Probing large-scale wind structures in Vela X–1 using off-states with INTEGRAL

Vela X–1 is the prototype of the class of wind-fed accreting pulsars in high-mass X-ray binaries hosting a supergiant donor. We have analysed in a systematic way 10 years of INTEGRAL data of Vela X–1 (22–50 keV) and we found that when outside the X-ray eclipse, the source undergoes several luminosity drops where the hard X-rays luminosity goes below ∼3 × 1035 erg s−1, becoming undetected by INTEGRAL. These drops in the X-ray flux are usually referred to as ‘off-states’ in the literature. We have investigated the distribution of these off-states along the Vela X–1 ∼ 8.9 d orbit, finding that their orbital occurrence displays an asymmetric distribution, with a higher probability to observe an off-state near the pre-eclipse than during the post-eclipse. This asymmetry can be explained by scattering of hard X-rays in a region of ionized wind, able to reduce the source hard X-ray brightness preferentially near eclipse ingress. We associate this ionized large-scale wind structure with the photoionization wake produced by the interaction of the supergiant wind with the X-ray emission from the neutron star. We emphasize that this observational result could be obtained thanks to the accumulation of a decade of INTEGRAL data, with observations covering the whole orbit several times, allowing us to detect an asymmetric pattern in the orbital distribution of off-states in Vela X–1.

Generation of representation models for complex systems using Lagrangian functions

In this article, a new methodology is presented to obtain representation models for a priori relation z = u(x1, x2, . . . ,xn) (1), with a known an experimental dataset zi; x1i ; x2i ; x3i ; . . . ; xni i=1;2;...;p· In this methodology, a potential energy is initially defined over each possible model for the relationship (1), what allows the application of the Lagrangian mechanics to the derived system. The solution of the Euler–Lagrange in this system allows obtaining the optimal solution according to the minimal action principle. The defined Lagrangian, corresponds to a continuous medium, where a n-dimensional finite elements model has been applied, so it is possible to get a solution for the problem solving a compatible and determined linear symmetric equation system. The computational implementation of the methodology has resulted in an improvement in the process of get representation models obtained and published previously by the authors.

A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.