We study orbital evolution of multiple Earth-mass protoplanets in their natal protoplanetary disk. Our aim is to explore the interplay between migration of protoplanets driven by the disk gravity, their growth by pebble accretion, and accretion heating which affects gas in their neighbourhood. Radiation hydrodynamic (RHD) simulations in 2D and 3D are used to model the problem. We find that the heating torque, i.e. the torque exerted by asymmetric hot underdense gas near accreting protoplanets, significantly changes the migration. Specifically, it excites orbital eccentricities of migrating protoplanets, thus preventing their capture in chains of mean-motion resonances. The protoplanets then undergo numerous close encounters and form giant planet cores by mutual collisions. Additionally, if inclinations also become excited, we describe a new mechanism that can form binary planets by means of consecutive two-body and three-body encounters, with the assistance of the disk gravity. Finally, our 3D RHD simulations reveal a complex distortion of the gas flow near an accreting protoplanet, driven by baroclinic perturbations and convection. For specific temperature-dependent opacities of the disk, an instability is triggered which redistributes gas around the protoplanet and leads to an oscillatory migration,...

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<p>We use numerical simulations to examine the fragmentation of protostellar discs via gravitational instability (GI), a proposed formation mechanism for gas-giant planets and brown dwarfs. To accurately model heating and cooling, we have implemented radiative transfer (RT) in the TreeSPH code Gasoline, using the flux-limited diffusion approximation coupled to photosphere boundary cooling. We present 3D radiation hydrodynamics simulations of discs that are gravitationally unstable in the inner 40 AU; these discs do not fragment because the cooling times are too long. In prior work, one of these discs was found to fragment; however, we demonstrate that this resulted from an over-estimate of the photosphere cooling rate. Fragmentation via GI does not appear to be a viable formation mechanism in the inner 40 AU.</p> <p>We also present simulations of GI in the outer regions of discs, near 100 AU, where we find GI to be a viable formation mechanism. We give a detailed framework that explains the link between cooling and fragmentation: spiral arms grow on a scale determined by the linear gravitational instability, have a characteristic width determined by the balance of heating and cooling, and fragment if this width is less than twice their Hill radius. This framework is consistent with the fragmentation and initial fragment masses observed in our simulations. We apply the framework to discs modelled with the commonly-used beta-prescription cooling and calculate the critical cooling rate for the first time, with results that are consistent with previous estimates measured from numerical experiments.</p> <p>RT is fundamentally important in the star formation process. Non-ionizing radiation heats the gas and prevents small-scale fragmentation. Ionizing radiation from massive stars is an important feedback mechanism and may disrupt giant molecular clouds. We present methods and tests for our implementation of ionizing radiation, using the Optically-Thin Variable Eddington Tensor method.</p> / Doctor of Philosophy (PhD)

This thesis describes efforts to improve the realism of numerical models of giant planet formation and migration in an attempt to better understand these processes. A new approach has been taken to the modelling of accretion, designed to mimic reality by allowing gas to accumulate upon a protoplanetary surface. Implementing this treatment in three-dimensional self-gravity radiation hydrodynamics calculations provides an excellent model for planet growth, allowing an exploration of the factors that affect accretion. Moreover, these calculations have also been extended to investigate the migration of protoplanets through their parent discs as they grow. When focusing on the growth of non-migrating protoplanets, the models are performed using small sections of disc, enabling excellent resolution right down to the core; gas structures and flow can be resolved on scales from ~ 10^4 to 10^11 metres. Using radiative transfer, these models reveal the importance of opacity in determining the accretion rates. For the low mass protoplanets, equivalent in mass to a giant planet core (~ 10 M⊕), the accretion rates were found to increase by up to an order of magnitude for a factor of 100 reduction in the grain opacity of the parent circumstellar disc. However, even these low opacities lead to growth rates that are an order of magnitude slower than those obtained in locally-isothermal conditions. For high mass protoplanets (>~ 100M⊕), the accretion rates show very little dependence upon opacity. Nevertheless, the rates obtained using radiative transfer are still lower than those obtained in locally-isothermal models by a factor of ~2, due to the release of accretion energy as heat. Only high mass protoplanets are found to be capable of developing circumplanetary discs, and this ability is dependent upon the opacity, as are the scaleheights of such discs. However, their radial extents were found to be independent of the opacity and the protoplanet mass, all reaching ≈ RH/3, inline with analytic predictions. Migration is investigated using global models, ensuring a self-consistently evolved disc. Using locally-isothermal calculations, it was found that the capture radius of an accreting sink particle, used to model a protoplanet without a surface, must be small (<< RH) to yield migration timescales consistent with linear theory of Type I migration. In the low mass regime of Type I migration, accreting sinks with such small radii yield timescales consistent with those models in which a protoplanetary surface is used. However, for high mass protoplanets, undergoing Type II migration, the surface treatment leads to faster rates of migration, indicating the importance of a realistic accretion model. Using radiative transfer, with high opacities, leads to a factor of ~ 3 increase in the migration timescale of the lowest mass protoplanets, improving their chances of survival. As suitable gas giant progenitors, their survival is key to understanding the growth of giant planets. An unexpected result of the radiative transfer was a reduction in the migration timescale of high mass planets. This appears to be a result of the less thoroughly evacuated gaps created by planets in non-locally-isothermal discs, which affects the corotation torque.

