Richard P. Nelson

Queen Mary, University of London, Londinium, England, United Kingdom

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Publications (72)279.99 Total impact

  • Gavin A. L. Coleman · Richard P. Nelson
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    ABSTRACT: We present the results of planet formation N-body simulations based on a comprehensive physical model that includes planetary mass growth through mutual embryo collisions and planetesimal/boulder accretion, viscous disc evolution, planetary migration and gas accretion onto planetary cores. The main aim of this study is to determine which set of model parameters leads to the formation of planetary systems that are similar to the compact low mass multi-planet systems that have been discovered by radial velocity surveys and the Kepler mission. We vary the initial disc mass, solids-to-gas ratio and the sizes of the boulders/planetesimals, and for a restricted volume of the parameter space we find that compact systems containing terrestrial planets, super-Earths and Neptune-like bodies arise as natural outcomes of the simulations. Disc models with low values of the solids-to-gas ratio can only form short-period super-Earths and Neptunes when small planetesimals/boulders provide the main source of accretion, since the mobility of these bodies is required to overcome the local isolation masses for growing embryos. The existence of short-period super-Earths around low metallicity stars provides strong evidence that small, mobile bodies (planetesimals, boulders or pebbles) played a central role in the formation of the observed planets.
    No preview · Article · Jan 2016
  • Samuel Richard · Richard P. Nelson · Orkan M. Umurhan
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    ABSTRACT: We present the results of 2D and 3D hydrodynamic simulations of idealized protoplanetary discs that examine the formation and evolution of vortices by the vertical shear instability (VSI). In agreement with recent work, we find that discs with radially decreasing temperature profiles and short thermal relaxation time-scales, are subject to the axisymmetric VSI. In three dimensions, the resulting velocity perturbations give rise to quasi-axisymmetric potential vorticity perturbations that break-up into discrete vortices, in a manner that is reminiscent of the Rossby wave instability. Discs with very short thermal evolution time-scales (i.e. {\tau}<0.1 local orbit periods) develop strong vorticity perturbations that roll up into vortices that have small aspect ratios ({\chi}<2) and short lifetimes (~ a few orbits). Longer thermal time-scales give rise to vortices with larger aspect ratios (6<{\chi}<10), and lifetimes that depend on the entropy gradient. A steeply decreasing entropy profile leads to vortex lifetimes that exceed the simulation run times of hundreds of orbital periods. Vortex lifetimes in discs with positive or weakly decreasing entropy profiles are much shorter, being 10s of orbits at most, suggesting that the subcritical baroclinic instability plays an important role in sustaining vortices against destruction through the elliptical instability. Applied to the outer regions of protoplanetary discs, where the VSI is most likely to occur, our results suggest that vortices formed by the VSI are likely to be short lived structures.
    No preview · Article · Jan 2016 · Monthly Notices of the Royal Astronomical Society
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    Oliver Gressel · Neal J. Turner · Richard P. Nelson · Colin P. McNally
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    ABSTRACT: Protoplanetary disks are believed to accrete onto their central T Tauri star because of magnetic stresses. Recently published shearing box simulations indicate that Ohmic resistivity, ambipolar diffusion and the Hall effect all play important roles in disk evolution. In the presence of a vertical magnetic field, the disk remains laminar between 1-5au, and a magnetocentrifugal disk wind forms that provides an important mechanism for removing angular momentum. Questions remain, however, about the establishment of a true physical wind solution in the shearing box simulations because of the symmetries inherent in the local approximation. We present global MHD simulations of protoplanetary disks that include Ohmic resistivity and ambipolar diffusion, where the time-dependent gas-phase electron and ion fractions are computed under FUV and X-ray ionization with a simplified recombination chemistry. Our results show that the disk remains laminar, and that a physical wind solution arises naturally in global disk models. The wind is sufficiently efficient to explain the observed accretion rates. Furthermore, the ionization fraction at intermediate disk heights is large enough for magneto-rotational channel modes to grow and subsequently develop into belts of horizontal field. Depending on the ionization fraction, these can remain quasi-global, or break-up into discrete islands of coherent field polarity. The disk models we present here show a dramatic departure from our earlier models including Ohmic resistivity only. It will be important to examine how the Hall effect modifies the evolution, and to explore the influence this has on the observational appearance of such systems, and on planet formation and migration.
