Properties of the Lindemann Mechanism in Phase Space

We study the planar and scalar reductions of the nonlinear Lindemann mechanism of unimolecular decay. First, we establish that the origin, a degenerate critical point, is globally asymptotically stable. Second, we prove there is a unique scalar solution (the slow manifold) between the horizontal and vertical isoclines. Third, we determine the concavity of all scalar solutions in the nonnegative quadrant. Fourth, we establish that each scalar solution is a centre manifold at the origin given by a Taylor series. Moreover, we develop the leading-order behaviour of all planar solutions as time tends to infinity. Finally, we determine the asymptotic behaviour of the slow manifold at infinity by showing that it is a unique centre manifold for a fixed point at infinity.Comment: 27 pages, 6 figure

The reprocessing features in the X-ray spectrum of the NELG MCG-5-23-16

We present results from the spectral analysis of the Seyfert 1.9 galaxy MCG-5-23-16, based on ASCA, BeppoSAX, Chandra and XMM-Newton observations. The spectrum of this object shows a complex iron Kalpha emission line, which is best modeled by a superposition of a narrow and a broad (possibly relativistic) iron line, together with a Compton reflection component. Comparing results from all (six) available observations, we do not find any significant variation in the flux of both line components. The moderate flux continuum variability (about 25% difference between the brightest and faintest states), however, does not permit us to infer much about the location of the line-emitting material. The amount of Compton reflection is lower than expected from the total iron line EW, implying either an iron overabundance or that one of the two line components (most likely the narrow one) originates in Compton-thin matter.Comment: Accepted for publication in A&

Analysis of Superoscillatory Wave Functions

Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory functions was presented and it was shown that superoscillatory quantum mechanical wave functions should exhibit a number of counter-intuitive physical effects. Following up on this work, we here present more general methods which allow the calculation of superoscillatory wave functions with custom-designed physical properties. We give concrete examples and we prove results about the limits to superoscillatory behavior. We also give a simple and intuitive new explanation for the exponential computational cost of superoscillations.Comment: 20 pages, several figure

Many-Body Rate Limit on Photoassociation of a Bose-Einstein Condensate

We briefly report on zero-temperature photoassociation of a Bose-Einstein condensate, focusing on the many-body rate limit for atom-molecule conversion. An upgraded model that explicitly includes spontaneous radiative decay leads to an unanticipated shift in the position of the photoassociation resonance, which affects whether the rate (constant) maximizes or saturates, as well as the limiting value itself. A simple analytical model agrees with numerical experiments, but only for high density. Finally, an explicit comparison with the two-body unitary limit, set by the size of the condensate, finds that the many-body rate limit is generally more strict.Comment: 4 pages, 3 figures, 59 references. v2: discussion added; to appear in PR

Magnetic games between a planet and its host star: the key role of topology

Magnetic interactions between a star and a close-in planet are postulated to be a source of enhanced emissions and to play a role in the secular evolution of the orbital system. Close-in planets generally orbit in the sub-alfv\'enic region of the stellar wind, which leads to efficient transfers of energy and angular momentum between the star and the planet. We model the magnetic interactions occurring in close-in star-planet systems with three-dimensional, global, compressible magneto-hydrodynamic numerical simulations of a planet orbiting in a self-consistent stellar wind. We focus on the cases of magnetized planets and explore three representative magnetic configurations. The Poynting flux originating from the magnetic interactions is an energy source for enhanced emissions in star-planet systems. Our results suggest a simple geometrical explanation for ubiquitous on/off enhanced emissions associated with close-in planets, and confirm that the Poynting fluxes can reach powers of the order of $10^{19}$ W. Close-in planets are also showed to migrate due to magnetic torques for sufficiently strong stellar wind magnetic fields. The topology of the interaction significantly modifies the shape of the magnetic obstacle that leads to magnetic torques. As a consequence, the torques can vary by at least an order of magnitude as the magnetic topology of the interaction varies.Comment: 15 pages, 6 figures, accepted for publication in The Astrophysical Journa