Sequences Of Constant Rest Mass Research Articles

Quasi-stationary sequences of hyper-massive neutron stars with exotic equations of state

In this work, we study the effect of differential rotation, finite temperature and strangeness on the quasi stationary sequences of hyper massive neutron stars (HMNS). We generate constant rest mass sequences of differentially rotating and uniformly rotating stars. The nucleonic matter relevant to the star interior is described within the framework of the relativistic mean field model with the DD2 parameter set. We also consider the strange $\Lambda$ hyperons using the BHB$\Lambda\phi$ equation of state (EoS). Additionally, we probe the behaviour of neutron stars (NS) with these compositions at different temperatures. We report that the addition of hyperons to the EoS produces a significant boost to the spin-up phenomenon. Moreover, increasing the temperature can make the spin-up more robust. We also study the impact of strangeness and thermal effects on the T/W instability. Finally, we analyse equilibrium sequences of a NS following a stable transition from differential rotation to uniform rotation. The decrease in frequency relative to angular momentum loss during this transition is significantly smaller for EoS containing hyperons, compared to nucleonic EoS.

Constant circulation sequences of binary neutron stars and their spin characterization

For isentropic fluids, dynamical evolution of a binary system conserves the baryonic mass and circulation; therefore, sequences of constant rest mass and constant circulation are of particular importance. In this work, we present the extension of our Compact Object CALculator (\cocal{}) code to compute such quasiequilibria and compare them with the well-known corotating and irrotational sequences, the latter being the simplest, zero-circulation case. The circulation as a measure of the spin for a neutron star in a binary system has the advantage of being exactly calculable since it is a local quantity. To assess the different measures of spin, such as the angular velocity of the star, the quasilocal, dimensionless spin parameter $J/M^2$, or the circulation $\mathcal{C}$, we first compute sequences of single, uniformly rotating stars and describe how the different spin diagnostics are related to each other. The connection to spinning binary systems is accomplished through the concept of circulation and the use of the constant rotational velocity formulation. Finally, we explore a modification of the latter formulation that naturally leads to differentially rotating binary systems.

Critical mass, moment of inertia and universal relations of rapidly rotating neutron stars with exotic matter

We calculate moment of inertia of neutron star with different exotic constituents such as hyperons and antikaon condensates and study its variation with mass and spin frequency. The sets of equation-of-state (EoS), generated within the framework of relativistic mean field model with density-dependent couplings are adopted for the purpose. We follow the quasi-stationary evolution of rotating stars along the constant rest mass sequences, that varies considerably with different constituents in the EoS. We also explore the universal relations associated with some of the normalized properties, such as critical mass and moment of inertia for specific EoS or as a matter of fact constituents of the dense matter. Deviations in the universal relations for moment of inertia are observed at higher compactness. This study presents important results concerning the properties of neutron stars, that could be observationally verified in the near future using Square Kilometer Array telescope.

Quasiequilibrium models for triaxially deformed rotating compact stars

Quasiequilibrium models of rapidly rotating triaxially deformed stars are computed in general relativistic gravity, assuming a conformally flat spatial geometry (Isenberg-Wilson-Mathews formulation) and a polytropic equation of state. Highly deformed solutions are calculated on the initial slice covered by spherical coordinate grids, centered at the source, in all angular directions up to a large truncation radius. Constant rest mass sequences are calculated from nearly axisymmetric to maximally deformed triaxial configurations. Selected parameters are to model (proto-) neutron stars; the compactness is $M/R=0.001$, 0.1, 0.14, and 0.2 for polytropic index $n=0.3$ and $M/R=0.001$, 0.1, 0.12, and 0.14 for $n=0.5$, where $M/R$ refers to that of a nonrotating spherical star having the same rest mass. We confirmed that the triaxial solutions exist for these parameters as in the case of Newtonian polytropes. However, it is also found that the triaxial sequences become shorter for higher compactness, and those disappear at a certain large compactness for the $n=0.5$ case. In the scenario of the contraction of proto-neutron stars being subject to strong viscosity and rapid cooling, it is plausible that, once the viscosity driven secular instability sets in during the contraction, the proto-neutron stars are always maximally deformed triaxial configurations, as long as the compactness and the equation of state parameters allow such triaxial sequences. Detection of gravitational waves from such sources may be used as another probe for the nuclear equation of state.

Approximate matching of analytic and numerical solutions for rapidly rotating neutron stars

We investigate the properties of a closed-form analytic solution recently found by Manko et al. (2000) for the exterior spacetime of rapidly rotating neutron stars. For selected equations of state we numerically solve the full Einstein equations to determine the neutron star spacetime along constant rest mass sequences. The analytic solution is then matched to the numerical solutions by imposing the condition that the quadrupole moment of the numerical and analytic spacetimes be the same. For the analytic solution we consider, such a matching condition can be satisfied only for very rapidly rotating stars. When solutions to the matching condition exist, they belong to one of two branches. For one branch the current octupole moment of the analytic solution is very close to the current octupole moment of the numerical spacetime; the other branch is more similar to the Kerr solution. We present an extensive comparison of the radii of innermost stable circular orbits (ISCOs) obtained with a) the analytic solution, b) the Kerr metric, c) an analytic series expansion derived by Shibata and Sasaki (1998) and d) a highly accurate numerical code. In most cases where a corotating ISCO exists, the analytic solution has an accuracy consistently better than the Shibata-Sasaki expansion. The numerical code is used for tabulating the mass-quadrupole and current-octupole moments for several sequences of constant rest mass.

Rapidly Rotating Strange Stars for a New Equation of State of Strange Quark Matter

For a new equation of state of strange quark matter, we construct equilibrium sequences of rapidly rotating strange stars in general relativity. The sequences are the normal and supramassive evolutionary sequences of constant rest mass. We also calculate equilibrium sequences for a constant value of Ω corresponding to the most rapidly rotating pulsar PSR 1937+21. In addition, we calculate the radius of the marginally stable orbit and its dependence on Ω, relevant for modeling of kilohertz quasi-periodic oscillations in X-ray binaries.

General relativistic models of binary neutron stars in quasiequilibrium

We perform fully relativistic calculations of binary neutron stars in corotating, circular orbit. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to lose energy and slowly spiral inwards. However, since inspiral occurs on a time scale much longer than the orbital period, we can treat the binary to be in quasiequilibrium. In this approximation, we integrate a subset of the Einstein equations coupled to the relativistic equation of hydrostatic equilibrium to solve the initial value problem for binaries of arbitrary separation. We adopt a polytropic equation of state to determine the structure and maximum mass of neutron stars in close binaries for polytropic indices $n=1,$ 1.5 and 2. We construct sequences of constant rest-mass and locate turning points along energy equilibrium curves to identify the onset of orbital instability. In particular, we locate the innermost stable circular orbit and its angular velocity. We construct the first contact binary systems in full general relativity. These arise whenever the equation of state is sufficiently soft $(n\ensuremath{\gtrsim}1.5).$ A radial stability analysis reveals no tendency for neutron stars in close binaries to collapse to black holes prior to merger.

Binary Neutron Stars in General Relativity: Quasiequilibrium Models

We perform fully relativistic calculations of binary neutron stars in quasi-equilibrium circular orbits. We integrate Einstein's equations together with the relativistic equation of hydrostatic equilibrium to solve the initial value problem for equal-mass binaries of arbitrary separation. We construct sequences of constant rest mass and identify the innermost stable circular orbit and its angular velocity. We find that the quasi-equilibrium maximum allowed mass of a neutron star in a close binary is slightly larger than in isolation.