local ecology.

More realistic planetesimal masses alter Kuiper belt formation models and add stochasticity

Much of the modern Kuiper belt is thought to be the result of Neptune’s migration through a primordial belt of planetesimals, possibly interrupted by an instability amongst the giant planets. While most prior work has employed massless test particles to study this Kuiper belt formation process, we perform simulations here that include the gravitational effects of the primordial planetesimal belt consisting of ∼105 massive bodies. In our simulations, Neptune unlocks from resonance with the other giant planets and begins to migrate outward due to interactions with planetesimals before a planetary orbital instability is triggered, and afterward, residual Neptunian migration completes the formation of the modern Kuiper belt. Compared to past simulations using massless test particles, our present work exhibits a number of notable differences. First, Neptune’s planetary resonance unlocking requires the Neptunian 3:2 mean motion resonance to sweep much of the primordial disk interior to 30 au prior to the giant planet instability. This generates a pre-instability population of planetesimals that is significantly lower in semimajor axis, eccentricity, and inclination than predicted by many prior models, and this effect persists after the instability. Second, direct scattering between Pluto-mass bodies and other small bodies removes material from Neptunian resonances significantly more efficiently than the resonant dropout resulting from small changes in Neptune’s semimajor axis during scattering between Pluto-mass bodies and Neptune. Consequently, the primordial population of Pluto-mass bodies may be as few as ∼200 objects. Finally, our simulation end states display a wide variety of orbital distributions, and straightforward relationships between final bulk Kuiper belt properties and Neptune’s migration or initial planetesimal properties largely elude us. In particular, we find that the rapid, stochastic planetary orbital evolution occurring during the giant planet instability can significantly alter final Kuiper belt properties such as its inclination dispersion and the prominence of resonant populations. This complicates efforts to use modern Kuiper belt properties to confidently constrain early solar system events and conditions, including planetary orbital migration and the primordial Kuiper belt’s characteristics.

The eccentric Koza–Lidov mechanism as the cause of exocomet transits of KIC 8462852

ABSTRACT KIC 8462852 is a star in the Kepler field that exhibits almost unique behaviour. The deep, irregular, and aperiodic dips in its light curve have been interpreted as the breakup of a large exocomet on a highly eccentric orbit whose post-disruption material obscures the star. It is hypothesized that a nearby M-dwarf, recently confirmed to be bound to the system, could be exciting planetesimals in a source belt to high eccentricities if its orbit is highly misaligned with the belt: an effect known as the ‘Eccentric Kozai–Lidov Mechanism’. To quantify how often this effect is expected to occur, this paper presents a Monte Carlo model of wide binary stars with embedded, misaligned planetesimal belts. These belts collisionally erode over time until they are excited to high eccentricities on secular time-scales by a companion star if its orbit is sufficiently misaligned. The large planetesimals then produce an observable dimming signature in the light curve for a set period of time which may or may not overlap with similar events. The model finds that, for dimming events that persist for 100 yr, the most likely companion stars are located at 102−104 au, the most likely belts are at 102−103 au and the system age is most likely to be 102−103 Myr. However, the probability of observing one or more stars exhibiting this phenomenon in the Kepler field is 1.3 × 10−3, such that it is unlikely this mechanism is driving the observations of KIC 8462852.

Secondary gas in debris discs released following the decay of long-lived radioactive nuclides, catastrophic, or resurfacing collisions

ABSTRACT Kuiper-like belts of planetesimals orbiting stars other than the Sun are most commonly detected from the thermal emission of small dust produced in collisions. Emission from gas, most notably CO, highlights the cometary nature of these planetesimals. Here, we present models for the release of gas from comet-like bodies in these belts, both due to their thermophysical evolution, most notably the decay of long-lived radioactive nuclides, and collisional evolution, including catastrophic and gentler resurfacing collisions. We show that the rate of gas release is not proportional to the rate of dust release, if non-catastrophic collisions or thermal evolution dominate the release of CO gas. In this case, care must be taken when inferring the composition of comets. Non-catastrophic collisions dominate the gas production at earlier times than catastrophic collisions, depending on the properties of the planetesimal belt. We highlight the importance of the thermal evolution of comets, including crucially the decay of long-lived radioactive nuclides, as a source of CO gas around young (<50 Myr) planetary systems, if large (10–100 km) planetesimals are present.

