223 research outputs found
Dynamics and Origin of the 2:1 Orbital Resonances of the GJ 876 Planets
(Abridged) A dynamical fit has placed the two planets about the star GJ 876
in coplanar orbits deep in 3 resonances at the 2:1 mean-motion commensurability
with small libration amplitudes. The libration of both lowest order mean-motion
resonance variables, theta_1 and theta_2, and the secular resonance variable,
theta_3, about 0 deg. differs from the familiar geometry of the Io-Europa pair,
where theta_2 and theta_3 librate about 180 deg. By considering a condition for
stable simultaneous librations of theta_1 and theta_2, we show that the GJ 876
geometry results because of the large orbital eccentricities e_i, whereas the
very small e_i in the Io-Europa system lead to the latter's geometry.
Surprisingly, the GJ 876 resonance configuration remains stable for e_1 up to
0.86 and for amplitude of libration of theta_1 approaching 45 deg. with the
current e_i. We find that inward migration of the outer planet of the GJ 876
system results in certain capture into the observed resonances if initially e_1
<0.06 and e_2<0.03 and the migration rate |(da_2/dt)/a_2| < 0.03(a_2/AU)^{-3/2}
yr^{-1}. The bound on the migration rate is easily satisfied by migration due
to planet-nebula interaction. If there is no eccentricity damping, eccentricity
growth is rapid with continued migration within the resonance, with e_i
exceeding the observed values after a further reduction in the semi-major axes
a_i of only 7%. With eccentricity damping (de_i/dt)/e_i = -K|(da_i/dt)/a_i|,
the e_i reach equilibrium values that remain constant for arbitrarily long
migration within the resonances. The equilibrium e_i are close to the observed
e_i for K=100 (K=10) if there is migration and damping of the outer planet only
(of both planets). It is as yet unclear that planet-nebula interaction can
produce the large value of K required to obtain the observed eccentricities.Comment: 23 pages, including 8 figures; uses AASTeX v5.0; minor additions;
accepted for publication in Ap
Concentration of atomic hydrogen diffused into silicon in the temperature range 900–1300 °C
Boron-doped Czochralski silicon samples with [B]~1017 cm−3 have been heated at various temperatures in the range 800–1300 °C in an atmosphere of hydrogen and then quenched. The concentration of [H-B] pairs was measured by infrared localized vibrational mode spectroscopy. It was concluded that the solubility of atomic hydrogen is greater than [Hs] = 5.6 × 1018 exp( − 0.95 eV/kT)cm−3 at the temperatures investigated
Surface and grain-boundary scattering in nanometric Cu films
We report a quantitative analysis of both surface and grain-boundary scattering in Cu thin films with independent variation in film thickness (27 to 158 nm) and grain size (35 to 425 nm) in samples prepared by subambient temperature film deposition followed by annealing. Film resistivities of carefully characterized samples were measured at both room temperature and at 4.2 K and were compared with physical models that include the effects of surface and grain-boundary scattering. Grain-boundary scattering is found to provide the strongest contribution to the resistivity increase. However, a weaker, but significant, role is observed for surface scattering. We find that the data are best fit when the Mayadas and Shatzkes\u27 model of grain-boundary scattering and the Fuchs and Sondheimer\u27s model of surface scattering resistivity contributions are combined using Matthiessen\u27s rule (simple addition of resistivities). This finding implies that grain-boundary scattering preserves the component of electron momentum parallel to the grain-boundary plane. Using Matthiessen\u27s rule, we find our data are well described by a grain-boundary reflection coefficient of 0.43 and a surface specularity coefficient of 0.52. This analysis finds a significantly lower contribution from surface scattering than has been reported in previous works and we attribute this difference to the careful quantitative microstructural characterization performed on our samples. The effects of surface roughness, impurities, voids, and interactions between surface and grain-boundary scattering are also examined and their importance is evaluated
The Gibbs-Thomson formula at small island sizes - corrections for high vapour densities
In this paper we report simulation studies of equilibrium features, namely
circular islands on model surfaces, using Monte-Carlo methods. In particular,
we are interested in studying the relationship between the density of vapour
around a curved island and its curvature-the Gibbs-Thomson formula. Numerical
simulations of a lattice gas model, performed for various sizes of islands,
don't fit very well to the Gibbs-Thomson formula. We show how corrections to
this form arise at high vapour densities, wherein a knowledge of the exact
equation of state (as opposed to the ideal gas approximation) is necessary to
predict this relationship. Exploiting a mapping of the lattice gas to the Ising
model one can compute the corrections to the Gibbs-Thomson formula using high
field series expansions. We also investigate finite size effects on the
stability of the islands both theoretically and through simulations. Finally
the simulations are used to study the microscopic origins of the Gibbs-Thomson
formula. A heuristic argument is suggested in which it is partially attributed
to geometric constraints on the island edge.Comment: 27 pages including 7 figures, tarred, gzipped and uuencoded. Prepared
using revtex and espf.sty. To appear in Phys. Rev.
