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

Coronal structure of the cTTS V2129 Oph

The nature of the magnetic coupling between T Tauri stars and their disks determines not only the mass accretion process but possibly the spin evolution of the central star. We have taken a recently-published surface magnetogram of one moderately-accreting T Tauri star (V2129 Oph) and used it to extrapolate the geometry of its large-scale field. We determine the structure of the open (wind-bearing) field lines, the closed (X-ray bright) field lines and those potentially accreting field lines that pass through the equatorial plane inside the Keplerian co-rotation radius. We consider a series of models in which the stellar magnetic field is opened up by the outward pressure of the hot coronal gas at a range of radii. As this radius is increased, accretion takes place along simpler field structures and impacts on fewer sites at the stellar surface. This is consistent with the observed variation in the Ca II IRT and HeI lines which suggests that accretion in the visible hemisphere is confined to a single high-latitude spot. By determining the density and velocity of the accretion flows, we find that in order to have most of the total mass accretion rate impacting on a single high-latitude region we need disk material to accrete from approximately 7R*, close to the Keplerian co-rotation radius at 6.8R*. We also calculate the coronal density and X-ray emission measure. We find that both the magnitude and rotational modulation of the emission measure increase as the source surface is increased. For the field structure of V2129 Oph which is dominantly octupolar, the emission forms a bright, high-latitude ring that is always in view as the star rotates. Since the accretion funnels are not dense enough to cause significant scattering of coronal X-ray photons, they provide only a low rotational modulation of around 10% at most.Comment: 10 pages, 9 figure

Revealing the fastest component of the DG Tau outflow through X-rays

Some T Tauri stars show a peculiar X-ray spectrum that can be modelled by two components with different absorbing column densities. We seek to explain the soft X-ray component in DG Tau, the best studied of these sources, with an outflow model, taking observations at other wavelengths into consideration. We constrain the outflow properties through spectral fitting and employ simple semi-analytical formulae to describe properties of a shock wave that heats up the X-ray emitting region. The X-ray emission is consistent with its arising from the fastest and innermost component of the optically detected outflow. Only a small fraction of the total mass loss is required for this X-ray emitting component. Our favoured model requires shock velocities between 400 and 500 km/s. For a density >10^5 /cm^3 all dimensions of the shock cooling zone are only a few AU, so even in optical observations this cannot be resolved. This X-ray emission mechanism in outflows may also operate in other, less absorbed T Tauri stars, in addition to corona and accretion spots.Comment: 7, pages, 4 figures, accepted by A&

Theory of Combined Photoassociation and Feshbach Resonances in a Bose-Einstein Condensate

We model combined photoassociation and Feshbach resonances in a Bose-Einstein condensate, where the shared dissociation continuum allows for quantum interference in losses from the condensate, as well as a dispersive-like shift of resonance. A simple analytical model, based on the limit of weakly bound molecules, agrees well with numerical experiments that explicitly include dissociation to noncondensate modes. For a resonant laser and an off-resonant magnetic field, constructive interference enables saturation of the photoassociation rate at user-friendly intensities, at a value set by the interparticle distance. This rate limit is larger for smaller condensate densities and, near the Feshbach resonance, approaches the rate limit for magnetoassociation alone. Also, we find agreement with the unitary limit--set by the condensate size--only for a limited range of near-resonant magnetic fields. Finally, for a resonant magnetic field and an off-resonant laser, magnetoassociation displays similar quantum interference and a dispersive-like shift. Unlike photoassociation, interference and the fieldshift in resonant magnetoassociation is tunable with both laser intensity and detuning. Also, the dispersive-like shift of the Feshbach resonance depends on the size of the Feshbach molecule, and is a signature of non-universal physics in a strongly interacting system.Comment: 10 pages, 5 figures, 82 reference

Cosmography: Cosmology without the Einstein equations

How much of modern cosmology is really cosmography? How much of modern cosmology is independent of the Einstein equations? (Independent of the Friedmann equations?) These questions are becoming increasingly germane -- as the models cosmologists use for the stress-energy content of the universe become increasingly baroque, it behoves us to step back a little and carefully disentangle cosmological kinematics from cosmological dynamics. The use of basic symmetry principles (such as the cosmological principle) permits us to do a considerable amount, without ever having to address the vexatious issues of just how much "dark energy", "dark matter", "quintessence", and/or "phantom matter" is needed in order to satisfy the Einstein equations. This is the sub-sector of cosmology that Weinberg refers to as "cosmography", and in this article I will explore the extent to which cosmography is sufficient for analyzing the Hubble law and so describing many of the features of the universe around us.Comment: 7 pages; uses iopart.cls setstack.sty. Based on a talk presented at ACRGR4, the 4th Australasian Conference on General Relativity and Gravitation, Monash University, Melbourne, January 2004. To appear in the proceedings, in General Relativity and Gravitatio

X-ray reprocessing in Seyfert Galaxies: simultaneous XMM-Newton/BeppoSAX observations

We selected a sample of eight bright unobscured (at least at the iron line energy) Seyfert Galaxies observed simultaneously by XMM-Newton and BeppoSAX, taking advantage of the complementary characteristics of the two missions. The main results of our analysis can be summarized as follows: narrow neutral iron lines are confirmed to be an ubiquitous component in Seyfert spectra; none of the analyzed sources shows unambiguously a broad relativistic iron line; all the sources of our sample (with a single exception) show the presence of a Compton reflection component; emission lines from ionized iron are observed in some sources; peculiar weak features around 5-6 keV (possibly arising from rotating spots on the accretion disk) are detected in two sources. The scenario emerging from these results strongly requires some corrections for the classical model of reprocessing from the accretion disk. As for materials farther away from the Black Hole, our results represent a positive test for the Unification Model, suggesting the presence of the torus in (almost) all sources, even if unobscured.Comment: Accepted for publication in A&

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