DDA 2015 – Tidal Effects in Late Stage Accretion

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Session: Planet Formation II

Kevin Graves (Purdue)


We model the effects of tidal dissipation in the late stages of planetary accretion. We investigate the tidal dissipation during close encounters between embryos and nearly-formed planets using a modified version of the N-body integrator SyMBA. We calculate a total energy lost due to tides per close encounter and estimate the change in velocities of the bodies at each encounter. We measure the effects on the dynamics, evolution, and final outcome of the planets. Our initial results show a clear separation between the tidal and non-tidal case for a relatively strong tidal dissipation factor. We compare these results to traditional late stage simulations both with and without fragmentation.


  • Overview of late-stage terrestrial planet accretion
    • a few dozen embryos
    • a few thousand planetesimals
    • Morby 2012
    • giant plant migration?
      • increases AMD of inner solar system
      • must therefore start with a lower deficit
    • AMD: Jacobson & Morbidelli 2014
  • Tidal effects on planetary embryos
    • Lots of heat generation from various processes $\rightarrow$ magma oceans
    • Simple model for energy loss during a close encounter (Kaula & Harris 1973): tides
      • free parameters: tidal Love numbers, dissipation param
    • combine to a “tidal parameter”: $\frac{h_2 (k_2 + 1)}{Q}$
    • Tidal effects in an n-body integrator
      • no tides vs. strong tides:
        • plot: mass concentration (Chambers 2013) vs AMD
        • strong tides: higher mass concentration with AMD
        • weak tides: inverse

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