29,337 research outputs found
Viscoelastic Tidal Dissipation in Giant Planets and Formation of Hot Jupiters Through High-Eccentricity Migration
We study the possibility of tidal dissipation in the solid cores of giant
planets and its implication for the formation of hot Jupiters through
high-eccentricity migration. We present a general framework by which the tidal
evolution of planetary systems can be computed for any form of tidal
dissipation, characterized by the imaginary part of the complex tidal Love
number, , as a function of the forcing
frequency . Using the simplest viscoelastic dissipation model (the
Maxwell model) for the rocky core and including the effect of a nondissipative
fluid envelope, we show that with reasonable (but uncertain) physical
parameters for the core (size, viscosity and shear modulus), tidal dissipation
in the core can accommodate the tidal-Q constraint of the Solar system gas
giants and at the same time allows exoplanetary hot Jupiters to form via tidal
circularization in the high-e migration scenario. By contrast, the often-used
weak friction theory of equilibrium tide would lead to a discrepancy between
the Solar system constraint and the amount of dissipation necessary for high-e
migration. We also show that tidal heating in the rocky core can lead to modest
radius inflation of the planets, particularly when the planets are in the
high-eccentricity phase () during their high-e migration. Finally,
as an interesting by-product of our study, we note that for a generic tidal
response function , it is possible that spin
equilibrium (zero torque) can be achieved for multiple spin frequencies (at a
given ), and the actual pseudo-synchronized spin rate depends on the
evolutionary history of the system.Comment: 10 pages, 8 figures, MNRAS in pres
Effects of Zeeman field on a Spin Bose-Metal phase
We consider Zeeman field effects on a Spin Bose-Metal (SBM) phase on a
two-leg triangular ladder. This phase was found in a spin-1/2 model with ring
exchanges [D. N. Sheng et. al., Phys. Rev. B {\bf 79}, 205112 (2009)], and was
also proposed to appear in an interacting electronic model with longer-ranged
repulsion [Lai et. al., Phys. Rev. B {\bf 81}, 045105 (2010)]. Using
bosonization of a spinon-gauge theory, we study the stability of the SBM phase
and its properties under the field. We also explore phases arising from
potential instabilities of the SBM; in all cases, we find a gap to spin-1
excitations while spin-nematic correlations are power law. We discuss
two-dimensional analogues of these phases where spinons can pair with their own
species.Comment: 10 pages, 6 figure
Effects of impurities in Spin Bose-Metal phase on a two-leg triangular strip
We study effects of nonmagnetic impurities in a Spin Bose-Metal (SBM) phase
discovered in a two-leg triangular strip spin-1/2 model with ring exchanges (D.
N. Shenget al, arXiv:0902.4210). This phase is a quasi-1D descendant of a 2D
spin liquid with spinon Fermi sea, and the present study aims at interpolating
between the 1D and 2D cases. Different types of defects can be treated as local
energy perturbations, which we find are always relevant. As a result, a
nonmagnetic impurity generically cuts the system into two decoupled parts. We
calculate bond energy and local spin susceptibility near the defect, both of
which can be measured in experiments. The Spin Bose-Metal has dominant
correlations at characteristic incommensurate wavevectors that are revealed
near the defect. Thus, the bond energy shows a static texture oscillating as a
function of distance from the defect and decaying as a slow power law. The
local spin susceptibility also oscillates and actually {\it increases} as a
function of distance from the defect, similar to the effect found in the 1D
chain [S. Eggert and I. Affleck, Phys. Rev. Lett. {\bf 75}, 934 (1995)]. We
calculate the corresponding power law exponents for the textures as a function
of one Luttinger parameter of the SBM theory.Comment: 6 pages, 1 figur
Two-band electronic metal and neighboring spin liquid (spin Bose-metal) on a zigzag strip with longer-ranged repulsion
We consider an electronic model for realizing the Spin Bose-metal (SBM) phase
on a 2-leg triangular strip --a spin liquid phase found by D. N. Sheng et al
[Phys. Rev. B {\bf 79}, 205112 (2009)] in a spin-1/2 model with ring exchanges.
The SBM can be viewed as a "C1S2" Mott insulator of electrons where the overall
charge transporting mode is gapped out. We start from a two-band "C2S2" metal
and consider extended repulsion motivated by recent ab initio derivation of
electronic model for -ET spin liquid material [K. Nakamura et al, J.
