We investigate the formation of terrestrial planets in the late stage of planetary formation using two-planet model. At that time, the protostar has formed for about 3 Myr and the gas disk has dissipated. In the model, the perturbations from Jupiter and Saturn are considered. We also consider variations of the mass of outer planet, and the initial eccentricities and inclinations of embryos and planetesimals. Our results show that, terrestrial planets are formed in 50 Myr, and the accretion rate is about $60% - 80%$. In each simulation, 3 - 4 terrestrial planets are formed inside "Jupiter" with masses of $0.15 - 3.6 M_{\oplus}$. In the $0.5 - 4$ AU, when the eccentricities of planetesimals are excited, planetesimals are able to accrete material from wide radial direction. The plenty of water material of the terrestrial planet in the Habitable Zone may be transferred from the farther places by this mechanism. Accretion could also happen a few times between two major planets only if the outer planet has a moderate mass and the small terrestrial planet could survive at some resonances over time scale of $10^8$ yr. In one of our simulations, com-mensurability of the orbital periods of planets is very common. Moreover, a librating-circulating 3:2 configuration of mean motion resonance is found.
Deep Dive into Simulations for Terrestrial Planets Formation.
We investigate the formation of terrestrial planets in the late stage of planetary formation using two-planet model. At that time, the protostar has formed for about 3 Myr and the gas disk has dissipated. In the model, the perturbations from Jupiter and Saturn are considered. We also consider variations of the mass of outer planet, and the initial eccentricities and inclinations of embryos and planetesimals. Our results show that, terrestrial planets are formed in 50 Myr, and the accretion rate is about $60% - 80%$. In each simulation, 3 - 4 terrestrial planets are formed inside “Jupiter” with masses of $0.15 - 3.6 M_{\oplus}$. In the $0.5 - 4$ AU, when the eccentricities of planetesimals are excited, planetesimals are able to accrete material from wide radial direction. The plenty of water material of the terrestrial planet in the Habitable Zone may be transferred from the farther places by this mechanism. Accretion could also happen a few times between two major planets only if the o
Since the discovery of the first extrasolar planet around Solar-Type star, the detection of the extrasolar planets develops rapidly. To date, more than 300 planets are found orbiting their center stars beyond our solar system, including 35 multiple planetary systems. Recently, scientists have found evidences of methane and carbon dioxide in the atmosphere of a Hot-Jupiter (HD 189733 b) (http://planetquest.jpl.nasa.gov). Of ∼ 300 known extrasolar planets, the minimum mass is generally several Jupiter masses. There are also several terrestrial planets (Super-Earth), but their orbital characteristic is unsuitable for the formation or development of life. Along with the development of survey techniques and incoming high definition space missions, people will definitely discover more and more Earth-like planets in the extrasolar planetary systems. The research of formation and evolution of the terrestrial planet now becomes important topics in astrophysics, astrobiology, astrochemistry and so on.
Planet formation has certain order (Zhou et al. 2005), and Jupiter-like planets at greater distance are formed faster than those near the Sun. It is generally believed that the planet formation may experience the following stages: The grains condensed in the initial stage grow to km-sized planetesimals in the early stage, and then, in the middle stage, Moon-to-Mars sized embryos are formed by accretion of the planetesimals. The size of embryos correlates with the feeding zone of the planetesimals. According to the formula of Hill radius: R H = r(m/3M ⊙ ) 1/3 (where r,m are the heliocentric distance and the mass of planetesimal), the distant planetesimals have wider feeding zones, so the formed embryos are larger. When the embryos grow to the core of mass (∼ 10M ⊕ ), runaway accretion may take place accordingly. With more atmosphere accreted, the embryos contract, growing ever denser and more massive, eventually collapse to form giant Jovian planets (Hu & Xu 2008;Ida & Lin 2004). However, at the same period, the inner planetesimals accrete in respective accretion scope, and then the embryos of terrestrial planet (namely kind of the terrestrial planet core matter) are formed. At the end of the third stage, it is around that the protostar has formed for about 3 Myr, the gas disk has dissipated. A few larger bodies with low e and i are in crowds of planetesimals with certain eccentricities e, and inclinations i. In the late stage, the terrestrial planetary embryos are excited to high eccentricity orbit by gravitational perturbation. Then, the orbital crossing makes the planets accreting material in the broader radial area. Solid residue is either scattered out of the planetary system or accreted by the massive planet. However, it also has the possibility of being captured at the resonance position of the major planets (Nagasawa & Ida 2000;Hu & Xu 2008).
Taking our Solar System as the background, Chambers (2001) made a study of terrestrial planet formation in the late stage by numerical simulations. He set 150 -160 Moon-to-Mars size planetary embryos in the area of 0.3 -2.0 AU, include gravitational perturbations from Jupiter and Saturn. He also examined two initial mass distributions: approximately uniform masses, and a bimodal mass distribution. The results show that 2 -4 planets are formed in 50 Myr, and finally survive over 200 Myr timescale. The space distribution and concentration (see Section 4 in Chambers (2001)) of planets formed in the simulations are similar to our solar system. However, the planets produced by the simulations usually have eccentric orbits with higher eccentricities e, and inclinations i than Venus. Raymond, Quinn & Lunine (2004, 2006) also studied the formation of terrestrial planets. In the simulations, they took into account Jupiter’s gravitational perturbation, wider distribution of material (0.5 -4.5 AU) and higher resolution. The results confirm a leading hypothesis for the origin of Earth’s water: they may come from the material in the outer area by impacts in the late stage of planet formation. Raymond, Mandell, & Sigurdsson (2006) explored the planet formation under planetary migration of the giant. In the simulations, super Hot Earth form interior to the migrating giant planet, and water-rich, Earthsize terrestrial planet are present in the Habitable Zone (0.8 -1.5 AU) and can survive over 10 8 yr timescale.
In our model, Solar System is taken as the background. But several changes are worth noting : 1) we use twoplanet (Jupiter and Saturn, see Fig. 1) model. 2) in the model, Jupiter and Saturn are supposed to be formed at the beginning of the simulation, with two swarms of planetesimals distributed among 0.5 -4.2 AU and 6.2 -9.6 AU respectively. 3) The initial eccentricities and inclinations of planetesimals are considered. 4) The variations of the mass of Saturn are examined. 5) The exchange of material in the radial direction is also studied by the parameter of water mass fraction.
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