Inner edges of planetesimal belts: collisionally eroded or truncated?

ABSTRACT The radial structure of debris discs can encode important information about their dynamical and collisional history. In this paper, we present a three-phase analytical model to analyse the collisional evolution of solids in debris discs, focusing on their joint radial and temporal dependence. Consistent with previous models, we find that as the largest planetesimals reach collisional equilibrium in the inner regions, the surface density of dust and solids becomes proportional to ∼r2 within a certain critical radius. We present simple equations to estimate the critical radius and surface density of dust as a function of the maximum planetesimal size and initial surface density in solids (and vice versa). We apply this model to Atacama Large Millimeter/submillimeter Array observations of seven wide debris discs. We use both parametric and non-parametric modelling to test if their inner edges are shallow and consistent with collisional evolution. We find that four out of seven have inner edges consistent with collisional evolution. Three of these would require small maximum planetesimal sizes below 10 km, with HR 8799’s disc potentially lacking solids larger than a few centimetres. The remaining systems have inner edges that are much sharper, which requires maximum planetesimal sizes ≳ 10 km. Their sharp inner edges suggest they could have been truncated by planets, which JWST could detect. In the context of our model, we find that the seven discs require surface densities below a Minimum Mass Solar Nebula, avoiding the so-called disc mass problem. Finally, during the modelling of HD 107146 we discover that its wide gap is split into two narrower ones, which could be due to two low-mass planets formed within the disc.

The high-albedo, low polarization disk around HD 114082 that harbors a Jupiter-sized transiting planet

Aims. We present new optical and near-infrared images of the debris disk around the F-type star HD 114082 in the Scorpius-Centaurus OB association. We obtained direct imaging observations and analyzed the TESS photometric time series data of this target with the goal of searching for planetary companions to HD 114082 and characterizing the morphology of the debris disk and the scattering properties of dust particles. Methods. HD 114082 was observed with the VLT/SPHERE instrument in different modes – the IRDIS camera in the K band (2.0–2.3 μm) together with the IFS in the Y, J, and H bands (0.95–1.66 μm) using the angular differential imaging technique as well as IRDIS in the H band (1.5–1.8 μm) and ZIMPOL in the I_PRIME band (0.71–0.87 μm) using the polarimetric differential imaging technique. To constrain the basic geometrical parameters of the disk and the scattering properties of dust grains, scattered light images were fitted with a 3D model for single scattering in an optically thin dust disk using a Markov chain Monte Carlo approach. We performed aperture photometry to derive the scattering and polarized phase functions, the polarization fraction, and the spectral scattering albedo for the dust particles in the disk. This method was also used to obtain the reflectance spectrum of the disk and, in turn, to retrieve the disk color and study the dust reflectivity in comparison to the debris disk HD 117214. We also performed the modeling of the HD 114082 light curve measured by TESS using models for planet transit and stellar activity to put constraints on the radius of the detected planet and its orbit. Last, we searched for additional planets in the system by combining archival radial velocity data, astrometry, and direct imaging. Results. The debris disk HD 114082 appears as an axisymmetric debris belt with a radius of ~0.37″ (35 au), an inclination of ~83°, and a wide inner cavity. Dust particles in HD 114082 have a maximum polarization fraction of ~17% and a higher reflectivity when compared to the debris disk HD 117214. This high reflectivity results in a spectral scattering albedo of ~0.65 for the HD 114082 disk at near-infrared wavelengths. The disk reflectance spectrum exhibits a red color at the position of the planetesimal belt and shows no obvious features, whereas that of HD 117214 might indicate the presence of CO2 ice. The analysis of TESS photometric data reveals a transiting planetary companion to HD 114082 with a radius of ~1 RJup on an orbit with a semimajor axis of 0.7 ± 0.4 au. No additional planet was detected in the system when we combined the SPHERE images with constraints from astrometry and radial velocity. We reach deep sensitivity limits down to ~5 MJup at 50 au and ~10 MJup at 30 au from the central star.