    Preview · Article · Jan 2015 · The Astrophysical Journal
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    Jaehan Bae · Lee Hartmann · Zhaohuan Zhu · Richard P. Nelson
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    ABSTRACT: We improve on our previous treatments of long-term evolution of protostellar disks by explicitly solving disk self-gravity in two dimensions. The current model is an extension of the one-dimensional layered accretion disk model of Bae et al. We find that gravitational instability (GI)-induced spiral density waves heat disks via compressional heating (i.e. $P\rm{d}V$ work), and can trigger accretion outbursts by activating the magnetorotational instability (MRI) in the magnetically inert disk dead-zone. The GI-induced spiral waves propagate well inside of gravitationally unstable region before they trigger outbursts at $R \lesssim 1$ AU where GI cannot be sustained. This long-range propagation of waves cannot be reproduced with the previously used local $\alpha$ treatments for GI. In our standard model where zero dead-zone residual viscosity ($\alpha_{\rm rd}$) is assumed, the GI-induced stress measured at the onset of outbursts is locally as large as $0.01$ in terms of the generic $\alpha$ parameter. However, as suggested in our previous one-dimensional calculations, we confirm that the presence of a small but finite $\alpha_{\rm rd}$ triggers thermally-driven bursts of accretion instead of the GI + MRI-driven outbursts that are observed when $\alpha_{\rm rd}=0$. The inclusion of non-zero residual viscosity in the dead-zone decreases the importance of GI soon after mass feeding from the envelope cloud ceases. During the infall phase while the central protostar is still embedded, our models stay in a quiescent accretion phase with $\dot{M}_{acc}\sim10^{-8}-10^{-7}~M_{\odot}~{\rm yr^{-1}}$ over $60~\%$ of the time and spend less than $15~\%$ of the infall phase in accretion outbursts.
    Preview · Article · Sep 2014 · The Astrophysical Journal
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    Gavin A. L. Coleman · Richard P. Nelson
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    ABSTRACT: We present N-body simulations of planetary system formation in thermally-evolving, viscous disc models. The simulations incorporate type I migration (including corotation torques and their saturation), gap formation, type II migration, gas accretion onto planetary cores, and gas disc dispersal through photoevaporation. The aim is to examine whether or not the oligarchic growth scenario, when combined with self-consistent disc models and up-to-date prescriptions for disc-driven migration, can produce planetary systems similar to those that have been observed. The results correlate with the initial disc mass. Low mass discs form close-packed systems of terrestrial-mass planets and super-Earths. Higher mass discs form multiple generations of planets, with masses in the range 10 < mp < 45M_Earth. These planets generally type I migrate into the inner disc, because of corotation torque saturation, where they open gaps and type II migrate into the central star. Occasionally, a final generation of low-to-intermediate mass planets forms and survives due to gas disc dispersal. No surviving gas giants were formed in our simulations. Analysis shows that these planets can only survive migration if a core forms and experiences runaway gas accretion at orbital radii r > 10 au prior to the onset of type II migration. We conclude that planet growth above masses mp > 10M_Earth during the gas disc life time leads to corotation torque saturation and rapid inward migration, preventing the formation and survival of gas giants. This result is in contrast to the success in forming gas giant planets displayed by some population synthesis models. This discrepancy arises, in part, because the type II migration prescription adopted in the population synthesis models causes too large a reduction in the migration speed when in the planet dominated regime.
