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Tim D. Pearce

Publications and source records attributed to Tim D. Pearce.

At least 19 recordsLinked to original sources

Direct Imaging Discovery of Giant Exoplanet $\beta$ Pictoris d: A Decade-Long Game of Hide-and-Seek

We report the direct imaging discovery of a third exoplanet in the $\beta$ Pictoris system. We detect $\beta$ Pictoris d ($\beta$ Pic d) in non-coronagraphic observations obtained with VLT/ERIS as well as multi-epoch archival datasets from JWST/NIRCam and VLT/SPHERE. Astrometric measurements over an 11-year baseline demonstrate that it is consistent with a gravitationally-bound source with orbital motion. Joint multi-planet orbit fits of all three planets in the system yield a semi-major axis of $26.0^{+2.2}_{-6.1}$ au and inclination $89.0^{+0.7}_{-0.6}$ deg for planet d. $\beta$ Pic d has a larger orbital semi-major axis than the other known planets in the system, but is coplanar with the inner two planets, and its orbit is consistent with sculpting the inner edge of the debris disk. $\beta$ Pic d has a contrast of $\Delta L^{\prime}=12.11\pm0.15$ mag, with colors and luminosity that closely match those of 51 Eri b, another exoplanet in the $\beta$ Pictoris moving group. Its VLT/ERIS and JWST/NIRCam colors are distinct from those of free-floating planetary-mass objects of a similar age and temperature. Its red $F410M-F444W$ color indicates strong CO$_2$ absorption in its atmosphere and suggests significant enhancement in metals compared to free-floating objects. From the ATMO hot-start evolutionary models, we estimate an effective temperature of $600^{+45}_{-60}$ K and mass of $2.4\pm0.6$ $M_{\rm Jup}$, which also closely matches similar estimates for 51 Eri b. $\beta$ Pic d is among the lowest-mass exoplanets imaged from the ground. This discovery highlights the deep sensitivity achievable with ground-based imaging in the mid-infrared and the discovery potential of future high-contrast observations with the Extremely Large Telescope.

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Environmental interactions in Class II systems and their impact on the disk-planet architecture

Protoplanetary disks evolve in clustered environments where interactions with nearby stars and interstellar gas are common. Such environmental processes, including stellar flybys and gas infall, can significantly perturb disk structures over the disk lifetime and potentially influence the evolution of embedded planets. We investigate how environmental interactions affect the architecture of Class II systems that host both a disk and already-formed planets, and assess their impact on disk structure and dynamics, as well as planetary evolution. We performed 3D simulations using the Phantom SPH code, including multiple dust species treated with a dust-as-particles approach that accounts for dust back-reaction on the gas. We modeled a disk hosting two planets in a 2:1 mean-motion resonance and subjected the system to two types of perturbations: an infalling gaseous cloudlet and a stellar flyby. Infall and flyby perturbations change the disk morphology and dynamical state. Infalling gas increases the disk mass and angular momentum, dynamically exciting the dust and producing eccentric, multi-ring dust structures. The stellar flyby truncates the disk, compacting the dust distribution radially and enhancing episodic radial migration of dust grains. These processes excite eccentricity in both gas and dust, leading to distinct accretion pathways for the planets. In particular, the flyby promotes inward dust migration, which may enhance solid accretion onto the planets, while infall preferentially increases the accretion rate of the inner planet. Environmental interactions during the Class II phase can reshape disk-planet systems, imprinting dynamical signatures that may persist into later evolutionary stages. Both late infall and stellar flybys influence the growth and composition of planets; in particular, infall events can lead to the formation of eccentric, narrow debris disks.

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Viscously Stirring Particle Disks into Lorentzians and Gaussians to Infer Dynamical and Collisional Masses (ARKS XIII)

Disks (Keplerian or otherwise, particulate or fluid) are often assumed to have densities that drop off vertically as Gaussians. Recent mm-wave imaging of circumstellar debris disks contradicts this assumption, revealing vertical profiles in dust that resemble Lorentzians. As part of the ARKS ALMA Large Program, we show how Lorentzians and Gaussians define an evolutionary sequence for disks of gravitationally scattering (viscously stirring) particles. When orbits are crossing and eccentricities $e \gg$ inclinations $i$, each scattering can change a particle's inclination by $\pm \,\Delta i \propto i$. A random walk with fixed steps in $\Delta i/i = \Delta \ln i$ produces a thick, log normal tail at large $i$ that leads to Lorentzian tails in density. This result holds independent of the origin of the large eccentricities, which may characterize either the stirrers or the objects being stirred; what matters is that relative motions parallel to the disk midplane are faster than perpendicular motions, and that vertical displacements during encounters are smaller than horizontal displacements. After enough scatterings, $i$ comes into equipartition with $e$, $\Delta i$ stops exponentiating, and the vertical density relaxes to a Gaussian. We identify four regimes of dispersion-dominated viscous stirring, three of which are out-of-equipartition and where $i$ is stirred faster than $e$. The stirrers for ARKS debris disks may range from Pluto to a few times Mars in size, and be sufficiently few as to be collisionless. Or the stirrers may be even smaller, and be so numerous and collide so frequently that they source the collisional cascades that produce observable dust.

