The dressed nonrelativistic electron in a magnetic field

We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the $x_{3}$-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 $x_{3}$-axis, we consider the reduced Hamiltonian associated with the total momentum along the $x_{3}$-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 $x_{3}$-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, $\tau$ 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 $\tau$ 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 ($\geq$0.5 A.U.), no later than a few times $10^7$ years of birth.Comment: aasms4 LaTeX, 1 figure, accepted to Ap.J. Letter

Toward a homogeneous set of transiting planet parameters

With 40 or more transiting exoplanets now known, the time is ripe to seek patterns and correlations among their observed properties, which may give important insights into planet formation, structure, and evolution. This task is made difficult by the widely different methodologies that have been applied to measure their properties in individual cases. Furthermore, in many systems our knowledge of the planet properties is limited by the knowledge of the properties of the parent stars. To address these difficulties we have undertaken the first comprehensive analysis of the data for 23 transiting planets using a uniform methodology. We revisit several of the recently proposed correlations, and find new ones involving the metallicity of the parent stars.Comment: 4 pages including figures. To appear in Proceedings of IAU Symposium 253, "Transiting Planets", May 2008, Cambridge, M

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)