STABILITY ANALYSIS OF RELATIVISTIC POLYTROPES

We study the relativistic self-gravitating, hydrostatic spheres with a polytropic equation of state, considering structures with the polytropic indices n=1(0.5)3 and illustrate the results for the relativistic parameters σ=0−0.75. We determine the critical relativistic parameter at which the mass of the polytrope has a maximum value and represents the first mode of radial instability. For n=1(0.5)2.5, stable relativistic polytropes occur for σ less than the critical values 0.42, 0.20, 0.10, and 0.04, respectively, while unstable relativistic polytropes are obtained when σ is greater than the same values. When n=3.0 and σ>0.5, energetically unstable solutions occur. The results of critical values are in full agreement with those evaluated by several authors. Comparisons between analytical and numerical solutions of the given relativistic functions provide a maximum relative error of order 10−3.

Radial instability of trapping polytropic spheres

We complete the stability study of general-relativistic spherically symmetric polytropic perfect fluid spheres, concentrating our attention on the newly discovered polytropes containing region of trapped null geodesics. We compare the methods of treating the dynamical stability based on the equation governing infinitesimal radial pulsations of the polytropes and the related Sturm–Liouville eigenvalue equation for the eigenmodes governing the pulsations, to the methods of stability analysis based on the energetic considerations. Both methods are applied to determine the stability of the polytropes governed by the polytropic index [Formula: see text] in the whole range [Formula: see text], and the relativistic parameter [Formula: see text] given by the ratio of the central pressure and energy density, restricted by the causality limit. The critical values of the adiabatic index for stability are determined, together with the critical values of the relativistic parameter [Formula: see text]. For the dynamical approach, we implemented a numerical method which is independent on the choice of the trial function, and compare its results with the standard trial function approach. We found that the energetic and dynamic method give nearly the same critical values of [Formula: see text]. We found that all the configurations having trapped null geodesics are unstable according to both methods.

Consideration of the Competing Factors in Calculations of the Characteristics of Non-Magnetic Degenerate Dwarfs

Using the equation of state of the electron-nuclear model at high densities and the mechanical equilibrium equation, we have investigated the influence of interparticle interactions and the axial rotation on the macroscopic characteristics (mass, surface shape) of massive degenerate dwarfs. We propose a method of solving the equilibrium equation in the case of rotation that uses the basis of universal functions of the radial variable. The conditions, under which the axial rotation can compensate for a weight loss of the mass due to the Coulomb interactions, have been established. The maximal value of the relativistic parameter, at which the stability is disturbed, is determined within the general theory of relativity (GTR).

Relativistic elliptic matrix tops and finite Fourier transformations

We consider a family of classical elliptic integrable systems including (relativistic) tops and their matrix extensions of different types. These models can be obtained from the “off-shell” Lax pairs, which do not satisfy the Lax equations in general case but become true Lax pairs under various conditions (reductions). At the level of the off-shell Lax matrix, there is a natural symmetry between the spectral parameter z and relativistic parameter [Formula: see text]. It is generated by the finite Fourier transformation, which we describe in detail. The symmetry allows one to consider z and [Formula: see text] on an equal footing. Depending on the type of integrable reduction, any of the parameters can be chosen to be the spectral one. Then another one is the relativistic deformation parameter. As a by-product, we describe the model of N2 interacting GL(M) matrix tops and/or M2 interacting GL(N) matrix tops depending on a choice of the spectral parameter.

The Discovery of the Most Accelerated Binary Pulsar

Pulsars in relativistic binary systems have emerged as fantastic natural laboratories for testing theories of gravity, the most prominent example being the double pulsar, PSR J0737–3039. The HTRU-South Low Latitude pulsar survey represents one of the most sensitive blind pulsar surveys taken of the southern Galactic plane to date, and its primary aim has been the discovery of new relativistic binary pulsars. Here we present our binary pulsar searching strategy and report on the survey’s flagship discovery, PSR J1757–1854. A 21.5-ms pulsar in a relativistic binary with an orbital period of 4.4 hours and an eccentricity of 0.61, this double neutron star (DNS) system is the most accelerated pulsar binary known, and probes a relativistic parameter space not yet explored by previous pulsar binaries.

Modulationally stable envelope solitons in astrophysical magnetoplasmas with degenerate relativistic electrons

The formation and propagation characteristics of small-amplitude magnetoacoustic dark/grey solitons are investigated in a semi relativistic degenerate magnetoplasma whose constituents are electrons and singly ionized positive ions. For this purpose, the electrons are assumed to follow the degeneracy pressure law through the Chandrasekhar equation of state, while the inertial cold ions are taken as non-degenerate and magnetized. By solving the one-fluid quantum magnetohydrodynamic (QMHD) model with the aid of a reductive perturbation technique, a nonlinear Schrödinger (NLS) equation is derived for weakly nonlinear envelope magnetoacoustic solitons. The NLS equation admits the existence of stable excitations, e.g. dark and grey solitons for which the condition $P/Q<0$ holds. Numerical results reveal that the variation of plasma number density, magnetic field strength, relativistic parameter $({\it\eta}_{e0})$ and the quantum parameter $(H)$ significantly modify the profiles of the envelope magnetoacoustic solitons. The present results are important to understanding of the nonlinear dynamics of magnetoacoustic solitons in astrophysical dense magnetoplasmas (viz., white dwarfs, magnetars, neutron stars, etc.), where the relativistic degeneracy effects play a vital role in collective interactions.