The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables
The Hamiltonian theory of Earth rotation, known as the Kinoshita-Souchay
theory, operates with nonosculating Andoyer elements. This situation parallels
a similar phenomenon that often happens (but seldom gets noticed) in orbital
dynamics, when the standard Lagrange-type or Delaunay-type planetary equations
unexpectedly render nonosculating orbital elements. In orbital mechanics,
osculation loss happens when a velocity-dependent perturbation is plugged into
the standard planetary equations. In attitude mechanics, osculation is lost
when an angular-velocity-dependent disturbance is plugged in the standard
dynamical equations for the Andoyer elements. We encounter exactly this
situation in the theory of Earth rotation, because this theory contains an
angular-velocity-dependent perturbation (the switch from an inertial frame to
that associated with the precessing ecliptic of date).
While the osculation loss does not influence the predictions for the figure
axis of the planet, it considerably alters the predictions for the
instantaneous spin-axis' orientation. We explore this issue in great detail
Tidal friction in close-in satellites and exoplanets. The Darwin theory re-visited
This report is a review of Darwin's classical theory of bodily tides in which
we present the analytical expressions for the orbital and rotational evolution
of the bodies and for the energy dissipation rates due to their tidal
interaction. General formulas are given which do not depend on any assumption
linking the tidal lags to the frequencies of the corresponding tidal waves
(except that equal frequency harmonics are assumed to span equal lags).
Emphasis is given to the cases of companions having reached one of the two
possible final states: (1) the super-synchronous stationary rotation resulting
from the vanishing of the average tidal torque; (2) the capture into a 1:1
spin-orbit resonance (true synchronization). In these cases, the energy
dissipation is controlled by the tidal harmonic with period equal to the
orbital period (instead of the semi-diurnal tide) and the singularity due to
the vanishing of the geometric phase lag does not exist. It is also shown that
the true synchronization with non-zero eccentricity is only possible if an
extra torque exists opposite to the tidal torque. The theory is developed
assuming that this additional torque is produced by an equatorial permanent
asymmetry in the companion. The results are model-dependent and the theory is
developed only to the second degree in eccentricity and inclination
(obliquity). It can easily be extended to higher orders, but formal accuracy
will not be a real improvement as long as the physics of the processes leading
to tidal lags is not better known.Comment: 30 pages, 7 figures, corrected typo
Refined parameters and spectroscopic transit of the super-massive planet HD147506b
In this paper, we report a refined determination of the orbital parameters
and the detection of the Rossiter-McLaughlin effect of the recently discovered
transiting exoplanet HD147506b (HAT-P-2b). The large orbital eccentricity at
the short orbital period of this exoplanet is unexpected and is distinguishing
from other known transiting exoplanets. We performed high-precision radial
velocity spectroscopic observations of HD147506 (HAT-P-2) with the new
spectrograph SOPHIE, mounted on the 1.93 m telescope at the Haute-Provence
observatory (OHP). We obtained 63 new measurements, including 35 on May 14 and
20 on June 11, when the planet was transiting its parent star. The radial
velocity (RV) anomaly observed illustrates that HAT-P-2b orbital motion is set
in the same direction as its parent star spin. The sky-projected angle between
the normal of the orbital plane and the stellar spin axis, \lambda = 0.2 +12.2
-12.5 deg, is consistent with zero. The planetary and stellar radii were
re-determined, yielding R_p = 0.951 +0.039 -0.053 R_Jup, R_s = 1.416 +0.040
-0.062 R_Sun. The mass M_p = 8.62 +0.39 -0.55 M_Jup and radius of HAT-P-2b
indicate a density of 12.5 +2.6 -3.6 g cm^{-3}, suggesting an object in between
the known close-in planets with typical density of the order of 1 g cm^{-3},
and the very low-mass stars, with density greater than 50 g cm^{-3}.Comment: Submitted to A&A; V2: Replaced by accepted versio
Decay of isolated surface features driven by the Gibbs-Thomson effect in analytic model and simulation
A theory based on the thermodynamic Gibbs-Thomson relation is presented which
provides the framework for understanding the time evolution of isolated
nanoscale features (i.e., islands and pits) on surfaces. Two limiting cases are
predicted, in which either diffusion or interface transfer is the limiting
process. These cases correspond to similar regimes considered in previous works
addressing the Ostwald ripening of ensembles of features. A third possible
limiting case is noted for the special geometry of "stacked" islands. In these
limiting cases, isolated features are predicted to decay in size with a power
law scaling in time: A is proportional to (t0-t)^n, where A is the area of the
feature, t0 is the time at which the feature disappears, and n=2/3 or 1. The
constant of proportionality is related to parameters describing both the
kinetic and equilibrium properties of the surface. A continuous time Monte
Carlo simulation is used to test the application of this theory to generic
surfaces with atomic scale features. A new method is described to obtain
macroscopic kinetic parameters describing interfaces in such simulations.