    Preview · Article · Aug 2014 · Monthly Notices of the Royal Astronomical Society
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    Richard P Nelson · Phil Hellary · Stephen M Fendyke · Gavin Coleman
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    ABSTRACT: Observations of extrasolar planets are providing new opportunities for furthering our understanding of planetary formation processes. In this paper, we review planet formation and migration scenarios and describe some recent simulations that combine planetary accretion and gas-disc-driven migration. While the simulations are successful at forming populations of low- and intermediate-mass planets with short orbital periods, similar to those that are being observed by ground- and space-based surveys, our models fail to form any gas giant planets that survive migration into the central star. The simulation results are contrasted with observations, and areas of future model development are discussed.
    Preview · Article · Mar 2014 · Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences
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    ABSTRACT: The great diversity of extrasolar planetary systems has challenged our understanding of how planets form, and how their orbits evolve as they form. Among the various processes that may account for this diversity, the gravitational interaction between planets and their parent protoplanetary disc plays a prominent role in shaping young planetary systems. Planet-disc forces are large, and the characteristic times for the evolution of planets orbital elements are much shorter than the lifetime of protoplanetary discs. The determination of such forces is challenging, because it involves many physical mechanisms and it requires a detailed knowledge of the disc structure. Yet, the intense research of the past few years, with the exploration of many new avenues, represents a very significant improvement on the state of the discipline. This chapter reviews current understanding of planet-disc interactions, and highlights their role in setting the properties and architecture of observed planetary systems.
    Full-text · Article · Dec 2013
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    Richard P. Nelson · Oliver Gressel · Orkan M. Umurhan
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    ABSTRACT: We analyse the stability and non-linear dynamics of power-law accretion disc models. These have mid-plane densities that follow radial power laws and have either temperature or entropy distributions that are strict power-law functions of cylindrical radius, R. We employ two different hydrodynamic codes to perform high-resolution 2D axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the disc scaleheight, the thermal relaxation time of the fluid and the disc viscosity. We present an accompanying stability analysis of the problem, based on asymptotic methods, that we use to guide our interpretation of the simulation results. We find that axisymmetric disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of perturbations whose most obvious character is modes with horizontal and vertical wavenumbers that satisfy |kR/kZ| ≫ 1. Instability occurs only when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time-scale. These discs appear to exhibit the Goldreich-Schubert-Fricke or `vertical shear' linear instability. Closer inspection of the simulation results uncovers the growth of two distinct modes. The first are characterized by very short radial wavelength perturbations that grow rapidly at high latitudes in the disc, and descend down towards the mid-plane on longer time-scales. We refer to these as `finger modes' because they display kR/kZ ≫ 1. The second appear at slightly later times in the main body of the disc, including near the mid-plane. These `body modes' have somewhat longer radial wavelengths. Early on they manifest themselves as fundamental breathing modes, but quickly become corrugation modes as symmetry about the mid-plane is broken. The corrugation modes are a prominent feature of the non-linear saturated state, leading to strong vertical oscillation of the disc mid-plane. In a viscous disc with aspect ratio H/r = 0.05, instability is found to operate when the viscosity parameter α < 4 × 10-4. In three dimensions the instability generates a quasi-turbulent flow, and the associated Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches α ˜ 10-3 by the end of the simulation. The evolution and saturation of the vertical shear instability in astrophysical disc models which include realistic treatments of the thermal physics has yet to be examined. Should it occur on either global or local scales, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties and observational appearance.