ASTROD I: Mission Concept and Venus Flybys

ASTROD I with one spacecraft ranging optically with ground stations is a first step for a full ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) mission. The goals are testing relativity with the relativistic parameter γ measured to 10~7, measuring solar-system parameters more precisely, and improving the present-day sensitivity for gravitational wave detection using Doppler tracking by radio waves. In this paper, we present the mission concept and the orbit design for ASTROD I with an emphasis on Venus flybys. The spacecraft is to be launched into an inner solar orbit with initial period about 290 days to encounter Venus twice to receive gravity-assistance for achieving shorter period (165 days or less) to reach the other side of the Sun for a sooner measurement of Shapiro time delay. For a launch on June 17, 2010, after two encounters with Venus, the orbital period can be shortened to 165 days and the spacecraft orbit reaches inside Mercury orbit. After about 400 days from launch, the spacecraft will arrive at the other side of the Sun and the relativistic parameter γ can be determined to 0.1 ppm or better. A simulation of the accuracy for determining the relativistic parameters γ and β, and the solar quadrupole parameter J2 gives 10−7, 10−7 and 10−8 for their respective uncertainties. In this simulation, we assume a 10 ps timing accuracy and 10−13 m/s2(Hz)1/2 at frequency f ~ 100μHz inertial sensor/accelerometer noise. Other orbits separated by synodic periods of Venus can readily be found. We discuss the sensitivity and noise reduction requirements, the atmosphere transmission noise, timing noise, spacecraft environmental noise, test-mass sensor back-action, and test mass-spacecraft control-loop noise and stiffness. In the second Venus flyby, the ASTROD I could also be swung into an elliptic 360-day orbit and stay near opposite side of the Sun for many good measurements of the Shapiro time delays — 19 times in 10 years. This is an interesting alternative. In the two Venus flybys, Venus multiple moments can be determined very precisely. In this paper, we also review ASTROD and discuss its gravitational-wave sensitivities.

Mini-ASTROD: Mission Concept

Advances in laser physics and its applications triggered the proposition and development of Laser Astrodynamics. Mini-ASTROD is a down-scaled version of ASTROD (Astro-dynamical Space Test of Relativity using Optical Devices). This mission concept has one spacecraft carrying a payload of a telescope, six lasers, and a clock together with ground stations (ODSN: Optical Deep Space Network) to test the optical scheme and yet give important scientific results. These scientific results include a better measurement of the relativistic parameters (γ to 1 ppm, β to a few ppm and others with improvement), a better sensitivity (several times better) in using the optical Doppler tracking method for detecting gravitational waves, a potential of measuring the solar angular momentum via the Lense-Thirring effect and measurement of many solar system parameters more precisely. These enable us to build a more precise ephemeris and astrodynamics. The weight of this spacecraft is estimated to be about 300–350 kg with a payload of about 100–120 kg. The spacecraft goes into an inner solar orbit with several options. One option is with period 304 days as for the inner spacecraft of the standard two-spacecraft ASTROD mission concept and it takes about 900 days to reach the other side of the Sum relative to the Earth. Another option is to launch with initial period about 290 days and to pass by Venus twice to receive gravity-assistance for achieving shorter periods. For a launch on November 15, 2008, after two encounters with Venus, the orbital period can be shortened to 165 days. After about 400 days from launch, the spacecraft will arrive at the other side of the Sun and the relativistic parameter γ can be determined to 1 ppm. We discuss the payload configuration and outlook for technological developments to reach the mission goals, and summarize the conclusions and recommendations of the first and second organizational meeting for the Mini-ASTROD study.

Relativistic Models for a GAIA-Like Astrometry Mission

A non-perturbative general relativistic approach to global astrometry was developed by de Felice et al. (1998) to handle satellite astrometry data in a genuine relativistic framework. In this contribution, the framework above has been further exploited to account for stellar motions and parallax. Because of the relevance that accurate knowledge (to 10−5 or better) of the relativistic parameter γ has to fundamental physics, a Parametrized Post-Newtonian (PPN) model has also been implemented, which allows the direct estimation of γ along with the astrometric parameters. These models have been tested on end-to-end simulations of the mission GAIA. The results show that, within the limitation of the simulation and the assumptions of the adopted model, measurements accurate to 100 μarcsec of large arcs among stars repeated over a few years can be modelled to establish a dense reference frame with a precision of a few tens of μarcseconds. Moreover, our experiments indicate that γ can be estimated to better than 10−6.