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GLOBAL MODELS OF PLANETARY SYSTEM FORMATION
G. A. L. Coleman and R. P. Nelson
Astronomy Unit, Queen Mary University of London
Introduction
With the number of confirmed exoplanets now exceeding 1000, models that explain the formation and evolution of these systems are clearly required. We have examined the diversity of planets and planetary systems that arise from oligarchic growth and gas accretion onto massive cores, by means of N-body simulations combined with a sophisticated disc model. Our simulations use a modified version of the Mercury-6 symplectic integrator (Chambers 1999), and include the following physical components: · · · · A self-consistent thermally evolving viscous disc model Planetary migration: Type I and II, including corotation torques and their possible saturation (Paardekooper et al 2011), and the influence of orbital eccentricity (Fendyke & Nelson 2014) and inclination Gas disc dispersal induced by photoevaporation (Dullemond et al 2007) Gas accretion onto cores with masses that exceed 3 MEarth (Movshovitz et al 2010)

Limited Planetary Growth
Simulations in discs with mass 1x MMSN underwent limited planetary growth, where no gas accreted onto protoplanets. Slow planetary growth resulted from the relatively low mass of solids in the disc, and one consequence of this is that planets underwent limited orbital migration during the lifetime of the gas disc. Simulations that displayed this mode of formation generally resulted in the formation of numerous terrestrial planets, with a large range of semi-major axes, accompanied by a small number of volatile-rich super-Earths with masses less than 7 MEarth and semi-major axes less than 2 AU.

Simulations
We ran a suite of 40 simulations, where the initial conditions of the solid component consisted of 36 embryos of mass 0.3 MEarth and 1000s of planetesimals embedded in gaseous discs around Solar mass stars. Initial disc masses ranged between 1-5x the minimum mass solar nebula model (MMSN), with planetesimal radii of 1 and 10 km. We considered metallicities of Solar and 2x Solar. Simulations ran for 10 Myr or until no planets remained in the disc due to the effects of migration.

Conclusions
·

Figure 2 ­ Plots showing planetary masses, semi-major axes and eccentricities for the initial 700 Kyr (top panel) and the full 10 Myr (bottom panel) of a 5xMMSN simulation.

Figure 1 ­ Migration contours showing migration behaviour for a 5xMMSN disc with a single protoplanet highlighted in black. Blue contours imply outward migration. Red contours imply inward migration.

· · ·

Kamikaze Planets and Late Forming Survivors
Simulations with enhanced disc masses/metallicities resulted in significant growth of protoplanets, enabling gaseous envelopes to be accreted. These more massive planets underwent outward type I migration due by corotation torques, until they reached zero-migration zones where corotation and Lindblad torques balance. Continued mass growth above ~ 10-20 MEarth causes saturation of the corotation torques, leading to rapid inward migration. Upon reaching semi-major axes less than 1 AU these planets open gaps in the disc and transition to slower type II migration. Figure 1 shows an example of this migration behaviour in a single-planetin-a-disc run. Rapid migration leaves insufficient time for significant gas accretion to occur prior to the planet migrating into the central star. For this reason our simulations fail to form giant planets that survive beyond the gas disc lifetime. The kamikaze planets formed in our simulations range from gas-poor Neptunes with masses ~ 15 MEarth to gas-rich giants with a maximum mass of 92 MEarth. One consequence of the rapid formation and migration of these kamikaze planets is that initially massive discs of solids are depleted within ~1-2 Myr. Later forming planets therefore often have higher gas mass fractions and an increased probability of survival against large-scale migration. Figure 2 shows the time evolution of semi-major axes, eccentricities and planetary masses for a 5x MMSN simulation. The upper panels show the first 0.7 Myr, and the lower panels show the full evolution over 10 Myr, illustrating the behaviour described above.

Out of 40 simulations, 23 formed surviving planetary systems. Surviving planets included: 3 rocky terrestrial and 95 volatile-rich terrestrial planets with masses less than 3 MEarth, 22 volatile-rich super-Earths and 6 gas-rich mini-Neptunes with masses ~3-10 MEarth, and one gas-rich Neptune of 13 MEarth. Figure 3 shows our surviving planets along with confirmed exoplanets and those within our Solar System. Low mass discs produce systems of numerous terrestrial planets and super-Earths with a wide ranges of semi-major axes. Numerous giant planets are formed in our simulations but most do not survive type I and II migration before full disc dispersal. Late forming gaseous planets have increased chances of survival, as their migration timescales exceed local disc lifetimes.

Contact email: g.coleman@qmul.ac.uk This project was funded by an STFC Studentship

Figure 3 ­ An M versus P diagram comparing confirmed exoplanets (red squares), Kepler candidates (green triangles) and Solar System planets (black diamonds) with our surviving planets (blue circles). The shaded grey region represents the habitable zone, whilst the dotted line corresponds to the inner boundary of our computational domain/disc model.

References
Coleman and Nelson, 2014, in prep Paardekooper et al, 2011, MNRAS, 410, 293 Fendyke & Nelson, 2014, MNRAS, 437, 96 Chambers, 1999, MNRAS, 304, 793 Dullemond et al, 2007, PPV, 555 Movshovitz et al, 2011, Icarus, 209, 616