Dependence Of The Final Mass Of A Gas Giant Planet On The Molecular Cloud Core Properties

Nearly1900extrasolar planets have been confirmed so far (seehttp://exoplanet.eu/). Observations of extrasolar planets have revealed the diversity ofplanetary system architectures. Especially, masses of giant planets appear to bediverse (0.3to20MJ), where MJis the Jupiter mass. The most striking features ofplanet masses are:(1) masses of most giant planets are less than3MJ;(2) Planets thatare more massive than10MJare very rare. Observational data also show that thenumber of giant planets around low mass stars is much less than that aroundsolar-type stars. It is suggested that the probability of observing a giant planetincreases with stellar mass. For a long time, our understanding of giant planets waslimited to the four outer planets in the Solar System. With the improvement of theextrasolar planet observation techniques, many people try to explain the diversity ofextrasolar planets.The diversity exhibits the complex environments of planet formation. Planets arebyproducts of star formation. Formation of planets connects with formation of starsthrough disks. Therefore, people first recognize that the physical properties of starshave noticeable influence on the formation of planets. It has been found that stellarmetallicity affects the frequency of giant planets and heavy element mass in giantplanets. In recent years, planet population synthesis has been developed to explore theconnection between the diversity of protoplanetary disks and the diversity ofextrasolar planets. The model must be simplified in order to keep the problem tractable and to set a large number of initial conditions. On the one hand the planetformation model is simplified; on the other hand the disk model is also simplified.However, we do not know whether the simplified model still conserves the overallproperties of the emerging planet population. Therefore, planet population synthesis isunable to self-consistently explain the diversity of extrasolar planets.In this paper, we study how a gas giant planet grows in the protoplanetary diskand how the properties of molecular cloud cores determine the final mass of a gasgiant planet. We suggested that the diversity of extrasolar planets might originate fromthe diversity of molecular cloud cores. We first provide a self-consistent planetformation model, in which the formulae for the solid core growth and the gasaccretion onto the core are the functions of protoplanetary disk properties. Our diskmodel is a one-dimensionally long time evolution model, in which the properties ofthe molecular cloud core determine the disk properties.We find that the evolutionary behaviors of giant planets at different semimajoraxes are significantly different. At <3AU, the solid core is too small to trigger therunaway gas accretion and the planet mass is dominated by the solid core mass and isvery small. The planet mass increases with radius because the solid core increaseswith radius. At3AU, the protoplanet just has enough mass to trigger the runaway gasaccretion within the disk lifetime and the planet mass increases sharply. At3-5AU,the protoplanet core mass increases with radius, the rate of the quasi-statical growth ofthe planetary envelope gradually increases and the trigger of the runaway gasaccretion is advanced. Therefore, the planet mass gradually increases with radius. At5 -20AU, the planet is massive enough to open a deep gap. The upper limit of theplanet mass is determined by the disk viscosity. The final mass is2MJand falls in avery narrow range over the wide range of orbital radius in this region. At20-37AU,the planet mass decreases rapidly with radius. As the radius increases, the growth rateof the protoplanetary core decreases and the trigger of the runaway gas accretion isgradually delayed. The planet does not have time to gain mass enough to open thedeep gap. Beyond37AU, the surface densities of both planetesimals and gas decreasewith radius. The planetary core mass decreases with radius since the core growth ratedecreases with radius. The planet can only accrete a small amount of gas and the finalmass is small.We suggest a formation mechanism of super-Jupiters in the framework of thecore accretion model of planet formation. A super-Jupiter can form under thecondition that a disk is gravitationally unstable (high viscosity) when a protoplanetopens the deep gap. Our calculations infer that the upper limit of super-Jupiter massesand the range of semi-major axes and the occurrence rate of super-Jupiters increasewith the central star mass. We also show that the super-Jovian planet forms moreeasily around massive stars. We find that gas giant planets should commonly existaround various stellar masses.Comparing with observations, our model could explain the range and the mostfrequent values of observed masses of gas giant planets. Our calculations couldinterpret the observed pileup of gas giants at>1AU and the distinct deficit of gasgiants at0.05to1AU. Our calculations indicate that it is difficult to form gas giant planets outside20AU and the intermediate mass planets might be found at15-30AU as the observing technique advances.