510 research outputs found
Mean motion resonances at high eccentricities: the 2:1 and the 3:2 interior resonances
Mean motion resonances [MMRs] play an important role in the formation and
evolution of planetary systems and have significantly influenced the orbital
properties and distribution of planets and minor planets in the solar system as
well as exo-planetary systems. Most previous theoretical analyses have focused
on the low-to-moderate eccentricity regime, but with new discoveries of high
eccentricity resonant minor planets and even exoplanets, there is increasing
motivation to examine MMRs in the high eccentricity regime. Here we report on a
study of the high eccentricity regime of MMRs in the circular planar restricted
three-body problem. Non-perturbative numerical analyses of the 2:1 and the 3:2
interior resonances are carried out for a wide range of secondary-to-primary
mass ratio, and for a wide range of eccentricity of the test particle. The
surface-of-section technique is used to study the phase space structure near
resonances. We identify transitions in phase space at certain critical
eccentricities related to the geometry of resonant orbits; new stable libration
zones appear at high eccentricity at libration centers shifted from those at
low eccentricities. We present novel results on the mass and eccentricity
dependence of the resonance libration centers and their widths in semi-major
axis. Our results show that MMRs have sizable libration zones at high
eccentricities, comparable to those at lower eccentricities.Comment: 16 pages. Submitted to AAS Journal
Standard Model Mass Spectrum in Inflationary Universe
We work out the Standard Model (SM) mass spectrum during inflation with
quantum corrections, and explore its observable consequences in the squeezed
limit of non-Gaussianity. Both non-Higgs and Higgs inflation models are studied
in detail. We also illustrate how some inflationary loop diagrams can be
computed neatly by Wick-rotating the inflation background to Euclidean
signature and by dimensional regularization.Comment: 62 pages, JHEP accepted versio
Neutrino Signatures in Primordial Non-Gaussianities
We study the cosmological collider phenomenology of neutrinos in an effective
field theory. The mass spectrum of neutrinos and their characteristic
oscillatory signatures in the squeezed limit bispectrum are computed. Both
dS-covariant and slow-roll corrections are considered, so is the scenario of
electroweak symmetry breaking during inflation. Interestingly, we show that the
slow-roll background of the inflaton provides a chemical potential for the
neutrino production. The chemical potential greatly amplifies the oscillatory
signal and makes the signal observably large for heavy neutrinos without the
need of fine tuning.Comment: 31 pages, JHEP accepted versio
Stability and Motion around Equilibrium Points in the Rotating Plane-Symmetric Potential Field
This study presents a study of equilibrium points, periodic orbits,
stabilities, and manifolds in a rotating plane symmetric potential field. It
has been found that the dynamical behaviour near equilibrium points is
completely determined by the structure of the submanifolds and subspaces. The
non-degenerate equilibrium points are classified into twelve cases. The
necessary and sufficient conditions for linearly stable, non resonant unstable
and resonant equilibrium points are established. Furthermore, the results show
that a resonant equilibrium point is a Hopf bifurcation point. In addition, if
the rotating speed changes, two non degenerate equilibria may collide and
annihilate each other. The theory developed here is lastly applied to two
particular cases, motions around a rotating, homogeneous cube and the asteroid
1620 Geographos. We found that the mutual annihilation of equilibrium points
occurs as the rotating speed increases, and then the first surface shedding
begins near the intersection point of the x axis and the surface. The results
can be applied to planetary science, including the birth and evolution of the
minor bodies in the Solar system, the rotational breakup and surface mass
shedding of asteroids, etc.Comment: 38 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1403.040
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