95 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
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 : II. Collapse dynamics and gravitational radiation
We have performed hydrodynamic simulations of relativistic rotational supernova core collapse in axisymmetry and have computed the gravitational radiation emitted by such an event. The Einstein equations are formulated using the conformally flat metric approximation, and the corresponding hydrodynamic equations are written as a first-order flux-conservative hyperbolic system. Details of the methodology and of the numerical code have been given in an accompanying paper. We have simulated the evolution of 26 models in both Newtonian and relativistic gravity. The initial configurations are di erentially rotating relativistic 4=3-polytropes in equilibrium which have a central density of 10^10 g cm^−3. Collapse is initiated by decreasing the
adiabatic index to some prescribed fixed value. The equation of state consists of a polytropic and a thermal part for a more realistic treatment of shock waves. Any microphysics like electron capture and neutrino transport is neglected. Our simulations show that the three di erent types of rotational supernova core collapse and gravitational waveforms identified in previous Newtonian simulations (regular collapse, multiple bounce collapse, and rapid collapse) are also present in relativistic gravity. However, rotational core collapse with multiple bounces is only possible in a much narrower parameter range in relativistic gravity. The relativistic models cover almost the same range of gravitational wave amplitudes (4x10^−21 <= h^TT 3x10^−20 for a source at a distance of 10 kpc) and frequencies (60 Hz <= ν <= 1000 Hz) as the corresponding Newtonian ones. Averaged over all models, the total energy radiated in the form of gravitational waves is 8.2 10^−8 Moc^2 in the relativistic case, and 3.6 10^−8 Moc^2 in the Newtonian case. For all collapse models that are of the same type in both Newtonian and relativistic gravity, the gravitational wave signal is of lower amplitude. If the collapse type changes, either weaker or stronger signals are found in the relativistic case. For a given model, relativistic gravity can cause a large increase of the characteristic signal frequency of up to a factor of five, which may have important consequences for the signal detection. Our study implies that the prospects for detection of gravitational wave signals from axisymmetric supernova rotational core collapse do not improve when taking into account relativistic gravity. The gravitational wave signals obtained in our study are within the sensitivity range of the first generation laser interferometer detectors if the source is located within the Local Group. An online catalogue containing the gravitational wave signal amplitudes and spectra of all our models is available at the URL http://www.mpa-garching.mpg.de/Hydro/hydro.html.Font Roda, Jose Antonio, [email protected]
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
Generic Gravitational Wave Signals from the Collapse of Rotating Stellar Cores
We perform general relativistic simulations of stellar core collapse to a proto-neutron star, using a microphysical equation of state as well as an approximate description of deleptonization. We show that for a wide variety of rotation rates and profiles the gravitational wave burst signals from the core bounce are of a generic type, known as Type I in the literature. In our systematic study, using both general relativity and Newtonian gravity, we identify and individually quantify the micro- and macrophysical mechanisms leading to this result, i.e. the effects of rotation, the equation of state, and deleptonization. Such a generic type of signal templates will likely facilitate a more efficient search in current and future gravitational wave detectors of both interferometric and resonant type
Axisymmetric simulations of magnetorotational core collapse: approximate inclusion of general relativistic effects
We continue our investigations of the magnetorotational collapse of stellar cores by discussing simulations performed with a modified Newtonian gravitational potential that mimics general relativistic effects. The approximate TOV gravitational potential used in our simulations captures several basic features of fully relativistic simulations quite well. In particular, it is able to correctly reproduce the behavior of models that show a qualitative change both of the dynamics and the gravitational wave signal when switching from Newtonian to fully relativistic simulations. For models where the dynamics and gravitational wave signals are already captured qualitatively correctly by a Newtonian potential, the results of the Newtonian and the approximate TOV models differ quantitatively. The collapse proceeds to higher densities with the approximate TOV potential, allowing for a more efficient amplification of the magnetic field by differential rotation. The strength of the saturation fields (∼10^15 G at the surface of the inner core) is a factor of two to three higher than in Newtonian gravity. Due to the more efficient field amplification, the influence of magnetic fields is considerably more pronounced than in the Newtonian case for some of the models. As in the Newtonian case, sufficiently strong magnetic fields slow down the core’s rotation and trigger a secular contraction phase to higher densities. More clearly than in Newtonian models, the collapsed cores of these models exhibit two different kinds of shock generation. Due to magnetic braking, a first shock wave created during the initial centrifugal bounce at subnuclear densities does not suffice for ejecting any mass, and the temporarily stabilized core continues to collapse to supranuclear densities. Another stronger shock wave is generated during the second bounce as the core exceeds nuclear matter density. The gravitational wave signal of these models does not fit into the standard classification. Therefore, in the first paper of this series we introduced a new type of gravitational wave signal, which we call type IV or “magnetic type”. This signal type is more frequent for the approximate relativistic potential than for the Newtonian one. Most of our weak-field models are marginally detectable with the current LIGO interferometer for a source located at a distance of 10 kpc. Strongly magnetized models emit a substantial fraction of their GW power at very low frequencies. A flat spectrum between 10 Hz and <∼100 kHz denotes the generation of a jet-like hydromagnetic outflow.Aloy Toras, Miguel Angel, [email protected]
Gravitational waves from relativistic rotational core collapse
We present results from simulations of axisymmetric relativistic rotational
core collapse. The general relativistic hydrodynamic equations are formulated
in flux-conservative form and solved using a high-resolution shock-capturing
scheme. The Einstein equations are approximated with a conformally flat
3-metric. We use the quadrupole formula to extract waveforms of the
gravitational radiation emitted during the collapse. A comparison of our
results with those of Newtonian simulations shows that the wave amplitudes
agree within 30%. Surprisingly, in some cases, relativistic effects actually
diminish the amplitude of the gravitational wave signal. We further find that
the parameter range of models suffering multiple coherent bounces due to
centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure
- …