Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings

Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. These (static) condensates can be found analytically because the relevant Hartree-Fock and gap equations can be reduced to the nonlinear Schr\"odinger equation, whose deformations are governed by the mKdV and AKNS integrable hierarchies, respectively. Recently, Thies et al have shown that time-dependent Hartree-Fock solutions describing baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation, and can be mapped directly to classical string solutions in AdS3. Here we propose a geometric perspective for this result, based on the generalized Weierstrass spinor representation for the embedding of 2d surfaces into 3d spaces, which explains why these well-known integrable systems underlie these various Gross-Neveu gap equations, and why there should be a connection to classical string theory solutions. This geometric viewpoint may be useful for higher dimensional models, where the relevant integrable hierarchies include the Davey-Stewartson and Novikov-Veselov systems.Comment: 27 pages, 1 figur

Accreting Neutron Stars in Low-Mass X-Ray Binary Systems

Using the Rossi X-ray Timing Explorer (RossiXTE), astronomers have discovered that disk-accreting neutron stars with weak magnetic fields produce three distinct types of high-frequency X-ray oscillations. These oscillations are powered by release of the binding energy of matter falling into the strong gravitational field of the star or by the sudden nuclear burning of matter that has accumulated in the outermost layers of the star. The frequencies of the oscillations reflect the orbital frequencies of gas deep in the gravitational field of the star and/or the spin frequency of the star. These oscillations can therefore be used to explore fundamental physics, such as strong-field gravity and the properties of matter under extreme conditions, and important astrophysical questions, such as the formation and evolution of millisecond pulsars. Observations using RossiXTE have shown that some two dozen neutron stars in low-mass X-ray binary systems have the spin rates and magnetic fields required to become millisecond radio-emitting pulsars when accretion ceases, but that few have spin rates above about 600 Hz. The properties of these stars show that the paucity of spin rates greater than 600 Hz is due in part to the magnetic braking component of the accretion torque and to the limited amount of angular momentum that can be accreted in such systems. Further study will show whether braking by gravitational radiation is also a factor. Analysis of the kilohertz oscillations has provided the first evidence for the existence of the innermost stable circular orbit around dense relativistic stars that is predicted by strong-field general relativity. It has also greatly narrowed the possible descriptions of ultradense matter.Comment: 22 pages, 7 figures, updated list of sources and references, to appear in "Short-period Binary Stars: Observation, Analyses, and Results", eds. E.F. Milone, D.A. Leahy, and D. Hobill (Dordrecht: Springer, http://www.springerlink.com

Generalized Flows around Neutron Stars

In this chapter, we present a brief and non-exhaustive review of the developments of theoretical models for accretion flows around neutron stars. A somewhat chronological summary of crucial observations and modelling of timing and spectral properties are given in sections 2 and 3. In section 4, we argue why and how the Two-Component Advective Flow (TCAF) solution can be applied to the cases of neutron stars when suitable modifications are made for the NSs. We showcase some of our findings from Monte Carlo and Smoothed Particle Hydrodynamic simulations which further strengthens the points raised in section 4. In summary, we remark on the possibility of future works using TCAF for both weakly magnetic and magnetic Neutron Stars.Comment: 15 pages, 7 figures. arXiv admin note: text overlap with arXiv:1901.0084

Interpretation of Binary Pulsar Observations

The nature, dynamics and evolution of the three known radio pulsar binaries are discussed. The system containing 1913+16 appears to comprise two ~1.4 M⊙ components, and to undergo orbital decay as predicted by general relativity. It is proposed that 1913+16 has a neutron star companion and that 0655+64 and 0820+02 have white dwarf companions which should be observable optically

