73 research outputs found
Numerical models for stationary superfluid neutron stars in general relativity with realistic equations of state
We present a numerical model for uniformly rotating superfluid neutron stars,
for the first time with realistic microphysics including entrainment, in a
fully general relativistic framework. We compute stationary and axisymmetric
configurations of neutron stars composed of two fluids, namely superfluid
neutrons and charged particles (protons and electrons), rotating with different
rates around a common axis. Both fluids are coupled by entrainment, a
non-dissipative interaction which in case of a non-vanishing relative velocity
between the fluids, causes the fluid momenta being not aligned with the
respective fluid velocities. We extend the formalism by Comer and Joynt (2003)
in order to calculate the equation of state (EoS) and entrainment parameters
for an arbitrary relative velocity. The resulting entrainment matrix fulfills
all necessary sum rules and in the limit of small relative velocity our results
agree with Fermi liquid theory ones, derived to lowest order in the velocity.
This formalism is applied to two new nuclear equations of state which are
implemented in the numerical model. We are able to obtain precise equilibrium
configurations. Resulting density profiles and moments of inertia are discussed
employing both EoSs, showing the impact of entrainment and the dependence on
the EoS.Comment: 18 pages, 10 figures, minor changes to match published version in
PRD, a typo present in Eq.A1 in the published version has been correcte
Isolated horizons in numerical relativity: constructing the excised Kerr spacetime in Dirac gauge
Using a constrained formalism for Einstein equations in Dirac gauge, we
propose to compute excised quasistationary initial data for black hole
spacetimes in full general relativity. Vacuum spacetime settings are
numerically constructed by using the isolated horizon formalism; we especially
tackle the conformal metric part of our equations, assuming global
stationarity. We show that a no-boundary treatment can be used on the horizon
for the equation related to the conformal metric. We relate this finding to
previous suggestions in the literature, and use our results to assess the
widely used conformally flat approximation for computing black hole initial
data.Comment: 3 pages, 1 figure; to appear in the proceedings of the 12th Marcel
Grossmann meeting on general relativit
Global numerical simulations of the rise of vortex-mediated pulsar glitches in full general relativity
In this paper, we study in detail the role of general relativity on the
global dynamics of giant pulsar glitches as exemplified by Vela. For this
purpose, we carry out numerical simulations of the spin up triggered by the
sudden unpinning of superfluid vortices. In particular, we compute the exchange
of angular momentum between the core neutron superfluid and the rest of the
star within a two-fluid model including both (non-dissipative) entrainment
effects and (dissipative) mutual friction forces. Our simulations are based on
a quasi-stationary approach using realistic equations of state (EoSs). We show
that the evolution of the angular velocities of both fluids can be accurately
described by an exponential law. The associated characteristic rise time
, which can be precisely computed from stationary
configurations only, has a form similar to that obtained in the Newtonian
limit. However, general relativity changes the structure of the star and leads
to additional couplings between the fluids due to frame-dragging effects. As a
consequence, general relativity can have a large impact on the actual value of
: the errors incurred by using Newtonian gravity are thus
found to be as large as for the models considered. Values of the
rise time are calculated for Vela and compared with current observational
limits. Finally, we study the amount of gravitational waves emitted during a
glitch. Simple expressions are obtained for the corresponding characteristic
amplitudes and frequencies. The detectability of glitches through gravitational
wave observatories is briefly discussed.Comment: 19 pages, 12 figures, minor changes to match version to be published
in MNRA
Spectral Methods for Numerical Relativity
Version published online by Living Reviews in Relativity.International audienceEquations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods where, typically, the various functions are expanded onto sets of orthogonal polynomials or functions. A theoretical introduction on spectral expansion is first given and a particular emphasis is put on the fast convergence of the spectral approximation. We present then different approaches to solve partial differential equations, first limiting ourselves to the one-dimensional case, with one or several domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. One then turns to results obtained by various groups in the field of General Relativity by means of spectral methods. First, works which do not involve explicit time-evolutions are discussed, going from rapidly rotating strange stars to the computation of binary black holes initial data. Finally, the evolutions of various systems of astrophysical interest are presented, from supernovae core collapse to binary black hole mergers
An excision scheme for black holes in constrained evolution formulations: spherically symmetric case
Excision techniques are used in order to deal with black holes in numerical
simulations of Einstein equations and consist in removing a topological sphere
containing the physical singularity from the numerical domain, applying instead
appropriate boundary conditions at the excised surface. In this work we present
recent developments of this technique in the case of constrained formulations
of Einstein equations and for spherically symmetric spacetimes. We present a
new set of boundary conditions to apply to the elliptic system in the
fully-constrained formalism of Bonazzola et al. (2004), at an arbitrary
coordinate sphere inside the apparent horizon. Analytical properties of this
system of boundary conditions are studied and, under some assumptions, an
exponential convergence toward the stationary solution is exhibited for the
vacuum spacetime. This is verified in numerical examples, together with the
applicability in the case of the accretion of a scalar field onto a
Schwarzschild black hole. We also present the successful use of the excision
technique in the collapse of a neutron star to a black hole, when excision is
switched on during the simulation, after the formation of the apparent horizon.