Stars form via the gravitational collapse of molecular clouds during which time the protostellar object contracts by over seven orders of magnitude. If all the angular momentum present in the natal cloud was conserved during collapse, stars would approach rotational velocities rapid enough to tear themselves apart within just a few Myr. In contrast to this, observations of pre-main sequence rotation rates are relatively slow (∼ 1 − 15 days) indicating that significant quantities of angular momentum must be removed from the star. I use observations of fully convective pre-main sequence stars in two well-studied, nearby regions of star formation (namely the Orion Nebula Cluster and Taurus-Auriga) to determine the removal rate of stellar angular momentum. I find the accretion disc-hosting stars to be rotating at a slower rate and contain less specific angular momentum than the disc-less stars. I interpret this as indicating a period of accretion disc-regulated angular momentum evolution followed by near-constant rotational evolution following disc dispersal. Furthermore, assuming that the age spread inferred from the Hertzsprung-Russell diagram constructed for the star forming region is real, I find that the removal rate of angular momentum during the accretion-disc hosting phase to be more rapid than that expected from simple disc-locking theory whereby contraction occurs at a fixed rotation period. This indicates a more efficient process of angular momentum removal must operate, most likely in the form of an accretion-driven stellar wind or outflow emanating from the star-disc interaction. The initial circumstellar envelope that surrounds a protostellar object during the earliest stages of star formation is rotationally flattened into a disc as the star contracts. An effective viscosity, present within the disc, enables the disc to evolve: mass accretes inwards through the disc and onto the star while momentum migrates outwards, forcing the outer regions of the disc to expand. I used spatially resolved submillimetre detections of the dust and gas components of protoplanetary discs, gathered from the literature, to measure the radial extent of discs around low-mass pre-main sequence stars of ∼ 1−10 Myr and probe their viscous evolution. I find no clear observational evidence for the radial expansion of the dust component. However, I find tentative evidence for the expansion ofthe gas component. This suggests that the evolution of the gas and dust components of protoplanetary discs are likely governed by different astrophysical processes. Observations of jets and outflows emanating from protostars and pre-main sequence stars highlight that it may also be possible to remove angular momentum from the circumstellar material. Using the sample of spatially resolved protoplanetary discs, I find no evidence for angular momentum removal during disc evolution. I also use the spatially resolved debris discs from the Submillimetre Common-User Bolometer Array-2 Observations of Nearby Stars survey to constrain the amount of angular momentum retained within planetary systems. This sample is compared to the protoplanetary disc angular momenta and to the angular momentum contained within pre-stellar cores. I find that significant quantities of angular momentum must be removed during disc formation and disc dispersal. This likely occurs via magnetic braking during the formation of the disc, via the launching of a disc or photo-evaporative wind, and/or via ejection of planetary material following dynamical interactions.

