A giant planet embedded in a protoplanetary disk creates a gap. This process is important for both theory and observation. Using results of a survey for a wide parameter range with two-dimensional hydrodynamic simulations, we constructed an empirical formula for the gap structure (i.e., the radial surface density distribution), which can reproduce the gap width and depth obtained by two-dimensional simulations. This formula enables us to judge whether an observed gap is likely to be caused by an embedded planet or not. The propagation of waves launched by the planet is closely connected to the gap structure. It makes the gap wider and shallower as compared with the case where an instantaneous wave damping is assumed. The hydrodynamic simulations show that the waves do not decay immediately at the launching point of waves, even when the planet is as massive as Jupiter. Based on the results of hydrodynamic simulations, we also obtained an empirical model of wave propagation and damping in cases of deep gaps. The one-dimensional gap model with our wave propagation model is able to reproduce the gap structures in hydrodynamic simulations well. In the case of a Jupiter-mass planet, we also found that the waves with a smaller wavenumber (e.g., m = 2) are excited and transport the angular momentum to a location far away from the planet. The wave with m = 2 is closely related with a secondary wave launched by a site opposite from the planet.
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机译：嵌入原行星盘中的巨型行星会产生一个间隙。这个过程对于理论和观察都很重要。使用二维流体动力学模拟对宽参数范围的调查结果，我们为间隙结构（即径向表面密度分布）建立了经验公式，该公式可以再现通过二维模拟获得的间隙宽度和深度。该公式使我们能够判断观察到的间隙是否可能是由嵌入的行星引起的。行星发射的波的传播与间隙结构紧密相连。与假定瞬时波衰减的情况相比，它使间隙变宽和变浅。流体动力学模拟表明，即使行星像木星一样大，波也不会在波的发射点立即衰减。基于流体动力学模拟的结果，我们还获得了在深间隙情况下波传播和阻尼的经验模型。具有我们的波传播模型的一维间隙模型能够很好地再现流体动力学模拟中的间隙结构。对于木星质量的行星，我们还发现具有较小波数（例如m = 2）的波被激发并将角动量传输到远离行星的位置。 m = 2的波与行星相反位置发射的二次波密切相关。
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