573 research outputs found
General relativistic hydrodynamics in curvilinear coordinates
In this paper we report on what we believe is the first successful
implementation of relativistic hydrodynamics, coupled to dynamical spacetimes,
in spherical polar coordinates without symmetry assumptions. We employ a
high-resolution shock-capturing scheme, which requires that the equations be
cast in flux-conservative form. One example of such a form is the :Valencia"
formulation, which has been adopted in numerous applications, in particular in
Cartesian coordinates. Here we generalize this formulation to allow for a
reference-metric approach, which provides a natural framework for calculations
in curvilinear coordinates. In spherical polar coordinates, for example, it
allows for an analytical treatment of the singular r and sin(\theta) terms that
appear in the equations. We experiment with different versions of our
generalized Valencia formulation in numerical implementations of relativistic
hydrodynamics for both fixed and dynamical spacetimes. We consider a number of
different tests -- non-rotating and rotating relativistic stars, as well as
gravitational collapse to a black hole -- to demonstrate that our formulation
provides a promising approach to performing fully relativistic astrophysics
simulations in spherical polar coordinates.Comment: 14 pages, 8 figures, version to be published in PR
Numerical Relativity in Spherical Polar Coordinates: Off-center Simulations
We have recently presented a new approach for numerical relativity
simulations in spherical polar coordinates, both for vacuum and for
relativistic hydrodynamics. Our approach is based on a reference-metric
formulation of the BSSN equations, a factoring of all tensor components, as
well as a partially implicit Runge-Kutta method, and does not rely on a
regularization of the equations, nor does it make any assumptions about the
symmetry across the origin. In order to demonstrate this feature we present
here several off-centered simulations, including simulations of single black
holes and neutron stars whose center is placed away from the origin of the
coordinate system, as well as the asymmetric head-on collision of two black
holes. We also revisit our implementation of relativistic hydrodynamics and
demonstrate that a reference-metric formulation of hydrodynamics together with
a factoring of all tensor components avoids problems related to the coordinate
singularities at the origin and on the axes. As a particularly demanding test
we present results for a shock wave propagating through the origin of the
spherical polar coordinate system.Comment: 13 pages, 11 figures; matches version published in PR
Dynamic system classifier
Stochastic differential equations describe well many physical, biological and
sociological systems, despite the simplification often made in their
derivation. Here the usage of simple stochastic differential equations to
characterize and classify complex dynamical systems is proposed within a
Bayesian framework. To this end, we develop a dynamic system classifier (DSC).
The DSC first abstracts training data of a system in terms of time dependent
coefficients of the descriptive stochastic differential equation. Thereby the
DSC identifies unique correlation structures within the training data. For
definiteness we restrict the presentation of DSC to oscillation processes with
a time dependent frequency {\omega}(t) and damping factor {\gamma}(t). Although
real systems might be more complex, this simple oscillator captures many
characteristic features. The {\omega} and {\gamma} timelines represent the
abstract system characterization and permit the construction of efficient
signal classifiers. Numerical experiments show that such classifiers perform
well even in the low signal-to-noise regime.Comment: 11 pages, 8 figure
Magneto-elastic oscillations of neutron stars with dipolar magnetic fields
By means of two dimensional, general-relativistic, magneto-hydrodynamical
simulations we investigate the oscillations of magnetized neutron star models
(magnetars) including the description of an extended solid crust. The aim of
this study is to understand the origin of the QPOs observed in the giant flares
of SGRs. We confirm the existence of three different regimes: (a) a weak
magnetic field regime B<5 x 10^13 G, where crustal shear modes dominate the
evolution; (b) a regime of intermediate magnetic fields 5 x 10^13 G<B< 10^15 G,
where Alfv\'en QPOs are mainly confined to the core of the neutron star and the
crustal shear modes are damped very efficiently; and (c) a strong field regime
B>10^15 G, where magneto-elastic oscillations reach the surface and approach
the behavior of purely Alfv\'en QPOs. When the Alfv\'en QPOs are confined to
the core of the neutron star, we find qualitatively similar QPOs as in the
absence of a crust. The lower QPOs associated with the closed field lines of
the dipolar magnetic field configuration are reproduced as in our previous
simulations without crust, while the upper QPOs connected to the open field
lines are displaced from the polar axis. Additionally, we observe a family of
edge QPOs. Our results do not leave much room for a crustal-mode interpretation
of observed QPOs in SGR giant flares, but can accommodate an interpretation of
these observations as originating from Alfv\'en-like, global, turning-point
QPOs in models with dipolar magnetic field strengths in the narrow range of 5 x
10^15 G < B < 1.4 x 10^16 G. This range is somewhat larger than estimates for
magnetic field strengths in known magnetars. The discrepancy may be resolved in
models including a more complicated magnetic field structure or with models
taking superfluidity of the neutrons and superconductivity of the protons in
the core into account.Comment: 25 pages, 17 figures, 7 tables, minor corrections to match published
version in MNRA
Constraining properties of high-density matter in neutron stars with magneto-elastic oscillations
We discuss torsional oscillations of highly magnetised neutron stars
(magnetars) using two-dimensional, magneto-elastic-hydrodynamical simulations.
