Simulations of the formation and evolution of isolated dwarf galaxies - II. Angular momentum as a second parameter

We show results based on a large suite of N-Body/SPH simulations of isolated, flat dwarf galaxies, both rotating and non-rotating. The main goal is to investigate possible mechanisms to explain the observed dichotomy in radial stellar metallicity profiles of dwarf galaxies: dwarf irregulars (dIrr) and flat, rotating dwarf ellipticals (dE) generally possess flat metallicity profiles, while rounder and non-rotating dEs show strong negative metallicity gradients. These simulations show that flattening by rotation is key to reproducing the observed characteristics of flat dwarf galaxies, proving particularly efficient in erasing metallicity gradients. We propose a "centrifugal barrier mechanism" as an alternative to the previously suggested "fountain mechanism" for explaining the flat metallicity profiles of dIrrs and flat, rotating dEs. While only flattening the dark-matter halo has little influence, the addition of angular momentum slows down the infall of gas, so that star formation (SF) and the ensuing feedback are less centrally concentrated, occurring galaxy-wide. Additionally, this leads to more continuous SFHs by preventing large-scale oscillations in the SFR ("breathing"), and creates low density holes in the ISM, in agreement with observations of dIrrs. Our general conclusion is that rotation has a significant influence on the evolution and appearance of dwarf galaxies, and we suggest angular momentum as a second parameter (after galaxy mass as the dominant parameter) in dwarf galaxy evolution. Angular momentum differentiates between SF modes, making our fast rotating models qualitatively resemble dIrrs, which does not seem possible without rotation.Comment: Accepted for publication in MNRAS | 19 pages, 20 figures | extra online content available (animations) : on the publisher's website / on the YouTube channel for the astronomy department of the University of Ghent : http://www.youtube.com/user/AstroUGent / YouTube playlist specifically for this article : http://www.youtube.com/user/AstroUGent#grid/user/EFAA5AAE5C5E474

Kinemetry: a generalisation of photometry to the higher moments of the line-of-sight velocity distribution

We present a generalisation of surface photometry to the higher-order moments of the line-of-sight velocity distribution of galaxies observed with integral-field spectrographs. The generalisation follows the approach of surface photometry by determining the best fitting ellipses along which the profiles of the moments can be extracted and analysed by means of harmonic expansion. The assumption for the odd moments (e.g. mean velocity) is that the profile along an ellipse satisfies a simple cosine law. The assumption for the even moments (e.g velocity dispersion) is that the profile is constant, as it is used in surface photometry. We find that velocity profiles extracted along ellipses of early-type galaxies are well represented by the simple cosine law (with 2% accuracy), while possible deviations are carried in the fifth harmonic term which is sensitive to the existence of multiple kinematic components, and has some analogy to the shape parameter of photometry. We compare the properties of the kinematic and photometric ellipses and find that they are often very similar. Finally, we offer a characterisation of the main velocity structures based only on the kinemetric parameters which can be used to quantify the features in velocity maps (abridged).Comment: 17 pages, 11 figures. MNRAS in press. High resolution version of the paper is available at http://www.strw.leidenuniv.nl/sauron/papers/krajnovic2005_kinemetry.pdf and software implementation of the method is freely available at http://www-astro.physics.ox.ac.uk/~dxk/idl

Fine-Structure Classification of Multiqubit Entanglement by Algebraic Geometry

We present a fine-structure entanglement classification under stochastic local operation and classical communication (SLOCC) for multiqubit pure states. To this end, we employ specific algebraic-geometry tools that are SLOCC invariants, secant varieties, to show that for $n$-qubit systems there are $\lceil\frac{2^{n}}{n+1}\rceil$ entanglement families. By using another invariant, $\ell$-multilinear ranks, each family can be further split into a finite number of subfamilies. Not only does this method facilitate the classification of multipartite entanglement, but it also turns out to be operationally meaningful as it quantifies entanglement as a resource.Comment: 11 pages, 2 figures, Minor changes, Published versio

Modeling Age Patterns of Under-5 Mortality: Results From a Log-Quadratic Model Applied to High-Quality Vital Registration Data

