Energy shedding during nonlinear self-focusing of optical beams

Self-focusing of intense laser beams and pulses of light in real nonlinear media is in general accompanied by material losses that require corrections to the conservative Nonlinear Schrödinger equations describing their propagation. Here we examine loss mechanisms that exist even in lossless media and are caused by shedding of energy away from the self-trapping beam making it to relax to an exact solution of lower energy. Using the conservative NLS equations with absorbing boundary conditions we show that energy shedding not only occurs during the initial reshaping process but also during oscillatory propagation induced by saturation of the nonlinear effect. For pulsed input we also show that, depending on the sign and magnitude of dispersion, pulse splitting, energy shedding, collapse or stable self-focusing may result

Atmospheric Escape from Hot Jupiters

The extra-solar planet HD209458b has been found to have an extended atmosphere of escaping atomic hydrogen (Vidal-Madjar et al. 2003), suggesting that ``hot Jupiters'' closer to their parent stars could evaporate. Here we estimate the atmospheric escape (so called evaporation rate) from hot Jupiters and their corresponding life time against evaporation. The calculated evaporation rate of HD209458b is in excellent agreement with the HI Lyman-alpha observations. We find that the tidal forces and high temperatures in the upper atmosphere must be taken into account to obtain reliable estimate of the atmospheric escape. Because of the tidal forces, we show that there is a new escape mechanism at intermediate temperatures at which the exobase reaches the Roche lobe. From an energy balance, we can estimate plausible values for the planetary exospheric temperatures, and thus obtain typical life times of planets as a function of their mass and orbital distance.Comment: A&A Letters, in pres

Reversible skew laurent polynomial rings and deformations of poisson automorphisms

A skew Laurent polynomial ring S = R[x(+/- 1); alpha] is reversible if it has a reversing automorphism, that is, an automorphism theta of period 2 that transposes x and x(-1) and restricts to an automorphism gamma of R with gamma = gamma(-1). We study invariants for reversing automorphisms and apply our methods to determine the rings of invariants of reversing automorphisms of the two most familiar examples of simple skew Laurent polynomial rings, namely a localization of the enveloping algebra of the two-dimensional non-abelian solvable Lie algebra and the coordinate ring of the quantum torus, both of which are deformations of Poisson algebras over the base field F. Their reversing automorphisms are deformations of Poisson automorphisms of those Poisson algebras. In each case, the ring of invariants of the Poisson automorphism is the coordinate ring B of a surface in F-3 and the ring of invariants S-theta of the reversing automorphism is a deformation of B and is a factor of a deformation of F[x(1), x(2), x(3)] for a Poisson bracket determined by the appropriate surface

Bayesian multiscale deconvolution applied to gamma-ray spectroscopy

A common task in gamma-ray astronomy is to extract spectral information, such as model constraints and incident photon spectrum estimates, given the measured energy deposited in a detector and the detector response. This is the classic problem of spectral “deconvolution” or spectral inversion. The methods of forward folding (i.e., parameter fitting) and maximum entropy “deconvolution” (i.e., estimating independent input photon rates for each individual energy bin) have been used successfully for gamma-ray solar flares (e.g., Rank, 1997; Share and Murphy, 1995). These methods have worked well under certain conditions but there are situations were they don’t apply. These are: 1) when no reasonable model (e.g., fewer parameters than data bins) is yet known, for forward folding; 2) when one expects a mixture of broad and narrow features (e.g., solar flares), for the maximum entropy method; and 3) low count rates and low signal-to-noise, for both. Low count rates are a problem because these methods (as they have been implemented) assume Gaussian statistics but Poisson are applicable. Background subtraction techniques often lead to negative count rates. For Poisson data the Maximum Likelihood Estimator (MLE) with a Poisson likelihood is appropriate. Without a regularization term, trying to estimate the “true” individual input photon rates per bin can be an ill-posed problem, even without including both broad and narrow features in the spectrum (i.e., amultiscale approach). One way to implement this regularization is through the use of a suitable Bayesian prior. Nowak and Kolaczyk (1999) have developed a fast, robust, technique using a Bayesian multiscale framework that addresses these problems with added algorithmic advantages. We outline this new approach and demonstrate its use with time resolved solar flare gamma-ray spectroscopy

Detection of oxygen and carbon in the hydrodynamically escaping atmosphere of the extrasolar planet HD209458b

Four transits of the planet orbiting the star HD209458 were observed with the STIS spectrograph on board HST. The wavelength domain (1180-1710A) includes HI as well as CI, CII, CIV, NV, OI, SI, SiII, SiIII and SiIV lines. During the transits, absorptions are detected in HI, OI and CII (5+/-2%, 13+/-4.5% and 7.5+/-3.5%, respectively). No absorptions are detected for other lines. The 5% mean absorption over the whole HI Lyman alpha line is consistent with the previous detection at higher resolution (Vidal-Madjar et al. 2003). The absorption depths in OI and CII show that oxygen and carbon are present in the extended upper atmosphere of HD209458b. These species must be carried out up to the Roche lobe and beyond, most likely in a state of hydrodynamic escape.Comment: 6 pages, 4 figures, 1 table, submitted to ApJ Letters, revised version with slightly revisited absorption depth estimate

Energetic proton spectra in the 11 June 1991 solar flare

The June 11, 1991 gamma-ray flare seen by the Compton Gamma-ray Observatory (CGRO) displays several features that make it a dynamic and rich event. It is a member of a class of long duration gamma-ray events with both 2.223 MeV and greater than 8 MeV emission for hours after the impulsive phase. It also contains an inter-phase between the impulsive and extended phases that presents a challenge to the standard gamma-ray line (GRL) flare picture. This phase has strong 2.223 MeV emission and relatively weak 4.44 MeV emission indicative of a very hard parent proton spectrum. However, this would indicate emission greater than 8 MeV, which is absent from this period. We present the application of new spectroscopy techniques to this phase of the flare in order to present a reasonable explanation for this seemly inconsistent picture