43 research outputs found
Dynamics of Convergent Migration and Mean Motion Resonances in Planetary Systems.
Recent observations of solar systems orbiting other stars show that exoplanets display an enormous range of physical properties and that planetary systems display a diverse set of architectures, which motivate further studies in planetary dynamics. Part of the richness of this dynamical problem arises from the intrinsic complexity of -body systems, even in the absence of additional forces. The realm of physical behavior experienced by such systems is enormous, and includes mean motion resonances (MMR), secular interactions, and sensitive dependence on the initial conditions (chaos). Additional complications arise from other forces that are often present: During the early stages of evolution, circumstellar disks provide torques that influence orbital elements, and turbulent fluctuations act on young planets. Over longer time scales, solar systems are affected by tidal forces from both stars and planets, and by general relativistic corrections that lead to orbital precession. This thesis addresses a subset of these dynamical problems, including the capture rates of planets into MMR, collision probabilities for migrating rocky planets interacting with Jovian planets, and the exploration of the ``nodding'' phenomenon (where systems move in and out of MMR). This latter effect can have important implications for interpreting transit timing variations (TTV), a method to detect smaller planets due to their interaction with larger transiting bodies.PhDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107050/1/jaketchm_1.pd
Effects of Turbulence, Eccentricity Damping, and Migration Rate on the Capture of Planets into Mean Motion Resonance
Pairs of migrating extrasolar planets often lock into mean motion resonance
as they drift inward. This paper studies the convergent migration of giant
planets (driven by a circumstellar disk) and determines the probability that
they are captured into mean motion resonance. The probability that such planets
enter resonance depends on the type of resonance, the migration rate, the
eccentricity damping rate, and the amplitude of the turbulent fluctuations.
This problem is studied both through direct integrations of the full 3-body
problem, and via semi-analytic model equations. In general, the probability of
resonance decreases with increasing migration rate, and with increasing levels
of turbulence, but increases with eccentricity damping. Previous work has shown
that the distributions of orbital elements (eccentricity and semimajor axis)
for observed extrasolar planets can be reproduced by migration models with
multiple planets. However, these results depend on resonance locking, and this
study shows that entry into -- and maintenance of -- mean motion resonance
depends sensitively on migration rate, eccentricity damping, and turbulence.Comment: 43 pages including 14 figures; accepted for publication in The
Astrophysical Journa
Orbital Instabilities in a Triaxial Cusp Potential
This paper constructs an analytic form for a triaxial potential that
describes the dynamics of a wide variety of astrophysical systems, including
the inner portions of dark matter halos, the central regions of galactic
bulges, and young embedded star clusters. Specifically, this potential results
from a density profile of the form , where the radial
coordinate is generalized to triaxial form so that . Using the resulting analytic form of the potential, and the
corresponding force laws, we construct orbit solutions and show that a robust
orbit instability exists in these systems. For orbits initially confined to any
of the three principal planes, the motion in the perpendicular direction can be
unstable. We discuss the range of parameter space for which these orbits are
unstable, find the growth rates and saturation levels of the instability, and
develop a set of analytic model equations that elucidate the essential physics
of the instability mechanism. This orbit instability has a large number of
astrophysical implications and applications, including understanding the
formation of dark matter halos, the structure of galactic bulges, the survival
of tidal streams, and the early evolution of embedded star clusters.Comment: 50 pages, accepted for publication in Ap
The Future Evolution of White Dwarf Stars Through Baryon Decay and Time Varying Gravitational Constant
Motivated by the possibility that the fundamental ``constants'' of nature
could vary with time, this paper considers the long term evolution of white
dwarf stars under the combined action of proton decay and variations in the
gravitational constant. White dwarfs are thus used as a theoretical laboratory
to study the effects of possible time variations, especially their implications
for the future history of the universe. More specifically, we consider the
gravitational constant to vary according to the parametric relation , where the time scale is the same order as
the proton lifetime. We then study the long term fate and evolution of white
dwarf stars. This treatment begins when proton decay dominates the stellar
luminosity, and ends when the star becomes optically thin to its internal
radiation.Comment: 12 pages, 10 figures, accepted to Astrophysics and Space Scienc
MEAN MOTION RESONANCES IN EXOPLANET SYSTEMS: AN INVESTIGATION INTO NODDING BEHAVIOR
Motivated by the large number of extrasolar planetary systems that are near mean motion resonances, this paper explores a related type of dynamical behavior known as “nodding”. Here, the resonance angle of a planetary system executes libration (oscillatory motion) for several cycles, circulates for one or more cycles, and then enters once again into libration. This type of complicated dynamics can affect our interpretation of observed planetary systems that are in or near mean motion resonance. This work shows that planetary systems in (near) mean motion resonance can exhibit nodding behavior, and outlines the portion of parameter space where it occurs. This problem is addressed using both full numerical integrations of the planetary systems and via model equations obtained through expansions of the disturbing function. In the latter approach, we identify the relevant terms that allow for nodding. The two approaches are in agreement, and show that nodding often occurs when a small body is in an external mean motion resonance with a larger planet. As a result, the nodding phenomenon can be important for interpreting observations of transit timing variations, where the existence of smaller bodies is inferred through their effects on larger, observed transiting planets. For example, in actively nodding planetary systems, both the amplitude and frequency of the transit timing variations depend on the observational time window. Subject headings: planets and satellites: dynamical evolution and stability — planets and satellites: formation — planet-disk interactions – 2 – 1