Information about how the risk of death varies with age within the 0-5 age range represents critical evidence for guiding health policy. This paper proposes a new model for summarizing regularities about how under-5 mortality is distributed by detailed age. The model is based on a newly compiled database that contains under-5 mortality information by detailed age in countries with high-quality vital registration systems, covering a wide array of mortality levels and patterns. The model uses a log-quadratic approach, predicting a full mortality schedule between age 0 and 5 on the basis of only 1 or 2 parameters. With its larger number of age groups, the proposed model offers greater flexibility than existing models both in terms of entry parameters and model outcomes. We present applications of this model for evaluating and correcting under-5 mortality information by detailed age in countries with problematic mortality data

The Peculiar Motions of Early-Type Galaxies in Two Distant Regions. IV. The Photometric Fitting Procedure

The EFAR project is a study of 736 candidate early-type galaxies in 84 clusters lying in two regions towards Hercules-Corona Borealis and Perseus-Cetus at distances $cz \approx 6000-15000$ km/s. In this paper we describe a new method of galaxy photometry adopted to derive the photometric parameters of the EFAR galaxies. The algorithm fits the circularized surface brightness profiles as the sum of two seeing-convolved components, an $R^{1/4}$ and an exponential law. This approach allows us to fit the large variety of luminosity profiles displayed by the EFAR galaxies homogeneously and to derive (for at least a subset of these) bulge and disk parameters. Multiple exposures of the same objects are optimally combined and an optional sky-fitting procedure has been developed to correct for sky subtraction errors. Extensive Monte Carlo simulations are analyzed to test the performance of the algorithm and estimate the size of random and {\it systematic} errors. Random errors are small, provided that the global signal-to-noise ratio of the fitted profiles is larger than $\approx 300$. Systematic errors can result from 1) errors in the sky subtraction, 2) the limited radial extent of the fitted profiles, 3) the lack of resolution due to seeing convolution and pixel sampling, 4) the use of circularized profiles for very flattened objects seen edge-on and 5) a poor match of the fitting functions to the object profiles. Large systematic errors are generated by the widely used simple $R^{1/4}$ law to fit luminosity profiles when a disk component, as small as 20% of the total light, is present.Comment: 47 pages, Latex File, aaspp4.sty, flushrt.sty, 16 Postscript figures, to appear in ApJ

The Polynomial Waring Problem and the Determinant

The symmetric rank of a polynomial P is the minimum number of d-th powers of linear forms necessary to sum to P. Questions pertaining to the rank and decomposition of symmetric forms or polynomials are of classic interest. Work on this topic dates back to the mid 1800’s to J. J. Sylvester. Many questions have been resolved since Sylvester’s work, yet many more questions have arisen. In recent years, certain polynomials including detn, the determinant of an n × n matrix of indeterminates, have become central in the study of rank problems. Symmetric border rank of a polynomial P is the minimum r such that P is in the Zariski closure of polynomials with symmetric rank r. It bounds and is closely related to rank. This dissertation demonstrates new lower bounds for the symmetric border rank of the polynomial detn. We prove this result using methods from algebraic geometry and representation theory. In addition to the lower bounds for symmetric border rank of detn, we present a lower bound for symmetric border rank of a related polynomial, perm3. We conclude by giving future directions for continuing this project. The first direction is to use the methods from algebraic geometry and representation theory used in this dissertation to study permn. With the new lower bound on symmetric border rank of perm3 we know that there are only 3 possible values for symmetric border rank of perm3. One could ask which of the 3 possible values for symmetric border rank of perm3 is the correct value

Decomposability of Tensors

Tensor decomposition is a relevant topic, both for theoretical and applied mathematics, due to its interdisciplinary nature, which ranges from multilinear algebra and algebraic geometry to numerical analysis, algebraic statistics, quantum physics, signal processing, artificial intelligence, etc. The starting point behind the study of a decomposition relies on the idea that knowledge of elementary components of a tensor is fundamental to implement procedures that are able to understand and efficiently handle the information that a tensor encodes. Recent advances were obtained with a systematic application of geometric methods: secant varieties, symmetries of special decompositions, and an analysis of the geometry of finite sets. Thanks to new applications of theoretic results, criteria for understanding when a given decomposition is minimal or unique have been introduced or significantly improved. New types of decompositions, whose elementary blocks can be chosen in a range of different possible models (e.g., Chow decompositions or mixed decompositions), are now systematically studied and produce deeper insights into this topic. The aim of this Special Issue is to collect papers that illustrate some directions in which recent researches move, as well as to provide a wide overview of several new approaches to the problem of tensor decomposition