Our model is able to explain both the low- and high-frequency quasi-periodic
oscillations (QPOs) observed in magnetars. The analysis of these oscillations
provides constraints on the breakout magnetic-field strength, on the
fundamental QPO frequency, and on the frequency of a particularly excited
overtone. More importantly, we show how to use this information to generically
constraint properties of high-density matter in neutron stars, employing
Bayesian analysis. In spite of current uncertainties and computational
approximations, our model-dependent Bayesian posterior estimates for SGR
1806-20 yield a magnetic-field strength G and a crust thickness of km, which are both in remarkable agreement with
observational and theoretical expectations, respectively (1- error bars
are indicated). Our posteriors also favour the presence of a superfluid phase
in the core, a relatively low stellar compactness, , indicating a
relatively stiff equation of state and/or low mass neutron star, and high shear
speeds at the base of the crust, cm/s. Although the
procedure laid out here still has large uncertainties, these constraints could
become tighter when additional observations become available.Comment: 14 pages, 8 figures, 6 tables, submitted to MNRA
Coherent magneto-elastic oscillations in superfluid magnetars
We study the effect of superfluidity on torsional oscillations of highly
magnetised neutron stars (magnetars) with a microphysical equation of state by
means of two-dimensional, magnetohydrodynamical- elastic simulations. The
superfluid properties of the neutrons in the neutron star core are treated in a
parametric way in which we effectively decouple part of the core matter from
the oscillations. Our simulations confirm the existence of two groups of
oscillations, namely continuum oscillations that are confined to the neutron
star core and are of Alfv\'enic character, and global oscillations with
constant phase and that are of mixed magneto-elastic type. The latter might
explain the quasi-periodic oscillations observed in magnetar giant flares,
since they do not suffer from the additional damping mechanism due to phase
mixing, contrary to what happens for continuum oscillations. However, we cannot
prove rigorously that the coherent oscillations with constant phase are normal
modes. Moreover, we find no crustal shear modes for the magnetic field
strengths typical for magnetars.We provide fits to our numerical simulations
that give the oscillation frequencies as functions of magnetic field strength
and proton fraction in the core.Comment: 16 pages, 12 figures, accepted by MNRA
Modulating the magnetosphere of magnetars by internal magneto-elastic oscillations
We couple internal torsional, magneto-elastic oscillations of highly
magnetized neutron stars (magnetars) to their magnetospheres. The corresponding
axisymmetric perturbations of the external magnetic field configuration evolve
as a sequence of linear, force-free equilibria that are completely determined
by the background magnetic field configuration and by the perturbations of the
magnetic field at the surface. The perturbations are obtained from simulations
of magneto-elastic oscillations in the interior of the magnetar. While such
oscillations can excite travelling Alfv\'en waves in the exterior of the star
only in a very limited region close to the poles, they still modulate the near
magnetosphere by inducing a time-dependent twist between the foot-points of
closed magnetic field lines that exit the star at a polar angle rad. Moreover, we find that for a dipole-like background magnetic field
configuration the magnetic field modulations in the magnetosphere, driven by
internal oscillations, can only be symmetric with respect to the equator. This
is in agreement with our previous findings, where we interpreted the observed
quasi-periodic oscillations in the X-ray tail of magnetar bursts as driven by
the family of internal magneto-elastic oscillations with symmetric magnetic
field perturbations.Comment: 9 pages, 5 figures, 2 tables, Accepted by MNRA
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