Planet migration: self-gravitating radiation hydrodynamical models of protoplanets with surfaces

We calculate radial migration rates of protoplanets in laminar minimum mass solar nebula discs using three-dimensional self-gravitating radiation hydrodynamical (RHD) models. The protoplanets are free to migrate, whereupon their migration rates are measured. For low mass protoplanets (10-50 M_\oplus) we find increases in the migration timescales of up to an order of magnitude between locally-isothermal and RHD models. In the high-mass regime the migration rates are changed very little. These results are arrived at by calculating migration rates in locally-isothermal models, before sequentially introducing self-gravity, and radiative transfer, allowing us to isolate the effects of the additional physics. We find that using a locally-isothermal equation of state, without self-gravity, we reproduce the migration rates obtained by previous analytic and numerical models. We explore the impact of different protoplanet models, and changes to their assumed radii, upon migration. The introduction of self-gravity gives a slight reduction of the migration rates, whilst the inertial mass problem, which has been proposed for high mass protoplanets with circumplanetary discs, is reproduced. Upon introducing radiative transfer to models of low mass protoplanets (\approx 10 M_\oplus), modelled as small radius accreting point masses, we find outward migration with a rate of approximately twice the analytic inward rate. However, when modelling such a protoplanet in a more realistic manner, with a surface which enables the formation of a deep envelope, this outward migration is not seen.Comment: 21 pages, 21 figure

Planetesimal Formation In Self-Gravitating Discs

We study particle dynamics in local two-dimensional simulations of self-gravitating accretion discs with a simple cooling law. It is well known that the structure which arises in the gaseous component of the disc due to a gravitational instability can have a significant effect on the evolution of dust particles. Previous results using global simulations indicate that spiral density waves are highly efficient at collecting dust particles, creating significant local over-densities which may be able to undergo gravitational collapse. We expand on these findings, using a range of cooling times to mimic the conditions at a large range of radii within the disc. Here we use the Pencil Code to solve the 2D local shearing sheet equations for gas on a fixed grid together with the equations of motion for solids coupled to the gas solely through aerodynamic drag force. We find that spiral density waves can create significant enhancements in the surface density of solids, equivalent to 1-10cm sized particles in a disc following the profiles of Clarke (2009) around a solar mass star, causing it to reach concentrations several orders of magnitude larger than the particles mean surface density. We also study the velocity dispersion of the particles, finding that the spiral structure can result in the particle velocities becoming highly ordered, having a narrow velocity dispersion. This implies low relative velocities between particles, which in turn suggests that collisions are typically low energy, lessening the likelihood of grain destruction. Both these findings suggest that the density waves that arise due to gravitational instabilities in the early stages of star formation provide excellent sites for the formation of large, planetesimal-sized objects.Comment: 11 pages, 8 figures, accepted for publication in MNRA

On the convergence of the critical cooling timescale for the fragmentation of self-gravitating discs

We carry out simulations of gravitationally unstable discs using a Smoothed Particle Hydrodynamics (SPH) code and a grid-based hydrodynamics code, FARGO, to understand the previous non-convergent results reported by Meru & Bate (2011a). We obtain evidence that convergence with increasing resolution occurs with both SPH and FARGO and in both cases we find that the critical cooling timescale is larger than previously thought. We show that SPH has a first-order convergence rate while FARGO converges with a second-order rate. We show that the convergence of the critical cooling timescale for fragmentation depends largely on the numerical viscosity employed in both SPH and FARGO. With SPH, particle velocity dispersion may also play a role. We show that reducing the dissipation from the numerical viscosity leads to larger values of the critical cooling time at a given resolution. For SPH, we find that the effect of the dissipation due to the numerical viscosity is somewhat larger than had previously been appreciated. In particular, we show that using a quadratic term in the SPH artificial viscosity (beta_{SPH}) that is too low appears to lead to excess dissipation in gravitationally unstable discs, which may affect any results that sensitively depend on the thermodynamics, such as disc fragmentation. We show that the two codes converge to values of the critical cooling timescale, beta_{crit} > 20 (for a ratio of specific heats of gamma=5/3), and perhaps even as large as beta_{crit} \approx 30. These are approximately 3-5 times larger than has been found by most previous studies. This is equivalent to a maximum gravitational stress that a disc can withstand without fragmenting of alpha_{GI,crit} \approx 0.013-0.02, which is much smaller than the values typically used in the literature. It is therefore easier for self-gravitating discs to fragment than has been concluded from most past studies.Comment: Accepted for publication by MNRAS. 26 pages, 17 figure

