The Most Luminous Galaxies

Ultraluminous galaxies in the local universe (z$\leq$0.2) emit the bulk of their energy in the mid and far-infrared. The multiwavelength approach to these objects has shown that they are advanced mergers of gas-rich spiral galaxies. Galaxy-galaxy collisions took place on all cosmological time-scales, and nearby mergers serve as local analogs to gain insight into the physical processes that lead to the formation and trans-formation of galaxies in the more distant universe. Here I review multiwavelength observations --with particular emphasis on recent results obtained with ISO-- of mergers of massive galaxies driving the formation of: 1) luminous infrared galaxies, 2) elliptical galaxy cores, 3) luminous dust-enshrouded extranuclear starbursts, 4) symbiotic galaxies that host AGNs, and 5) tidal dwarf galaxies. The most important implication for studies on the formation of galaxies at early cosmological timescales is that the distant analogs to the local ultraluminous infrared galaxies are invisible in the ultraviolet and optical wavelength rest-frames and should be detected as sub-millimeter sources with no optical counterparts.Comment: 12 pages, 6 figures. Invited Review at the Conference Lighthouses of the universe. August 6-10, 2001 (Garching, Germany

Intrinsic rotation in tokamaks: theory

Self-consistent equations for intrinsic rotation in tokamaks with small poloidal magnetic field $B_p$ compared to the total magnetic field $B$ are derived. The model gives the momentum redistribution due to turbulence, collisional transport and energy injection. Intrinsic rotation is determined by the balance between the momentum redistribution and the turbulent diffusion and convection. Two different turbulence regimes are considered: turbulence with characteristic perpendicular lengths of the order of the ion gyroradius, $\rho_i$, and turbulence with characteristic lengths of the order of the poloidal gyroradius, $(B/B_p) \rho_i$. Intrinsic rotation driven by gyroradius scale turbulence is mainly due to the effect of neoclassical corrections and of finite orbit widths on turbulent momentum transport, whereas for the intrinsic rotation driven by poloidal gyroradius scale turbulence, the slow variation of turbulence characteristics in the radial and poloidal directions and the turbulent particle acceleration can be become as important as the neoclassical and finite orbit width effects. The magnetic drift is shown to be indispensable for the intrinsic rotation driven by the slow variation of turbulence characteristics and the turbulent particle acceleration. The equations are written in a form conducive to implementation in a flux tube code, and the effect of the radial variation of the turbulence is included in a novel way that does not require a global gyrokinetic formalism.Comment: 88 pages, 4 figure

Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry

Gyrokinetic theory is based on an asymptotic expansion in the small parameter $\epsilon$, defined as the ratio of the gyroradius and the characteristic length of variation of the magnetic field. In this article, this ordering is strictly implemented to compute the electrostatic gyrokinetic phase-space Lagrangian in general magnetic geometry to order $\epsilon^2$. In particular, a new expression for the complete second-order gyrokinetic Hamiltonian is provided, showing that in a rigorous treatment of gyrokinetic theory magnetic geometry and turbulence cannot be dealt with independently. The new phase-space gyrokinetic Lagrangian gives a Vlasov equation accurate to order $\epsilon^2$ and a Poisson equation accurate to order $\epsilon$. The final expressions are explicit and can be implemented into any simulation without further computations.Comment: 55 pages. Version with typo in equation (135) corrected. The second term in the second line of (135) was missing the subindex that indicates that only the perpendicular component of the gradient enters this ter

Radial penetration of flux surface shaping in tokamaks

Using analytic calculations, the effects of the edge flux surface shape and the toroidal current profile on the penetration of flux surface shaping are investigated in a tokamak. It is shown that the penetration of shaping is determined by the poloidal variation of the poloidal magnetic field on the surface. This fact is used to investigate how different flux surface shapes penetrate from the edge. Then, a technique to separate the effects of magnetic pressure and tension in the Grad-Shafranov equation is presented and used to calculate radial profiles of strong elongation for nearly constant current profiles. Lastly, it is shown that more hollow toroidal current profiles are significantly better at conveying shaping from the edge to the core.Comment: 11 pages, 13 figure

The origin of Scorpius X-1

We have used multi-wavelength observations of high precision to derive the space velocity and compute the orbit around the Galactic Centre of the prototype X-ray binary Scorpius X-1. An origin in the local spiral arm of the Milky Way is ruled out. The galactocentric kinematics of Scorpius X-1 is similar to that of the most ancient stars and globular clusters of the inner Galactic halo. Most probably, this low-mass X-ray binary was formed by a close encounter in a globular cluster. However, it cannot be ruled out that a natal supernova explosion launched Scorpius X-1 into an orbit like this from a birth place in the galactic bulge. In any case, the Galactocentric orbit indicates that Scorpius X-1 was formed more than 30 Myrs ago.Comment: 4 pages, 1 figure. Animation and high resolution figures can be retrived from the NRAO press release: http://www.aoc.nrao.edu/epo/pr/2003/scox1

Turbulent momentum pinch of diamagnetic flows in a tokamak

The ion toroidal rotation in a tokamak consists of an $E\times B$ flow due to the radial electric field and a diamagnetic flow due to the radial pressure gradient. The turbulent pinch of toroidal angular momentum due to the Coriolis force studied in previous work is only applicable to the $E\times B$ flow. In this Letter, the momentum pinch for the rotation generated by the radial pressure gradient is calculated and is compared with the Coriolis pinch. This distinction is important for subsonic flows or the flow in the pedestal where the two types of flows are similar in size and opposite in direction. In the edge, the different pinches due to the opposite rotations can result in intrinsic momentum transport that gives significant rotation peaking.Comment: 5 pages and 3 figure

Topological superconducting phase in helical Shiba chains

Recently, it has been suggested that topological superconductivity and Majorana end states can be realized in a chain of magnetic impurities on the surface of an s-wave superconductor when the magnetic moments form a spin helix as a result of the RKKY interaction mediated by the superconducting substrate. Here, we investigate this scenario theoretically by developing a tight-binding Bogoliubov-de Gennes description starting from the Shiba bound states induced by the individual magnetic impurities. While the resulting model Hamiltonian has similarities with the Kitaev model for one-dimensional spinless p-wave superconductors, there are also important differences, most notably the long-range nature of hopping and pairing as well as the complex hopping amplitudes. We use both analytical and numerical approaches to explore the consequences of these differences for the phase diagram and the localization properties of the Majorana end states when the Shiba chain is in a topological superconducting phase.Comment: 14 pages, 9 figures, minor changes, references added; published versio