An Exact Study of Rigidly and Rapidly Rotating Stars in General Relativity with Application to the Crab Pulsar

Bonazzola, S.; Schneider, J.

doi:10.1086/152965

Cited by 42 publications

(33 citation statements)

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“…Most authors studying rapid rotation have adopted the approach of Bardeen & Wagoner (1971), which explicitly assumes an isotropic stress tensor and is thus incompatible with electromagnetic Ðelds. Building on earlier work of Bonazzola & Maschio (1971) and Bonazzola & Schneider (1974), Bonazzola et al (1993) present a formulation which allows for the most general stress-energy tensor consistent with a spacetime having the properties of stationarity, axisymmetry, and circularity. The metric for such a spacetime can be expressed as…”

Section: Formalismmentioning

confidence: 99%

Effects of Strong Magnetic Fields on Neutron Star Structure

Cardall

Prakash

Lattimer

2001

ApJ

322

348

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We study static neutron stars with poloidal magnetic Ðelds and a simple class of electric current distributions consistent with the requirement of stationarity. For this class of electric current distributions, we Ðnd that magnetic Ðelds are too large for static conÐgurations to exist when the magnetic force pushes a sufficient amount of mass o †-center that the gravitational force points outward near the origin in the equatorial plane. (In our coordinates an outward gravitational force corresponds to L ln g tt /Lr [ 0, where t and r are respectively time and radial coordinates and is coefficient of dt2 in the line element.) g tt For the equations of state (EOSs) employed in previous work, we obtain conÐgurations of higher mass than had been reported ; we also present results with more recent EOSs. For all EOSs studied, we Ðnd that the maximum mass among these static conÐgurations with magnetic Ðelds is noticeably larger than the maximum mass attainable by uniform rotation, and that for Ðxed values of baryon number the maximum mass conÐgurations are all characterized by an o †-center density maximum.

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Section: Formalismmentioning

confidence: 99%

Effects of Strong Magnetic Fields on Neutron Star Structure

Cardall

Prakash

Lattimer

2001

ApJ

322

348

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“…The numerical calculation of these objects was the subject of papers by several authors (see Bonazzola & Schneider 1974;Wilson 1972;Butterworth & Ipser 1975, 1976Friedman et al 1986Friedman et al , 1989Lattimer et al 1990;Komatsu et al 1989aKomatsu et al , 1989bEriguchi et al 1994;Stergioulas & Friedman 1995;Bonazzola et al 1993; for reviews see Friedman 1998 andStergioulas 1998).…”

Section: Introductionmentioning

confidence: 99%

Highly accurate calculation of rotating neutron stars

Ansorg¹,

Kleinwächter²,

Meinel³

2003

A&A

105

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Abstract. We give a detailed description of the recently developed multi-domain spectral method for constructing highly accurate general-relativistic models of rapidly rotating stars. For both "ordinary" and "critical" configurations, we show using representative examples, how the accuracy improves as the order of the approximation increases. As well as homogeneous fluid bodies, we also discuss models of polytropic and strange stars.

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“…It is possible to use approximations in the form of truncated k-expansions (e.g. Byrd & Freeman 1971) or from fitting functions (Abramowitz & Stegun 1964;Bonazzola & Schneider 1974). This enables a significant reduction of the execution time, but high accuracy can generally not be reached on field and potential values.…”

Section: Notations and Assumptionsmentioning

confidence: 99%

“…We are not aware of any method aiming to estimate Eqs. (2) or (4) rigorously for toroidal configurations (see Bonazzola & Schneider 1974). Our goal is to provide the community with efficient tools to investigate the structure, stability and dynamical evolution of self-gravitating tori, discs and rings 1 , which are ubiquitous objects in the Universe.…”

Section: Introductionmentioning

confidence: 99%

Solutions of the axi-symmetric Poisson equation from elliptic integrals

Huré

2005

A&A

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Abstract. In a series of two papers, we present numerical, integral-based methods to compute accurately the self-gravitating field and potential induced by tri-dimensional, axially symmetric fluids, with a special regard for tori, discs and rings. This first article is concerned with a fully numerical approach. Complex shapes, small/large aspect ratios, important density gradients and compact/extended systems can be accounted for. Loop singularities in the Poisson integrals are carefully treated from kernel splitting and/or density splitting. Field components are obtained from density splitting: the local density field is separated into a vertically homogeneous contribution for which the integrable singularity is known in a closed form, plus a "residual" contribution which yields a regular integrand. This technique is exact in the vertically homogeneous limit. The potential is computed from double splitting: kernel splitting (to isolate explicitly the singular function), followed by density splitting. In each two directions, numerical quadratures are performed using a dynamical mesh (very efficient for flat and extended systems), combined with a high-order, irregular-spacing scheme. Global performances are demonstrated through a few test-configurations. The accuracy is potentially very high, and can reach the computer precision (for simple geometries and smooth density profiles). In terms of computing time to precision ratio, present methods are asymptotically more efficient than classical finite-difference methods. These can be employed either as a "Poisson-solver" or only to compute a sub-set of Dirichlet/Neumann-type boundary conditions in order to initialize spectral/finite-difference/finite element methods. As an example of an astrophysical application, we determine the structure of an uniformly rotating polytrope belonging to the compressible, Dyson-Wong sequence. In a second paper (Paper II), we show that singularities are integrable analytically for geometrically thin systems where the density is of the form ρ ∝ z n . Improvements and extensions (such as the non-axi-symmetric case) are possible and discussed.

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An Exact Study of Rigidly and Rapidly Rotating Stars in General Relativity with Application to the Crab Pulsar

Cited by 42 publications

References 0 publications

Effects of Strong Magnetic Fields on Neutron Star Structure

Effects of Strong Magnetic Fields on Neutron Star Structure

Highly accurate calculation of rotating neutron stars

Solutions of the axi-symmetric Poisson equation from elliptic integrals

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