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

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

The Suzaku X-ray spectrum of NGC 3147. Further insights on the best "true" Seyfert 2 galaxy candidate

NGC 3147 is so far the most convincing case of a "true" Seyfert 2 galaxy, i.e. a source genuinely lacking the Broad Line Regions. We obtained a Suzaku observation with the double aim to study in more detail the iron line complex, and to check the Compton-thick hypothesis for the lack of observed optical broad lines. The Suzaku XIS and HXD/PIN spectra of the source were analysed in detail. The line complex is composed of at least two unresolved lines, one at about 6.45 keV and the other one at about 7 keV, most likely identified with Fe XVII/XIX, the former, and Fe XXVI, the latter. The high-ionization line can originate either in a photoionized matter or in an optically thin thermal plasma. In the latter case, an unusually high temperature is implied. In the photoionized model case, the large equivalent width can be explained either by an extreme iron overabundance or by assuming that the source is Compton-thick. In the Compton-thick hypothesis, however, the emission above 2 keV is mostly due to a highly ionized reflector, contrary to what is usually found in Compton-thick Seyfert 2s, where reflection from low ionized matter dominates. Moreover, the source flux varied between the XMM-Newton and the Suzaku observations, taken 3.5 years apart, confirming previous findings and indicating that the size of the emitting region must be smaller than a parsec. The hard X-ray spectrum is also inconclusive on the Compton-thick hypothesis. Weighting the various arguments, a "true" Seyfert 2 nature of NGC 3147 seems to be still the most likely explanation, even if the "highly ionized reflector" Compton-thick hypothesis cannot at present be formally rejected.Comment: 6 pages, accepted for publication in Astronomy & Astrophysic