A mixed stirring mechanism for debris discs with giant and dwarf planetary perturbations

ABSTRACT 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 exploring the evolution of debris discs over 1 Gyr, combining the gravitational perturbations of both dwarf planets embedded in the discs, and an interior giant planet. Our systems were somewhat modelled after the architecture of the outer Solar system: a Solar mass star, a single massive giant planet at 30 au (MGP = 10 to 316 M⊕), and a debris disc formed by 100 massive dwarf planets and 1000 massless particles (MDD = 3.16 to 31.6 M⊕). We present the evolution of both the disc and the giant planet after 1 Gyr. The time evolution of the average eccentricity and inclination of the disc is strongly dependent on the giant planet mass as well as on the remaining disc mass. We also found that efficient stirring is achieved even with small disc masses. In general, we find that a mixed mechanism is more efficient in the stirring of cold debris discs than either mechanism acting in isolation.

Potential effects of stellar winds on gas dynamics in debris disks leading to observable belt winds

Context. Gas has been successfully detected in many extrasolar systems around mature stars aged between 10 Myr and ∼1 Gyr that include planetesimal belts. Gas in these mature disks is thought to be released from planetesimals and has been modeled using a viscous disk approach where the gas expands inwards and outwards from the belt where it is produced. Therefore, the gas has so far been assumed to make up the circumstellar disk orbiting the star; however, at low densities, this may not be an adequate assumption, as the gas could be blown out by the stellar wind instead. Aims. In this paper, we aim to explore the timeframe in which a gas disk transitions to such a gas wind and whether this information can be used to determine the stellar wind properties around main sequence stars, which are otherwise difficult to obtain. Methods. We developed an analytical model for A to M stars that can follow the evolution of gas outflows and target the moment of transition between a disk or a wind in order to make a comparison with current observations. The crucial criterion here is the gas density for which gas particles are no longer protected from the impact of stellar wind protons at high velocities and on radial trajectories. Results. We find that: (1) belts with a radial width, ΔR, with gas densities <7 (ΔR/50 au)−1 cm−3, would create a wind rather than a disk, which would explain the recent outflowing gas detection in NO Lup; (2) the properties of this belt wind can be used to measure stellar wind properties such as their densities and velocities; (3) very early-type stars can also form gas winds due to the star’s radiation pressure, instead of a stellar wind; (4) debris disks with low fractional luminosities, f, are more likely to create gas winds, which could be observed with current facilities. Conclusions. Systems containing low gas masses, such as Fomalhaut or TWA 7, or more generally, debris disks with fractional luminosities of f ≲ 10−5(L⋆/L⊙)−0.37 or stellar luminosity ≳20 L⊙ (A0V or earlier) are more likely to create gas outflows (or belt winds) than gas disks. Gas that is observed to be outflowing at high velocity in the young system NO Lup could be an example of such belt winds. Future observing predictions in this wind region should account for the stellar wind in the attempt to detect the gas. The detection of these gas winds is possible with ALMA (CO and CO+ could serve as good wind tracers). This would allow us to constrain the stellar wind properties of main-sequence stars, as these properties are otherwise difficult to measure, since, for example, there are no successful measures around A stars at present.

