177 research outputs found
Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation
We study non-linear axisymmetric pulsations of rotating relativistic stars
using a general relativistic hydrodynamics code under the assumption of a
conformal flatness. We compare our results to previous simulations where the
spacetime dynamics was neglected. The pulsations are studied along various
sequences of both uniformly and differentially rotating relativistic polytropes
with index N = 1. We identify several modes, including the lowest-order l = 0,
2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes.
Differential rotation significantly lowers mode frequencies, increasing
prospects for detection by current gravitational wave interferometers. We
observe an extended avoided crossing between the l = 0 and l = 4 first
overtones, which is important for correctly identifying mode frequencies in
case of detection. For uniformly rotating stars near the mass-shedding limit,
we confirm the existence of the mass-shedding-induced damping of pulsations,
though the effect is not as strong as in the Cowling approximation. We also
investigate non-linear harmonics of the linear modes and notice that rotation
changes the pulsation frequencies in a way that would allow for various
parametric instabilities between two or three modes to take place. We assess
the detectability of each obtained mode by current gravitational wave detectors
and outline how the empirical relations that have been constructed for
gravitational wave asteroseismology could be extended to include the effects of
rotation.Comment: 24 pages, 20 figures; minor corrections, added extended discussion
and one figure in one subsectio
A learning approach to the detection of gravitational wave transients
We investigate the class of quadratic detectors (i.e., the statistic is a
bilinear function of the data) for the detection of poorly modeled
gravitational transients of short duration. We point out that all such
detection methods are equivalent to passing the signal through a filter bank
and linearly combine the output energy. Existing methods for the choice of the
filter bank and of the weight parameters rely essentially on the two following
ideas: (i) the use of the likelihood function based on a (possibly
non-informative) statistical model of the signal and the noise, (ii) the use of
Monte-Carlo simulations for the tuning of parametric filters to get the best
detection probability keeping fixed the false alarm rate. We propose a third
approach according to which the filter bank is "learned" from a set of training
data. By-products of this viewpoint are that, contrarily to previous methods,
(i) there is no requirement of an explicit description of the probability
density function of the data when the signal is present and (ii) the filters we
use are non-parametric. The learning procedure may be described as a two step
process: first, estimate the mean and covariance of the signal with the
training data; second, find the filters which maximize a contrast criterion
referred to as deflection between the "noise only" and "signal+noise"
hypothesis. The deflection is homogeneous to the signal-to-noise ratio and it
uses the quantities estimated at the first step. We apply this original method
to the problem of the detection of supernovae core collapses. We use the
catalog of waveforms provided recently by Dimmelmeier et al. to train our
algorithm. We expect such detector to have better performances on this
particular problem provided that the reference signals are reliable.Comment: 22 pages, 4 figure
Relativistic simulations of the phase-transition-induced collapse of neutron stars
An increase in the central density of a neutron star may trigger a phase
transition from hadronic matter to deconfined quark matter in the core, causing
it to collapse to a more compact hybrid-star configuration. We present a study
of this, building on previous work by Lin et al. (2006). We follow them in
considering a supersonic phase transition and using a simplified equation of
state, but our calculations are general relativistic (using 2D simulations in
the conformally flat approximation) as compared with their 3D Newtonian
treatment. We also improved the treatment of the initial phase transformation,
avoiding the introduction of artificial convection. As before, we find that the
emitted gravitational-wave spectrum is dominated by the fundamental
quasi-radial and quadrupolar pulsation modes but the strain amplitudes are much
smaller than suggested previously, which is disappointing for the detection
prospects. However, we see significantly smaller damping and observe a
nonlinear mode resonance which substantially enhances the emission in some
cases. We explain the damping mechanisms operating, giving a different view
from the previous work. Finally, we discuss the detectability of the
gravitational waves, showing that the signal-to-noise ratio for current or
second generation interferometers could be high enough to detect such events in
our Galaxy, although third generation detectors would be needed to observe them
out to the Virgo cluster, which would be necessary for having a reasonable
event rate.Comment: 28 pages, 27 figures. Minor changes to be consistent with published
versio
Dynamic migration of rotating neutron stars due to a phase transition instability
Using numerical simulations based on solving the general relativistic
hydrodynamic equations, we study the dynamics of a phase transition in the
dense core of isolated rotating neutron stars, triggered by the back bending
instability reached via angular momentum loss. In particular, we investigate
the dynamics of a migration from an unstable configuration into a stable one,
which leads to a mini-collapse of the neutron star and excites sizeable
pulsations in its bulk until it acquires a new stable equilibrium state. We
consider equations of state with softening at high densities, a simple analytic
one with a mixed hadron-quark phase in an intermediate pressure interval and
pure quark matter at very high densities, and a microphysical one that has a
first-order phase transition, originating from kaon condensation. Although the
marginally stable initial models are rigidly rotating, we observe that during
the collapse (albeit little) differential rotation is created. We analyze the
