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تسجيل مستخدم جديدToward a Deterministic Model of Planetary Formation IV: Effects of Type-I Migration
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In a further development of a deterministic planet-formation model (Ida & Lin 2004), we consider the effect of type-I migration of protoplanetary embryos due to their tidal interaction with their nascent disks. During the early embedded phase of protostellar disks, although embryos rapidly emerge in regions interior to the ice line, uninhibited type-I migration leads to their efficient self-clearing. But, embryos continue to form from residual planetesimals at increasingly large radii, repeatedly migrate inward, and provide a main channel of heavy element accretion onto their host stars. During the advanced stages of disk evolution (a few Myr), the gas surface density declines to values comparable to or smaller than that of the minimum mass nebula model and type-I migration is no longer an effective disruption mechanism for mars-mass embryos. Over wide ranges of initial disk surface densities and type-I migration efficiency, the surviving population of embryos interior to the ice line has a total mass several times that of the Earth. With this reservoir, there is an adequate inventory of residual embryos to subsequently assemble into rocky planets similar to those around the Sun. But, the onset of efficient gas accretion requires the emergence and retention of cores, more massive than a few M_earth, prior to the severe depletion of the disk gas. The formation probability of gas giant planets and hence the predicted mass and semimajor axis distributions of extrasolar gas giants are sensitively determined by the strength of type-I migration. We suggest that the observed fraction of solar-type stars with gas giant planets can be reproduced only if the actual type-I migration time scale is an order of magnitude longer than that deduced from linear theories.
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The ubiquity of planets and diversity of planetary systems reveal planet formation encompass many complex and competing processes. In this series of papers, we develop and upgrade a population synthesis model as a tool to identify the dominant physic
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d by the disk structure. Theoretical models suggest that planets form in protostellar disk regions with an inactive neutral ``dead zone near the mid plane, sandwiched together by partially ionized surface layers where magnetorotational instability is active. Due to a transition in the abundance of dust grains, the active layers thickness decreases abruptly near the ice line. Over a range of modest accretion rates ($sim 10^{-9}-10^{-8} M_odot$ yr$^{-1}$), the change in the angular momentum transfer rate leads to local surface density and pressure distribution maxima near the ice line. The azimuthal velocity becomes super-Keplerian and the grains accumulate in this transition zone. This barrier locally retains protoplanetary cores and enhances the heavy element surface density to the critical value needed to initiate efficient gas accretion. It leads to a preferred location and epoch of gas giant formation. We simulate and reproduce the observed frequency and mass-period distribution of gas giants around solar type stars without having to greatly reduce the type I migration strength. The mass function of the short-period planets can be utilized to calibrate the efficiency of type I migration and to extrapolate the fraction of stars with habitable terrestrial planets.
We study the effects of diffusion on the non-linear corotation torque, or horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for which the width of the horseshoe region is much smaller than the scale height of the disc. In the
absence of diffusion, the non-linear corotation torque saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can act to sustain the corotation torque. In the limit of very strong diffusion, the linear corotation torque is recovered. For the case of thermal diffusion, this limit corresponds to having a locally isothermal equation of state. We present some simple models that are able to capture the dependence of the torque on diffusive processes to within 20% of the numerical simulations.
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