Using debris disk observations to infer substellar companions orbiting within or outside a parent planetesimal belt

Context. Alongside a debris disk, substellar companions often exist in the same system. The companions influence the dust dynamics via their gravitational potential. Aims. We analyze whether the effects of secular perturbations, originating from a substellar companion, on the dust dynamics can be investigated with spatially resolved observations. Methods. We numerically simulated the collisional evolution of narrow and eccentric cold planetesimal belts around a star of spectral type A3 V that are secularly perturbed by a substellar companion that orbits either closer to or farther from the star than the belt. Our model requires a perturber on an eccentric orbit (e ≳ 0.3) that is both far from and more massive than the collisionally dominated belt around a luminous central star. Based on the resulting spatial dust distributions, we simulated spatially resolved maps of their surface brightness in the K, N, and Q bands and at wavelengths of 70 µm and 1300 µm. Results. Assuming a nearby debris disk seen face-on, we find that the surface brightness distribution varies significantly with observing wavelength, for example between the N and Q band. This can be explained by the varying relative contribution of the emission of the smallest grains near the blowout limit. The orbits of both the small grains that form the halo and the large grains close to the parent belt precess due to the secular perturbations induced by a substellar companion orbiting inward of the belt. The halo, being composed of older grains, trails the belt. The magnitude of the trailing decreases with increasing perturber mass and hence with increasing strength of the perturbations. We recovered this trend in synthetic maps of surface brightness by fitting ellipses to lines of constant brightness. Systems with an outer perturber do not show a uniform halo precession since the orbits of small grains are strongly altered. We identified features of the brightness distributions suitable for distinguishing between systems with a potentially detectable inner or outer perturber, especially with a combined observation with JWST/MIRI in the Q band tracing small grain emission and with ALMA at millimeter wavelengths tracing the position of the parent planetesimal belt.

Evidence for the Disruption of a Planetary System During the Formation of the Helix Nebula

The persistence of planetary systems after their host stars evolve into their post-main-sequence phase is poorly constrained by observations. Many young white dwarf systems exhibit infrared excess emission and/or spectral absorption lines associated with a reservoir of dust (or planetesimals) and its accretion. However, most white dwarfs are too cool to sufficiently heat any circumstellar dust to detectable levels of emission. The Helix Nebula (NGC 7293) is a young, nearby planetary nebula; observations at mid- and far-infrared wavelengths have revealed excess emission associated with its central white dwarf (WD 2226-210). The origin of this excess is ambiguous. It could be a remnant planetesimal belt, a cloud of comets, or the remnants of material shed during the post-asymptotic giant branch (post-AGB) phase. Here we combine infrared (Stratospheric Observatory for Infrared Astronomy, Spitzer, Herschel) and millimeter (Atacama Large Millimeter/submillimeter Array) observations of the system to determine the origin of this excess using multiwavelength imaging and radiative transfer modeling. We find the data are incompatible with a compact remnant planetesimal belt or post-AGB disk, and conclude the dust most likely originates from deposition by a cometary cloud. The measured dust mass, and lifetime of the constituent grains, implies disruption of several thousand Hale–Bopp equivalent comets per year to fuel the observed excess emission around the Helix Nebula’s white dwarf.

High-resolution ALMA and HST imaging of κCrB: a broad debris disc around a post-main-sequence star with low-mass companions