Phys. Soc. Jpn. {\bf 78}, 083710(2009)]. Using weak coupling renormalization
group analysis, we find that the extended interactions allow much wider C2S2
metallic phase than in the Hubbard model with on-site repulsion only. An
eight-fermion Umklapp term plays a crucial role in producing a Mott insulator
but can not be treated in weak coupling. We use Bosonization to extend the
analysis to intermediate coupling and study phases obtained out of the C2S2
metal upon increasing overall repulsion strength, finding that the SBM phase is
a natural outcome for extended interactions.Comment: 12 pages, 9 figure
Insulating phases of electrons on a zigzag strip in the orbital magnetic field
We consider electrons on a two-leg triangular ladder at half-filling and in
an orbital magnetic field. In a two-band regime in the absence of the field,
the electronic system remains conducting for weak interactions since there is
no four-fermion Umklapp term. We find that in the presence of the orbital field
there is a four-fermion Umklapp and it is always relevant for repulsive
interactions. Thus in this special ladder, the combination of the orbital
magnetic field and interactions provides a mechanism to drive metal-insulator
transition already at weak coupling. We discuss properties of the possible
resulting phases C0S2 and various C0S1 and C0S0.Comment: 7 pages, 4 figures, 2 table
Non-radial Oscillations in Rotating Giant Planets with Solid Cores: Application to Saturn and its Rings
Recent observations have revealed evidence for the global oscillations of
Jupiter and Saturn, which can potentially provide a new window into the
interior structure of giant planets. Motivated by these observations, we study
the non-radial oscillation modes of giant planets containing a solid core. Our
calculations include the elastic response of the core and consider a wide range
of possible values of the core shear modulus. While the elasticity of the core
only slightly changes the frequencies of acoustic modes, which reside mostly in
the fluid envelope, it adds two new classes of shear modes that are largely
confined to the core. We also calculate the effects of the Coriolis force on
the planetary oscillation modes. In addition to changing the mode frequencies,
the Coriolis force can cause the shear modes to mix with the f-modes. Such
mixing occurs when the frequencies of the shear mode and the f-mode are close
to each other, and results in "mixed modes" with similar properties that are
slightly split in frequency. We discuss our results in light of the recent work
by Hedman & Nicholson (2013), which revealed the presence of density waves in
Saturn's C-ring that appear to be excited by the gravitational perturbations
associated with the f-mode oscillations within Saturn. We find that the fine
splitting in wave frequencies observed in the rings can in principle be
explained by the rotation-induced mixing between core shear modes and f-modes,
possibly indicating the presence of a solid core within Saturn. However, in our
current calculations, which assume rigid-body rotation and include only
first-order rotational effects, significant fine-tuning in the planetary model
parameters is needed in order to achieve these mode mixings and to explain the
observed fine frequency splitting. We briefly discuss other effects that may
modify the f-modes and facilitate mode mixing.Comment: 35 pages, 12 figures, submitted to Icaru
Chaotic Dynamics of Stellar Spin in Binaries and the Production of Misaligned Hot Jupiters
Many exoplanetary systems containing hot Jupiters are observed to have highly
misaligned orbital axes relative to the stellar spin axes. Kozai-Lidov
oscillations of orbital eccentricity/inclination induced by a binary companion,
in conjunction with tidal dissipation, is a major channel for the production of
hot Jupiters. We demonstrate that gravitational interaction between the planet
and its oblate host star can lead to chaotic evolution of the stellar spin axis
during Kozai cycles. As parameters such as the planet mass and stellar rotation
period vary, periodic islands can appear in an ocean of chaos, in a manner
reminiscent of other dynamical systems. In the presence of tidal dissipation,
the complex spin evolution can leave an imprint on the final spin-orbit
misalignment angles.Comment: 26 pages, 13 figures. Includes supplementary materials. To be
published in the September 12, 2014 edition of Science Magazine. For
additional information, please visit
http://astro.cornell.edu/~dong/sciencepaper.htm
Eccentricity and Spin-Orbit Misalignment in Short-Period Stellar Binaries as a Signpost of Hidden Tertiary Companions
Eclipsing binaries are observed to have a range of eccentricities and
spin-orbit misalignments (stellar obliquities). Whether such properties are
primordial, or arise from post-formation dynamical interactions remains
uncertain. This paper considers the scenario in which the binary is the inner
component of a hierarchical triple stellar system, and derives the requirements
that the tertiary companion must satisfy in order to raise the eccentricity and
obliquity of the inner binary. Through numerical integrations of the secular
octupole-order equations of motion of stellar triples, coupled with the spin
precession of the oblate primary star due to the torque from the secondary, we
obtain a simple, robust condition for producing spin-orbit misalignment in the
inner binary: In order to excite appreciable obliquity, the precession rate of
the stellar spin axis must be smaller than the orbital precession rate due to
the tertiary companion. This yields quantitative requirements on the mass and
orbit of the tertiary. We also present new analytic expressions for the maximum
eccentricity and range of inclinations allowing eccentricity excitation
(Lidov-Kozai window), for stellar triples with arbitrary masses and including
the non-Keplerian potentials introduced by general relativity, stellar tides
and rotational bulges. The results of this paper can be used to place
constraints on unobserved tertiary companions in binaries that exhibit high
eccentricity and/or spin-orbit misalignment, and will be helpful in guiding
efforts to detect external companions around stellar binaries. As an
application, we consider the eclipsing binary DI Herculis, and identify the
requirements that a tertiary companion must satisfy to produce the observed
spin-orbit misalignment.Comment: 19 pages, 15 figures, accepted for publication in MNRA
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