论文标题

倾斜天王星:碰撞与旋转 - 轨道共振

Tilting Uranus: Collisions versus Spin--Orbit Resonance

论文作者

Rogoszinski, Zeeve, Hamilton, Douglas P.

论文摘要

在本文中,我们调查了天王星的98 $^{\ circ} $倾斜是否是一个世俗的旋转轨道共振的副产品,假设地球起源于太阳。在这个位置,天王星的旋转进动频率足够快,可以与位于土星以外的另一个星球产生共鸣。使用数值集成,我们表明在过去的许多太阳系配置中可能进行共振捕获是可能的,但是将行星倾斜到90 $^{\ circ} $所需的时间尺度是$ \ sim \ sim \ sim \!10^{8} $ yr的顺序 - 时间 - 时间很长。共振踢可以将行星倾斜到$ \ sim \!10^{7} $ yr中的显着40 $^{\ circ} $,只有在条件是理想的情况下。我们还为天王星大倾斜的起源重新审视了碰撞假设。我们通过新的碰撞代码考虑了多种影响,该代码通过总结撞击器所赋予的角动量来构建行星。由于气体积聚赋予了地球旋转角动量的未知但可能很大一部分,因此我们比较了倾斜,直到,直到,旋转和非启动行星的不同碰撞模型。我们发现1 $ m _ {\ oplus} $打击足以解释地球当前的旋转状态,但是两个$ 0.5 \,m _ {\ oplus} $碰撞产生更好的可能性。最后,我们研究了混合模型,并表明共鸣必须产生至少$ \ sim \!40^{\ circ} $的倾斜度,以实现对碰撞模型的任何明显改进。因为旋转轨道共振很难将天王星的倾斜度驱动到98 $^{\ circ} $,即使在这些理想条件下,巨大的影响似乎不可避免。

In this paper, we investigate whether Uranus's 98$^{\circ}$ obliquity was a by-product of a secular spin-orbit resonance assuming that the planet originated closer to the Sun. In this position, Uranus's spin precession frequency is fast enough to resonate with another planet located beyond Saturn. Using numerical integration, we show that resonance capture is possible in a variety of past solar system configurations, but that the timescale required to tilt the planet to 90$^{\circ}$ is of the order $\sim\!10^{8}$ yr -- a timespan that is uncomfortably long. A resonance kick could tilt the planet to a significant 40$^{\circ}$ in $\sim\!10^{7}$ yr only if conditions were ideal. We also revisit the collisional hypothesis for the origin of Uranus's large obliquity. We consider multiple impacts with a new collisional code that builds up a planet by summing the angular momentum imparted from impactors. Because gas accretion imparts an unknown but likely large part of the planet's spin angular momentum, we compare different collisional models for tilted, untilted, spinning, and nonspinning planets. We find that a 1 $M_{\oplus}$ strike is sufficient to explain the planet's current spin state, but that two $0.5\,M_{\oplus}$ collisions produce better likelihoods. Finally, we investigate hybrid models and show that resonances must produce a tilt of at least $\sim\!40^{\circ}$ for any noticeable improvements to the collision model. Because it is difficult for spin-orbit resonances to drive Uranus's obliquity to 98$^{\circ}$ even under these ideal conditions, giant impacts seem inescapable.

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