Dans les disques protoplanétaires, les grains micrométriques croissent jusqu'à atteindre des tailles de planétésimaux avant de finalement former des planètes. Cependant,des études dynamiques ont montré qu'une fois que les grains atteignent une taille critique, ils dérivent rapidement vers l'étoile et y sont accrétés. Ce problème est connu comme la barrière de dérive radiale. De plus, des expériences en laboratoire ont montré que les grains peuvent fragmenter ou rebondir et ainsi arrêter la croissance avant les tailles kilométriques.Afin de passer outre ces barrières, plusieurs méthodes ont été proposés comme les pièges à particules (dans les vortex ou les sillons planétaires) qui demandent des évolutions dynamiques à grande échelle. Dans ce travail, nous choisissons d'étudier les propriétés intrinsèques de la poussière pendant leur croissance et plus particulièrement leur porosité.Nous développons un modèle d'évolution de la porosité pendant la croissance en fonction de la masse des grains pour plusieurs régimes d'expansion/compression (Kataoka et al. 2013, Okuzumi et al. 2012) et l'implémentons dans notre code SPH bifluide (Barrière-Fouchet et al. 2005). Nous trouvons que la croissance des grains poreux est accélérée en comparaison aux grains compacts et leur taille peut atteindre plusieurs kilomètres. De surcroît,la dérive est légèrement ralentie pour les grains poreux qui peuvent croître jusqu'à de plus grandes tailles avant de commencer à dériver vers l'étoile. Nous constatons aussi que les grains des régions externes du disque grossissent plus que quand l'effet de la porosité est négligé. Ces deux mécanismes peuvent aider les grains à outrepasser la barrière de dérive radiale, notamment en passant dans le régime de traînée de Stokes, et ainsi former des planétésimaux.Nous étudions aussi l'effet de la fragmentation et du rebond sur le comportement des grains. En considérant un seuil de fragmentation constant, nous observons que la croissance de grains poreux est retardée un temps par la fragmentation mais qu'elle se poursuit vers de grandes tailles et par conséquent, permet de passer outre les problèmes dus à la fragmentation et à la dérive radiale. Cependant, les grains très poreux sont plus fragiles et peuvent se fragmenter plus facilement entraînant une accrétion massive des poussières dans l'étoile. De plus, nous montrons que les effets du rebond peuvent être négligés devant ceux de la fragmentation.Enfin, nous observons également que la taille des monomères et du paramètre de viscosité turbulente peut avoir une influence sur l'évolution de la porosité et donc de la poussière dans le disque.La porosité permet donc de favoriser la croissance des grains et accélérer le découplage des grains. Les grains très poreux peuvent être plus sensibles à la fragmentation.Cependant, les effets collectifs de la poussière couplés à la porosité peuvent aider les grains à outrepasser les barrières de formation planétaire. La barrière de rebond peut être négligée dans le cas de grains poreux devant les autres barrières. Enfin,l'intensité de la turbulence altère la croissance et ainsi le devenir de la poussière.La taille des monomères modifie le facteur de remplissage sans toutefois impacter le découplage des grains dans les parties internes / In protoplanetary discs, micron-sized grains should grow up to planetesimal sizes in order to ultimately form planets. However, dynamical studies show that once they reach a critical size, they drift rapidly into the accreting star. This is known as the radial-drift barrier. Moreover, laboratory experiments have shown that grains can fragment or bounce, stopping the growth towards planetesimal sizes.In order to overcome those barriers, several methods have been proposed such as particles traps (e.g. vortices or planet gaps) which all involve large-scale dynamics.In this work, we choose to investigate the intrinsic properties of the grains during their growth, in particular their porosity.We thus consider the growth of grains with variable porosity as a function of their mass in several regimes of compression/expansion (Kataoka et al. 2013, Okuzumiet al. 2012) and implement it in our 3D SPH two-fluid code (Barrière-Fouchetet al. 2005).We find that growth is accelerated for porous grains that can reach kilometersizes. On the other hand, drift is slightly slowed down for porous grains that can grow up to larger sizes before drifting towards the star. As a result, grains in the outer regions of the disc reach larger sizes than when porosity is neglected. Those two mechanisms can help grains overcome the radial-drift barrier and form planetesimals.The Stokes drag regime appears to play a substantial part in maintaining grains in the disc.Considering a constant fragmentation threshold, we also find out that growth is delayed because of fragmentation but reaching large sizes and thus overcoming problems due to fragmentation and radial drift is still possible. However, very fluffy grains are fragile and can be easily disrupted leading to a massive accretion of dust into the star. Moreover, we show that the effects due to dust bouncing can be neglected compared to fragmentation.Finally, we investigate the influence of the size of monomers and -parameter on the evolution of porosity and then dust in the disc.Dust growth is accelerated by porosity and thus promotes grains decoupling. Very fluffy grains are more affected by fragmentation. However, dust collective effects and porosity can help grains to overcome planet formation barriers. Besides,the bouncing barrier can be neglected in the case of porous dust compared to other barriers. Finally, the intensity of turbulence can alter the growth and so the outcome of dust. The size of monomers modifies the grain filling factor without impacting dust decoupling in the inner parts of the disc

