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

Extensive population synthesis of isolated neutron stars with field decay

We perform population synthesis studies of different types of neutron stars taking into account the magnetic field decay. For the first time, we confront our results with observations using {\it simultaneously} the Log N -- Log S distribution for nearby isolated neutron stars, the Log N -- Log L distribution for magnetars, and the distribution of radio pulsars in the $P$ -- $\dot P$ diagram. We find that our theoretical model is consistent with all sets of data if the initial magnetic field distribution function follows a log-normal law with $\sim 13.25$ and $\sigma_{\log B_0}\sim 0.6$. The typical scenario includes about 10% of neutron stars born as magnetars, significant magnetic field decay during the first million years of a NS life. Evolutionary links between different subclasses may exist, although robust conclusions are not yet possible. We apply the obtained field distribution and the model of decay to study long-term evolution of neuton stars till the stage of accretion from the interstellar medium. It is shown that though the subsonic propeller stage can be relatively long, initially highly magnetized neutron stars ($B_0 > \sim 10^{13}$ G) reach the accretion regime within the Galactic lifetime if their kick velocities are not too large. The fact that in previous studies made $>$10 years ago, such objects were not considered results in a slight increase of the Accretor fraction in comparison with earlier conclusions. Most of the neutron stars similar to the Magnificent seven are expected to become accreting from the interstellar medium after few billion years of their evolution. They are the main predecestors of accreting isolated neutron stars.Comment: 4 pages, conference "Astrophysics of Neutron Stars - 2010" in honor of M. Ali Alpar, Izmir, Turke

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

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&

Sink limitations to yield in wheat : how could it be reduced?

Ponència presentada al International Workshop on Increasing Wheat Yield Potential, CIMMYT, Obregón, Mèxic, del 20 al 24 de març de 2006.Further genetic gains in wheat yield are required to match expected increases in demand. This may require the identification of physiological attributes able to produce such improvement, as well as the genetic bases controlling those traits in order to facilitate their manipulation. In the present paper, a theoretical framework of source and sink limitation to wheat yield is presented and the fine-tuning of crop development as an alternative for increasing yield potential is discussed. Following a top-down approach, most crop physiologists have agreed that the main attribute explaining past genetic gains in yield was harvest index (HI). By virtue of previous success, no further gains may be expected in HI and an alternative must be found. Using a bottom-up approach, the present paper firstly provides evidence on the generalized sink-limited condition of grain growth, determining that for further increases in yield potential, sink strength during grain filling has to be increased. The focus should be on further increasing grain number per m2, through fine-tuning pre-anthesis developmental patterns. The phase of rapid spike growth period (RSGP) is critical for grain number determination and increasing spike growth during pre-anthesis would result in an increased number of grains. This might be achieved by lengthening the duration of the phase (though without altering flowering time), as there is genotypic variation in the proportion of pre-anthesis time elapsed either before or after the onset of the stem elongation phase. Photoperiod sensitivity during RSGP could be then used as a genetic tool to further increase grain number, since slower development results in smoother floret development and more floret primordia achieve the fertile floret stage, able to produce a grain. Far less progress has been achieved on the genetic control of this attribute. None of the well-known major Ppd alleles seems to be consistently responsible for RSGP sensitivity. Alternatives for identifying the genetic factors responsible for this sensitivity (e.g. quantitative trait locus (QTL) identification in mapping populations) are being considered