    Preview · Article · Nov 2013 · Monthly Notices of the Royal Astronomical Society
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    Stephen M. Fendyke · Richard P. Nelson
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    ABSTRACT: We present the results of high-resolution 2D simulations of low-mass planets on fixed eccentric orbits embedded in protoplanetary discs. The aim of this study is to determine how the strength of the sustained, non-linear corotation torque experienced by embedded planets varies as a function of orbital eccentricity, disc parameters and planetary mass. In agreement with previous work we find that the corotation torque diminishes as orbital eccentricity, e, increases. Analysis of the time-averaged streamlines in the disc demonstrates that the width of the horseshoe region narrows as the eccentricity increases, and we suggest that this narrowing largely explains the observed decrease in the corotation torque. We employ three distinct methods for estimating the strength of the unsaturated corotation torque from our simulations, and provide an empirical fit to these results. We find that a simple model where the corotation torque, ΓC, decreases exponentially with increasing eccentricity [i.e. ΓC ∝ exp (−e/ef)] provides a good global fit to the data with an e-folding eccentricity, ef, that scales linearly with the disc scale height at the planet location. We confirm that this model provides a good fit for planet masses of 5 and 10 M⊕ in our simulations. The formation of planetary systems is likely to involve significant planet–planet interactions that will excite eccentric orbits, and this is likely to influence disc-driven planetary migration through modification of the corotation torque. Our results suggest that high fidelity models of planetary formation should account for these effects.
    Preview · Article · Oct 2013 · Monthly Notices of the Royal Astronomical Society
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    Oliver Gressel · Richard P. Nelson · Neal J. Turner · Udo Ziegler
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    ABSTRACT: We present global hydrodynamic and magnetohydrodynamic (MHD) simulations with mesh refinement of accreting planets embedded in protoplanetary disks (PPDs). The magnetized disk includes Ohmic resistivity that depends on the overlying mass column, leading to turbulent surface layers and a dead zone near the midplane. The main results are: (i) The accretion flow in the Hill sphere is intrinsically 3D for hydrodynamic and MHD models. Net inflow toward the planet is dominated by high latitude flows. A circumplanetary disk (CPD) forms. Its midplane flows outward in a pattern whose details differ between models. (ii) Gap opening magnetically couples and ignites the dead zone near the planet, leading to stochastic accretion, a quasi-turbulent flow in the Hill sphere and a CPD whose structure displays high levels of variability. (iii) Advection of magnetized gas onto the rotating CPD generates helical fields that launch magnetocentrifugally driven outflows. During one specific epoch a highly collimated, one-sided jet is observed. (iv) The CPD's surface density $\sim30{\rm\,g\,cm^{-2}}$, small enough for significant ionization and turbulence to develop. (v) The accretion rate onto the planet in the MHD simulation reaches a steady value $8 \times 10^{-3} {\rm M_\oplus yr^{-1}}$, and is similar in the viscous hydrodynamic runs. Our results suggest that gas accretion onto a forming giant planet within a magnetized PPD with dead zone allows rapid growth from Saturnian to Jovian masses. As well as being relevant for giant planet formation, these results have important implications for the formation of regular satellites around gas giant planets.
    Preview · Article · Sep 2013 · The Astrophysical Journal
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    Arnaud Pierens · Richard P. Nelson
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    ABSTRACT: Several circumbinary planets have been detected by the Kepler mission. Recent work has emphasized the difficulty of forming these planets at their observed locations. It has been suggested that these planets formed further out in their discs and migrated in to locations where they are observed. We examine the orbital evolution of planets embedded in circumbinary disc models for the three systems Kepler-16, Kepler-34 and Kepler-35. The aims are: to explore the plausibility of a formation scenario in which cores form at large distances from the binaries and undergo inward migration and gas accretion as the gas disc disperses; to determine which sets of disc parameters lead to planets whose final orbits provide reasonable fits to the observed systems. We performed simulations of a close binary system interacting with circumbinary discs with differing aspect ratios, and viscous stress parameters. Once the binary+disc system reaches quasi-equilibrium we embed a planet in the disc and examine its evolution under the action of binary and disc forces. We consider fully-formed planets with masses equal to those inferred from Kepler data, and low-mass cores that migrate and accrete gas while the gas disc is being dispersed. A typical outcome for all systems is stalling of inward migration as the planet enters the inner cavity formed by the binary system. The circumbinary disc becomes eccentric and the disc eccentricity forces the planet into a noncircular orbit. For each of the Kepler-16b, Kepler-34b and Kepler-35b systems we obtain planets whose parameters agree reasonably well with the observational data. The simulations presented here provide support for a formation scenario in which a core forms, migrates inward and accretes gas, but accurate fitting of the observed Kepler systems is likely to require disc models that are significantly more sophisticated in terms of their input physics.