In this thesis, I study numerical and semi-analytical models of self-gravitating protostellar discs, with the aim of furthering our understanding of the role of disc-self gravity in planet formation. At the time of writing, the ALMA era of observational astronomy is upon us. Therefore, I place my research into this context with synthetic images of both numerical and semi-analytical models. I begin with an examination into the apparent lack of convergence, with increasing resolution, of the fragmentation boundary in Smoothed Particle Hydrodynamics (SPH) simulations of a protostellar disc. I run a suite of SPH with different numerical implementations, and find that even very similar implementations can fundamentally change the final answer. I analyse a suite of SPH simulations that fragment to form gravitationally bound objects, with the motivation of informing future population synthesis model development. I find that fragment-fragment and fragment-disc interaction dominates the orbital evolution of the system even at very early times, and any attempt to produce a population of objects from the gravitational instability process must include these interactions. Before a disc fragments, it will go through a self-gravitating phase. If the disc cools globally on a timescale such that it is balanced by heating due to gravitational stresses, the disc will be in a state of quasi-equilibrium. So long as the disc mass is sufficiently low, and spirals are sufficiently tightly wound, then angular momentum transport can be described by the local approximation, for which there is an analytical description. Using this analytical description, I develop an existing 1D model into 3D, and examine a wide range of parameter space for which disc self-gravity produces significant non-axisymmetry. Using radiative transfer calculations coupled with synthetic observations, I determine that there is a very narrow range of parameter space in which a disc will have sufficiently large gravitational stresses so as to produce detectable spirals, but the stresses not be so large as to cause the disc to fragment. By developing a simple analytical prescription for dust, I show that this region of parameter space can be broadened considerably. However, it requires grains that are large enough to become trapped by pressure maxima in the disc, so I conclude that if self-gravitating spiral arms are detected in the continuum, it is likely that at least some grain growth has taken place.

L'existence de molécules interstellaires soulève une question, ces molécules sont-elles les mêmes molécules que nous voyons dans le système Solaire aujourd'hui ? C'est une question toujours ouverte qui implique des conséquences profondes. Il est possible d’éclaircir cette question en étant capables de retracer l'héritage d'un groupe de molécules chimiquement liées, ce que nous appelons un réservoir. Le meilleur outil pour retracer l'héritage des réservoirs sont les rapports isotopiques. L'élément qui montre les plus grandes variations du rapport isotopique dans le système Solaire est l'azote. Ces variations indiquent que le rapport isotopique de l'azote est sensible aux conditions physiques de la formation des étoiles.L'objectif principal de cette thèse est d'identifier les réservoirs d'azote à différents étapes de la formation des étoiles et des planètes. La première étape de cette entreprise était d'identifier le rapport isotopique de la masse principal d'azote du milieu interstellaire local aujourd'hui.Cela a été déterminé égale à 323 ± 30 à partir du rapport CN/C 15 N mesuré dans le disque protoplanétaire autour de TW Hya. Parallèlement à cela, nous avons également mesuré un rapport HCN/HC 15 N=128 ± 36 dans le disque protoplanétaire autour de MWC 480. Ces rapports isotopiques très distinctes mesurées sur les disques protoplanétaires sont une indication claire de la présence d'au moins deux réservoirs d'azote dans les disques protoplanétaires. La façon dont ces réservoirs se séparent est cependant inconnue. Cela pourrait peut-être se produire en raison de réactions de fractionnement chimique ayant lieu dans les cœurs prestellaires. Nous avions donc comme objectif d'obtenir une mesure précise et directe du rapport isotopique de l'azote des molécules d'HCN dans le cœur prestellaire L1498.Pour obtenir cette mesure, l'obstacle le plus important à surmonter était due aux anomalies hyperfines des molécules d'HCN. Ces anomalies hyperfines sont induites par le chevauchement des composants hyperfins. Ceci sont particulièrement sensibles à la densité de colonne d'HCN, mais aussi au champ de vitesses et aux largeurs de raies. Ainsi les anomalies hyperfines sont un outil de mesure de l'abondance d'HCN permettant aussi de sonder la cinématique des cœurs prestellaires.Pour reproduire avec précision les anomalies hyperfines, et ainsi mesurer des densités de colonne précises d'HCN, nous avions besoin d'explorer un espace de paramètres dégénéré