Stellar Models in General Relativity

Neutron stars are some of the most fascinating objects in Nature. Essentially all aspects of physics seems to be represented inside them. Their cores are likely to contain deconfined quarks, hyperons and other exotic phases of matter in which the strong interaction is the dominant force. The inner region of their solid crust is penetrated by superfluid neutrons and their magnetic fields may reach well over 1012 Gauss. Moreover, their extreme mean densities, well above the densities of nuclei, and their rapid rotation rates makes them truly relativistic both in the special as well as in the general sense. This thesis deals with a small subset of these phenomena. In particular the exciting possibility of trapping of gravita-tional waves is examined from a theoretical point of view. It is shown that the standard condition R < 3M is not essential to the trapping mechanism. This point is illustrated using the elegant tool provided by the optical geometry. It is also shown that a realistic equation of state proposed in the literature allows stable neutron star models with closed circular null orbits, something which is closely related to trapped gravitational waves. Furthermore, the general relativistic theory of elasticity is reviewed and applied to stellar models. Both static equilibrium as well as radially oscillating configurations with elasticsources are examined. Finally, Killing tensors are considered and their applicability to modeling of stars is discussed

Astrophysical parameters of LS 2883 and implications for the PSR B1259-63 gamma-ray binary

Only a few binary systems with compact objects display TeV emission. The physical properties of the companion stars represent basic input for understanding the physical mechanisms behind the particle acceleration, emission, and absorption processes in these so-called gamma-ray binaries. Here we present high-resolution and high signal-to-noise optical spectra of LS 2883, the Be star forming a gamma-ray binary with the young non-accreting pulsar PSR B1259-63, showing it to rotate faster and be significantly earlier and more luminous than previously thought. Analysis of the interstellar lines suggests that the system is located at the same distance as (and thus is likely a member of) Cen OB1. Taking the distance to the association, d = 2.3 kpc, and a color excess of E(B – V) = 0.85 for LS 2883 results in MV ≈ –4.4. Because of fast rotation, LS 2883 is oblate (R eq sime 9.7 R ☉ and R pole sime 8.1 R ☉) and presents a temperature gradient (T eq≈ 27,500 K, log g eq = 3.7; T pole≈ 34,000 K, log g pole = 4.1). If the star did not rotate, it would have parameters corresponding to a late O-type star. We estimate its luminosity at log(L */L ☉) sime 4.79 and its mass at M * ≈ 30 M ☉. The mass function then implies an inclination of the binary system i orb ≈ 23°, slightly smaller than previous estimates. We discuss the implications of these new astrophysical parameters of LS 2883 for the production of high-energy and very high-energy gamma rays in the PSR B1259-63/LS 2883 gamma-ray binary system. In particular, the stellar properties are very important for prediction of the line-like bulk Comptonization component from the unshocked ultrarelativistic pulsar wind.

A Self-Organizing Multiple-View Representation of 3D Objects

We explore representation of 3D objects in which several distinct 2D views are stored for each object. We demonstrate the ability of a two-layer network of thresholded summation units to support such representations. Using unsupervised Hebbian relaxation, we trained the network to recognise ten objects from different viewpoints. The training process led to the emergence of compact representations of the specific input views. When tested on novel views of the same objects, the network exhibited a substantial generalisation capability. In simulated psychophysical experiments, the network's behavior was qualitatively similar to that of human subjects.

Compact Representations for Fast Nonrigid Registration of Medical Images

We develop efficient techniques for the non-rigid registration of medical images by using representations that adapt to the anatomy found in such images. Images of anatomical structures typically have uniform intensity interiors and smooth boundaries. We create methods to represent such regions compactly using tetrahedra. Unlike voxel-based representations, tetrahedra can accurately describe the expected smooth surfaces of medical objects. Furthermore, the interior of such objects can be represented using a small number of tetrahedra. Rather than describing a medical object using tens of thousands of voxels, our representations generally contain only a few thousand elements. Tetrahedra facilitate the creation of efficient non-rigid registration algorithms based on finite element methods (FEM). We create a fast, FEM-based method to non-rigidly register segmented anatomical structures from two subjects. Using our compact tetrahedral representations, this method generally requires less than one minute of processing time on a desktop PC. We also create a novel method for the non-rigid registration of gray scale images. To facilitate a fast method, we create a tetrahedral representation of a displacement field that automatically adapts to both the anatomy in an image and to the displacement field. The resulting algorithm has a computational cost that is dominated by the number of nodes in the mesh (about 10,000), rather than the number of voxels in an image (nearly 10,000,000). For many non-rigid registration problems, we can find a transformation from one image to another in five minutes. This speed is important as it allows use of the algorithm during surgery. We apply our algorithms to find correlations between the shape of anatomical structures and the presence of schizophrenia. We show that a study based on our representations outperforms studies based on other representations. We also use the results of our non-rigid registration algorithm as the basis of a segmentation algorithm. That algorithm also outperforms other methods in our tests, producing smoother segmentations and more accurately reproducing manual segmentations.