    Preview · Article · Jul 2013 · Astronomy and Astrophysics
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    Giammarco Campanella · Richard P. Nelson · Craig B. Agnor
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    ABSTRACT: We analyse the dynamics of the multiple planet system HD 181433. This consists of two gas giant planets (c and d) with msin i = 0.65 MJup and 0.53 MJup orbiting with periods 975 and 2468 days, respectively. The two planets appear to be in a 5:2 mean motion resonance, as this is required for the system to be dynamically stable. A third planet with mass m_b sin i = 0.023 MJup orbits close to the star with orbital period 9.37 days. Each planet orbit is significantly eccentric, with current values estimated to be e_b = 0.39, e_c = 0.27 and e_d = 0.47. In this paper we assess different scenarios that may explain the origin of these eccentric orbits, with particular focus on the innermost body, noting that the large eccentricity of planet b cannot be explained through secular interaction with the outer pair. We consider a scenario in which the system previously contained an additional giant planet that was ejected during a period of dynamical instability among the planets. N-body simulations are presented that demonstrate that during scattering and ejection among the outer planets a close encounter between a giant and the inner body can raise e_b to its observed value. We consider the possibility that an undetected planet in the system increases the secular forcing of planet b by the exterior giant planets, but we find that the resulting eccentricity is not large enough to agree with the observed one. We also consider a scenario in which the spin-down of the central star causes the system to pass through secular resonance. Spin-down rates below the critical value lead to longterm capture of planet b in secular resonance, driving the eccentricity toward unity. If additional short-period low mass planets are present in the system, however, we find that mutual scattering can release planet b from the secular resonance, leading to a system with orbital parameters similar to those observed today.
    Preview · Article · May 2013 · Monthly Notices of the Royal Astronomical Society
  • Orkan M. Umurhan · Richard P. Nelson · Oliver Gressel
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    ABSTRACT: The terrestrial planet formation regions of protoplanetary disks are generally sufficiently cold to be con- sidered non-magnetized and, consequently, dynamically inactive. However, recent investigations of these so-called "Dead-Zones" indicate the possibility that disks with strong mean radial temperature gradients can support instabilities associated with disk-normal gradients of the basic Keplerian shear profile. This process, known as the Goldreich-Schubert-Fricke (GSF) instability, is the instability of short radial wavelength inertial modes and depends wholly on the presence of vertical gradients of the mean Keplerian (zonal) flow. We report here high resolution fully nonlinear axisymmetric numerical studies of this instability and find a number of features including how, in the nonlinear saturated state, unstable discs become globally distorted, with strong vertical oscillations occurring at all radii due to local instability. We find that nonaxisymmetric numerical experiments are accompanied by significant amounts angular momentum transport (α ~ 0001). This instability should be operating in the Dead-Zones of protoplanetary disks at radii greater than 10-15 AU in minimum mass solar nebula models.
    No preview · Article · Apr 2013 · The European Physical Journal Conferences
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    Richard P. Nelson · Oliver Gressel · Orkan M. Umurhan
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    ABSTRACT: (Abridged) We analyse the stability and evolution of power-law accretion disc models. These have midplane densities that follow radial power-laws, and have either temperature or entropy distributions that are power-law functions of cylindrical radius. We employ two different hydrodynamic codes to perform 2D-axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the thermal relaxation time of the fluid, and the viscosity. We present a stability analysis of the problem that we use to interpret the simulation results. We find that disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of modes with wavenumber ratios |k_R/k_Z| >> 1 when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time scale. These discs are subject to the Goldreich-Schubert-Fricke (GSF) or `vertical shear' linear instability. Development of the instability involves excitation of vertical breathing and corrugation modes in the disc, with the corrugation modes in particular being a feature of the nonlinear saturated state. Instability operates when the dimensionless disc kinematic viscosity nu < 10^{-6} (Reynolds numbers Re>H c_s/nu > 2500). In 3D the instability generates a quasi-turbulent flow, and the Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches alpha ~ 6 x 10^{-4} by the end of the simulation. The vertical shear instability in disc models which include realistic thermal physics has yet to be examined. Should it occur, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties, and observational appearance.