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Exocometary physics: material release and tails

Despite decades of observations, the physical processes governing mass loss from small bodies beyond our Solar System remain poorly constrained. These exocomets are often treated as analogs of Solar System comet, yet the stellar environments they inhabit spans a wide range in terms of luminosity, stellar winds, and evolutionary stage, leading to potentially very diverse physical behaviors. Within our Solar System, small bodies lose material through a range of mechanisms, including sublimation, desorption, impacts, and/or sputtering. Once released, the composition and dynamics of the ejecta are then altered by additional processes, such as dust sublimation, ionization, and radiation pressure. In extrasolar systems, these mechanisms unfold under vastly different radiative and plasma conditions, leading to a rich diversity of mass-loss pathways and observable signatures. This work reviews our understanding of the mechanisms driving mass loss from small bodies and the subsequent evolution of ejecta in diverse stellar environments. We compare the physical and chemical mechanisms that drive gas and dust production, and investigate how they scale with stellar luminosity, temperature, and activity. We then examine the processes that modify the composition of the ejecta (e.g., dust sublimation, dissociation, or ionisation) and its dynamics (e.g., radiation pressure or stellar winds). To illustrate how these processes vary across different stellar environments, we use four well-studied planetary systems as case studies: the Sun, $\beta$ Pictoris, AU Microscopii, and WD 1145+017. By exploring how cometary tails behave under such diverse conditions, this work provides a physical framework for interpreting exocometary activity and sheds light on why A-type stars, such as the famous $\beta$ Pictoris, are over-represented in the population of exocomet-hosting stars.

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The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) III: The vertical structure of debris disks

Debris disks -- collisionally sustained belts of dust and sometimes gas around main sequence stars -- are remnants of planet formation processes and are found in systems ${\gtrsim}10$ Myr old. Millimeter-wavelength observations are particularly important, as the grains probed by these observations are not strongly affected by radiation pressure and stellar winds, allowing them to probe the dynamics of large bodies producing dust. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) is analyzing high-resolution observations of 24 debris disks to enable the characterization of debris disk substructures across a large sample for the first time. For the most highly inclined disks, it is possible to recover the vertical structure of the disk. We aim to model and analyze the most highly inclined systems in the ARKS sample in order to uniformly extract the vertical dust distributions for a sample of well-resolved debris disks. We employed both parametric and nonparametric methods to constrain the vertical dust distributions for the most highly inclined ARKS targets. We find a broad range of aspect ratios, revealing a wide diversity in vertical structure, with a range of best-fit parametric values of $0.0026 \leq h_{\rm HWHM} \leq 0.193$ and a median best-fit value of $h_{\rm HWHM}=0.021$. The results obtained by nonparametric modeling are generally consistent with the parametric modeling results. We find that five of the 13 disks are consistent with having total disk masses less than that of Neptune (17 $M_{\oplus}$), assuming stirring by internal processes (self-stirring and collisional and frictional damping). Furthermore, most systems show a significant preference for a Lorentzian vertical profile rather than a Gaussian.

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The SPace-based InterFerometer Feasibility (SPIFF) Project: Enabling Future High-Resolution Astronomy Across the EM Spectrum