Simulation and analytic theory are compared directly, using measurements of the
simulation to determine the constants of the analytic theory. Agreement between
the two is very good over a range of surface parameters, suggesting that the
analytic theory properly captures the necessary physics. It is anticipated that
the simulation will be useful in modeling complex surface geometries often seen
in experiments on physical surfaces, for which application of the analytic
model is not straightforward.Comment: RevTeX (with .bbl file), 25 pages, 7 figures from 9 Postscript files
embedded using epsf. Submitted to Phys. Rev. B A few minor changes made on
9/24/9
Tidal torques. A critical review of some techniques
We point out that the MacDonald formula for body-tide torques is valid only
in the zeroth order of e/Q, while its time-average is valid in the first order.
So the formula cannot be used for analysis in higher orders of e/Q. This
necessitates corrections in the theory of tidal despinning and libration
damping.
We prove that when the inclination is low and phase lags are linear in
frequency, the Kaula series is equivalent to a corrected version of the
MacDonald method. The correction to MacDonald's approach would be to set the
phase lag of the integral bulge proportional to the instantaneous frequency.
The equivalence of descriptions gets violated by a nonlinear
frequency-dependence of the lag.
We explain that both the MacDonald- and Darwin-torque-based derivations of
the popular formula for the tidal despinning rate are limited to low
inclinations and to the phase lags being linear in frequency. The
Darwin-torque-based derivation, though, is general enough to accommodate both a
finite inclination and the actual rheology.
Although rheologies with Q scaling as the frequency to a positive power make
the torque diverge at a zero frequency, this reveals not the impossible nature
of the rheology, but a flaw in mathematics, i.e., a common misassumption that
damping merely provides lags to the terms of the Fourier series for the tidal
potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the
magnitudes of the terms, too, get changed. Reinstating of this detail tames the
infinities and rehabilitates the "impossible" scaling law (which happens to be
the actual law the terrestrial planets obey at low frequencies).Comment: arXiv admin note: sections 4 and 9 of this paper contain substantial
text overlap with arXiv:0712.105
Mercury's Moment of Inertia from Spin and Gravity Data
Earth-based radar observations of the spin state of Mercury at 35 epochs between 2002 and 2012 reveal that its spin axis is tilted by (2.04 plus or minus 0.08) arc min with respect to the orbit normal. The direction of the tilt suggests that Mercury is in or near a Cassini state. Observed rotation rate variations clearly exhibit an 88-day libration pattern which is due to solar gravitational torques acting on the asymmetrically shaped planet. The amplitude of the forced libration, (38.5 plus or minus 1.6) arc sec, corresponds to a longitudinal displacement of ∼450 m at the equator. Combining these measurements of the spin properties with second-degree gravitational harmonics (Smith et al., 2012) provides an estimate of the polar moment of inertia of MercuryC/MR2 = 0.346 plus or minus 0.014, where M and R are Mercury's mass and radius. The fraction of the moment that corresponds to the outer librating shell, which can be used to estimate the size of the core, is Cm/C = 0.431 plus or minus 0.025
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