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Title: Compact planetary systems perturbed by an inclined companion. II. Stellar spin-orbit evolution

Abstract

The stellar spin orientation relative to the orbital planes of multiplanet systems is becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an inclined outer companion. Our study is based on classical secular theory, using a vectorial approach developed in a separate paper. When planet-planet perturbations are truncated at the second order in eccentricity and mutual inclination, and the planet-companion perturbations are developed at the quadrupole order, the problem becomes integrable. The motion is composed of a uniform precession of the whole system around the total angular momentum, and in the rotating frame, the evolution is periodic. Here, we focus on the relative motion associated with the oscillations of the inclination between the planet system and the outer orbit and of the obliquities of the star with respect to the two orbital planes. The solution is obtained using a powerful geometric method. With this technique, we identify four different regimes characterized by the nutation amplitude of the stellar spin axis relative to the orbital plane of the planets. In particular, the obliquity of the star reaches its maximum when the system is in the Cassini regime where planets havemore » more angular momentum than the star and where the precession rate of the star is similar to that of the planets induced by the companion. In that case, spin-orbit oscillations exceed twice the inclination between the planets and the companion. Even if the mutual inclination is only ≅ 20°, this resonant case can cause the spin-orbit angle to oscillate between perfectly aligned and retrograde values.« less

Authors:
;  [1]
  1. Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637 (United States)
Publication Date:
OSTI Identifier:
22365726
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 789; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; COMPACTS; DISTURBANCES; EVOLUTION; INCLINATION; L-S COUPLING; ORBITS; OSCILLATIONS; PERIODICITY; PERTURBATION THEORY; PLANETS; SATELLITES; SPIN; SPIN ORIENTATION; STABILITY; STARS

Citation Formats

Boué, Gwenaël, and Fabrycky, Daniel C., E-mail: boue@imcce.fr. Compact planetary systems perturbed by an inclined companion. II. Stellar spin-orbit evolution. United States: N. p., 2014. Web. doi:10.1088/0004-637X/789/2/111.
Boué, Gwenaël, & Fabrycky, Daniel C., E-mail: boue@imcce.fr. Compact planetary systems perturbed by an inclined companion. II. Stellar spin-orbit evolution. United States. doi:10.1088/0004-637X/789/2/111.
Boué, Gwenaël, and Fabrycky, Daniel C., E-mail: boue@imcce.fr. Thu . "Compact planetary systems perturbed by an inclined companion. II. Stellar spin-orbit evolution". United States. doi:10.1088/0004-637X/789/2/111.
@article{osti_22365726,
title = {Compact planetary systems perturbed by an inclined companion. II. Stellar spin-orbit evolution},
author = {Boué, Gwenaël and Fabrycky, Daniel C., E-mail: boue@imcce.fr},
abstractNote = {The stellar spin orientation relative to the orbital planes of multiplanet systems is becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an inclined outer companion. Our study is based on classical secular theory, using a vectorial approach developed in a separate paper. When planet-planet perturbations are truncated at the second order in eccentricity and mutual inclination, and the planet-companion perturbations are developed at the quadrupole order, the problem becomes integrable. The motion is composed of a uniform precession of the whole system around the total angular momentum, and in the rotating frame, the evolution is periodic. Here, we focus on the relative motion associated with the oscillations of the inclination between the planet system and the outer orbit and of the obliquities of the star with respect to the two orbital planes. The solution is obtained using a powerful geometric method. With this technique, we identify four different regimes characterized by the nutation amplitude of the stellar spin axis relative to the orbital plane of the planets. In particular, the obliquity of the star reaches its maximum when the system is in the Cassini regime where planets have more angular momentum than the star and where the precession rate of the star is similar to that of the planets induced by the companion. In that case, spin-orbit oscillations exceed twice the inclination between the planets and the companion. Even if the mutual inclination is only ≅ 20°, this resonant case can cause the spin-orbit angle to oscillate between perfectly aligned and retrograde values.},
doi = {10.1088/0004-637X/789/2/111},
journal = {Astrophysical Journal},
number = 2,
volume = 789,
place = {United States},
year = {Thu Jul 10 00:00:00 EDT 2014},
month = {Thu Jul 10 00:00:00 EDT 2014}
}
  • The non-resonant secular dynamics of compact planetary systems are modeled by a perturbing function that is usually expanded in eccentricity and absolute inclination with respect to the invariant plane. Here, the expressions are given in a vectorial form which naturally leads to an expansion in eccentricity and mutual inclination. The two approaches are equivalent in most cases, but the vectorial one is specially designed for those cases where an entire quasi-coplanar system tilts to a large degree. Moreover, the vectorial expressions of the Hamiltonian and of the equations of motion are slightly simpler than those given in terms of themore » usual elliptical elements. We also provide the secular perturbing function in vectorial form expanded in semi-major axis ratio allowing for arbitrary eccentricities and inclinations. The interaction between the equatorial bulge of a central star and its planets is also provided, as is the relativistic periapse precession of any planet induced by the central star. We illustrate the use of this representation to follow the secular oscillations of the terrestrial planets of the solar system and for Kozai cycles which may take place in exoplanetary systems.« less
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