    Preview · Article · Sep 2012
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    ABSTRACT: By carrying out two-dimensional two-fluid global simulations, we have studied the response of dust to gap formation by a single planet in the gaseous component of a protoplanetary disk - the so-called "dust filtration" mechanism. We have found that a gap opened by a giant planet at 20 AU in a \alpha=0.01, \dot{M}=10^{-8} Msun/yr disk can effectively stop dust particles larger than 0.1 mm drifting inwards, leaving a sub-millimeter dust cavity/hole. However, smaller particles are difficult to filter by a planet-induced gap due to 1) dust diffusion, and 2) a high gas accretion velocity at the gap edge. An analytic model is also derived to understand what size particles can be filtered by the gap edge. Finally, with our updated understanding of dust filtration, we have computed Monte-Carlo radiative transfer models with variable dust size distributions to generate the spectral energy distributions (SEDs) of disks with gaps. By comparing with transitional disk observations (e.g. GM Aur), we have found that dust filtration alone has difficulties to deplete small particles sufficiently to explain the near-IR deficit of transitional disks, except under some extreme circumstances. The scenario of gap opening by multiple planets studied previously suffers the same difficulty. One possible solution is by invoking both dust filtration and dust growth in the inner disk. In this scenario, a planet induced gap filters large dust particles in the disk, and the remaining small dust particles passing to the inner disk can grow efficiently without replenishment from fragmentation of large grains. Predictions for ALMA have also been made based on all these scenarios. We conclude that dust filtration with planet(s) in the disk is a promising mechanism to explain submm observations of transitional disks but it may need to be combined with other processes (e.g. dust growth) to explain the near-IR deficit.
    Preview · Article · May 2012 · The Astrophysical Journal
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    Oliver Gressel · Richard P. Nelson · Neal J. Turner
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    ABSTRACT: (Abridged) Planetesimals embedded in a protoplanetary disc are stirred by gravitational torques exerted by density fluctuations in the surrounding turbulence. In particular, planetesimals in a disc supporting fully developed magneto-rotational turbulence are readily excited to velocity dispersions above the threshold for catastrophic disruption, halting planet formation. We aim to examine the stirring of planetesimals lying instead in a magnetically-decoupled midplane dead zone, stirred only by spiral density waves propagating out of the disc's magnetically-coupled turbulent surface layers. We extend previous studies to include a wider range of disc models, and explore the effects of varying the disc column density and external magnetic field strength. [...] The strength of the stirring is found to be independent of the gas surface density, which is contrary to the increase with disc mass expected from a simple linear wave picture. The discrepancy arises from the shearing out of density waves as they propagate into the dead zone, resulting in density structures near the midplane that exert weaker stochastic torques on average. We provide a simple analytic fit to our numerically obtained torque amplitudes that accounts for this effect. The stirring on the other hand depends sensitively on the net vertical magnetic flux, up to a saturation level above which magnetic forces dominate in the turbulent layers. For the majority of our models, the equilibrium planetesimal velocity dispersions lie between the thresholds for disrupting strong and weak aggregates, suggesting that collision outcomes will depend on material properties. However, discs with relatively weak magnetic fields yield reduced stirring, and their dead zones provide safe-havens even for the weakest planetesimals against collisional destruction.