A plethora of astronomical science cases can only be achieved with high angular resolution observations, and we can expect the number of these to grow as astronomers are constrained by the size limitations of single-aperture space telescopes, making space-based interferometry inevitable. However, the enabling technologies do not have flight heritage at the system level, and the concept remains immature to much of the community, meaning no direct-detection synthetic-aperture space-based interferometer has yet flown and an opportunity exists for the UK to take a world leading role. Here we propose the SPace-based InterFerometry Feasibility (SPIFF) Project as a program to address both issues simultaneously by: 1) completing a thorough survey of the science cases across the EM spectrum that would directly benefit from, or be impossible without, space-based interferometry; 2) down selecting key requirements via a Science Traceability Matrix mapping exercise; 3) host a workshop for the UK astronomical community to consolidate these findings; 4) build a technology demonstration mission to raise TRL and achieve flight heritage of critical technologies. Such a program positions the UK as the partner of choice for any future NASA or ESA space-based interferometry mission, allowing the UK to lead groundbreaking scientific discoveries, while also directly benefiting the UK industrial base by advancing domestic exportable technologies and building direct synergy with other UK space priorities. Indeed, the UK is uniquely positioned to lead in space-based interferometry, possessing a rare trifecta of domestic strengths: world-class expertise in ground-based interferometry and space-based instrumentation; commercial entities developing mission-critical technologies; and scientists whose research spans the full range of science cases that would benefit directly from space-based interferometry.

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Fomalhaut's debris disc is not dominated by primordial Plutos

A key challenge in debris-disc science is that we do not know the masses of debris discs, nor the sizes of the largest debris bodies. This is because modern observations can only detect objects up to centimetre sizes, whilst larger planetesimals, which dominate disc mass, remain hidden. We must therefore use other arguments, such as dynamics, to indirectly infer disc masses and body sizes. This paper presents a new method, applicable to narrow debris discs like Fomalhaut. We argue that such discs cannot be too massive, nor the largest bodies too large, otherwise they would self-scatter and the disc would be much broader than observed. Using n-body dynamics and collisional theory, we demonstrate that the mass of Fomalhaut's disc cannot be dominated by primordial Plutos. Instead, if the mass is dominated by primordial bodies, then they should have radii below $300^{+80}_{-70}$ km ($0.3 \pm 0.1$ RPluto) and above $5^{+20}_{-4}$ km. Such bodies would each have less than 1 per cent the mass of Pluto. Our conclusions are robust to additional physics, including shepherding planets and collisional damping. Our results provide independent, dynamical support for the idea that the masses of bright debris discs are dominated by objects smaller than Pluto.

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HD 44892: The youngest (or oldest?) gas-harbouring debris disc around an intermediate mass star

We present the first detections of gas around a 2.1 Myr old debris disc-bearing intermediate-mass star, HD 44892. Gas is detected both in $^{12}$CO (2-1) emission through ALMA Band 6 observations and in absorption in Ca II K and H, seen with high-resolution UVES spectroscopy. $^{13}$CO and C$^{18}$O (2-1) are not detected. The star exhibits a 12 $\mu$m fractional excess of $7.86^{+0.11}_{-2.27}$, placing it in the transition stage between protoplanetary and debris discs. Our detection of 1.3 mm emission yields the dust mass of 0.019$\pm$0.009 $M_{\oplus}$ assuming 115 K temperature. The $^{13}$CO non-detection places an upper limit on CO gas mass of $\sim$10$^{-2}$ $M_{\oplus}$. The $^{12}$CO detection yields a CO gas mass of (7.86$\pm$2.05)$\times$10$^{-5}$ $M_{\oplus}$ or (1.62$\pm$0.17)$\times$10$^{-4}$ $M_{\oplus}$ assuming a gas temperature of 20 K or 50 K, respectively. These should be considered as lower limits since $^{12}$CO emission may be optically thick. With UVES, we find variability in Ca II K and H lines, which can be interpreted by transiting circumstellar gas, ruling out interstellar absorption as their origin. Both the dust mass, which is within an order of magnitude of HD 141569, and the gas mass derived here indicate a late gas dispersal stage of the protoplanetary disc. Through our analysis we deem the alternative age of 800 Myr unlikely.

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Theory of Exozodi Sources and Dust Evolution

Exozodiacal dust disks (exozodis) are populations of warm (~300K) or hot (~1000K) dust, located in or interior to a star's habitable zone, detected around ~25% of main-sequence stars as excess emission over the stellar photosphere at mid- or near-infrared wavelengths. Often too plentiful to be explained by an in-situ planetesimal belt, exozodi dust is usually thought to be transported inwards from further out in the system. There is no consensus on which (if any) of various proposed dynamical models is correct, yet it is vital to understand exozodis given the risk they pose to direct imaging and characterisation of Earth-like planets. This article reviews current theoretical understanding of the origin and evolution of exozodi dust. It also identifies key questions pertinent to the potential for exozodis to impact exoplanet imaging and summarises current understanding of the answer to them informed by exozodi theory. These address how exozodi dust is delivered, its size and spatial distribution, and the effect of its composition on exozodi observability, as well as the connection between hot and warm exozodis. Also addressed are how common different exozodi levels are and how that level can be predicted from system properties, as well as the features that planets impart in dust distributions and how exozodis affect a planet's physical properties and habitability. We conclude that exozodis present both a problem and an opportunity, e.g., by introducing noise that makes planets harder to detect, but also identifying systems in which ingredients conducive to life, like water and volatiles, are delivered to the habitable zone.

