Formation of a proto-Jovian envelope for various planetary accretion rates

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Abstract
The formation of a proto-Jovian envelope has been simulated on the basis of a core accretion model and the maximum mass that a proto-Jovian planet can have while keeping its envelope gravitationally stable, called the critical core mass, has also been investigated extensively over a wide range of the core accretion rate. The value of the critical core mass has been found to depend strongly on the core accretion rate; for example, it is less than or equal to for the typical accretion rates for Uranus and Neptune. Furthermore, through simulations of the quasi-static evolution of the envelope beyond the critical core mass, we have found that the characteristic times of envelope contraction are and for the cases where the core accretion rates are per year, per year and per year, respectively. Also, in the last case, the core mass of the Jovian planet can be estimated to be about . We conclude that if a given one of the Jovian planets of our solar system has a core smaller than about , it is very hard to see how the core could have attracted a gaseous envelope from our solar nebula and formed the Jovian envelope. Determination of the sizes of the cores in our Jovian planets should give fruitful information for the theory of the formation of our solar system.