Post-oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems

By Ji-lin Zhou, D. Lin, Yi-sui Sun. 2007

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In the sequential accretion model, planets form through the sedimentation of dust, cohesive collisions of planetesimals, and coagulation of protoplanetary embryos prior to the onset of efficient gas accretion. As progenitors of terrestrial planets and the cores of gas giant planets, embryos have comparable masses and are separated by the full width of their feeding zones after the oligarchic growth. Within this context, we investigate the orbit-crossing time (Tc) of protoplanetary systems with equal planetary masses and initial separation k0 scaled by their mutual Hill radii ("EMS systems"). In a gas-free environment, log [Tc/(1 yr)] ≃ A + B log (k0/2.3), where A and B are functions of the planetary masses and initial eccentricities. This power law is caused by a random-walk diffusion of velocity dispersion σ(t) in the EMS systems. The diffusion also leads to (1) a Rayleigh distribution of eccentricities with probability P(t) = (e/σ2) exp [-e2/(2σ2)] at time t and (2) an evolution of average eccentricity ∝t1/2. As evidence of this chaotic diffusion, the observed eccentricities of known extrasolar planets obey a Rayleigh distribution. In a gaseous environment, as embryos become well separated (with k0 ≃ 6-12), their orbit-crossing tendency is suppressed by tidal drag, and their growth is stalled as their orbits are circularized. We evaluate the isolation masses of the embryos, which determine the probability of gas giant formation, as a function of the dust and gas surface densities.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/e81c7e0b945fd3e998ce75c72278ea642b297083

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Citations in the corpus

• Tidal dissipation in planet-hosting stars: damping of spin-orbit misalignment and survival of hot Jupiters (2011, background): “…are formed through dynamical planet- ⋆ Email: dong@astro.cornell.edu planet scatterings (e.g., Rasio & Ford 1996; Weidenschilling & Marzari 1996; Zhou et al. 2007; Chatterjee et al. 2008; Juric & Tremaine 2008) and more importantly, through secular interactions between multiple planets or…”
• Spacing of Kepler Planets: Sculpting by Dynamical Instability (2015, background): “For systems where there are more than 2 planets, there is yet no theoretical understanding for the origin of dynamical instability (see attempts by, e.g. Chambers et al. 1996; Zhou et al. 2007; Quillen 2011).”
• BREEDING SUPER-EARTHS AND BIRTHING SUPER-PUFFS IN TRANSITIONAL DISKS (2015, methodology): “…exceeds∼0.1 of the orbit crossing timescale tX (the factor of 0.1 is empirically determined by Iwasaki et al. 2001; see also Kominami & Ida 2002).8 Zhou et al. (2007) give the following empirical fitting formulae for tX for an ensemble of nine equal-mass protocores situated at a mean semimajor…”
• TOWARD A DETERMINISTIC MODEL OF PLANETARY FORMATION. VI. DYNAMICAL INTERACTION AND COAGULATION OF MULTIPLE ROCKY EMBRYOS AND SUPER-EARTH SYSTEMS AROUND SOLAR-TYPE STARS (2010, methodology): “…time (timescales on which orbital crossing starts) of each pair (i, j ) of the embryos is calculated, following the fitting formula obtained by Zhou et al. (2007) with some slight modifications: log ( τcross TK ) = A + B log ( b 2.3rH ) , (A1) where TK is the Keplerian time at the mean a(=…”
• Toward a Deterministic Model of Planetary Formation. IV. Effects of Type I Migration (2008, background): “…the expansion of the feeding zones due to collisions among the isolated cores after a significant depletion of disk gas (Kominami & Ida 2002; Zhou et al. 2007), although this effect influences the results only slightly (it is important in inner regions in which cores are significantly…”
• MAKE SUPER-EARTHS, NOT JUPITERS: ACCRETING NEBULAR GAS ONTO SOLID CORES AT 0.1 AU AND BEYOND (2014, background): “Because tcross is extremely sensitive to oligarchs’ spacings and their initial eccentricities and inclinations (see Figure 1 of Zhou et al. 2007), the required nebular depletion factors can vary by orders of magnitude.”
• TRANSIT TIMING OBSERVATIONS FROM KEPLER. IV. CONFIRMATION OF FOUR MULTIPLE-PLANET SYSTEMS BY SIMPLE PHYSICAL MODELS (2012, background): “For non-resonant cases, non-zero eccentricities would only serve to bring the planets closer together at conjunctions, making them more unstable (Duncan et al. 1989; Zhou et al. 2007).”