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The HR 8799 Debris Disc: Shaped by Planetary Migration and a Possible Fifth Outermost Planet

Context. The HR 8799 system, hosting four giant planets between a warm and cold debris disc, and an extended dusty tail beyond, serves as an ideal laboratory for studying planetary formation and evolution. The debris discs have been observed across various wavelengths, and the planetary properties are well-constrained. Nonetheless, there are still open questions regarding the role of the planets in shaping the debris discs. Aims. We investigate the system's evolution with the aim of understanding how planetary migration shapes its architecture, both in terms of planets and the disc. Methods. We performed $N$-body simulations to model the HR 8799 system. We examined the orbital evolution of the known four super-Jupiter planets through the course of simple, imposed migration in a gaseous disc as they perturb an external, massless planetesimal disc. We also explore the impact of introducing a fifth planet on the dynamical and morphological aspects of the disc. Results. The planets migrate outward as a result of their imposed interactions with the gaseous disc while maintaining their resonant configuration. This outward migration excites the planetesimal disc, producing a transient scattered population. While a four-planet system partially reproduces the observed cavity between the star and the cold debris disc, the inclusion of a fifth low-mass planet appears to be crucial for better reproducing key morphological aspects of the cold debris disc. Conclusions. This model provides a novel explanation for the architecture of HR 8799. Outward planetary migration, combined with mean motion resonant interactions and a fifth, low-mass planet, can effectively replicate the observed planetary architecture and cold debris disc characteristics. Our findings underscore the potential important role of planetary migration in shaping debris discs.

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Hot exozodiacal dust around Fomalhaut: The MATISSE perspective

Excess over the stellar photospheric emission of main-sequence stars has been found in interferometric near-infrared observations, and is attributed to the presence of hot exozodiacal dust (HEZD). As part of our effort to detect and characterize HEZD around the nearby A3 V star Fomalhaut, we carried out the first interferometric observations with the MATISSE instrument at the VLTI in the photometric bands L and M for the Fomalhaut system. Assuming a dust distribution either as a narrow ring or spherical shell for modeling the HEZD, we aim to constrain the HEZD parameters by generating visibilities and fitting them to the MATISSE data using different approaches. The L band data provide a marginal detection of circumstellar radiation, potentially caused by the presence of HEZD, which is only the second detection of HEZD emission in the L band. An analysis of the data with different fitting approaches showed that the best-fit values for the HEZD parameters are consistent with those of previous Fomalhaut observations, which underlines the functionality of MATISSE. Assuming a dust ring, it would have an inner ring radius of \(0.11\ \mathrm{au}\), an outer ring radius of \(0.12\ \mathrm{au}\), a narrow dust grain size distribution around a dust grain radius constrained by \(0.53\ \mu\mathrm{m}\), and a total dust mass of \(3.25\times 10^{-10}\ \rm{M}_{\oplus}\). Finally, the results indicate that the choice of the geometric model has a more significant impact on the derived dust-to-star flux ratio than the specific fitting approach applied. Since different dust-to-star flux ratios can result from the applied fitting approaches, this also has an impact on the parameter values of the HEZD around Fomalhaut and most likely for other HEZD systems. Moreover, further NIR and MIR data are required for a more comprehensive description of the emission originating in the vicinity of Fomalhaut.

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Review and prospects of hot exozodiacal dust research for future exo-Earth direct imaging missions

Hot exozodiacal dust is dust in the innermost regions of planetary systems, at temperatures around 1000K to 2000K, and commonly detected by near-infrared interferometry. The phenomenon is poorly understood and has received renewed attention as a potential risk to a planned future space mission to image potentially habitable exoplanets and characterize their atmospheres (exo-Earth imaging) such as the Habitable Worlds Observatory (HWO). In this article, we review the current understanding of hot exozodiacal dust and its implications for HWO. We argue that the observational evidence suggests that the phenomenon is most likely real and indeed caused by hot dust, although conclusive proof in particular of the latter statement is still missing. Furthermore, we find that there exists as of yet no single model that is able to successfully explain the presence of the dust. We find that it is plausible and not unlikely that large amounts of hot exozodiacal dust in a system will critically limit the sensitivity of exo-Earth imaging observations around that star. It is thus crucial to better understood the phenomenon in order to be able to evaluate the actual impact on such a mission, and current and near-future observational opportunities for acquiring the required data exist. At the same time, hot exozodiacal dust (and warm exozodiacal dust closer to a system's habitable zone) has the potential to provide important context for HWO observations of rocky, HZ planets, constraining the environment in which these planets exist and hence to determine why a detected planet may be capable to sustain life or not.