Denisiuk-type reflection holography display with sillenite crystals for imaging and interferometry of small objects

A novel setup for imaging and interferometry through reflection holography with Bi12TiPO20(BTO) sillenite photorefractive crystals is proposed. A variation of the lensless Denisiuk arrangement was developed resulting in a compact, robust and simple interferometer. A red He-Ne laser was used as light source and the holographic recording occurred by diffusion with the grating vector parallel to the crystal [0 0 1]-axis. In order to enhance the holographic image quality and reduce noise a polarizing beam splitter (PBS) was positioned at the BTO input and the crystal was tilted around the [0 0 1]-axis. This enabled the orthogonally polarized transmission and diffracted beams to be separated by the PBS, providing the holographic image only. The possibility of performing deformation and strain analysis as well as vibration measurement of small objects was demonstrated. (C) 2007 Elsevier B.V. All rights reserved.

Very-long-baseline radio interferometry surveys of the compact structure in active galactic nuclei.

Very-long-baseline radio interferometry (VLBI) imaging surveys have been undertaken since the late 1970s. The sample sizes were initially limited to a few tens of objects but the snapshot technique has now allowed samples containing almost 200 sources to be studied. The overwhelming majority of powerful compact sources are asymmetric corejects of one form or another, most of which exhibit apparent superluminal motion. However 5-10% of powerful flat-spectrum sources are 100-parsec (pc)-scale compact symmetric objects; these appear to form a continuum with the 1-kpc-scale double-lobed compact steep-spectrum sources, which make up 15-20% of lower frequency samples. It is likely that these sub-galactic-size symmetric sources are the precursors to the large-scale classical double sources. There is a surprising peak around 90 degrees in the histogram of misalignments between the dominant source axes on parsec and kiloparsec scales; this seems to be associated with sources exhibiting a high degree of relativistic beaming. VLBI snapshot surveys have great cosmological potential via measurements of both proper motion and angular size vs. redshift as well as searches for gravitational "millilensing."

Compact steep-spectrum sources and the unified scheme.

The compact steep-spectrum sources (CSSs) are an interesting class of objects which are of subgalactic dimensions; they occur more frequently in high-frequency surveys because their spectra often turn over at lower frequencies. We have estimated the symmetry parameters of a well-defined sample of CSSs and compared these with the larger 3CR sources of similar luminosity to understand the evolution and the consistency of CSSs with the unified scheme. We suggest that the majority of CSSs are likely to be young sources advancing outward through an asymmetric, inhomogeneous environment to form the larger ones. The radio properties of the CSSs are consistent with the unified scheme, where the axes of the quasars are seen closer to the line of sight while the radio galaxies lie closer to the plane of the sky. We discuss how radio polarization observations may be used to probe whether the physical conditions in the central regions of the CSSs are different from the larger ones. We present a simple scenario where the depolarization and high rotation measures seen in many CSSs can be consistent with the low rotation measures of cores in the more extended quasars and suggest further observations to test this scenario.

