Applications of the Gauss-Bonnet theorem to gravitational lensing

In this geometrical approach to gravitational lensing theory, we apply the Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit. We find that the focusing of the light rays emerges here as a topological effect, and we introduce a new method to calculate the deflection angle from the Gaussian curvature of the optical metric. As examples, the Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are discussed within this framework.Comment: 10 pages, 1 figure, IoP styl

Electron-phonon interaction at the Be(0001) surface

We present a first principle study of the electron-phonon (e-p) interaction at the Be(0001) surface. The real and imaginary part of the e-p self energy are calculated for the surface state in the binding energy range from the $\bar{\Gamma}$ point to the Fermi level. Our calculation shows an overall good agreement with several photoemission data measured at high and low temperatures. Additionally, we show that the energy derivative of real part of the self-energy presents a strong temperature and energy variation close to $E_{F}$, making it difficult to measure its value just at $E_{F}$.Comment: Accepted in Phys. Rev. Lett., 5 figure

Roche Lobe Overflow from Dwarf Stellar Systems

We use both analytical analyses and numerical simulations to examine the evolution of residual gas within tidally-limited dwarf galaxies and globular clusters. If the gas sound speed exceeds about 10% of the central velocity dispersion, as is the case for ionized gas within small stellar systems, the gas shall have significant density at the tidal radius, and the gas may be lost on timescales as short as a few times the sound crossing time of the system. In colder systems, the density at the tidal radius is much lower, greatly reducing the mass loss rate, and the system may retain its gas for a Hubble time. The tidally removed gas shall follow an orbit close to that of the original host system, forming an extended stream of ionized, gaseous debris. Tidal mass loss severely limits the ability of dwarf systems to continuously form stars. The ordinary gas content in many dwarf galaxies is fully ionized during high red-shift epochs, possibly preventing star formation in some systems, leading to the formation of starless, dark-matter concentrations. In either the field or in the center of galaxy clusters, ionized gas may be retained by dwarf galaxies, even though its sound speed may be comparable to or even exceed the velocity dispersion. These processes may help to explain some observed differences among dwarf galaxy types, as well as observations of the haloes of massive galaxies.Comment: 28 pages, LaTeX, AASTex macro

Modelling the dynamical evolution of the Bootes dwarf spheroidal galaxy

We investigate a wide range of possible evolutionary histories for the recently discovered Bootes dwarf spheroidal galaxy, a Milky Way satellite. By means of N-body simulations we follow the evolution of possible progenitor galaxies of Bootes for a variety of orbits in the gravitational potential of the Milky Way. The progenitors considered cover the range from dark-matter-free star clusters to massive, dark-matter dominated outcomes of cosmological simulations. For each type of progenitor and orbit we compare the observable properties of the remnant after 10 Gyr with those of Bootes observed today. Our study suggests that the progenitor of Bootes must have been, and remains now, dark matter dominated. In general our models are unable to reproduce the observed high velocity dispersion in Bootes without dark matter. Our models do not support time-dependent tidal effects as a mechanism able to inflate significantly the internal velocity dispersion. As none of our initially spherical models is able to reproduce the elongation of Bootes, our results suggest that the progenitor of Bootes may have had some intrinsic flattening. Although the focus of the present paper is the Bootes dwarf spheroidal, these models may be of general relevance to understanding the structure, stability and dark matter content of all dwarf spheroidal galaxies.Comment: 10 pages, 7 figures, accepted by MNRA

Decoupled and inhomogeneous gas flows in S0 galaxies

A recent analysis of the "Einstein" sample of early-type galaxies has revealed that at any fixed optical luminosity Lb S0 galaxies have lower mean X-ray luminosity Lx per unit Lb than ellipticals. Following a previous analytical investigation of this problem (Ciotti & Pellegrini 1996), we have performed 2D numerical simulations of the gas flows inside S0 galaxies in order to ascertain the effectiveness of rotation and/or galaxy flattening in reducing the Lx/Lb ratio. The flow in models without SNIa heating is considerably ordered, and essentially all the gas lost by the stars is cooled and accumulated in the galaxy center. If rotation is present, the cold material settles in a disk on the galactic equatorial plane. Models with a time decreasing SNIa heating host gas flows that can be much more complex. After an initial wind phase, gas flows in energetically strongly bound galaxies tend to reverse to inflows. This occurs in the polar regions, while the disk is still in the outflow phase. In this phase of strong decoupling, cold filaments are created at the interface between inflowing and outflowing gas. Models with more realistic values of the dynamical quantities are preferentially found in the wind phase with respect to their spherical counterparts of equal Lb. The resulting Lx of this class of models is lower than in spherical models with the same Lb and SNIa heating. At variance with cooling flow models, rotation is shown to have only a marginal effect in this reduction, while the flattening is one of the driving parameters for such underluminosity, in accordance with the analytical investigation.Comment: 32 pages LaTex file, plus 5 .ps figures and macro aasms4.sty -- Accepted on Ap