    Full-text · Article · Feb 2012 · Monthly Notices of the Royal Astronomical Society
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    Phil Hellary · Richard P. Nelson
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    ABSTRACT: We present the results of N-body simulations of planetary system formation in radiatively-inefficient disc models, where positive corotation torques may counter the rapid inward migration of low-mass planets driven by Lindblad torques. The aim of this work is to examine the nature of planetary systems that arise from oligarchic growth in such discs. We adapt the commonly used Mercury-6 symplectic integrator by including simple prescriptions for planetary migration (types I and II), planetary atmospheres that enhance the probability of planetesimal accretion by protoplanets, gas accretion on to forming planetary cores, and gas disc dispersal. We perform a suite of simulations for a variety of disc models with power-law surface density and temperature profiles, with a focus on models in which unsaturated corotation torques can drive outward migration of protoplanets. In some models, we account for the quenching of corotation torques which arises when planetary orbits become eccentric. Approximately half of our simulations lead to the successful formation of gas giant planets with a broad range of masses and semimajor-axes. Giant planetary masses range from being approximately equal to that of Saturn up to approximately twice that of Jupiter. The semimajor-axes of these range from being ∼0.2 au up to ∼75 au, with disc models that drive stronger outward migration favouring the formation of longer period giant planets. Out of a total of 20 giant planets being formed in our simulation suite, we obtain three systems that contain two giants. No super-Earth or Neptune-mass planets were present in the final stages of our simulations, in contrast to the large abundance of such objects being discovered in observation surveys. This result arises because of rapid inward migration suffered by massive planetary cores that form early in the disc lifetime (for which the corotation torques saturate), combined with gas accretion on to massive cores which leads them to become gas giants. Numerous low-mass planets are formed and survive in the simulations, with masses ranging from a few tenths of an Earth mass up to ∼3 Earth masses. Simulations in which the quenching of corotation torques for planets on modestly eccentric orbits was included failed to produce any giant planets, apparently because Lindblad torques induce rapid inward migration of planetary cores in these systems. We conclude that convergent migration induced by corotation torques operating during planetary formation can enhance the growth rate of planetary cores, but these often migrate into the central star because corotation torques saturate. Outward migration of planetary cores of modest mass can lead to the formation of gas giant planets at large distances from the central star, similar to those observed recently through direct imaging surveys. The excitation of planetary eccentricities through planet–planet scattering during oligarchic growth may quench the effects of corotation torques, however, such that inward migration is driven by Lindblad torques.
    Preview · Article · Dec 2011 · Monthly Notices of the Royal Astronomical Society
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    Zhaohuan Zhu · Lee Hartmann · Richard P. Nelson · Charles F. Gammie
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    ABSTRACT: We present two-dimensional hydrodynamic simulations of self-gravitating protostellar disks subject to axisymmetric, continuing mass loading from an infalling envelope and irradiation from the central star to explore the growth of gravitational instability (GI) and disk fragmentation. We assume that the disk is built gradually and smoothly by the infall, resulting in good numerical convergence. We confirm that for disks around solar-mass stars, infall at high rates at radii beyond ~50 AU leads to disk fragmentation. At lower infall rates, however, irradiation suppresses fragmentation. We find that, once formed, the fragments or clumps migrate inward on typical type I timescales of ~2 × 103 yr initially, but with a stochastic component superimposed due to their interaction with the GI-induced spiral arms. Migration begins to deviate from the type I timescale when the clump becomes more massive than the local disk mass, and/or when the clump begins to form a gap in the disk. As they migrate, clumps accrete from the disk at a rate between 10–3 and 10–1M J yr–1, consistent with analytic estimates that assume a 1-2 Hill radii cross section. The eventual fates of these clumps, however, diverge depending on the migration speed: 3 out of 13 clumps in our simulations become massive enough (brown dwarf mass range) to open gaps in the disk and essentially stop migrating; 4 out of 13 are tidally destroyed during inward migration; and 6 out of 13 migrate across the inner boundary of the simulated disks. A simple analytic model for clump evolution explains the different fates of the clumps and reveals some limitations of two-dimensional simulations. Overall, our results indicate that fast migration, accretion, and tidal destruction of the clumps pose challenges to the scenario of giant planet formation by GI in situ, although we cannot address whether or not remnant solid cores can survive after tidal stripping. The models where the massive clumps are not disrupted and open gaps may be relevant to the formation of close binary systems similar to Kepler 16. A clump formed by GI-induced fragmentation can be as large as 10 AU and as luminous as 2 × 10–3L ☉, which will be easily detectable with ALMA, but its lifetime before dynamically collapsing is only ~1000 years.