Galaxy threshing and the origin of ultra-compact dwarf galaxies in the Fornax cluster

A recent all-object spectroscopic survey centred on the Fornax cluster of galaxies has discovered a population of subluminous and extremely compact members, called 'ultra-compact dwarf' (UCD) galaxies. In order to clarify the origin of these objects, we have used self-consistent numerical simulations to study the dynamical evolution a nucleated dwarf galaxy would undergo if orbiting the centre of the Fornax cluster and suffering from its strong tidal gravitational field. We find that the outer stellar components of a nucleated dwarf are removed by the strong tidal field of the cluster, whereas the nucleus manages to survive as a result of its initially compact nature. The developed naked nucleus is found to have physical properties (e. g. size and mass) similar to those observed for UCDs. We also find that although this formation process does not have a strong dependence on the initial total luminosity of the nucleated dwarf, it does depend on the radial density profile of the dark halo in the sense that UCDs are less likely to be formed from dwarfs embedded in dark matter haloes with central 'cuspy' density profiles. Our simulations also suggest that very massive and compact stellar systems can be rapidly and efficiently formed in the central regions of dwarfs through the merging of smaller star clusters. We provide some theoretical predictions on the total number and radial number density profile of UCDs in a cluster and their dependencies on cluster masses.

Spline Subdivision Schemes for Compact Sets. A Survey

Dedicated to the memory of our colleague Vasil Popov January 14, 1942 – May 31, 1990 * Partially supported by ISF-Center of Excellence, and by The Hermann Minkowski Center for Geometry at Tel Aviv University, Israel

The data type of spatial objects

A spatial object consists of data assigned to points in a space. Spatial objects, such as memory states and three dimensional graphical scenes, are diverse and ubiquitous in computing. We develop a general theory of spatial objects by modelling abstract data types of spatial objects as topological algebras of functions. One useful algebra is that of continuous functions, with operations derived from operations on space and data, and equipped with the compact-open topology. Terms are used as abstract syntax for defining spatial objects and conditional equational specifications are used for reasoning. We pose a completeness problem: Given a selection of operations on spatial objects, do the terms approximate all the spatial objects to arbitrary accuracy? We give some general methods for solving the problem and consider their application to spatial objects with real number attributes. © 2011 British Computer Society.

The Evolution of Massive Young Stellar Objects in the Large Magellanic Cloud

This thesis presents an analysis of the largest catalog to date of infrared spectra of massive young stellar objects in the Large Magellanic Cloud. Evidenced by their very different spectral features, the luminous objects span a range of evolutionary states from those most embedded in their natal molecular material to those that have dissipated and ionized their surroundings to form compact HII regions and photodissociation regions. We quantify the contributions of the various spectral features using the statistical method of principal component analysis. Using this analysis, we classify the YSO spectra into several distinct groups based upon their dominant spectral features: silicate absorption (S Group), silicate absorption and fine-structure line emission (SE), polycyclic aromatic hydrocarbon (PAH) emission (P Group), PAH and fine-structure line emission (PE), and only fine-structure line emission (E). Based upon the relative numbers of sources in each category, we are able to estimate the amount of time massive YSOs spend in each evolutionary stage. We find that approximately 50% of the sources have ionic fine-structure lines, indicating that a compact HII region forms about half-way through the YSO lifetime probed in our study. Of the 277 YSOs we collected spectra for, 41 have ice absorption features, indicating they are surrounded by cold ice-bearing dust particles. We have decomposed the shape of the ice features to probe the composition and thermal history of the ice. We find that most the CO2 ice is embedded a polar ice matrix that has been thermally processed by the embedded YSO. The amount of thermal processing may be correlated with the luminosity of the YSO. Using the Australia Telescope Compact Array, we imaged the dense gas around a subsample of our sources in the HII complexes N44, N105, N113, and N159 using HCO+ and HCN as dense gas tracers. We find that the molecular material in star forming environments is highly clumpy, with clumps that range from subparsec to ~2 parsecs in size and with masses between 10^2 to 10^4 solar masses. We find that there are varying levels of star formation in the clumps, with the lower-mass clumps tending to be without massive YSOs. These YSO-less clumps could either represent an earlier stage of clump to the more massive YSO-bearing ones or clumps that will never form a massive star. Clumps with massive YSOs at their centers have masses larger than those with massive YSOs at their edges, and we suggest that the difference is evolutionary: edge YSO clumps are more advanced than those with YSOs at their centers. Clumps with YSOs at their edges may have had a significant fraction of their mass disrupted or destroyed by the forming massive star. We find that the strength of the silicate absorption seen in YSO IR spectra feature is well-correlated with the on-source HCO+ and HCN flux densities, such that the strength of the feature is indicative of the embeddedness of the YSO. We estimate that ~40% of the entire spectral sample has strong silicate absorption features, implying that the YSOs are embedded in circumstellar material for about 40% of the time probed in our study.