de 15 dimensions. Pour minimiser les dégénérescences nous avons obtenu un profil de densité basé sur des cartes du continuum de L1498. Ceci permettant de réduire à 12 dimensions l'espace des paramètres. L'exploration de cet espace de paramètre a été fait grâce à l'utilisation d'un méthode de minimisation MCMC. Grâce à cette exploration, nous avons obtenu HCN/HC 15 N = 338 ± 28 et HCN/H 13 CN = 45 ± 3. Les incertitudes sur ces valeurs sont limités par les erreurs de calibration et sont dé-terminés de manière non arbitraire par le méthode MCMC. Les implications de ces résultats sont discutées dans le chapitre de conclusion,où nous présentons également quelques perspectives sur l'avenir. / The existence of interstellar molecules raises the question, are thesemolecules the same molecules we see on the Solar system today? Thisis still an open question with far reaching consequences. Some lightmay be shed on this issue if we are able to trace the heritage of agroup of chemically linked molecules, a so-called reservoir. The besttool to trace the heritage of reservoirs are isotopic ratios. The elementthat shows the largest isotopic ratio variations in the Solar system isnitrogen. For this is an indication that the isotopic ratio of nitrogen issensitive to the physical conditions during star formation.The main objective of this thesis is to identify the reservoirs of ni-trogen at different stages of star and planet formation. The first stepin this endeavour was to identify the isotopic ratio of the bulk of ni-trogen in the local ISM today. This was determined to be 323 ± 30from the CN/C 15 N ratio in the protoplanetary disk around TW Hya.Along with it we also measured the HCN/HC 15 N= 128 ± 36 in theprotoplanetary disk around MWC 480. This very distinct nitrogen iso-topic ratios on protoplanetary disks are a clear indication that thereare at least two reservoirs of nitrogen in protoplanetary disks. Howthese reservoirs get separated is however unknown. This could pos-sibly happen due to chemical fractionation reactions taking place inprestellar cores. We therefore aimed to obtain an accurate direct mea-surement of the nitrogen isotopic ratio of HCN in the prestellar coreL1498.To obtain this measurement the most important hurdle to overcomewere the hyperfine anomalies of HCN. These hyperfine anomaliesarise due to the overlap of hyperfine components. They are especiallysensitive to the column density of HCN, but also to the velocity fieldand line widths. Thus hyperfine anomalies are a tool to measure theabundance of HCN and to probe the kinematics of prestellar cores.To accurately reproduce the hyperfine anomalies, and thus mea-sure accurate column densities for HCN, we needed to explore adegenerate parameter space of 15 dimensions. To minimise the de-generacies we have derived a density profile based on continuummaps of L1498. This reduced the parameter space to 12 dimensions.The exploration of this parameter space was done through the useof a MCMC minimisation method. Through this exploration we ob-tained HCN/HC 15 N = 338 ± 28 and HCN/H 13 CN = 45 ± 3. Theuncertainties on these values are calibration limited and determinednon-arbitrarily by the MCMC method. Implications of these resultsare discussed in the concluding chapter, where we also present somefuture perspectives.

Les observations de centaines de systèmes d’exoplanètes nous ont fourni un large échantillon de configurations orbitales. Les périodes orbitales figurent parmi les données les mieux connues et les plus étonnantes. Les Super-Terres, ces planètes caractérisées par une masse entre 1 et 20 masses terrestres et une période typiquement de moins de 100 jours, sont présentes autour de la plupart des étoiles. La distribution des rapports de leurs périodes orbitales défie les astrophysiciens : pendant leur formation et migration au sein de leur disque protoplanétaire, elles devraient former des chaînes de résonances de moyen mouvement, c’est-à-dire que les rapports des périodes orbitales de planètes voisines devraient être proches de fractions simples. Toutefois, la plupart des systèmes de Super-Terres ne sont pas résonants. Dans cette thèse, je traite les aspects clés des chaînes résonantes : leur formation, leur évolution et leur stabilité. Premièrement, j’introduis les idées modernes en théorie de formation planétaire, et les méthodes utilisées dans la thèse : la mécanique Hamiltonienne, le problème planétaire et la théorie perturbative. Deuxièmement, je présente le processus de capture en résonance de moyen mouvement du premier ordre k : k − 1 par migration convergente des planètes, avec une nouvelle description analytique de l’évolution planétaire qui en suit, et je décris la dynamique résonante dans le plan orbital commun. La description analytique est confirmée par des intégrations N-corps qui incluent les interactions disque-planète. Ensuite, je me base sur des résultats existants concernant l’évolution dissipative de deux planètes en résonance qui engendre la divergence de leurs demi-grands axes. Par une approche similaire, je présente une méthode statistique qui permet de déterminer dans quelle mesure l’architecture observée d’un système de trois planètes est compatible avec une histoire dynamique résonante dissipative. Je considère par la suite la stabilité des chaînes résonantes. Des études antérieures ont montré que l’absence de systèmes exoplanétaires