3,483 research outputs found
The dressed nonrelativistic electron in a magnetic field
We consider a nonrelativistic electron interacting with a classical magnetic
field pointing along the -axis and with a quantized electromagnetic
field. When the interaction between the electron and photons is turned off, the
electronic system is assumed to have a ground state of finite multiplicity.
Because of the translation invariance along the -axis, we consider the
reduced Hamiltonian associated with the total momentum along the -axis
and, after introducing an ultraviolet cutoff and an infrared regularization, we
prove that the reduced Hamiltonian has a ground state if the coupling constant
and the total momentum along the -axis are sufficiently small. Finally
we determine the absolutely continuous spectrum of the reduced Hamiltonian.Comment: typos correction
A non-grey analytical model for irradiated atmospheres. II: Analytical vs. numerical solutions
The recent discovery and characterization of the diversity of the atmospheres
of exoplanets and brown dwarfs calls for the development of fast and accurate
analytical models. We quantify the accuracy of the analytical solution derived
in paper I for an irradiated, non-grey atmosphere by comparing it to a
state-of-the-art radiative transfer model. Then, using a grid of numerical
models, we calibrate the different coefficients of our analytical model for
irradiated solar-composition atmospheres of giant exoplanets and brown dwarfs.
We show that the so-called Eddington approximation used to solve the angular
dependency of the radiation field leads to relative errors of up to 5% on the
temperature profile. We show that for realistic non-grey planetary atmospheres,
the presence of a convective zone that extends to optical depths smaller than
unity can lead to changes in the radiative temperature profile on the order of
20% or more. When the convective zone is located at deeper levels (such as for
strongly irradiated hot Jupiters), its effect on the radiative atmosphere is
smaller. We show that the temperature inversion induced by a strong absorber in
the optical, such as TiO or VO is mainly due to non-grey thermal effects
reducing the ability of the upper atmosphere to cool down rather than an
enhanced absorption of the stellar light as previously thought.
Finally, we provide a functional form for the coefficients of our analytical
model for solar-composition giant exoplanets and brown dwarfs. This leads to
fully analytical pressure-temperature profiles for irradiated atmospheres with
a relative accuracy better than 10% for gravities between 2.5m/s^2 and 250
m/s^2 and effective temperatures between 100 K and 3000 K. This is a great
improvement over the commonly used Eddington boundary condition.Comment: Accepted in A&A, models are available at
http://www.oca.eu/parmentier/nongrey or in CD
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
Inverse scattering at fixed energy for layered media
AbstractIn this article we show that exponentially decreasing perturbations of the sound speed in a layered medium can be recovered from the scattering amplitude at fixed energy. We consider the unperturbed equation utt = c02(xn)δu in ℝ×ℝ, where n ≥ 3. The unperturbed sound speed, c0(xn), is assumed to be bounded, strictly positive, and constant outside a bounded interval on the real axis. The perturbed sound speed, c(x), satisfies ¦c.(x) - co(xn)¦ < C exp(−δ¦x¦) for some δ > 0. Our work is related to the recent results of H. Isozaki (J. Diff. Eq. 138) on the case where c0 takes the constant values c+ and c− on the positive and negative half-lines, and R. Weder on the case c0 = c+ for xn > h, c0 = ch, for 0 < xn, < h, and c0 = c− for xn < 0 (IIMAS-UNAM Preprint 70, November, 1997)
Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks
Planetesimals in gaseous protoplanetary disks may grow by collecting dust
particles. Hydrodynamical studies show that small particles generally avoid
collisions with the planetesimals because they are entrained by the flow around
them. This occurs when , the Stokes number, defined as the ratio of the
dust stopping time to the planetesimal crossing time, becomes much smaller than
unity. However, these studies have been limited to the laminar case, whereas
these disks are believed to be turbulent. We want to estimate the influence of
gas turbulence on the dust-planetesimal collision rate and on the impact
speeds. We used three-dimensional direct numerical simulations of a fixed
sphere (planetesimal) facing a laminar and turbulent flow seeded with small
inertial particles (dust) subject to a Stokes drag. A no-slip boundary
condition on the planetesimal surface is modeled via a penalty method. We find
that turbulence can significantly increase the collision rate of dust particles
with planetesimals. For a high turbulence case (when the amplitude of turbulent
fluctuations is similar to the headwind velocity), we find that the collision
probability remains equal to the geometrical rate or even higher for , i.e., for dust sizes an order of magnitude smaller than in the laminar
case. We derive expressions to calculate impact probabilities as a function of
dust and planetesimal size and turbulent intensity
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