Relativistic Neutron Stars: Rheological Type Extensions of the Equations of State

Based on the Rheological Paradigm, one has extended the equations of state for relativistic spherically symmetric static neutron stars, taking into consideration the derivative of the matter pressure along the so-called director four-vector. The modified equations of state are applied to the model of a zero-temperature neutron condensate. This model includes one new parameter with the dimensionality of length, which describes the rheological type screening inside the neutron star. As an illustration of the new approach, one has considered the rheological type generalization of the non-relativistic Lane-Emden theory and found the numerical profiles of the pressure for a number of values of the new guiding parameter. One has found that the rheological type self-interaction makes the neutron star more compact, since the radius of the star, related to the first null of the pressure profile, decreases when the modulus of the rheological type guiding parameter grows.Comment: 14 pages, 1 figure, 1 tabl

Anisotropic stars as ultracompact objects in General Relativity

Anisotropic stresses are ubiquitous in nature, but their modeling in General Relativity is poorly understood and frame dependent. We introduce the first study on the dynamical properties of anisotropic self-gravitating fluids in a covariant framework. Our description is particularly useful in the context of tests of the black hole paradigm, wherein ultracompact objects are used as black hole mimickers but otherwise lack a proper theoretical framework. We show that: (i) anisotropic stars can be as compact and as massive as black holes, even for very small anisotropy parameters; (ii) the nonlinear dynamics of the 1+1 system is in good agreement with linearized calculations, and shows that configurations below the maximum mass are nonlinearly stable; (iii) strongly anisotropic stars have vanishing tidal Love numbers in the black-hole limit; (iv) their formation will usually be accompanied by gravitational-wave echoes at late times.Comment: 7+2 pages, 6 figures; v2: include extra material (general covariant framework for anisotropic fluids in General Relativity without symmetries and code validation); to appear in PR

Maximum mass and universal relations of rotating relativistic hybrid hadron-quark stars

We construct equilibrium models of uniformly and differentially rotating hybrid hadron-quark stars using equations of state (EOSs) with a first-order phase transition that gives rise to a third family of compact objects. We find that the ratio of the maximum possible mass of uniformly rotating configurations - the supramassive limit - to the Tolman-Oppenheimer-Volkoff (TOV) limit mass is not EOS-independent, and is between 1.15 and 1.31,in contrast with the value of 1.20 previously found for hadronic EOSs. Therefore, some of the constraints placed on the EOS from the observation of the gravitational wave event GW170817 do not apply to hadron-quark EOSs. However, the supramassive limit mass for the family of EOSs we treat is consistent with limits set by GW170817, strengthening the possibility of interpreting GW170817 with a hybrid hadron-quark EOSs. We also find that along constant angular momentum sequences of uniformly rotating stars, the third family maximum and minimum mass models satisfy approximate EOS-independent relations, and the supramassive limit of the third family is approximately 16.5 % larger than the third family TOV limit. For differentially rotating spheroidal stars, we find that a lower-limit on the maximum supportable rest mass is 123 % more than the TOV limit rest mass. Finally, we verify that the recently discovered universal relations relating angular momentum, rest mass and gravitational mass for turning-point models hold for hybrid hadron-quark EOSs when uniform rotation is considered, but have a clear dependence on the degree of differential rotation.Comment: 19 pages, 14 figures, submitted to EPJA Topical Issue "First joint gravitational wave and electromagnetic observations: Implications for nuclear and particle physics

Localization theorems for nonlinear eigenvalue problems

Let T : \Omega \rightarrow \bbC^{n \times n} be a matrix-valued function that is analytic on some simply-connected domain \Omega \subset \bbC. A point $\lambda \in \Omega$ is an eigenvalue if the matrix $T(\lambda)$ is singular. In this paper, we describe new localization results for nonlinear eigenvalue problems that generalize Gershgorin's theorem, pseudospectral inclusion theorems, and the Bauer-Fike theorem. We use our results to analyze three nonlinear eigenvalue problems: an example from delay differential equations, a problem due to Hadeler, and a quantum resonance computation.Comment: Submitted to SIMAX. 22 pages, 11 figure

Differentially-rotating neutron star models with a parametrized rotation profile

We analyze the impact of the choice rotation law on equilibrium sequences of relativistic differentially-rotating neutron stars in axisymmetry. The maximum allowed mass for each model is strongly affected by the distribution of angular velocity along the radial direction and by the consequent degree of differential rotation. In order to study the wide parameter space implied by the choice of rotation law, we introduce a functional form that generalizes the so called "j-const. law" adopted in all previous work. Using this new rotation law we reproduce the angular velocity profile of differentially-rotating remnants from the coalescence of binary neutron stars in various 3-dimensional dynamical simulations. We compute equilibrium sequences of differentially rotating stars with a polytropic equation of state starting from the spherically symmetric static case. By analyzing the sequences at constant ratio, T/|W|, of rotational kinetic energy to gravitational binding energy, we find that the parameters that best describe the binary neutron star remnants cannot produce equilibrium configurations with values of T/|W| that exceed 0.14, the criterion for the onset of the secular instability.Comment: Submitted to A&A, 6 pages, 3 figure

The ESPRI project: astrometric exoplanet search with PRIMA I. Instrument description and performance of first light observations

The ESPRI project relies on the astrometric capabilities offered by the PRIMA facility of the Very Large Telescope Interferometer for the discovery and study of planetary systems. Our survey consists of obtaining high-precision astrometry for a large sample of stars over several years and to detect their barycentric motions due to orbiting planets. We present the operation principle, the instrument's implementation, and the results of a first series of test observations. A comprehensive overview of the instrument infrastructure is given and the observation strategy for dual-field relative astrometry is presented. The differential delay lines, a key component of the PRIMA facility which was delivered by the ESPRI consortium, are described and their performance within the facility is discussed. Observations of bright visual binaries are used to test the observation procedures and to establish the instrument's astrometric precision and accuracy. The data reduction strategy for astrometry and the necessary corrections to the raw data are presented. Adaptive optics observations with NACO are used as an independent verification of PRIMA astrometric observations. The PRIMA facility was used to carry out tests of astrometric observations. The astrometric performance in terms of precision is limited by the atmospheric turbulence at a level close to the theoretical expectations and a precision of 30 micro-arcseconds was achieved. In contrast, the astrometric accuracy is insufficient for the goals of the ESPRI project and is currently limited by systematic errors that originate in the part of the interferometer beamtrain which is not monitored by the internal metrology system. Our observations led to the definition of corrective actions required to make the facility ready for carrying out the ESPRI search for extrasolar planets.Comment: 32 pages, 39 figures, Accepted for publication in Astronomy and Astrophysic

Nonlinear Analysis of Irregular Variables

The Fourier spectral techniques that are common in Astronomy for analyzing periodic or multi-periodic light-curves lose their usefulness when they are applied to unsteady light-curves. We review some of the novel techniques that have been developed for analyzing irregular stellar light or radial velocity variations, and we describe what useful physical and astronomical information can be gained from their use.Comment: 31 pages, to appear as a chapter in `Nonlinear Stellar Pulsation' in the Astrophysics and Space Science Library (ASSL), Editors: M. Takeuti & D. Sasselo