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JWST/NIRCam 4-5 $\mu$m Imaging of the Giant Planet AF Lep b

With a dynamical mass of $3 \, M_\mathrm{Jup}$, the recently discovered giant planet AF Lep b is the lowest-mass imaged planet with a direct mass measurement. Its youth and spectral type near the L/T transition make it a promising target to study the impact of clouds and atmospheric chemistry at low surface gravities. In this work, we present JWST/NIRCam imaging of AF Lep b. Across two epochs, we detect AF Lep b in F444W ($4.4 \, \mathrm{\mu m}$) with S/N ratios of $9.6$ and $8.7$, respectively. At the planet's separation of $320 \, \mathrm{mas}$ during the observations, the coronagraphic throughput is ${\approx}7\%$, demonstrating that NIRCam's excellent sensitivity persists down to small separations. The F444W photometry of AF Lep b affirms the presence of disequilibrium carbon chemistry and enhanced atmospheric metallicity. These observations also place deep limits on wider-separation planets in the system, ruling out $1.1 \, M_\mathrm{Jup}$ planets beyond $15.6 \, \mathrm{au}$ ($0.58$ arcsec), $1.1 \, M_\mathrm{Sat}$ planets beyond $27 \, \mathrm{au}$ ($1$ arcsec), and $2.8 \, M_\mathrm{Nep}$ planets beyond $67 \, \mathrm{au}$ ($2.5$ arcsec). We also present new Keck/NIRC2 $L'$ imaging of AF Lep b; combining this with the two epochs of F444W photometry and previous Keck $L'$ photometry provides limits on the long-term $3{-}5 \, \mathrm{\mu m}$ variability of AF Lep b on months-to-years timescales. AF Lep b is the closest-separation planet imaged with JWST to date, demonstrating that planets can be recovered well inside the nominal (50\% throughput) NIRCam coronagraph inner working angle.

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Debris disks around main-sequence stars

'Debris disks' are collections of small bodies around stars, such as the Asteroid Belt and Kuiper Belt in our Solar System. These disks are composed of objects smaller than planets, including asteroids, comets, dust, and dwarf planets. We detect debris disks around a significant fraction of stars, and these disks appear to be common components of planetary systems. Extrasolar debris disks have a broad range of locations, shapes and features. This chapter provides an introduction to debris disks around main-sequence stars. It summarises our understanding of the field, and covers a wide range of concepts from observations and theory. It describes how we detect extrasolar debris disks, what we see, and what these observations tell us. It also describes how debris disks evolve, and how they interact with planets. The chapter concludes by discussing several unsolved questions in debris-disk science.

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Increasing planet-stirring efficiency of debris disks by "projectile stirring" and "resonant stirring"

Extrasolar debris disks are detected by observing dust, which is thought to be released during planetesimal collisions. This implies that planetesimals are dynamically excited ("stirred"), such that collisions are sufficiently common and violent. The most frequently considered stirring mechanisms are self-stirring by disk self-gravity, and planet-stirring via secular interactions. However, these models face problems when considering disk mass, self-gravity, and planet eccentricity, leading to the possibility that other, unexplored mechanisms instead stir debris. We hypothesize that planet-stirring could be more efficient than the traditional secular model implies, due to two additional mechanisms. First, a planet at the inner edge of a debris disk can scatter massive bodies onto eccentric, disk-crossing orbits, which then excite debris ("projectile stirring"). Second, a planet can stir debris over a wide region via broad mean-motion resonances, both at and between nominal resonance locations ("resonant stirring"). Both mechanisms can be effective even for low-eccentricity planets, unlike secular-planet-stirring. We run N-body simulations across a broad parameter space, to determine the viability of these new stirring mechanisms. We quantify stirring levels using a bespoke program for assessing Rebound debris simulations, which we make publicly available. We find that even low-mass projectiles can stir disks, and verify this with a simple analytic criterion. We also show that resonant stirring is effective for planets above ~0.5 MJup. By proving that these mechanisms can increase planet-stirring efficiency, we demonstrate that planets could still be stirring debris disks even in cases where conventional (secular) planet-stirring is insufficient.

