56 research outputs found

### Model for an optically thick torus in local thermodynamic equilibrium around a black hole

We propose a simple model for an optically thick radiative torus in local
thermodynamic equilibrium around a Kerr black hole. The hydrodynamics
structure, which is not affected by the radiation field, is the same as for the
so--called polish doughnuts. Under the assumption of isentropic fluid and
polytropic equation of state, a simple stationary and axisymmetric solution to
the relativistic radiation hydrodynamics equations is possible, for which the
temperature of the torus scales like the specific enthalpy. The astrophysical
relevance of the model is briefly discussed.Comment: With updated bibliographyc informatio

### Very High Order \PNM Schemes on Unstructured Meshes for the Resistive Relativistic MHD Equations

In this paper we propose the first better than second order accurate method
in space and time for the numerical solution of the resistive relativistic
magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space
dimensions. The nonlinear system under consideration is purely hyperbolic and
contains a source term, the one for the evolution of the electric field, that
becomes stiff for low values of the resistivity. For the spatial discretization
we propose to use high order \PNM schemes as introduced in \cite{Dumbser2008}
for hyperbolic conservation laws and a high order accurate unsplit time
discretization is achieved using the element-local space-time discontinuous
Galerkin approach proposed in \cite{DumbserEnauxToro} for one-dimensional
balance laws with stiff source terms. The divergence free character of the
magnetic field is accounted for through the divergence cleaning procedure of
Dedner et al. \cite{Dedneretal}. To validate our high order method we first
solve some numerical test cases for which exact analytical reference solutions
are known and we also show numerical convergence studies in the stiff limit of
the RRMHD equations using \PNM schemes from third to fifth order of accuracy
in space and time. We also present some applications with shock waves such as a
classical shock tube problem with different values for the conductivity as well
as a relativistic MHD rotor problem and the relativistic equivalent of the
Orszag-Tang vortex problem. We have verified that the proposed method can
handle equally well the resistive regime and the stiff limit of ideal
relativistic MHD. For these reasons it provides a powerful tool for
relativistic astrophysical simulations involving the appearance of magnetic
reconnection.Comment: 24 pages, 6 figures, submitted to JC

### 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

### High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes

We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE)
finite volume scheme on unstructured triangular meshes that is high order
accurate in space and time and that also allows for time-accurate local time
stepping (LTS). The new scheme uses the following basic ingredients: a high
order WENO reconstruction in space on unstructured meshes, an element-local
high-order accurate space-time Galerkin predictor that performs the time
evolution of the reconstructed polynomials within each element, the computation
of numerical ALE fluxes at the moving element interfaces through approximate
Riemann solvers, and a one-step finite volume scheme for the time update which
is directly based on the integral form of the conservation equations in
space-time. The inclusion of the LTS algorithm requires a number of crucial
extensions, such as a proper scheduling criterion for the time update of each
element and for each node; a virtual projection of the elements contained in
the reconstruction stencils of the element that has to perform the WENO
reconstruction; and the proper computation of the fluxes through the space-time
boundary surfaces that will inevitably contain hanging nodes in time due to the
LTS algorithm. We have validated our new unstructured Lagrangian LTS approach
over a wide sample of test cases solving the Euler equations of compressible
gasdynamics in two space dimensions, including shock tube problems, cylindrical
explosion problems, as well as specific tests typically adopted in Lagrangian
calculations, such as the Kidder and the Saltzman problem. When compared to the
traditional global time stepping (GTS) method, the newly proposed LTS algorithm
allows to reduce the number of element updates in a given simulation by a
factor that may depend on the complexity of the dynamics, but which can be as
large as 4.7.Comment: 31 pages, 13 figure

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