We construct an analytic model for the gas accretion rate onto planets embedded in protoplanetary disks as a function of planetary mass, viscosity, scale height, and unperturbed surface density, and systematically study the long-term accretion and final masses of gas giant planets. We first derive an analytical formula for the surface density profile near the planetary orbit from considerations of the balance of force and dynamical stability. Using it in the empirical formula of normalized gas accretion rate that is derived based on hydrodynamic simulations, we then simulate the mass evolution of gas giant planets in viscously evolving disks. We finally determine the final mass as a function of semimajor axis of the planet. We find that the disk can be divided into three regions characterized by different processes by which the final mass is determined. In the inner region, the planet grows quickly and forms a deep gap to suppress the growth by itself before disk dissipation. The final mass shows the same trend as the mass determined by the viscous condition for gap opening, but is about 10 times larger than that. In the intermediate region, the disk's viscous diffusion limits gas accretion onto planets before deep gap formation. The final mass can be up to the disk mass, when the disk's viscous evolution occurs faster than disk evaporation. In the outer region, planets capture only tiny amounts of gas within the disk lifetime to form Neptune-like planets. We also derive analytic formulae for the final masses in the different regions and the locations of the boundaries, which are helpful to gain a systematic understanding of the masses of gas giant planets.
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