ABSTRACT $\kappa \,$ CrB is an ∼2.5 Gyr old K1 sub-giant star, with an eccentric exo-Jupiter at ∼2.8 au and a debris disc at tens of au. We present ALMA (Atacama Large Millimetre/submillimetre Array) Band 6 (1.3 mm) and Hubble Space Telescope scattered light (0.6$\, \mu$m) images, demonstrating $\kappa \,$CrB’s broad debris disc, covering an extent $50\!-\!180\,$au in the millimetre (peaking at 110 au), and $51\!-\!280\,$au in scattered light (peaking at 73 au). By modelling the millimetre emission, we estimate the dust mass as ${\sim }0.016\, {\rm M}_\oplus$, and constrain lower-limit planetesimal sizes as $D_{\rm {max}}{\gtrsim }1\,$km and the planetesimal belt mass as $M_{\rm {disc}}{\gtrsim }1\, {\rm M}_\oplus$. We constrain the properties of an outer body causing a linear trend in 17 yr of radial velocity data to have a semimajor axis 8–66 au and a mass $0.4\!-\!120\, M_{\rm {Jup}}$. There is a large inner cavity seen in the millimetre emission, which we show is consistent with carving by such an outer massive companion with a string of lower mass planets. Our scattered light modelling shows that the dust must have a high anisotropic scattering factor (g ∼ 0.8–0.9) but an inclination (i ∼ 30°–40°) that is inferred to be significantly lower than the i ∼ 61° millimetre inclination. The origin of such a discrepancy is unclear, but could be caused by a misalignment in the micrometre- and millimetre-sized dust. We place an upper limit on the CO gas mass of $M_{\rm {CO}}{\lt }(4.2\!-\!13) \times 10^{-7}\, {\rm M}_\oplus$, and show this to be consistent with levels expected from planetesimal collisions, or from CO-ice sublimation as $\kappa \,$CrB begins its giant branch ascent.

Vertical evolution of exocometary gas – I. How vertical diffusion shortens the CO lifetime

ABSTRACT Bright debris discs can contain large amounts of CO gas. This gas was thought to be a protoplanetary remnant until it was recently shown that it could be released in collisions of volatile-rich solids. As CO is released, interstellar UV radiation photodissociates CO producing CI, which can shield CO allowing a large CO mass to accumulate. However, this picture was challenged because CI is inefficient at shielding if CO and CI are vertically mixed. Here, we study for the first time the vertical evolution of gas to determine how vertical mixing affects the efficiency of shielding by CI. We present a 1D model that accounts for gas release, photodissociation, ionization, viscous evolution, and vertical mixing due to turbulent diffusion. We find that if the gas surface density is high and the vertical diffusion weak (αv/α < [H/r]2) CO photodissociates high above the mid-plane, forming an optically thick CI layer that shields the CO underneath. Conversely, if diffusion is strong (αv/α > [H/r]2) CI and CO become well mixed, shortening the CO lifetime. Moreover, diffusion could also limit the amount of dust settling. High-resolution ALMA observations could resolve the vertical distribution of CO and CI, and thus constrain vertical mixing and the efficiency of CI shielding. We also find that the CO and CI scale heights may not be good probes of the mean molecular weight, and thus composition, of the gas. Finally, we show that if mixing is strong the CO lifetime might not be long enough for CO to spread interior to the planetesimal belt where gas is produced.

LMT/AzTEC observations of Vega

ABSTRACT Vega is the prototypical debris disc system. Its architecture has been extensively studied at optical to millimetre wavelengths, revealing a near face-on, broad, and smooth disc with multiple distinct components. Recent millimetre-wavelength observations from ALMA spatially resolved the inner edge of the outer, cold planetesimal belt from the star for the first time. Here we present early science imaging observations of the Vega system with the AzTEC instrument on the 32-m LMT, tracing extended emission from the disc out to 150 au from the star. We compare the observations to three models of the planetesimal belt architecture to better determine the profile of the outer belt. A comparison of these potential architectures for the disc does not significantly differentiate between them with the modelling results being similar in many respects to the previous ALMA analysis, but differing in the slope of the outer region of the disc. The measured flux densities are consistent between the LMT (single dish) and ALMA (interferometric) observations after accounting for the differences in wavelength of observation. The LMT observations suggest the outer slope of the planetesimal belt is steeper than was suggested in the ALMA analysis. This would be consistent with the interferometric observations being mostly blind to structure at the disc outer edges, but the overall low signal to noise of the LMT observations does not definitively resolve the structure of the outer planetesimal belt.