emission of gravitational radiation, which in some models is amplified by mode
resonance effects, and assess its prospective detectability by interferometric
detectors. We expect that the most favorable conditions for dynamic migration
exist in very young magnetars. We find that the damping of the post-migration
pulsations strongly depends on the character of the equation of state
softening. The damping of pulsations in the models with the microphysical
equation of state is caused by dissipation associated with matter flowing
through the density jump at the edge of the dense core. If at work, this
mechanism dominates over all other types of dissipation, like bulk viscosity in
the exotic-phase core, gravitational radiation damping, or numerical viscosity.Comment: 23 pages, 18 figures, minor modification
"Mariage des Maillages": A new numerical approach for 3D relativistic core collapse simulations
We present a new 3D general relativistic hydrodynamics code for simulations
of stellar core collapse to a neutron star, as well as pulsations and
instabilities of rotating relativistic stars. It uses spectral methods for
solving the metric equations, assuming the conformal flatness approximation for
the three-metric. The matter equations are solved by high-resolution
shock-capturing schemes. We demonstrate that the combination of a finite
difference grid and a spectral grid can be successfully accomplished. This
"Mariage des Maillages" (French for grid wedding) approach results in high
accuracy of the metric solver and allows for fully 3D applications using
computationally affordable resources, and ensures long term numerical stability
of the evolution. We compare our new approach to two other, finite difference
based, methods to solve the metric equations. A variety of tests in 2D and 3D
is presented, involving highly perturbed neutron star spacetimes and
(axisymmetric) stellar core collapse, demonstrating the ability to handle
spacetimes with and without symmetries in strong gravity. These tests are also
employed to assess gravitational waveform extraction, which is based on the
quadrupole formula.Comment: 29 pages, 16 figures; added more information about convergence tests
and grid setu
Exploring the relativistic regime with Newtonian hydrodynamics: An improved effective gravitational potential for supernova simulations
We investigate the possibility to approximate relativistic effects in
hydrodynamical simulations of stellar core collapse and post-bounce evolution
by using a modified gravitational potential in an otherwise standard Newtonian
hydrodynamic code. Different modifications of the effective relativistic
potential introduced by Rampp & Janka (2002) are discussed. Corresponding
hydrostatic solutions are compared with solutions of the TOV equations, and
hydrodynamic simulations with two different codes are compared with fully
relativistic results. One code is applied for one- and two-dimensional
calculations with a simple equation of state, and employs either the modified
effective relativistic potential in a Newtonian framework or solves the general
relativistic field equations under the assumption of the conformal flatness
condition (CFC) for the three-metric. The second code allows for full-scale
supernova runs including a microphysical equation of state and neutrino
transport based on the solution of the Boltzmann equation and its moments
equations. We present prescriptions for the effective relativistic potential
for self-gravitating fluids to be used in Newtonian codes, which produce
excellent agreement with fully relativistic solutions in spherical symmetry,
leading to significant improvements compared to previously published
approximations. Moreover, they also approximate qualitatively well relativistic
solutions for models with rotation.Comment: 20 pages, 13 figures; corrected minor inaccuracies and added two
subsection
Relativistic simulations of rotational core collapse. I. Methods, initial models, and code tests
We describe an axisymmetric general relativistic code for rotational core
collapse. The code evolves the coupled system of metric and fluid equations
using the ADM 3+1 formalism and a conformally flat metric approximation of the
Einstein equations. The relativistic hydrodynamics equations are formulated as
a first-order flux-conservative hyperbolic system and are integrated using
high-resolution shock-capturing schemes based on Riemann solvers. We assess the
quality of the conformally flat metric approximation for relativistic core
collapse and present a comprehensive set of tests which the code successfully
passed. The tests include relativistic shock tubes, the preservation of the
rotation profile and of the equilibrium of rapidly and differentially rotating
neutron stars (approximated as rotating polytropes), spherical relativistic
core collapse, and the conservation of rest-mass and angular momentum in
dynamic spacetimes. The application of the code to relativistic rotational core
collapse, with emphasis on the gravitational waveform signature, is presented
in an accompanying paper.Comment: 18 pages, 12 figure
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
Exploring the relativistic regime with Newtonian hydrodynamics: II. An effective gravitational potential for rapid rotation
We present the generalization of a recently introduced modified gravitational
potential for self-gravitating fluids. The use of this potential allows for an
accurate approximation of general relativistic effects in an otherwise
Newtonian hydrodynamics code also in cases of rapid rotation. We test this
approach in numerical simulations of astrophysical scenarios related to compact
stars, like supernova core collapse with both a simplified and detailed
microphysical description of matter, and rotating neutron stars in equilibrium.
We assess the quality of the new potential, and demonstrate that it provides a
significant improvement compared to previous formulations for such potentials.
Newtonian simulations of compact objects employing such an effective
relativistic potential predict inaccurate pulsation frequencies despite the
excellent agreement of the collapse dynamics and structure of the compact
objects with general relativistic results. We analyze and discuss the reason
for this behavior.Comment: 15 pages, 12 figures, minor modification
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