On the formation of hot Neptunes and super-Earths

The discovery of short-period Neptune-mass objects, now including the remarkable system HD69830 (Lovis et al. 2006) with three Neptune analogues, raises difficult questions about current formation models which may require a global treatment of the protoplanetary disc. Several formation scenarios have been proposed, where most combine the canonical oligarchic picture of core accretion with type I migration (e.g. Terquem & Papaloizou 2007) and planetary atmosphere physics (e.g. Alibert et al. 2006). To date, published studies have considered only a small number of progenitors at late times. This leaves unaddressed important questions about the global viability of the models. We seek to determine whether the most natural model -- namely, taking the canonical oligarchic picture of core accretion and introducing type I migration -- can succeed in forming objects of 10 Earth masses and more in the innermost parts of the disc. This problem is investigated using both traditional semianalytic methods for modelling oligarchic growth as well as a new parallel multi-zone N-body code designed specifically for treating planetary formation problems with large dynamic range (McNeil & Nelson 2009). We find that it is extremely difficult for oligarchic tidal migration models to reproduce the observed distribution. Even under many variations of the typical parameters, we form no objects of mass greater than 8 Earth masses. By comparison, it is relatively straightforward to form icy super-Earths. We conclude that either the initial conditions of the protoplanetary discs in short-period Neptune systems were substantially different from the standard disc models we used, or there is important physics yet to be understood.Comment: 19 pages, 18 figures. Final version accepted to MNRAS 30 September 200

On the dynamics and collisional growth of planetesimals in misaligned binary systems

Context. Abridged. Many stars are members of binary systems. During early phases when the stars are surrounded by discs, the binary orbit and disc midplane may be mutually inclined. The discs around T Tauri stars will become mildly warped and undergo solid body precession around the angular momentum vector of the binary system. It is unclear how planetesimals in such a disc will evolve and affect planet formation. Aims. We investigate the dynamics of planetesimals embedded in discs that are perturbed by a binary companion on a circular, inclined orbit. We examine collisional velocities of the planetesimals to determine when they can grow through accretion. We vary the binary inclination, binary separation, D, disc mass, and planetesimal radius. Our standard model has D=60 AU, inclination=45 deg, and a disc mass equivalent to the MMSN. Methods. We use a 3D hydrodynamics code to model the disc. Planetesimals are test particles which experience gas drag, the gravitational force of the disc, the companion star gravity. Planetesimal orbit crossing events are detected and used to estimate collisional velocities. Results. For binary systems with modest inclination (25 deg), disc gravity prevents planetesimal orbits from undergoing strong differential nodal precession (which occurs in absence of the disc), and forces planetesimals to precess with the disc on average. For bodies of different size the orbit planes become modestly mutually inclined, leading to collisional velocities that inhibit growth. For larger inclinations (45 degrees), the Kozai effect operates, leading to destructively large relative velocities. Conclusions. Planet formation via planetesimal accretion is difficult in an inclined binary system with parameters similar to those considered in this paper. For systems in which the Kozai mechanism operates, the prospects for forming planets are very remote.Comment: 24 pages, 16 figures, recently published in Astronomy and Astrophysic

On the accumulation of planetesimals near disc gaps created by protoplanets

We have performed three-dimensional two-fluid (gas-dust) hydrodynamical models of circumstellar discs with embedded protoplanets (3 - 333 M\oplu) and small solid bodies (radii 10cm to 10m). We find that high mass planets (\gtrsim Saturn mass) open sufficiently deep gaps in the gas disc such that the density maximum at the outer edge of the gap can very efficiently trap metre-sized solid bodies. This allows the accumulation of solids at the outer edge of the gap as solids from large radii spiral inwards to the trapping region. This process of accumulation occurs fastest for those bodies that spiral inwards most rapidly, typically metre-sized boulders, whilst smaller and larger objects will not migrate sufficiently rapidly in the discs lifetime to benefit from the process. Around a Jupiter mass planet we find that bound clumps of solid material, as large as several Earth masses, may form, potentially collapsing under self-gravity to form planets or planetesimals. These results are in agreement with Lyra et al. (2009), supporting their finding that the formation of a second generation of planetesimals or of terrestrial mass planets may be triggered by the presence of a high mass planet.Comment: 14 pages, 10 figures. Accepted for publication in MNRA

Considerations on the accretion of Uranus and Neptune by mutual collisions of planetary embryos in the vicinity of Jupiter and Saturn

Modeling the formation of the ice giants Uranus and Neptune is a long-lasting problem in planetary science. Due to gas-drag, collisional damping, and resonant shepherding, the planetary embryos repel the planetesimals away from their reach and thus they stop growing (Levison et al. 2010). This problem persists independently of whether the accretion took place at the current locations of the ice giants or closer to the Sun. Instead of trying to push the runaway/oligarchic growth of planetary embryos up to 10-15 Earth masses, we envision the possibility that the planetesimal disk could generate a system of planetary embryos of only 1-3 Earth masses. Then we investigate whether these embryos could have collided with each other and grown enough to reach the masses of current Uranus and Neptune. Our results point to two major problems. First, there is typically a large difference in mass between the first and the second most massive core formed and retained beyond Saturn. Second, in many simulations the final planetary system has more than two objects beyond Saturn. The growth of a major planet from a system of embryos requires strong damping of eccentricities and inclinations from the disk of gas. But strong damping also favors embryos and cores to find a stable resonant configuration, so that systems with more than two surviving objects are found. In addition to these problems, in order to have substantial mutual accretion among embryos, it is necessary to assume that the surface density of the gas was several times higher than that of the minimum-mass solar nebula. However this contrasts with the common idea that Uranus and Neptune formed in a gas-starving disk, which is suggested by the relatively small amount of hydrogen and helium contained in the atmospheres of these planets. Only one of our simulations "by chance" successfully reproduced the structure of the outer Solar System.Comment: 16 pages; 15 color figures; accepted in Astronomy & Astrophysics; shortened abstrac