Secular chaos in white dwarf planetary systems: origins of metal pollution and short-period planetary companions

ABSTRACT Secular oscillations in multiplanet systems can drive chaotic evolution of a small inner body through non-linear resonant perturbations. This ‘secular chaos’ readily pushes the inner body to an extreme eccentricity, triggering tidal interactions or collision with the central star. We present a numerical study of secular chaos in systems with two planets and test particles using the ring-averaging method, with emphasis on the relationship between the planets’ properties and the time-scale and efficiency of chaotic diffusion. We find that secular chaos can excite extreme eccentricities on time-scales spanning several orders of magnitude in a given system. We apply our results to the evolution of planetary systems around white dwarfs (WDs), specifically the tidal disruption and high-eccentricity migration of planetesimals and planets. We find that secular chaos in a planetesimal belt driven by large (≳10 M⊕), distant ($\gtrsim 10 \, \mathrm{au}$) planets can sustain metal accretion on to a WD over Gyr time-scales. We constrain the total mass of planetesimals initially present within the chaotic zone by requiring that the predicted mass delivery rate to the Roche limit be consistent with the observed metal accretion rates of WDs with atmospheric pollution throughout the cooling sequence. Based on the occurrence of long-period exoplanets and exo-asteroid belts, we conclude that secular chaos can be a significant (perhaps dominant) channel for polluting solitary WDs. Secular chaos can also produce short-period planets and planetesimals around WDs in concert with various circularization mechanisms. We discuss prospects for detecting exoplanets driving secular chaos around WDs using direct imaging and microlensing.

A “no-drift” runaway pile-up of pebbles in protoplanetary disks

Context. Forming planetesimals from pebbles is a major challenge in our current understanding of planet formation. In a protoplanetary disk, pebbles drift inward near the disk midplane via gas drag and they may enter a zone of reduced turbulence (dead zone). In this context, we identified that the backreaction of the drag of pebbles onto the gas could lead to a runaway pile-up of pebbles, the so-called no-drift mechanism for the formation of planetesimals. Aims. We improve upon the previous study of planetesimal formation from accumulating pebbles via the no-drift mechanism by investigating the nature and characteristics of the resultant planetesimal belt. Methods. We performed 1D diffusion-advection simulations of drifting pebbles in the outer region of a modeled dead zone by including a pebble-gas backreaction to the radial drift of pebbles and including planetesimal formation via the streaming instability. We independently considered the parameters that regulate gas accretion (αacc) and vertical stirring of pebbles in the disk midplane (αmid). In this study, the pebble-to-gas mass flux (Fp/g) was fixed as a parameter. Results. We find that, for a constant Fp/g, after the criteria of the no-drift mechanism are satisfied, planetesimals initially form within a narrow ring whose width expands as accumulating pebbles radially diffuse over time. The system finally reaches a steady-state where the width of the planetesimal belt no longer changes, followed by a continuous formation of planetesimals. A non-negligible total mass of planetesimals (more than one Earth mass) is formed via the no-drift mechanism for a disk having Fp/g ≳ 0.1 for more than ~10–100 kyr with nominal parameters: a gas mass flux of ≳10−8 M⊙ yr−1, τs ≃ 0.01−0.1, αmid ≲ 10−4, and αacc ≃ 10−3−10−2 at r ≲ 10 au, where r, τs, αmid, and αacc are the heliocentric distance, the Stokes number, and the parameters in a dead zone controlling the efficiencies of vertical turbulent diffusion of pebbles (i.e., scale height of pebbles) and gas accretion of the α-disk (i.e., gas surface density), respectively.

Effect of the Planetesimal Belt on the Dynamics of the Restricted Problem of 2 + 2 Bodies

In this paper, we study the existence and stability of collinear and noncollinear equilibrium points within the frame of the perturbed restricted problem of 2 + 2 bodies by a planetesimal belt. We compare and investigate the corresponding results of the perturbed and unperturbed models. The impact of the planetesimal belt is observed on collinear and noncollinear equilibrium points. We demonstrate that all equilibrium points are unstable, and we numerically investigate the noncollinear equilibrium points. Finally, we emphasize that the proposed problem is a credible model for describing the capture of small bodies by a planet.