4,146 research outputs found
Hyperbolic character of the angular moment equations of radiative transfer and numerical methods
We study the mathematical character of the angular moment equations of
radiative transfer in spherical symmetry and conclude that the system is
hyperbolic for general forms of the closure relation found in the literature.
Hyperbolicity and causality preservation lead to mathematical conditions
allowing to establish a useful characterization of the closure relations. We
apply numerical methods specifically designed to solve hyperbolic systems of
conservation laws (the so-called Godunov-type methods), to calculate numerical
solutions of the radiation transport equations in a static background. The
feasibility of the method in any kind of regime, from diffusion to
free-streaming, is demonstrated by a number of numerical tests and the effect
of the choice of the closure relation on the results is discussed.Comment: 37 pags, 12 figures, accepted for publication in MNRA
Legendre expansion of the neutrino-antineutrino annihilation kernel: Influence of high order terms
We calculate the Legendre expansion of the rate of the process up to 3rd order extending previous results
of other authors which only consider the 0th and 1st order terms. Using
different closure relations for the moment equations of the radiative transfer
equation we discuss the physical implications of taking into account quadratic
and cubic terms on the energy deposition outside the neutrinosphere in a
simplified model. The main conclusion is that 2nd order is necessary in the
semi-transparent region and gives good results if an appropriate closure
relation is used.Comment: 14 pages, 4 figures. To be published in A&A Supplement Serie
Anisotropic thermal emission from magnetized neutron stars
The thermal emission from isolated neutron stars is not well understood. The
X-ray spectrum is very close to a blackbody but there is a systematic optical
excess flux with respect to the extrapolation to low energy of the best
blackbody fit. This fact, in combination with the observed pulsations in the
X-ray flux, can be explained by anisotropies in the surface temperature
distribution.We study the thermal emission from neutron stars with strong
magnetic fields in order to explain the origin of the anisotropy. We find
(numerically) stationary solutions in axial symmetry of the heat
transportequations in the neutron star crust and the condensed envelope. The
anisotropy in the conductivity tensor is included consistently. The presence of
magnetic fields of the expected strength leads to anisotropy in the surface
temperature. Models with toroidal components similar to or larger than the
poloidal field reproduce qualitatively the observed spectral properties and
variability of isolated neutron stars. Our models also predict spectral
features at energies between 0.2 and 0.6 keV.Comment: 18 pages, 19 figures, version accepted for publication in A&
The relevance of ambipolar diffusion for neutron star evolution
We study ambipolar diffusion in strongly magnetised neutron stars, with
special focus on the effects of neutrino reaction rates and the impact of a
superfluid/superconducting transition in the neutron star core. For
axisymmetric magnetic field configurations, we determine the deviation from
equilibrium induced by the magnetic force and calculate the velocity of
the slow, quasi-stationary, ambipolar drift. We study the temperature
dependence of the velocity pattern and clearly identify the transition to a
predominantly solenoidal flow. For stars without superconducting/superfluid
constituents and with a mixed poloidal-toroidal magnetic field of typical
magnetar strength, we find that ambipolar diffusion proceeds fast enough to
have a significant impact on the magnetic field evolution only at low core
temperatures, K. The ambipolar diffusion timescale
becomes appreciably shorter when fast neutrino reactions are present, because
the possibility to balance part of the magnetic force with pressure gradients
is reduced. We also find short ambipolar diffusion timescales in the case of
superconducting cores for K, due to the reduced interaction
between protons and neutrons. In the most favourable scenario, with fast
neutrino reactions and superconducting cores, ambipolar diffusion results in
advection velocities of several km/kyr. This velocity can substantially
reorganize magnetic fields in magnetar cores, in a way that can only be
confirmed by dynamical simulations.Comment: 14 pages, 11 figures, version accepted for publication in MNRA
Relativistic r-modes and shear viscosity
We derive the relativistic equations for stellar perturbations, including in
a consistent way shear viscosity in the stress-energy tensor, and we
numerically integrate our equations in the case of large viscosity. We consider
the slow rotation approximation, and we neglect the coupling between polar and
axial perturbations. In our approach, the frequency and damping time of the
emitted gravitational radiation are directly obtained. We find that,
approaching the inviscid limit from the finite viscosity case, the continuous
spectrum is regularized. Constant density stars, polytropic stars, and stars
with realistic equations of state are considered. In the case of constant
density stars and polytropic stars, our results for the viscous damping times
agree, within a factor two, with the usual estimates obtained by using the
eigenfunctions of the inviscid limit. For realistic neutron stars, our
numerical results give viscous damping times with the same dependence on mass
and radius as previously estimated, but systematically larger of about 60%.Comment: 8 pages, 7 figures, to appear in the Proceedings of the Albert
Einstein Century International Conference, Paris, France, July 200
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