The Evolution of Gravitationally Unstable Protoplanetary Disks: Fragmentation and Possible Giant Planet Formation

By Lucio Mayer, Thomas R. Quinn, James Wadsley, Joachim Stadel. 2003

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We carry out a large set of very high resolution, three-dimensional, smoothed particle hydrodynamics simulations describing the evolution of gravitationally unstable gaseous protoplanetary disks. We consider a broad range of initial disk parameters. Disk masses out to 20 AU range from 0.075 to 0.125 M☉, roughly consistent with the high end of the mass distribution inferred for disks around T Tauri stars. Minimum outer temperatures range from 30 to 100 K, as expected from studies of the early protosolar nebula and suggested by the modeling of the spectra of protoplanetary disks. The mass of the central star is also varied, although it is usually assumed to be equal to that of the Sun. Overall, the initial disks span minimum Q-parameters between 0.8 and 2, with most models having Q ~ 1.4. The disks are evolved assuming either a locally isothermal equation of state or an adiabatic equation of state with varying γ. Heating by (artificial) viscosity and shocks is included when the adiabatic equation of state is used. When condensations above a specific density threshold appear as a result of gravitational instability in a locally isothermal calculation, the equation of state is switched to adiabatic to account for the increased optical depth. We show that when a disk has a minimum Q-parameter less than 1.4, strong trailing spiral instabilities, typically three- or four-armed modes, form and grow until fragmentation occurs along the arms after about 5 mean disk orbital times. The resulting clumps contract quickly to densities several orders of magnitude higher than the initial disk density, and the densest of them survive even under adiabatic conditions. These clumps are stable to tidal disruption and merge quickly, leaving two to three protoplanets on fairly eccentric orbits (the mean eccentricity being around 0.2) after ~103 yr. Fragmentation is not strongly dependent on whether the disk starts from a marginally unstable state or gradually achieves it; we show that if the disk is allowed to grow in mass from a very light, very stable state over tens of orbital times, it still fragments at roughly the same mass and temperature as in the standard disk models. We show that the first stages of the instability, until the appearance of the overdensities, can be understood in terms of the maximum unstable Toomre wavelength and the local Jeans length. A high mass and force resolution are needed to correctly resolve both scales and follow the fragmentation process appropriately. Varying disk mass and temperature affects such physical scales and hence the typical masses of the protoplanets that form. Objects smaller than Saturn or a couple of times bigger than Jupiter can both be produced by fragmentation. Their final masses will then depend on the subsequent interactions and mergers with other clumps and on the accretion of disk material. The accretion rate depends on the disk thermodynamics and is negligible with adiabatic conditions. After ~103 yr the masses range from just below 1MJup to more than 7MJup, well in agreement with those of detected extrasolar planets.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/b7895b34d04c14d2108f5230bd72ad6e18e3a4e5

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Citations in the corpus

Extrasolar planet population synthesis I: Method, formation tracks and mass-distance distribution (2009, background): “These masses should be stable against self-gravitional collapse (Mayer et al. 2004).”
SPECTRAL AND PHOTOMETRIC DIAGNOSTICS OF GIANT PLANET FORMATION SCENARIOS (2011, background): “In recent years, this mechanism, which remains controversial in the inner ∼10 AU of a planetary system (Rafikov 2005), has been advocated largely by Boss (2000, 2007, 2010) and Mayer et al. (2002, 2004).”
Extrasolar planet population synthesis - II. Statistical comparison with observations (2009, background): “This lead to the hypothesis that a faster formation mechanism is needed to form Jovian planets, namely the gravitational instability model (Boss 2001; Mayer et al. 2004).”
The properties of brown dwarfs and low-mass hydrogen-burning stars formed by disc fragmentation (2008, background): “Both theory and simulations (Gammie 2001; Johnson & Gammie 2003; Rice et al. 2003, 2005; Mayer et al. 2004; Mejia et al. 2005; Stamatellos et al. 2007b) indicate that for disc fragmentation to occur, the cooling time must satisfy t COOL < C(γ) t ORB , 0.5 .”
Investigating fragmentation conditions in self-gravitating accretion discs (2005, background): “This process has been suggested as a mechanism both for forming gaseous planets in protostellar discs (Kuiper 1951; Boss 1998; Mayer et al. 2004), and for forming stars in active galactic discs (Goodman & Tan 2004).”
THE TWO MODES OF GAS GIANT PLANET FORMATION (2009, result): “Although the fate of these clumps is unknown, the results of Mayer et al. (2004) and SW2009 indicate that some condensations can survive.”
Smoothed Particle Hydrodynamics in Astrophysics (2010, methodology): “SPH has been successfully employed to study giant planet formation through the fragmentation of protoplanetary disks (Mayer et al., 2002, 2004), and to explore the interaction of high- and low-mass planets embedded in protoplanetary discs (Bate et al., 2003; Lufkin et al., 2004).”
The Burst Mode of Protostellar Accretion (2006, methodology): “Using either finite-difference (Boss 2003; Pickett et al. 2003; Mej́ia et al. 2005) or smoothed-particle hydrodynamics (Rice et al. 2003; Mayer et al. 2004) techniques, and either isothermal evolution or various recipes for heating, radiative cooling, and simplified radiative transfer, these…”
Improving Stellar and Planetary Parameters of Transiting Planet Systems: The Case of TrES-2 (2007, background): “…et al. 2006; Burrows et al. 2007), and their implications for competing giant planet formation models (e.g., Ida & Lin 2004a, 2004b; Kornet et al. 2005; Alibert et al. 2005; Boss 2000, 2002; Mayer et al. 2004), relies in turn on the accurate determination of chemical abundances of the host stars.”
Clumps in the outer disk by disk instability: Why they are initially gas giants and the legacy of disruption (2009, background): “f g= F(M) otherwise. Multiple simulations have shown that an initial hQi. 1:4 is required for an isothermal disk to fragment (e.g., Tomley et al., 1994; Nelson et al., 1998; Johnson and Gammie, 2003; Mayer et al., 2004; Durisen et al., 2007). Using hQi= 1:4 in equation (8) gives f g ˇ2:5, which corr”
Theory of Star Formation (2007, result): “At temperatures comparable to those in observed systems, disks with masses >∼ 0.1 M⊙ are candidates for having significant mass transport due to self-gravitating torques (Mayer et al., 2004).”
THE FORMATION MECHANISM OF GAS GIANTS ON WIDE ORBITS (2009, unknown): “Even more importantly, simulations by Mayer et al. (2004) and Boss (2005) indicate that the protoplanetary clumps can survive without migrating into the star.”
Planet formation and migration (2005, background): “Nonetheless, condensations may form even if the disk is unstable only against non– axisymmetric perturbations, providing the density gets high enough in the spiral arms (Boss 1998, Mayer et al 2004).”