Three-dimensional Interaction between a Planet and an Isothermal Gaseous Disk. II. Eccentricity Waves and Bending Waves
Three-dimensional Interaction between a Planet and an Isothermal Gaseous Disk. II. Eccentricity Waves and Bending Waves
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行星与等温气态盘之间的三维相互作用。
DOI：
10.1086/380992
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
W. Ward
中科院分区：
文献类型：
--
作者：
Hidekazu Tanaka;W. Ward
我们进行线性计算，调查三维密度波激发的行星在椭圆和倾斜轨道上的等温原行星盘。我们考虑的小行星在其轨道周围没有圆盘间隙。行星的偏心率和倾角被假定为小于盘的长宽比。这对于没有盘隙的行星来说是合理的。将具有非零小偏心率e和倾角i的行星激发的密度波分解为三个分量：e = i = 0的行星激发的密度波、偏心率波和弯曲波。偏心波与行星的非圆运动有关，而弯曲波则是由垂直于赤道面的运动激发的。在我们的公式中，这些波由相同的波动方程描述，只有扰动势不同。我们数值求解波动方程并计算波浪施加在行星上的力。这个力与震中运动的速度不平行。由所得到的力，我们还得到了近日点和升交点的偏心率、倾角和半径的演化率。这些轨道要素的特征演化时间约为300（r/1 Au）2年的最小质量星云盘中的地球大小的行星。偏心阻尼是由偏心波引起的，而倾斜阻尼是由于弯曲波的行星与小偏心和倾斜，没有磁盘间隙。这意味着，对于最低阶，偏心率和倾角的演变之间没有耦合。
We perform linear calculations to investigate three-dimensional density waves excited by planets on elliptical and inclined orbits in isothermal protoplanetary disks. We consider small planets that have no disk gap around their orbits. Eccentricities and inclinations of planets are assumed to be smaller than the disk aspect ratio. This is reasonable for planets with no disk gap. The density wave excited by a planet with nonzero small eccentricity e and inclination i is decomposed into three components: the waves by a planet with e = i = 0, the eccentricity waves, and the bending waves. The eccentricity waves are related to the noncircular motion of the planet, while the bending waves are excited by the motion normal to the equatorial plane. In our formulation, these waves are described by the same wave equations, and only the perturbing potentials are different. We numerically solve the wave equations and calculate the force exerted on the planet by the waves. The force is not parallel to the velocity of the epicycle motion. From the force obtained, we also find the evolution rates in the eccentricity, the inclination, and the longitudes of the perihelion and the ascending node. The characteristic evolution time of these orbital elements is about 300(r/1 AU)2 yr for Earth-sized planets in the minimum-mass nebula disk. Eccentricity damping is caused by eccentricity waves, while inclination damping is due to bending waves for planets with small eccentricities and inclinations and with no disk gap. This means that to lowest order there is no coupling between the evolutions of the eccentricity and the inclination.