Contributions to twentieth century total column ozone change from halocarbons, tropospheric ozone precursors, and climate change

We investigate ozone changes from preindustrial times to the present using a chemistry-climate model. The influence of changes in physical climate, ozone-depleting substances, N2O, and tropospheric ozone precursors is estimated using equilibrium simulations with these different factors set at either preindustrial or present-day values. When these effects are combined, the entire decrease in total column ozone from preindustrial to present day is very small (–1.8 DU) in the global annual average, though with significant decreases in total column ozone over large parts of the Southern Hemisphere during austral spring and widespread increases in column ozone over the Northern Hemisphere during boreal summer. A significant contribution to the total ozone column change is the increase in lower stratospheric ozone associated with the increase in ozone precursors (5.9 DU). Also noteworthy is the near cancellation of the global average climate change effect on ozone (3.5 DU) by the increase in N2O (–3.9 DU)

Improved photometry of SDSS crowded field images: Structure and dark matter content in the dwarf spheroidal galaxy Leo I

We explore how well crowded field point-source photometry can be accomplished with SDSS data: We present a photometric pipeline based on DoPhot, and tuned for analyzing crowded-field images from the SDSS. Using Monte Carlo simulations we show that the completeness of source extraction is above 80% to i < 21 (AB) and a stellar surface density of about 200 sq.amin. Hence, a specialized data pipeline can efficiently be used for e.g. nearby resolved galaxies in SDSS images, where the standard SDSS photometric package Photo, when applied in normal survey mode, gives poor results. We apply our pipeline to an area of about 3.55sq.deg. around the dwarf spheroidal galaxy (dSph) Leo I, and construct a high S/N star-count map of Leo I via an optimized filter in color-magnitude space (g,r,i). Although the radial surface-density profile of the dwarf deviates from the best fit empirical King model towards outer radii, we find no evidence for tidal debris out to a stellar surface-density of 4*10^(-3) of the central value. We determine the total luminosity of Leo I, and model its mass using the spherical and isotropic Jeans equation. Assuming that 'mass follows light' we constrain a lower limit of the total mass of the dSph to be (1.7+/-0.2)*10^7 Msol. Contrary, if the mass in Leo I is dominated by a constant density dark-matter (DM) halo, then the mass within the central 12' is (2+/-0.6)*10^8 Msol. This leads to a mass-to-light ratio of >>6 (Ic_sol), and possibly >75 if the DM halo dominates the mass and extends further out than 12'. In summary, our results show that Leo I is a symmetric, relaxed and bound system; this supports the idea that Leo I is a dark-matter dominated system.Comment: 13 pages, 11 figures; accepted for publication in A

Real-time wave excitation forces estimation: An application on the ISWEC device

Optimal control strategies represent a widespread solution to increase the extracted energy of a Wave Energy Converter (WEC). The aim is to bring the WEC into resonance enhancing the produced power without compromising its reliability and durability. Most of the control algorithms proposed in literature require for the knowledge of the Wave Excitation Force (WEF) generated from the incoming wave field. In practice, WEFs are unknown, and an estimate must be used. This paper investigates the WEF estimation of a non-linear WEC. A model-based and a model-free approach are proposed. First, a Kalman Filter (KF) is implemented considering the WEC linear model and the WEF modelled as an unknown state to be estimated. Second, a feedforward Neural Network (NN) is applied to map the WEC dynamics to the WEF by training the network through a supervised learning algorithm. Both methods are tested for a wide range of irregular sea-states showing promising results in terms of estimation accuracy. Sensitivity and robustness analyses are performed to investigate the estimation error in presence of un-modelled phenomena, model errors and measurement noise

Understanding uncertainty in temperature effects on vector-borne disease: A Bayesian approach

Extrinsic environmental factors influence the distribution and population dynamics of many organisms, including insects that are of concern for human health and agriculture. This is particularly true for vector-borne infectious diseases, like malaria, which is a major source of morbidity and mortality in humans. Understanding the mechanistic links between environment and population processes for these diseases is key to predicting the consequences of climate change on transmission and for developing effective interventions. An important measure of the intensity of disease transmission is the reproductive number $R_0$. However, understanding the mechanisms linking $R_0$ and temperature, an environmental factor driving disease risk, can be challenging because the data available for parameterization are often poor. To address this we show how a Bayesian approach can help identify critical uncertainties in components of $R_0$ and how this uncertainty is propagated into the estimate of $R_0$. Most notably, we find that different parameters dominate the uncertainty at different temperature regimes: bite rate from 15-25$^\circ$ C; fecundity across all temperatures, but especially $\sim$25-32$^\circ$ C; mortality from 20-30$^\circ$ C; parasite development rate at $\sim$15-16$^\circ$C and again at $\sim$33-35$^\circ$C. Focusing empirical studies on these parameters and corresponding temperature ranges would be the most efficient way to improve estimates of $R_0$. While we focus on malaria, our methods apply to improving process-based models more generally, including epidemiological, physiological niche, and species distribution models.Comment: 27 pages, including 1 table and 3 figure