The meatiest paper of my
PhD thesis focused on this process. (Read the details there.)
Suppose you have a gas-giant planet orbiting a star at 5 AU, and way out
at 1000 AU a stellar binary companion lurks in a high-inclination orbit.
Here's what can happen...
This movie is an attempt to visualize 3-dimensional orbital and spin
evolution. The inertial frame is indicated by the blue coordinates,
centered on the star HD 80606, with the binary companion HD 80607 in
the X-Y plane. The planet's orbit is shown in black, with an
arrowhead indicating the position of distance of closest approach
(periastron) and the sense of the orbital trajectory. The black stick
vector normal to the orbital plane. The red stick is the spin axis of the
host star at the center. The combatants in the center of the figure have
shadows on the three walls of the arena, to aid in visualizing the 3-D motion.
At first, the movie plays 80 Myr of evolution slowly, during which the
planetary orbit exhibits 3 Kozai cycles: oscillations in eccentricity
and inclination. These are nearly periodic, so the movie is sped up to
see the long-term effect of tidal friction during the eccentricity maxima.
The orbit is slowly drawn in. The eccentricity cycles are first quenched,
and we see it (today) in a monotonically damping state. In the future the
eccentricity damps out completely, forming a hot Jupiter.
As the planetary orbit undergoes Kozai oscillations and migrates through
tidal friction, at first its host star maintains its original orientation.
Its distant planet simply supplies no net torque to its rotational
bulge. As the migration plays out, eventually the spin takes note, and
starts precessing very quickly around the planetary orbit normal. The
final result is an angle of 50 degrees between the planetary orbit and the
stellar spin (the angle between the green and red sticks), the sky
projection of which has recently been measured via spectroscopy
This process also works for triple stars, and observations indicate that
delivering a large fraction of close binaries to their close orbits. The
time history of how close-binaries are built up is relevant to the
formation of blue
stragglers, so I have computed the e-logP
diagram as a
function of time, and studied whether the proper inital cut-off to period
is, say, 0.2 days, 6
days (preferred), or 30 days.
This process makes two predictions regarding angles in the final systems.
First, the outer binary and the inner orbit should prefer the values of
~40 degrees and ~140 degrees; this is a clear hallmark of Kozai cycles at
work. Some of the firstcitations
to this paper were optical
interferometry observations that confirmed this expectation for two
systems. A satisfactory observational study and analysis testing this
prediction may require new telescopes (and therefore require many many
Second, planetary systems are usually assumed to form in a disk, which
itself determines the spin direction of the star. Therefore alignment
between the planetary orbits and the host star's spin is expected, and it
is observed in the solar system. However, Kozai cycles from the binary
companion can torque the planetary orbit through many many cycles before
it settles as a hot Jupiter. Therefore spin-orbit mis-alignment
may be induced. Surprisingly, even retrograde (inclination > 90
degrees) misalignment angles would be rather common in this process, which
might be guessed from the movie above. Once the planet-star torques
dominate the planet-companion torques, the inclination is sealed in. The
planet cannot torque up (synchronize or parallelize) its host star spin,
via tidal friction in the star. If it could, the planet would be shortly
consumed. This prediction is interesting because the Rossiter-McLaughlin
effect, a spectroscopic distortion observable during planetary transits,
can probe the statistics
of (mis)alignment, and it is a promising way for
deciding how exo-Jupiters migrate to orbits of just a few days.