Legendre expansion of the neutrino-antineutrino annihilation kernel: Influence of high order terms

We calculate the Legendre expansion of the rate of the process $\nu + \bar{\nu} \leftrightarrow e^+ + e^-$ 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

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

Anisotropic convection in rotating proto-neutron stars

We study the conditions for convective instability in rotating, non-magnetic proto--neutron stars. The criteria that determine stability of nascent neutron stars are analogous to the Solberg--Hoiland conditions but including the presence of lepton gradients. Our results show that, for standard angular velocity profiles, convectively unstable modes with wave-vectors parallel to the rotation axis are suppressed by a stable angular momentum profile, while unstable modes with wave-vectors perpendicular to the axis remain unaltered. Since the wave-vector is perpendicular to the velocity perturbation, the directional selection of the unstable modes may result in fluid motions along the direction of the rotation axis. This occurs in rigidly rotating stars as well as in the inner core of differentially rotating stars. Our results provide a natural source of asymmetry for proto--neutron stars with the only requirement that angular velocities be of the order of the convective characteristic frequency.Comment: 5 pages, 4 figures, final version to appear in A&

Medición del ángulo Q mediante goniometría convencional y videofotogrametría en 3D. Correlación de los resultados

Este trabajo pretende demostrar la existencia de correlación entre la medición del ángulo Q estático mediante goniometría convencional y mediante videofotogrametría en 3D, para que en próximos estudios se pueda obviar la exploración previa por el método convencional

Population Synthesis of Isolated Neutron Stars with magneto-rotational evolution II: from radio-pulsars to magnetars

Population synthesis studies constitute a powerful method to reconstruct the birth distribution of periods and magnetic fields of the pulsar population. When this method is applied to populations in different wavelengths, it can break the degeneracy in the inferred properties of initial distributions that arises from single-band studies. In this context, we extend previous works to include $X$-ray thermal emitting pulsars within the same evolutionary model as radio-pulsars. We find that the cumulative distribution of the number of X-ray pulsars can be well reproduced by several models that, simultaneously, reproduce the characteristics of the radio-pulsar distribution. However, even considering the most favourable magneto-thermal evolution models with fast field decay, log-normal distributions of the initial magnetic field over-predict the number of visible sources with periods longer than 12 s. We then show that the problem can be solved with different distributions of magnetic field, such as a truncated log-normal distribution, or a binormal distribution with two distinct populations. We use the observational lack of isolated NSs with spin periods P>12 s to establish an upper limit to the fraction of magnetars born with B > 10^{15} G (less than 1\%). As future detections keep increasing the magnetar and high-B pulsar statistics, our approach can be used to establish a severe constraint on the maximum magnetic field at birth of NSs.Comment: 12 pages, 11 figures, 5 table