    Preview · Article · Nov 2011 · The Astrophysical Journal
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    Oliver Gressel · Richard P. Nelson · Neal J. Turner
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    ABSTRACT: (abridged) Accretion in protoplanetary discs is thought to be driven by [...] turbulence via the magnetorotational instability (MRI). Recent work has shown that a planetesimal swarm embedded in a fully turbulent disc is subject to strong excitation of the velocity dispersion, leading to collisional destruction of bodies with radii R_p < 100 km. Significant diffusion of planetesimal semimajor axes also arises, leading to large-scale spreading of the planetesimal population throughout the inner regions of the protoplanetary disc, in apparent contradiction of constraints provided by the distribution of asteroids within the asteroid belt. In this paper, we examine the dynamics of planetesimals embedded in vertically stratified turbulent discs, with and without dead zones. Our main aims are to examine the turbulent excitation of the velocity dispersion, and the radial diffusion, of planetesimals in these discs. We employ three dimensional MHD simulations [...], along with an equilibrium chemistry model [...] We find that planetesimals in fully turbulent discs develop large random velocities that will lead to collisional destruction/erosion for bodies with sizes below 100 km, and undergo radial diffusion on a scale \sim 2.5 au over a 5 Myr disc life time. But planetesimals in a dead zone experience a much reduced excitation of their random velocities, and equilibrium velocity dispersions lie between the disruption thresholds for weak and strong aggregates for sizes R_p < 100 km. We also find that radial diffusion occurs over a much reduced length scale \sim 0.25 au over the disc life time, this being consistent with solar system constraints. We conclude that planetesimal growth via mutual collisions between smaller bodies cannot occur in a fully turbulent disc. By contrast, a dead zone may provide a safe haven in which km-sized planetesimals can avoid mutual destruction through collisions.
    Full-text · Article · Apr 2011 · Monthly Notices of the Royal Astronomical Society
  • Richard P. Nelson · Sijme-Jan Paardekooper
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    ABSTRACT: The gravitational interaction between a protoplanetary disc and planetary sized bodies that form within it leads to the exchange of angular momentum, resulting in migration of the planets and possible gap formation in the disc for more massive planets. In this article, we review the basic theory of disc-planet interactions, and discuss the results of recent numerical simulations of planets embedded in protoplanetary discs. We consider the migration of low mass planets and recent developments in our understanding of so-called type I migration when a fuller treatment of the disc thermodynamics is included. We discuss the runaway migration of intermediate mass planets (so-called type III migration), and the migration of giant planets (type II migration) and the associated gap formation in this disc. The availability of high performance computing facilities has enabled global simulations of magnetised, turbulent discs to be computed, and we discuss recent results for both low and high mass planets embedded in such discs.
    No preview · Article · Feb 2011 · Journal of Computational and Theoretical Nanoscience

Publication Stats

3k Citations
279.99 Total Impact Points

Institutions

  • 1994-2015
    • Queen Mary, University of London
      • • School of Physics and Astronomy
      • • School of Mathematical Sciences
      Londinium, England, United Kingdom
  • 2006-2014
    • University of London
      Londinium, England, United Kingdom
  • 2011
    • University of Michigan
      • Department of Astronomy
      Ann Arbor, Michigan, United States
  • 2008
    • University of Hertfordshire
      • School of Physics, Astronomy and Mathematics
      Hatfield, England, United Kingdom
  • 1999
    • University of California, Santa Cruz
      Santa Cruz, California, United States
  • 1997
    • California Institute of Technology
      Pasadena, California, United States