Additive Entropies of degree-q and the Tsallis Entropy

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are derived. Notions of additivity, extensivity and homogeneity are clarified. The relation between mean code lengths in coding theory and various expressions for average entropies is discussed.Comment: 13 page

SINFONI's take on Star Formation, Molecular Gas, and Black Hole Masses in AGN

We present some preliminary (half-way) results on our adaptive optics spectroscopic survey of AGN at spatial scales down to 0.085arcsec. Most of the data were obtained with SINFONI which provides integral field capability at a spectral resolution of R~4000. The themes on which we focus in this contribution are: star formation around the AGN, the properties of the molecular gas and its relation to the torus, and the mass of the black hole.Comment: 5 pages, 2 figures. To appear in Science Perspectives for 3D Spectroscopy. ESO Astrophysics Symposia. Ed by M. Kissler-Patig, M. Roth and J. Wals

The destruction of inner planetary systems during high-eccentricity migration of gas giants

Hot Jupiters are giant planets on orbits a few hundredths of an AU. They do not share their system with low-mass close-in planets, despite these latter being exceedingly common. Two migration channels for hot Jupiters have been proposed: through a protoplanetary gas disc or by tidal circularisation of highly-eccentric planets. We show that highly-eccentric giant planets that will become hot Jupiters clear out any low-mass inner planets in the system, explaining the observed lack of such companions to hot Jupiters. A less common outcome of the interaction is that the giant planet is ejected by the inner planets. Furthermore, the interaction can implant giant planets on moderately-high eccentricities at semimajor axes $<1$ AU, a region otherwise hard to populate. Our work supports the hypothesis that most hot Jupiters reached their current orbits following a phase of high eccentricity, possibly excited by other planetary or stellar companions.Comment: Replaced with accepted versio

The effects of external planets on inner systems: multiplicities, inclinations, and pathways to eccentric warm Jupiters

We study how close-in systems such as those detected by Kepler are affected by the dynamics of bodies in the outer system. We consider two scenarios: outer systems of giant planets potentially unstable to planet--planet scattering, and wide binaries that may be capable of driving Kozai or other secular variations of outer planets' eccentricities. Dynamical excitation of planets in the outer system reduces the multiplicity of Kepler-detectable planets in the inner system in $\sim20-25\%$ of our systems. Accounting for the occurrence rates of wide-orbit planets and binary stars, $\approx18\%$ of close-in systems could be destabilised by their outer companions in this way. This provides some contribution to the apparent excess of systems with a single transiting planet compared to multiple, however, it only contributes at most $25\%$ of the excess. The effects of the outer dynamics can generate systems similar to Kepler-56 (two coplanar planets significantly misaligned with the host star) and Kepler-108 (two significantly non-coplanar planets in a binary). We also identify three pathways to the formation of eccentric warm Jupiters resulting from the interaction between outer and inner systems: direct inelastic collision between an eccentric outer and an inner planet, secular eccentricity oscillations that may "freeze out" when scattering resolves in the outer system; and scattering in the inner system followed by "uplift", where inner planets are removed by interaction with the outer planets. In these scenarios, the formation of eccentric warm Jupiters is a signature of a past history of violent dynamics among massive planets beyond $\sim1$ au.Comment: 24 pages, 19 figures. Accepted to MNRA

Monte Carlo Predictions of Far-Infrared Emission from Spiral Galaxies

We present simulations of Far Infrared (FIR) emission by dust in spiral galaxies, based on the Monte Carlo radiative transfer code of Bianchi, Ferrara & Giovanardi (1996). The radiative transfer is carried out at several wavelength in the Ultraviolet, optical and Near Infrared, to cover the range of the stellar Spectral Energy Distribution (SED). Together with the images of the galactic model, a map of the energy absorbed by dust is produced. Using Galactic dust properties, the spatial distribution of dust temperature is derived under the assumption of thermal equilibrium. A correction is applied for non-equilibrium emission in the Mid Infrared. Images of dust emission can then be produced at any wavelength in the FIR. We show the application of the model to the spiral galaxy NGC 6946. The observed stellar SED is used as input and models are produced for different star-dust geometries. It is found that only optically thick dust disks can reproduce the observed amount of FIR radiation. However, it is not possible to reproduce the large FIR scalelength suggested by recent observation of spirals at 200 um, even when the scalelength of the dust disk is larger than that for stars. Optically thin models have ratios of optical/FIR scalelengths closer to the 200um observations, but with smaller absolute scalelengths than optically thick cases. The modelled temperature distributions are compatible with observations of the Galaxy and other spirals. We finally discuss the approximations of the model and the impact of a clumpy stellar and dust structure on the FIR simulations.Comment: 19 pages, 6 figures, accepted by A&