A numerical algorithm for dissipative Keplerian particle discs

We present a numerical algorithm designed to study the evolution of a distribution of solid particles orbiting around the Sun that could be applied to similar systems in which f _c ≤ Ω/2π, where f _c is the frequency of collisions, and Ω is the orbital angular speed. A number of sample particles are used to represent the whole system. Binary collisions are treated in a novel way using a Monte Carlo method that works as follows. Orbits are locally sampled to compute the velocity dispersion. Then the velocity vectors of the sample particles are modified according to random collisions with virtual particles which have velocities taken from a normal distribution computed using the previously found local velocity dispersion. The energy and momentum taken up by the virtual particles are redistributed among the neighbours of the sample particle undergoing the collision, so that conservation laws are satisfied. Simulations using this model give an estimation of the final distribution of inclinations and the associated evolutionary time-scale.     

DO WE NEED TO MODEL PLATES AT ALL?

The historical method of obtaining equatorial coordinates for stars observed via astronomical photography has been to convert the measured coordinates to equatorial coordinates with the aid of a plate model which corrects for a variety of effects. However, we now have at our disposal novel smoothing techniques, of considerable generality, which in conjunction with modern star catalogues can reproduce the essence of the plate model while dramatically minimizing both the fortuitous and systematic errors of observation. In this paper we demonstrate that, with this technique and extant catalogues, one can obtain, with at least the same precision and better accuracy, the information necessary to transform the measured coordinates successfully into standard coordinates by a process that involves no sophisticated model for the plate. Using external checks we estimate the increase in accuracy to be of the order of 25 per cent.     

Automated classification of stellar spectra — II. Two-dimensional classification with neural networks and principal components analysis

We investigate the application of neural networks to the automation of MK spectral classification. The data set for this project consists of a set of over 5000 optical (3800–5200 Å) spectra obtained from objective prism plates from the Michigan Spectral Survey. These spectra, along with their two-dimensional MK classifications listed in the Michigan Henry Draper Catalogue, were used to develop supervised neural network classifiers. We show that neural networks can give accurate spectral type classifications (σ₆₈= 0.82 subtypes, σ_rms= 1.09 subtypes) across the full range of spectral types present in the data set (B2–M7). We show also that the networks yield correct luminosity classes for over 95 per cent of both dwarfs and giants with a high degree of confidence.   Stellar spectra generally contain a large amount of redundant information. We investigate the application of principal components analysis (PCA) to the optimal compression of spectra. We show that PCA can compress the spectra by a factor of over 30 while retaining essentially all of the useful information in the data set. Furthermore, it is shown that this compression optimally removes noise and can be used to identify unusual spectra.   This paper is a continuation of the work carried out by von Hippel et al. (Paper I).     

The Bootstrap Estimation of the Accuracy of Preliminary Orbit Determination

From the point of view of the non-parametric statistics, a general estimation method of the accuracy and con?dence interval of preliminary orbit determination is proposed for the occasion without any other information but observational data. Based on the bootstrap method, the estimation relies only on the observational data and does not require the precise orbit determination as a reference, or the assumption of normal distribution of observational errors. Numerical experiments show that this method is very simple in implementa- tion, and may serve as an easy accuracy evaluation for the preliminary orbit determination and for the follow-up employments.     

Sodium beacon tip–tilt determination with Rayleigh-aided auxiliary telescope technique

The usefulness of tracking the Rayleigh portion of a mesospheric sodium laser guide star as reference for absolute tip–tilt recovery in the frame of the auxiliary telescopes technique is shown. This approach leads to the reduction of the ground occupation needed to attain a given sky coverage by more than one order of magnitude. Speed, tracking precision, and the number of auxiliary telescopes are also reduced, making this new approach a more attractive one. The use of a low-altitude Rayleigh spot reinforces the fundamental limitations affecting this and other techniques, thus degrading significantly the quality of the recovered tip–tilt. However, it is shown that, provided adequate care is taken in the collection and treatment of data, an interesting tilt signal can still be retrieved.     

Bar dissolution in non-spherical halos

Dynamical evolution of N-body bars embedded in spherical and prolate dark matter halos is investigated. In particular, the configuration such that galactic disks are placed in the plane perpendicular to the equatorial plane of the prolate halos is considered. Such a configuration is frequently found in cosmological simulations. N-body disks embedded in a fixed external halo potential were simulated, so that the barred structure was formed via dynamical instability in initially cool disks. In the subsequent evolution, bars in prolate halos dissolved gradually with time, while the bar pattern in spherical halos remained almost unchanged until the end of simulations. The e-folding time of bars suggest that they could be destroyed in a time smaller than a Hubble time. This revised version was published online in August 2006 with corrections to the Cover Date.     

Seismic Inference using Genetic Algorithms

A flood of reliable seismic data will soon arrive. The migration to largertelescopes on the ground may free up 4-m class instruments for multi-sitecampaigns, and several forthcoming satellite missions promise to yieldnearly uninterrupted long-term coverage of many pulsating stars. We willthen face the challenge of determining the fundamental properties of thesestars from the data, by trying to match them with the output of ourcomputer models. The traditional approach to this task is to make informedguesses for each of the model parameters, and then adjust them iterativelyuntil an adequate match is found. The trouble is: how do we know that oursolution is unique, or that some other combination of parameters will notdo even better? Computers are now sufficiently powerful and inexpensivethat we can produce large grids of models and simply compare all ofthem to the observations. The question then becomes: what range ofparameters do we want to consider, and how many models do we want tocalculate? This can minimize the subjective nature of the process, but itmay not be the most efficient approach and it may give us a false sense ofsecurity that the final result is correct, when it is really justoptimal. I discuss these issues in the context of recent advances inthe asteroseismological analysis of white dwarf stars.