tokens: suppression of gas inflow into a massive core (Ikoma Hori 2012 ). For example, high opacities of dust grains in a disk reduce accumulation of a disk gas by a massive core (Lee et al. 2014 ; Lambrechts Lega 2017 ). Gas dynamics around a planet embedded in a disk would be another adjustment knob for the gas flow. Ormel et al. ( 2015 ) found that an isothermal gas flow from high altitude might escape from the gravitational sphere of a planet before accreting onto it. A rapid recycling of a disk gas regulates gas accretion onto a massive core, whereas in a non-isothermal case this recycling process would be limited by an entropy gradient between the ambient disk gas and the atmosphere (Cimerman et al. 2017 ; Kurokawa Tanigawa 2018 ). According to recent magnetohydrodynamic (MHD) simulations, the gas flow structure in a disk has two layers, which is similar to the layered accretion model (e.g., Gammie 1996 ). There can be a rapid gas flow driven by a disk wind near the disk surface due to the effect of magnetic braking (e.g., Bai Stone 2013 ; Suzuki et al. 2016 ), while the accretion flow would be weaker at the midplane of the disk. In fact, global ideal MHD simulations observed a supersonic accretion flow in the upper layer of a disk (Zhu Stone 2018 ). A rapid gas flow near the disk surface may put a brake on runaway gas accretion onto a planetary core. In this paper, we have investigated how a time-dependent layered accretion in a disk affects formation of super-Earths having H 2 /He atmospheres. We have performed N -body simulations for formation of close-in super-Earths, coupled with disk evolution based on MHD simulations and gas accretion onto a planetary core. Note that hydrogen can be generated from secondary processes such as degassing via oxidation of metallic iron by water (Abe et al. 2000 ) and H 2 O photolysis and escape from a planet via stellar X-ray and extreme ultraviolet (XUV) irradiations (e.g., Lammer et al. 2013 ) and interactions between the stellar plasma and a hydrogen atmosphere (e.g., Kislyakova et al. 2013 ). However, a long-term evolution of a super-Earth’s atmosphere after the formation stage (≳10 Myr) is beyond the scope of this paper. The paper is structured as follows: We present detailed descriptions of models in Section 2 . Results of gas accretion rates onto planetary cores and their orbital evolution are shown in Section 3 . The radial dependence of the occurrence rate of gas giants and the validity of our model are discussed in Section 4 . We summarize this study in the last section. 2. Model 2.1. Disk Evolution For the evolution of a protoplanetary disk including effects of magnetically driven disk winds, we adopt the model of Suzuki et al. ( 2016 ), in which the diffusion equation is given bywhere Σ g , Ω, c s , and H are the gas surface density, the Keplerian angular velocity, the sound speed, and the disk scale height, respectively. The first two terms on the right-hand side induce radial mass accretion
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