论文标题
低粘度2D轴的I型轨道偏心阻尼的配方
A recipe for orbital eccentricity damping in the type-I regime for low viscosity 2D-discs
论文作者
论文摘要
众所周知，间隙的开口取决于光盘的粘度。然而，偏心阻尼公式仅在高粘度下得出，忽略了部分间隙的开口。我们旨在获得一个简单的公式，以模拟低粘度光盘中I型制度的$ $ $ $缩影，即使是小行星也可能开始部分打开部分。我们对行星进行高分辨率的2D局部等温流体动力学模拟，其在具有不同纵横比和粘度不同的圆盘上的固定轨道上有不同的质量。我们确定地球所感觉到的扭矩和力量来推导迁移和偏心衰变时间尺度。我们首先找到了涡流出现的间隙深度的下限；这大致发生在I型和II型制度之间的过渡中。对于保持稳定的模拟，我们在消失的偏心率的极限上获得了与文献中当前使用的偏心率相似的偏置的限制，但准确地降低到$α= 3.16 \ times 10^{ - 5} $。我们记录了$ e $缩减的效率，这是观察到的差距深度和$ e $的功能：当星球打开足够深的差距时，就独立于$ e $观察到线性趋势；在较浅的差距下，这种线性趋势保留在低$ e $的情况下，而当$ e $与光盘的比例高度相当时，它会偏离更有效的阻尼。这两种趋势都可以从理论上理解，并通过简单的拟合公式复制。我们的合并拟合产生了一个简单的食谱，以实现$ n $ $ n $ damp type-i $ e $ damp的部分间隙开放行星，这与高分辨率2D 2D Hydro-Simulations一致。拟合的典型误差为几个百分之几，低于文献中广泛使用的I型扭矩公式的误差。这将允许在低粘度下对人群合成模型的类型I型制度的行星盘相互作用进行更加持续的处理。
It is known that gap opening depends on the disc's viscosity; however, eccentricity damping formulas have only been derived at high viscosities, ignoring partial gap opening. We aim at obtaining a simple formula to model $e$-damping of the type-I regime in low viscosity discs, where even small planets may start opening partial. We perform high resolution 2D locally isothermal hydrodynamical simulations of planets with varying masses on fixed orbits in discs with varying aspect ratios and viscosities. We determine the torque and power felt by the planet to derive migration and eccentricity damping timescales. We first find a lower limit to the gap depths below which vortices appear; this happens roughly at the transition between type-I and type-II regimes. For the simulations that remain stable, we obtain a fit to the observed gap depth in the limit of vanishing eccentricities that is similar to the one currently used in the literature but is accurate down to $α=3.16\times 10^{-5}$. We record the $e$-damping efficiency as a function of the observed gap depth and $e$: when the planet has opened a deep enough gap, a linear trend is observed independently of $e$; at shallower gaps this linear trend is preserved at low $e$, while it deviates to more efficient damping when $e$ is comparable to the disc's scale height. Both trends can be understood on theoretical grounds and are reproduced by a simple fitting formula. Our combined fits yield a simple recipe to implement type-I $e$-damping in $N$-body for partial gap opening planets that is consistent with high-resolution 2D hydro-simulations. The typical error of the fit is of the order of a few percent, and lower than the error of type-I torque formulas widely used in the literature. This will allow a more self-consistent treatment of planet-disc interactions of the type-I regime for population synthesis models at low viscosities.