This allows the accretion of matter remaining outside the excision surface and
for the stable long-term evolution of the newly formed black hole.Comment: 14 pages, 9 figures. New section added and changes included according
to published articl
Absorbing boundary conditions for simulation of gravitational waves with spectral methods in spherical coordinates
We present a new formulation of the multipolar expansion of an exact boundary
condition for the wave equation, which is truncated at the quadrupolar order.
Using an auxiliary function, that is the solution of a wave equation on the
sphere defining the outer boundary of the numerical grid, the absorbing
boundary condition is simply written as a perturbation of the usual Sommerfeld
radiation boundary condition. It is very easily implemented using spectral
methods in spherical coordinates. Numerical tests of the method show that very
good accuracy can be achieved and that this boundary condition has the same
efficiency for dipolar and quadrupolar waves as the usual Sommerfeld boundary
condition for monopolar ones. This is of particular importance for the
simulation of gravitational waves, which have dominant quadrupolar terms, in
General Relativity.Comment: 14 pages, 4 figures. Strongly modified version, accepted for
publication in Journal of Computational Physics (new title, new figures and
removal of the description of multidomain spectral methods
The explosion mechanism of core-collapse supernovae: progress in supernova theory and experiments
The explosion of core-collapse supernova depends on a sequence of events
taking place in less than a second in a region of a few hundred kilometers at
the center of a supergiant star, after the stellar core approaches the
Chandrasekhar mass and collapses into a proto-neutron star, and before a shock
wave is launched across the stellar envelope. Theoretical efforts to understand
stellar death focus on the mechanism which transforms the collapse into an
explosion. Progress in understanding this mechanism is reviewed with particular
attention to its asymmetric character. We highlight a series of successful
studies connecting observations of supernova remnants and pulsars properties to
the theory of core-collapse using numerical simulations. The encouraging
results from first principles models in axisymmetric simulations is tempered by
new puzzles in 3D. The diversity of explosion paths and the dependence on the
pre-collapse stellar structure is stressed, as well as the need to gain a
better understanding of hydrodynamical and MHD instabilities such as SASI and
neutrino-driven convection. The shallow water analogy of shock dynamics is
presented as a comparative system where buoyancy effects are absent. This
dynamical system can be studied numerically and also experimentally with a
water fountain. The potential of this complementary research tool for supernova
theory is analyzed. We also review its potential for public outreach in science
museums.Comment: 19 pages, 6 figures, invited review accepted for publication in PAS
Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue
Uniqueness problems in the elliptic sector of constrained formulations of
Einstein equations have a dramatic effect on the physical validity of some
numerical solutions, for instance when calculating the spacetime of very
compact stars or nascent black holes. The fully constrained formulation (FCF)
proposed by Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak is one of these
formulations. It contains, as a particular case, the approximation of the
conformal flatness condition (CFC) which, in the last ten years, has been used
in many astrophysical applications. The elliptic part of the FCF basically
shares the same differential operators as the elliptic equations in CFC scheme.
We present here a reformulation of the elliptic sector of CFC that has the
fundamental property of overcoming the local uniqueness problems. The correct
behavior of our new formulation is confirmed by means of a battery of numerical
simulations. Finally, we extend these ideas to FCF, complementing the
mathematical analysis carried out in previous studies.Comment: 17 pages, 5 figures. Minor changes to be consistent with published
versio
Rotating star initial data for a constrained scheme in numerical relativity
A new numerical code for computing stationary axisymmetric rapidly rotating
stars in general relativity is presented. The formulation is based on a fully
constrained-evolution scheme for 3+1 numerical relativity using the Dirac gauge
and maximal slicing. We use both the polytropic and MIT bag model equations of
state to demonstrate that the code can construct rapidly rotating neutron star
and strange star models. We compare numerical models obtained by our code and a
well-established code, which uses a different gauge condition, and show that
the two codes agree to high accuracy.Comment: Minor changes and one figure added. Version accepted for publication
in Class. Quant. Gra
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