1,493 research outputs found
Secular Evolution of Hierarchical Planetary Systems
(Abridged) We investigate the dynamical evolution of coplanar hierarchical
two-planet systems where the ratio of the orbital semimajor axes alpha=a_1/a_2
is small. The orbital parameters obtained from a multiple Kepler fit to the
radial velocity variations of a star are best interpreted as Jacobi coordinates
and Jacobi coordinates should be used in any analyses of hierarchical planetary
systems. An approximate theory that can be applied to coplanar hierarchical
two-planet systems with a wide range of masses m_j and orbital eccentricities
e_j is the octupole-level secular perturbation theory (OSPT). The OSPT shows
that if the ratio of the maximum orbital angular momenta, lambda \approx
(m_1/m_2) alpha^{1/2}, for given a_j is approximately equal to a critical value
lambda_{crit}, then libration of the difference in the longitudes of periapse,
w_1-w_2, about either 0 or 180 deg. is almost certain, with possibly large
amplitude variations of both e_j. We establish that the OSPT is highly accurate
for systems with alpha<0.1 and reasonably accurate even for systems with alpha
as large as 1/3, provided that alpha is not too close to a significant
mean-motion commensurability or above the stability boundary. The HD 168443
system is not in a secular resonance and its w_1-w_2 circulates. The HD 12661
system is the first extrasolar planetary system found to have w_1-w_2 librating
about 180 deg. The libration of w_1-w_2 and the large-amplitude variations of
both e_j in the HD 12661 system are consistent with the analytic results on
systems with lambda \approx lambda_{crit}. The HD 12661 system with the best-
fit orbital parameters and sin i = 1 is affected by the close proximity to the
11:2 commensurability, but small changes in the outer orbital period can result
in configurations that are not affected by mean-motion commensurabilities.Comment: 32 pages, including 8 figures; uses AASTeX v5.0; accepted for
publication in Ap
A Primordial Origin of the Laplace Relation Among the Galilean Satellites
Understanding the origin of the orbital resonances of the Galilean satellites
of Jupiter will constrain the longevity of the extensive volcanism on Io, may
explain a liquid ocean on Europa, and may guide studies of the dissipative
properties of stars and Jupiter-like planets. The differential migration of the
newly formed Galilean satellites due to interactions with a circumjovian disk
can lead to the primordial formation of the Laplace relation n_1 - 3 n_2 + 2
n_3 = 0, where the n_i are the mean orbital angular velocities of Io, Europa,
and Ganymede, respectively. This contrasts with the formation of the resonances
by differential expansion of the orbits from tidal torques from Jupiter.Comment: 13 pages, including 4 figures; uses scicite.st
Pre-K Counts in Pennsylvania for Youngsters' Early School Success: Authentic Outcomes for an Innovative Prevention and Promotion Initiative
Examines the research base for the efficacy of early childhood education. Evaluates Pennsylvania's Pre-K Counts programs, including participants' characteristics, impact and quality of programs and partnerships, lessons learned, and recommendations
On the Origin of Pluto's Small Satellites by Resonant Transport
The orbits of Pluto's four small satellites (Styx, Nix, Kerberos, and Hydra)
are nearly circular and coplanar with the orbit of the large satellite Charon,
with orbital periods nearly in the ratios 3:1, 4:1, 5:1, and 6:1 with Charon's
orbital period. These properties suggest that the small satellites were created
during the same impact event that placed Charon in orbit and had been pushed to
their current positions by being locked in mean-motion resonances with Charon
as Charon's orbit was expanded by tidal interactions with Pluto. Using the
Pluto-Charon tidal evolution models developed by Cheng et al. (2014), we show
that stable capture and transport of a test particle in multiple resonances at
the same mean-motion commensurability is possible at the 5:1, 6:1, and 7:1
commensurabilities, if Pluto's zonal harmonic . However, the test
particle has significant orbital eccentricity at the end of the tidal evolution
of Pluto-Charon in almost all cases, and there are no stable captures and
transports at the 3:1 and 4:1 commensurabilities. Furthermore, a non-zero
hydrostatic value of destroys the conditions necessary for multiple
resonance migration. Simulations with finite but minimal masses of Nix and
Hydra also fail to yield any survivors. We conclude that the placing of the
small satellites at their current orbital positions by resonant transport is
extremely unlikely.Comment: 22 pages, including 7 figures; accepted for publication in Icaru
Complete Tidal Evolution of Pluto-Charon
Both Pluto and its satellite Charon have rotation rates synchronous with
their orbital mean motion. This is the theoretical end point of tidal evolution
where transfer of angular momentum has ceased. Here we follow Pluto's tidal
evolution from an initial state having the current total angular momentum of
the system but with Charon in an eccentric orbit with semimajor axis (where is the radius of Pluto), consistent with its impact origin.
Two tidal models are used, where the tidal dissipation function
1/frequency and constant, where details of the evolution are strongly
model dependent. The inclusion of the gravitational harmonic coefficient
of both bodies in the analysis allows smooth, self consistent
evolution to the dual synchronous state, whereas its omission frustrates
successful evolution in some cases. The zonal harmonic can also be
included, but does not cause a significant effect on the overall evolution. The
ratio of dissipation in Charon to that in Pluto controls the behavior of the
orbital eccentricity, where a judicious choice leads to a nearly constant
eccentricity until the final approach to dual synchronous rotation. The tidal
models are complete in the sense that every nuance of tidal evolution is
realized while conserving total angular momentum - including temporary capture
into spin-orbit resonances as Charon's spin decreases and damped librations
about the same.Comment: 36 pages, including 18 figures; accepted for publication in Icaru
Scattering of coherent states on a single artificial atom
In this work we theoretically analyze a circuit QED design where propagating
quantum microwaves interact with a single artificial atom, a single Cooper pair
box. In particular, we derive a master equation in the so-called transmon
regime, including coherent drives. Inspired by recent experiments, we then
apply the master equation to describe the dynamics in both a two-level and a
three-level approximation of the atom. In the two-level case, we also discuss
how to measure photon antibunching in the reflected field and how it is
affected by finite temperature and finite detection bandwidth.Comment: 18 pages, 7 figure
Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium
Detonation propagation in a compressible medium wherein the energy release
has been made spatially inhomogeneous is examined via numerical simulation. The
inhomogeneity is introduced via step functions in the reaction progress
variable, with the local value of energy release correspondingly increased so
as to maintain the same average energy density in the medium, and thus a
constant Chapman Jouguet (CJ) detonation velocity. A one-step Arrhenius rate
governs the rate of energy release in the reactive zones. The resulting
dynamics of a detonation propagating in such systems with one-dimensional
layers and two-dimensional squares are simulated using a Godunov-type
finite-volume scheme. The resulting wave dynamics are analyzed by computing the
average wave velocity and one-dimensional averaged wave structure. In the case
of sufficiently inhomogeneous media wherein the spacing between reactive zones
is greater than the inherent reaction zone length, average wave speeds
significantly greater than the corresponding CJ speed of the homogenized medium
are obtained. If the shock transit time between reactive zones is less than the
reaction time scale, then the classical CJ detonation velocity is recovered.
The spatio-temporal averaged structure of the waves in these systems is
analyzed via a Favre averaging technique, with terms associated with the
thermal and mechanical fluctuations being explicitly computed. The analysis of
the averaged wave structure identifies the super-CJ detonations as weak
detonations owing to the existence of mechanical non-equilibrium at the
effective sonic point embedded within the wave structure. The correspondence of
the super-CJ behavior identified in this study with real detonation phenomena
that may be observed in experiments is discussed
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