Delay Of Planet Formation At Large Radius And The Outward Decrease In Mass And Gas Content Of Jovian Planets

In modern science, the model for the formation of the solar system is constructed under the framework of the nebula hypothesis. Although the nebula hypothesis is successful in general, describing detailed physical processes in the history of the solar system and interpreting all observations are challenges to researchers. Two outstanding observations that any theory must explain are planet masses and compositions. Terrestrial planets(Mercury, Venus, Earth, and Mars) have small masses and are composed of rocky material while Jovian planets(Jupiter, Saturn, Uranus, and Neptune) have large masses and contain both heavy elements and H, He. It seems that the difference between terrestrial planets and Jovian planets is understood. An observational fact is that the mass and gas content of Jovian planets decrease outward with the orbital radius from Jupiter except Neptune being almost the same as Uranus. The masses of Jupiter, Saturn, Uranus, and Neptune are 318, 95, 15, ?17M, respectively. Models for Jovian planets suggest that their masses of H and He are 307276-, 7664-, 0.55.0-,and ?- 7.45.0M, respectively.A prominent observation of the solar system is that mass and gas content of Jovian planets decrease outward with the orbital radius except Neptune being almost the same as Uranus. In previous studies, the solar nebula is assumed to preexist and the formation process of the solar nebula is not considered. It is therefore assumed that planet formation at different radius starts at the same time in the solar nebula. In this paper, we show that planet formation at different radius does not start at the same time and is delayed at large radius. We suggest that this delay might be one of the factors which cause the outward decrease of Jovian planet masses. The nebula starts to form from its inner part because of the inside-out collapse of its progenitorial molecular cloud core. Then the nebula expands outward due to viscosity. Material reaches small radius first, then large radius. So planet formation is delayed at large radius. The later the material reaches a planet’s location, the less time it has to gain mass and gas content. Hence, the delay tends to cause the outward decrease in mass and gas content of Jovian planets. Our nebula model shows that the material reaches Jupiter, Saturn, Uranus, and Neptune at yr,,,and yr, respectively. We discuss the effects of the time delay on Jovian planet masses in the framework of the core accretion model of planet formation. Saturn’s formation is not delayed by much time relative to Jupiter so that they both reach the rapid gas accretion phase and are gas giants. But the delay of Uranus and Neptune’s formation is long and might be one of the factors that cause them not to reach the rapid gas accretion before the gas nebula is dispersed. Saturn has less time to go through the rapid gas accretion. So Saturn’s mass and gas content are significantly less than Jupiter.From the calculation in the last section, Jupiter starts to form at yr1040.06′. After that, there is a large amount of material in the Jupiter region for a long time(several yr106). There is enough time and material for Jupiter to gain large mass and gas. It owns the largest mass and abundances of H and He among Jovian planets. Saturn starts to form at yr1057.06′, later than Jupiter but not much later. Both Jupiter and Saturn reach the rapid gas accretion phase within the lifetime of the solar nebula. They increase their mass significantly during this phase. So both Jupiter and Saturn are gas giants with large mass. The delay time of Saturn relative to Jupiter is comparable to the rapid gas accretion time. Saturn has less time to go through the rapid gas accretion. So Saturn’s mass and gas content are significantly less than Jupiter. Uranus and Neptune start to form at yr1050.16′ and yr1029.66′, respectively, much later than Jupiter and Saturn. The delay times of Uranus and Neptune relative to Jupiter are yr1010.16′ and yr1090.56′, respectively. The delay of Uranus’(and Neptune’s) formation is long and might be one of the factors that cause them not to reach the rapid gas accretion before the gas nebula is dispersed. So they are ice giants with much smaller mass than Jupiter and Saturn.In summary, we show that planet formation is delayed at large radius and the length of the delay increases with radius because the solar nebula starts to form from the inner part and then expands outward due to the action of viscosity. We illustrate that the outward decrease in mass and gas content of Jovian planets might be related to this delay in the framework of the core accretion model of planet formation. Our theory infers that the timescale of the rapid gas accretion should be on the order of yr105 and the core formation time plus the slow gas accretion time is on the order of yr106. These timescales are compatible with the core accretion model. In the framework of the gravitational instability model of planet formation, the time delay might not cause the outward decrease in mass and gas content of Jovian planets.