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The effect of sculpting planets on the steepness of debris-disc inner edges

Debris discs are our best means to probe the outer regions of planetary systems. Many studies assume that planets lie at the inner edges of debris discs, akin to Neptune and the Kuiper Belt, and use the disc morphologies to constrain those otherwise-undetectable planets. However, this produces a degeneracy in planet mass and semimajor axis. We investigate the effect of a sculpting planet on the radial surface-density profile at the disc inner edge, and show that this degeneracy can be broken by considering the steepness of the edge profile. Like previous studies, we show that a planet on a circular orbit ejects unstable debris and excites surviving material through mean-motion resonances. For a non-migrating, circular-orbit planet, in the case where collisions are negligible, the steepness of the disc inner edge depends on the planet-to-star mass ratio and the initial-disc excitation level. We provide a simple analytic model to infer planet properties from the steepness of ALMA-resolved disc edges. We also perform a collisional analysis, showing that a purely planet-sculpted disc would be distinguishable from a purely collisional disc and that, whilst collisions flatten planet-sculpted edges, they are unlikely to fully erase a planet's signature. Finally, we apply our results to ALMA-resolved debris discs and show that, whilst many inner edges are too steep to be explained by collisions alone, they are too flat to arise through completed sculpting by non-migrating, circular-orbit planets. We discuss implications of this for the architectures, histories and dynamics in the outer regions of planetary systems.

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Self-gravity of debris discs can strongly change the outcomes of interactions with inclined planets

Drastic changes in protoplanets' orbits could occur in the early stages of planetary systems through interactions with other planets and their surrounding protoplanetary or debris discs. The resulting planetary system could exhibit orbits with moderate to high eccentricities and/or inclinations, causing planets to perturb one another as well as the disc significantly. The present work studies the evolution of systems composed of an initially inclined planet and a debris disc. We perform N-body simulations of a narrow, self-gravitating debris disc and a single interior Neptune-like planet. We simulate systems with various initial planetary inclinations, from coplanar to polar configurations considering different separations between the planet and the disc. We find that except when the planet is initially on a polar orbit, the planet-disc system tends to reach a quasi-coplanar configuration with low vertical dispersion in the disc. When present, the Zeipel--Kozai--Lidov oscillations induced by the disc pump the planet's eccentricity and, in turn, affect the disc structure. We also find that the resulting disc morphology in most of the simulations looks very similar in both radial and vertical directions once the simulations are converged. This contrasts strongly with massless disc simulations, where vertical disc dispersion is set by the initial disc-planet inclination and can be high for initially highly inclined planets. The results suggest caution in interpreting an unseen planet's dynamical history based only on the disc's appearance.

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Astrometric Accelerations as Dynamical Beacons: A Giant Planet Imaged Inside the Debris Disk of the Young Star AF Lep

We present the direct imaging discovery of a giant planet orbiting the young star AF Lep, a 1.2 $M_{\odot}$ member of the 24 $\pm$ 3 Myr $β$ Pic moving group. AF Lep was observed as part of our ongoing high-contrast imaging program targeting stars with astrometric accelerations between Hipparcos and Gaia that indicate the presence of substellar companions. Keck/NIRC2 observations in $L'$ with the Vector Vortex Coronagraph reveal a point source, AF Lep b, at ${\approx}340$ mas which exhibits orbital motion at the 6-$σ$ level over the course of 13 months. A joint orbit fit yields precise constraints on the planet's dynamical mass of 3.2$^{+0.7}_{-0.6}$ $M_\mathrm{Jup}$, semi-major axis of $8.4^{+1.1}_{-1.3}$ au, and eccentricity of $0.24^{+0.27}_{-0.15}$. AF Lep hosts a debris disk located at $\sim$50 au, but it is unlikely to be sculpted by AF Lep b, implying there may be additional planets in the system at wider separations. The stellar inclination ($i_* = 54^{+11}_{-9} {}^\circ$) and orbital inclination ($i_o = 50^{+9}_{-12} {}^\circ$) are in good agreement, which is consistent with the system having spin-orbit alignment. AF Lep b is the lowest-mass imaged planet with a dynamical mass measurement and highlights the promise of using astrometric accelerations as a tool to find and characterize long-period planets.

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