430 research outputs found

### Oscillations of relativistic axisymmetric tori and implications for modelling kHz-QPOs in neutron-star X-ray binaries

We perform a global linear perturbative analysis, and investigate the
oscillation properties of relativistic, non-selfgravitating tori orbiting
around neutron stars in the slow rotation limit approximation. Extending the
work done in Schwarzschild and Kerr backgrounds, we consider the axisymmetric
oscillations of vertically integrated tori in the Hartle-Thorne spacetime. The
equilibrium models are constructed by selecting a number of different
non-Keplerian distributions of specific angular momentum, allowing for disc
sizes $L \sim 0.5 - 600$ gravitational radii. Our results, obtained after
solving a global eigenvalue problem to compute the xisymmetric $p$-modes,
indicate that such oscillation modes could account with most observed lower
($\nu_L$) and upper ($\nu_U$) high frequency quasi-periodic oscillations for
Sco X-1, and for some Z sources and Atoll sources with $\nu_L\ gtrsim 500$ Hz.
However, when $\nu_L \lesssim 500$ Hz, $p$-modes oscillations do not account
for the linear relation $\nu_U = A \nu_L + B$, $B \neq 0$ between the upper and
the lower high frequency quasi-periodic oscillations that are observed in
neutron star low-mass X-ray binaries.Comment: 8 pages, 4 figures, matches accepted version for publication in MNRA

### Oscillations of vertically integrated relativistic tori -II. Axisymmetric modes in a Kerr spacetime

This is the second of a series of papers investigating the oscillation
properties of relativistic, non-selfgravitating tori orbiting around black
holes. Extending the work done in a Schwarzschild background, we here consider
the axisymmetric oscillations of vertically integrated tori in a Kerr
spacetime. The tori are modeled with a number of different non-Keplerian
distributions of specific angular momentum and we discuss how the oscillation
properties depend on these and on the rotation of the central black hole. We
first consider a local analysis to highlight the relations between acoustic and
epicyclic oscillations in a Kerr spacetime and subsequently perform a global
eigenmode analysis to compute the axisymmetric p modes. In analogy with what
found in a Schwarzschild background, these modes behave as sound waves that are
modified by rotation and are globally trapped in the torus. For constant
distributions of specific angular momentum, the eigenfrequencies appear in a
sequence 2:3:4:... which is essentially independent of the size of the disc and
of the black hole rotation. For non-constant distributions of angular momentum,
on the other hand, the sequence depends on the properties of the disc and on
the spin of the black hole, becoming harmonic for sufficiently large tori. We
also comment on how p modes could explain the high frequency quasi-periodic
oscillations observed in low-mass X-ray binaries with a black hole candidate
and the properties of an equivalent model in Newtonian physics.Comment: 13 pages, MNRAS, in pres

### 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

### Measuring the black hole spin direction in 3D Cartesian numerical relativity simulations

We show that the so-called flat-space rotational Killing vector method for
measuring the Cartesian components of a black hole spin can be derived from the
surface integral of Weinberg's pseudotensor over the apparent horizon surface
when using Gaussian normal coordinates in the integration. Moreover, the
integration of the pseudotensor in this gauge yields the Komar angular momentum
integral in a foliation adapted to the axisymmetry of the spacetime. As a
result, the method does not explicitly depend on the evolved lapse $\alpha$ and
shift $\beta^i$ on the respective timeslice, as they are fixed to Gaussian
normal coordinates, while leaving the coordinate labels of the spatial metric
$\gamma_{ij}$ and the extrinsic curvature $K_{ij}$ unchanged. Such gauge fixing
endows the method with coordinate invariance, which is not present in integral
expressions using Weinberg's pseudotensor, as they normally rely on the
explicit use of Cartesian coordinates

### Trumpet Slices in Kerr Spacetimes

We introduce a new time-independent family of analytical coordinate systems
for the Kerr spacetime representing rotating black holes. We also propose a
(2+1)+1 formalism for the characterization of trumpet geometries. Applying this
formalism to our new family of coordinate systems we identify, for the first
time, analytical and stationary trumpet slices for general rotating black
holes, even for charged black holes in the presence of a cosmological constant.
We present results for metric functions in this slicing and analyze the
geometry of the rotating trumpet surface.Comment: 5 pages, 2 figures; version published in PR

### Air recovery assessment on high-pressure pneumatic systems

A computational simulation and experimental work of the fluid flow through the pneumatic circuit used in a stretch blow moulding machine is presented in this paper. The computer code is built around a zero-dimensional thermodynamic model for the air blowing and recycling containers together with a non-linear time-variant deterministic model for the pneumatic three stations single acting valve manifold, which, in turn, is linked to a quasi-one-dimensional unsteady flow model for the interconnecting pipes. The flow through the pipes accounts for viscous friction, heat transfer, cross-sectional area variation, and entropy variation. Two different solving methods are applied: the method of characteristics and the Harten-Lax-Van Leer (HLL) Riemann first-order scheme. The numerical model allows prediction of the air blowing process and, more significantly, permits determination of the recycling rate at each operating cycle. A simplified experimental set-up of the industrial process was designed, and the pressure and temperature were adequately monitored. Predictions of the blowing process for various configurations proved to be in good agreement with the measured results. In addition, a novel design of a valve manifold intended for the polyethylene terephthalate (PET) plastic bottle manufacturing industry is also presented.Peer ReviewedPostprint (author's final draft

### Dynamics of magnetized relativistic tori oscillating around black holes

We present a numerical study of the dynamics of magnetized, relativistic,
non-self-gravitating, axisymmetric tori orbiting in the background spacetimes
of Schwarzschild and Kerr black holes. The initial models have a constant
specific angular momentum and are built with a non-zero toroidal magnetic field
component, for which equilibrium configurations have recently been obtained. In
this work we extend our previous investigations which dealt with purely
hydrodynamical thick discs, and study the dynamics of magnetized tori subject
to perturbations which, for the values of the magnetic field strength
considered here, trigger quasi-periodic oscillations lasting for tens of
orbital periods. Overall, we have found that the dynamics of the magnetized
tori analyzed is very similar to that found in the corresponding unmagnetized
models. The spectral distribution of the eigenfrequencies of oscillation shows
the presence of a fundamental p mode and of a series of overtones in a harmonic
ratio 2:3:.... These simulations, therefore, extend the validity of the model
of Rezzolla et al.(2003a) for explaining the high-frequency QPOs observed in
the spectra of LMXBs containing a black-hole candidate also to the case of
magnetized discs with purely toroidal magnetic field distribution. If
sufficiently compact and massive, these oscillations can also lead to the
emission of intense gravitational radiation which is potentially detectable for
sources within the Galaxy.Comment: 10 pages,7 figures, submitted to MNRA

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