Asteroseismology and Interferometry

Asteroseismology provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Recent developments, including the first systematic studies of solar-like pulsators, have boosted the impact of this field of research within Astrophysics and have led to a significant increase in the size of the research community. In the present paper we start by reviewing the basic observational and theoretical properties of classical and solar-like pulsators and present results from some of the most recent and outstanding studies of these stars. We centre our review on those classes of pulsators for which interferometric studies are expected to provide a significant input. We discuss current limitations to asteroseismic studies, including difficulties in mode identification and in the accurate determination of global parameters of pulsating stars, and, after a brief review of those aspects of interferometry that are most relevant in this context, anticipate how interferometric observations may contribute to overcome these limitations. Moreover, we present results of recent pilot studies of pulsating stars involving both asteroseismic and interferometric constraints and look into the future, summarizing ongoing efforts concerning the development of future instruments and satellite missions which are expected to have an impact in this field of research.Comment: Version as published in The Astronomy and Astrophysics Review, Volume 14, Issue 3-4, pp. 217-36

Accreting Millisecond X-Ray Pulsars

Accreting Millisecond X-Ray Pulsars (AMXPs) are astrophysical laboratories without parallel in the study of extreme physics. In this chapter we review the past fifteen years of discoveries in the field. We summarize the observations of the fifteen known AMXPs, with a particular emphasis on the multi-wavelength observations that have been carried out since the discovery of the first AMXP in 1998. We review accretion torque theory, the pulse formation process, and how AMXP observations have changed our view on the interaction of plasma and magnetic fields in strong gravity. We also explain how the AMXPs have deepened our understanding of the thermonuclear burst process, in particular the phenomenon of burst oscillations. We conclude with a discussion of the open problems that remain to be addressed in the future.Comment: Review to appear in "Timing neutron stars: pulsations, oscillations and explosions", T. Belloni, M. Mendez, C.M. Zhang Eds., ASSL, Springer; [revision with literature updated, several typos removed, 1 new AMXP added

Combining dispersion modelling with synoptic patterns to understand the wind-borne transport into the UK of the bluetongue disease vector

Bluetongue, an economically important animal disease, can be spread over long distances by carriage of insect vectors (Culicoides biting midges) on the wind. The weather conditions which influence the midge’s flight are controlled by synoptic scale atmospheric circulations. A method is proposed that links wind-borne dispersion of the insects to synoptic circulation through the use of a dispersion model in combination with principal component analysis (PCA) and cluster analysis. We illustrate how to identify the main synoptic situations present during times of midge incursions into the UK from the European continent. A PCA was conducted on high-pass-filtered mean sea-level pressure data for a domain centred over north-west Europe from 2005 to 2007. A clustering algorithm applied to the PCA scores indicated the data should be divided into five classes for which averages were calculated, providing a classification of the main synoptic types present. Midge incursion events were found to mainly occur in two synoptic categories; 64.8% were associated with a pattern displaying a pressure gradient over the North Atlantic leading to moderate south-westerly flow over the UK and 17.9% of the events occurred when high pressure dominated the region leading to south-easterly or easterly winds. The winds indicated by the pressure maps generally compared well against observations from a surface station and analysis charts. This technique could be used to assess frequency and timings of incursions of virus into new areas on seasonal and decadal timescales, currently not possible with other dispersion or biological modelling methods

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure

The Formation and Evolution of the First Massive Black Holes

The first massive astrophysical black holes likely formed at high redshifts (z>10) at the centers of low mass (~10^6 Msun) dark matter concentrations. These black holes grow by mergers and gas accretion, evolve into the population of bright quasars observed at lower redshifts, and eventually leave the supermassive black hole remnants that are ubiquitous at the centers of galaxies in the nearby universe. The astrophysical processes responsible for the formation of the earliest seed black holes are poorly understood. The purpose of this review is threefold: (1) to describe theoretical expectations for the formation and growth of the earliest black holes within the general paradigm of hierarchical cold dark matter cosmologies, (2) to summarize several relevant recent observations that have implications for the formation of the earliest black holes, and (3) to look into the future and assess the power of forthcoming observations to probe the physics of the first active galactic nuclei.Comment: 39 pages, review for "Supermassive Black Holes in the Distant Universe", Ed. A. J. Barger, Kluwer Academic Publisher