3,304 research outputs found
On the Radii of Close-in Giant Planets
The recent discovery that the close-in extrasolar giant planet, HD209458b,
transits its star has provided a first-of-its-kind measurement of the planet's
radius and mass. In addition, there is a provocative detection of the light
reflected off of the giant planet, Boo b. Including the effects of
stellar irradiation, we estimate the general behavior of radius/age
trajectories for such planets and interpret the large measured radii of
HD209458b and Boo b in that context. We find that HD209458b must be a
hydrogen-rich gas giant. Furthermore, the large radius of close-in gas giant is
not due to the thermal expansion of its atmosphere, but to the high residual
entropy that remains throughout its bulk by dint of its early proximity to a
luminous primary. The large stellar flux does not inflate the planet, but
retards its otherwise inexorable contraction from a more extended configuration
at birth. This implies either that such a planet was formed near its current
orbital distance or that it migrated in from larger distances (0.5 A.U.),
no later than a few times years of birth.Comment: aasms4 LaTeX, 1 figure, accepted to Ap.J. Letter
Spectral theory for a mathematical model of the weak interaction: The decay of the intermediate vector bosons W+/-. I
We consider a Hamiltonian with cutoffs describing the weak decay of spin one
massive bosons into the full family of leptons. The Hamiltonian is a
self-adjoint operator in an appropriate Fock space with a unique ground state.
We prove a Mourre estimate and a limiting absorption principle above the ground
state energy and below the first threshold for a sufficiently small coupling
constant. As a corollary, we prove absence of eigenvalues and absolute
continuity of the energy spectrum in the same spectral interval.Comment: Correction of minor misprint
Coalescence in the 1D Cahn-Hilliard model
We present an approximate analytical solution of the Cahn-Hilliard equation
describing the coalescence during a first order phase transition. We have
identified all the intermediate profiles, stationary solutions of the noiseless
Cahn-Hilliard equation. Using properties of the soliton lattices, periodic
solutions of the Ginzburg-Landau equation, we have construct a family of ansatz
describing continuously the processus of destabilization and period doubling
predicted in Langer's self similar scenario
Twisting algebras using non-commutative torsors
Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can
be used to twist comodule algebras. After surveying and extending the
literature on the subject, we prove a theorem that affords a presentation by
generators and relations for the algebras obtained by such twisting. We give a
number of examples, including new constructions of the quantum affine spaces
and the quantum tori.Comment: 27 pages. Masuoka is a new coauthor. Introduction was revised.
Sections 1 and 2 were thoroughly restructured. The presentation theorem in
Section 3 is now put in a more general framework and has a more general
formulation. Section 4 was shortened. All examples (quantum affine spaces and
tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are
left unchange
Modeling Pressure-Ionization of Hydrogen in the Context of Astrophysics
The recent development of techniques for laser-driven shock compression of
hydrogen has opened the door to the experimental determination of its behavior
under conditions characteristic of stellar and planetary interiors. The new
data probe the equation of state (EOS) of dense hydrogen in the complex regime
of pressure ionization. The structure and evolution of dense astrophysical
bodies depend on whether the pressure ionization of hydrogen occurs
continuously or through a ``plasma phase transition'' (PPT) between a molecular
state and a plasma state. For the first time, the new experiments constrain
predictions for the PPT. We show here that the EOS model developed by Saumon
and Chabrier can successfully account for the data, and we propose an
experiment that should provide a definitive test of the predicted PPT of
hydrogen. The usefulness of the chemical picture for computing astrophysical
EOS and in modeling pressure ionization is discussed.Comment: 16 pages + 4 figures, to appear in High Pressure Researc
On the Origin of HD149026b
The high density of the close-in extrasolar planet HD149026b suggests the
presence of a huge core in the planet, which challenges planet formation
theory. We first derive constraints on the amount of heavy elements and
hydrogen/helium present in the planet: We find that preferred values of the
core mass are between 50 and 80 M_E. We then investigate the possibility of
subcritical core accretion as envisioned for Uranus and Neptune and find that
the subcritical accretion scenario is unlikely in the case of HD149026b for at
least two reasons: (i) Subcritical planets are such that the ratio of their
core mass to their total mass is above ~0.7, in contradiction with constraints
for all but the most extreme interior models of HD149026b; (ii) High accretion
rates and large isolation mass required for the formation of a subcritical core
of 30 M_E are possible only at specific orbital distances in a disk with a
surface density of dust equal to at least 10 times that of the minimum mass
solar nebula. This value climbs to 30 when considering a 50 M_E core. These
facts point toward two main routes for the formation of this planet: (i) Gas
accretion that is limited by a slow viscous inflow of gas in an evaporating
disk; (ii) A significant modification of the composition of the planet after as
accretion has stopped. These two routes are not mutually exclusive.
Illustrating the second route, we show that for a wide range of impact
parameters, giant impacts lead to a loss of the gas component of the planet and
thus may lead to planets that are highly enriched in heavy elements. In the
giant impact scenario, we expect an outer giant planet to be present.
Observational studies by imaging, astrometry and long term interferometry of
this system are needed to better narrow down the ensemble of possibilities.Comment: 29 pages, 8 figures, to appear in the 10 October 2006 issue of Ap
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