résonants n’est pas en contradiction avec le modèle de capture en résonance par migration dans le disque, si une phase d’instabilité est très commune après la disparition du disque. On observe un taux d’instabilité plus élevé dans les systèmes synthétiques plus compacts et peuplés par des planètes plus massives. Des simulations N-corps dédiées à l’étude de la stabilité des chaînes résonantes ont montré qu’il y a une masse planétaire maximale qui garantit la stabilité ; cette masse limite diminue si les planètes sont plus massives et/ou si la chaîne résonante est plus compacte. J’étudie la stabilité des chaînes résonantes de planètes en fonction de leur masse commune, et j’examine de façon analytique et numérique des cas spécifiques de systèmes comprenant deux ou trois planètes. Je découvre un mécanisme dynamique qui peut déclencher une excitation du système, et qui mène à une phase de rencontres proches et collisions. Ce mécanisme se généralise à différents nombres de planètes et/ou à des chaînes résonantes plus ou moins compactes, et donne une prédiction analytique de la masse critique qui est en accord qualitatif avec les expériences numériques mentionnées précédemment. Enfin, je décris un scénario dynamique qui peut expliquer la pollution des naines blanches en éléments lourds. Les systèmes planétaires compacts peuvent devenir instables pendant la phase de perte de masse qui marque la fin de l’évolution stellaire, et les impacts entre planètes génèrent des débris. En m’appuyant sur des résultats précédents, je montre que l’excentricité orbitale des débris qui résident en résonance de moyen mouvement avec une planète externe peut devenir suffisamment élevée pour que les débris soient engloutis par l’étoile, ce qui peut expliquer la pollution observée. / Observations of hundreds of exoplanetary systems have produced a huge sample of orbital configurations, and the orbital periods are one of their better constrained and most astonishing properties. A common type of exoplanets are the Super-Earths, which have a mass between 1 and 20 Earth masses and a typical period of less than 100 days. The period ratio distribution of these planets poses a challenge to astrophysicists: during their formation, still embedded in the protoplanetary disc, we expect them to form chains of mean motion resonances, where the period ratio of neighbouring planets is close to a low-integer ratio. However, most Super-Earth systems are not close to resonance. In this thesis, I discuss key dynamical aspects of resonant chains: their formation, their evolution and their stability. I first give an overview of our current understanding of planetary formation, and an introduction of the methods used in the thesis: the tools of Hamiltonian dynamics, the planetary problem and perturbation theory. Then, I present the process of capture of planets migrating in protoplanetary discs into first order k : k − 1 mean motion resonances, including a novel analytical description of the corresponding planetary evolution, and I describe the relevant aspects of resonant dynamics in the planar approximation. The analytical treatment is supported by numerical N-body simulations which include the planet-disc interactions. Next, I expand on previous results on two-planet dissipative evolution in mean motion resonance and the resulting divergence of the planets’ semi-major axes. With a similar approach, I present a statistical method which allows to determine to what extent the observed architecture of a three-planet system is compatible with a dissipative resonant dynamical history. I then address the main problem of the stability of resonant chains. Previous works have shown that the over-all lack of resonances in the exoplanet sample is not in contradiction with resonant capture, if a post-disc phase of planetary instabilities is extremely common. Higher rates of instabilities are observed in synthetic systems where planets are most massive and the configurations most compact. Specific N-body experiments on the stability of resonant chains found that there is a critical planetary mass allowed for stability, which decreases with increasing number of planets and/or increasing value of k in the chain. The origin of these instabilities was however not discussed. I study the stability of resonant chains of equal-mass planets in terms of their mass, investigating analytically and numerically specific cases of two- and threeplanet systems. I find a dynamical mechanism which can trigger an excitation of the system, leading to mutual close-encounters and collisions. This can be generalised to an arbitrary number of planets and/or value of k in the resonant chain, and gives an analytical prediction for the critical mass allowed for stability which agrees qualitatively with the aforementioned numerical experiments. Finally, I describe a dynamical scenario that can explain the pollution of White Dwarfs with heavy elements. The idea is that compact planetary systems become unstable during the mass-loss phase characterising the end of the stellar evolution, so that impacts among planets lead to the generation of collisional debris. Expanding on previous works, I show that debris residing in mean motion resonance with an outer planetary perturber can have their orbital eccentricity excited to largeenough values to be engulfed by the host star, causing the observed pollution.