DDA 2015 – Secular Star-Disk Coupling and the Origin of Exoplanetary Spin-Orbit Misalignments

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.

Christopher Spalding (CalTech) (Duncombe prize winner)


A recent paradigm shift in exoplanetary astronomy has come with the detection of a substantial number of planets possessing orbits that are misaligned with respect to the spin axes of their host stars. Moreover, observations of misalignments now include coplanar, multi-transiting systems, suggesting that these planets inherited their orbital planes from a protoplanetary disk which was once itself inclined with respect to the star. It has been proposed that mutual star-disk inclination may arise as a consequence of turbulence within the collapsing molecular cloud core, out of which both the star and its disk form. Alternatively, misalignments may be aRained later on, through secular interactions between the disk and companion stars. In this work, we examine the secular dynamics of the stellar spin axis arising in response to the gravitational and accretional torques communicated between the star and its disk throughout the epoch of star and planet formation. Our analysis shows that even though the disk forms from turbulent material, and is thus expected to exhibit a stochastic variation in its orientation with time during the star formation process, gravitational disk-star coupling adiabatically suppresses the excitation of mutual star-disk inclination under all reasonable parameter regimes. As such, the excitation of mutual star-protoplanetary disk inclination must occur later on in the disk’s lifetime, by way of an encounter with a secular resonance between stellar precession and the gravitational perturbations arising from an external potential, such as a binary companion.


  • Motivation: our solar system, Laplace 1796
    • Ecliptic disk oriented approx perp to Sun’s spin axis
    • Goldreich & Tremaine 1980:
      • disk-driven migration
      • Jupiters eaten by stars
        • Why aren’t observed hot Jupiters eaten?
    • $\rightarrow$ hot Jupiters should be aligned with their disks
    • But significant fraction is seriously misaligned!
      • Tends to be more massive planets
  • How to getmisalignments?
    • Disk-driven migration doesn’t work
    • High-eccentricity + tidal?
      • Cannot explain multi-transiting misaligned systems (Huber et al. 2013)
  • $\rightarrow$ Are disks really aligned with their stars?
  • Hypothesis 1: misalignment during formation
    • Spalding et al. 2014 (ApJ)
    • Cores are turbulent
    • Spin dir varies randomly by $\approx30^{\circ}$ every ~0.01 pc
    • Shell infall time $\approx 10^4$ yr
    • Disk adopts plane of whatever shell falls last (Bate et al. 2010)
    • Star-disk system forms misaligned
    • BUT: disk-star coupling?
      • Young stars spin rapidly $\rightarrow$ oblate
        • Dynamically equivalent to massive wire around point mass
        • $\rightarrow$ disk precession
      • Use Laplace-Lagrange secular theory
        • Disk annuli act as outer perturbers upon stellar irientation
        • $\rightarrow$ precession period ~100 years(!)
    • Numerical simulation — will star spin axis follow motion of disk?
      • Star trails disk, even though motion stochastic
  • Hypothesis 2: binary companion in orbit around star+disk — disktorquing
    • Companion causes $\gg 10^4$ yr precession
    • Star-disk coupling weakens with time
      • mass loss
      • stellar contraction
    • Spalding & Batygin 2014 (ApJ)
    • Eventually, disk-binary precession ~ star-disk precession
      • hits secular resonance, catapulting disk/star into retrograde orbits
    • Final inclination only depends upon initial binary inclination
  • Summary:
    • Gravitational star-disk coupling prevents misalignment early on.
    • Neighboring stars excite misalignments by was of a secular resonance.
    • Misalignments are consistent with disk-driven migration.

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