5,936 research outputs found
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&
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
Non-radial oscillation modes as a probe of density discontinuities in neutron stars
A phase transition occurring in the inner core of a neutron star could be
associated to a density discontinuity that would affect the frequency spectrum
of the non-radial oscillation modes in two ways. Firstly, it would produce a
softening of the equation of state, leading to more compact equilibrium
configurations and changing the frequency of the fundamental and pressure modes
of the neutron star. Secondly, a new non-zero frequency g-- mode would appear,
associated to each discontinuity. These discontinuity g--modes have typical
frequencies larger than those of g--modes previously studied in the literature
(thermal, core g-- modes, or g--modes due to chemical inhomogeneities in the
outer layers), and smaller than that of the fundamental mode; therefore they
should be distinguishable from the other modes of non radial oscillation. In
this paper we investigate how high density discontinuities change the frequency
spectrum of the non-radial oscillations, in the framework of the general
relativistic theory of stellar perturbations. Our purpose is to understand
whether a gravitational signal, emitted at the frequencies of the quasi normal
modes, may give some clear information on the equation of state of the neutron
star and, in particular, on the parameters that characterize the density
discontinuity. We discuss some astrophysical processes that may be associated
to the excitation of these modes, and estimate how much gravitational energy
should the modes convey to produce a signal detectable by high frequency
gravitational detectors.Comment: submitted to MNRA
Unstable g-modes in Proto-Neutron Stars
In this article we study the possibility that, due to non-linear couplings,
unstable g-modes associated to convective motions excite stable oscillating
g-modes. This problem is of particular interest, since gravitational waves
emitted by a newly born proto-neutron star pulsating in its stable g-modes
would be in the bandwidth of VIRGO and LIGO. Our results indicate that
nonlinear saturation of unstable modes occurs at relatively low amplitudes, and
therefore, even if there exists a coupling between stable and unstable modes,
it does not seem to be sufficiently effective to explain, alone, the excitation
of the oscillating g-modes found in hydrodynamical simulations.Comment: 10 pages, 3 figures, to appear on Class. Quant. Gra
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
Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space
Relying on known results of the Noether theory of symmetries extended to
constrained systems, it is shown that there exists an obstruction that prevents
certain tangent-space diffeomorphisms to be projectable to phase-space, for
generally covariant theories. This main result throws new light on the old fact
that the algebra of gauge generators in the phase space of General Relativity,
or other generally covariant theories, only closes as a soft algebra and not a
a Lie algebra.
The deep relationship between these two issues is clarified. In particular,
we see that the second one may be understood as a side effect of the procedure
to solve the first. It is explicitly shown how the adoption of specific
metric-dependent diffeomorphisms, as a way to achieve projectability, causes
the algebra of gauge generators (constraints) in phase space not to be a Lie
algebra --with structure constants-- but a soft algebra --with structure {\it
functions}.Comment: 22 pages, version to be published in Classical & Quantum Gravit
Faddeev-Jackiw approach to gauge theories and ineffective constraints
The general conditions for the applicability of the Faddeev-Jackiw approach
to gauge theories are studied. When the constraints are effective a new proof
in the Lagrangian framework of the equivalence between this method and the
Dirac approach is given. We find, however, that the two methods may give
different descriptions for the reduced phase space when ineffective constraints
are present. In some cases the Faddeev-Jackiw approach may lose some
constraints or some equations of motion. We believe that this inequivalence can
be related to the failure of the Dirac conjecture (that says that the Dirac
Hamiltonian can be enlarged to an Extended Hamiltonian including all first
class constraints, without changes in the dynamics) and we suggest that when
the Dirac conjecture fails the Faddeev-Jackiw approach fails to give the
correct dynamics. Finally we present some examples that illustrate this
inequivalence.Comment: 21 pages, Latex. To be published in Int. J. Mod. Phys.
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