Numerical solution of the radiative transfer equation: X-ray spectral formation from cylindrical accretion onto a magnetized neutron star

Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. To this aim, we have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system tau using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth tau produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. The algorithm has been implemented in the XSPEC package for X-ray spectral fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (> 10^{12} G), which is expected to be typical of accreting systems such as X-ray pulsars and supergiant fast X-ray transients.Comment: 13 pages, 20 figures, accepted for publication in A&

A new model for the X-ray continuum of the magnetized accreting pulsars

Accreting highly magnetized pulsars in binary systems are among the brightest X-ray emitters in our Galaxy. Although a number of high statistical quality broad-band (0.1-100 keV) X-ray observations are available, the spectral energy distribution of these sources is usually investigated by adopting pure phenomenological models, rather than models linked to the physics of accretion. In this paper, a detailed spectral study of the X-ray emission recorded from the high-mass X-ray binary pulsars Cen X-3, 4U 0115+63, and Her X-1 is carried out by using BeppoSAX and joined Suzaku+NuStar data, together with an advanced version of the compmag model. The latter provides a physical description of the high energy emission from accreting pulsars, including the thermal and bulk Comptonization of cyclotron and bremsstrahlung seed photons along the neutron star accretion column. The compmag model is based on an iterative method for solving second-order partial differential equations, whose convergence algorithm has been improved and consolidated during the preparation of this paper. Our analysis shows that the broad-band X-ray continuum of all considered sources can be self-consistently described by the compmag model. The cyclotron absorption features, not included in the model, can be accounted for by using Gaussian components. From the fits of the compmag model to the data we inferred the physical properties of the accretion columns in all sources, finding values reasonably close to those theoretically expected according to our current understanding of accretion in highly magnetized neutron stars. The updated version of the compmag model has been tailored to the physical processes that are known to occur in the columns of highly magnetized accreting neutron stars and it can thus provide a better understanding of the high energy radiation from these sources.Comment: 19 pages, 10 figures, accepted for publication in A&

RX J0440.9+4431: a persistent Be/X-ray binary in outburst

The persistent Be/X-ray binary RX J0440.9+4431 flared in 2010 and 2011 and has been followed by various X-ray facilities Swift, RXTE, XMM-Newton, and INTEGRAL. We studied the source timing and spectral properties as a function of its X-ray luminosity to investigate the transition from normal to flaring activity and the dynamical properties of the system. We have determined the orbital period from the long-term Swift/BAT light curve, but our determinations of the spin period are not precise enough to constrain any orbital solution. The source spectrum can always be described by a bulk-motion Comptonization model of black body seed photons attenuated by a moderate photoelectric absorption. At the highest luminosity, we measured a curvature of the spectrum, which we attribute to a significant contribution of the radiation pressure in the accretion process. This allows us to estimate that the transition from a bulk-motion-dominated flow to a radiatively dominated one happens at a luminosity of ~2e36 erg/s. The luminosity dependency of the size of the black body emission region is found to be $r_{BB} \propto L_X^{0.39\pm0.02}$. This suggests that either matter accreting onto the neutron star hosted in RX J0440.9+4431 penetrates through closed magnetic field lines at the border of the compact object magnetosphere or that the structure of the neutron star magnetic field is more complicated than a simple dipole close to the surfaceComment: Accepted for publication by A&

HMM-based anomaly interpretation for intelligent robots in Industry 4.0

We apply an anomaly detection method based on Hidden Markov Models and Hellinger distance to a Kairos mobile robot operating in the ICE lab, a research laboratory for Industry 4.0. Two main contributions are proposed: i) a decomposition of the Hellinger distance which allows to identify the causes of anomalous behaviours detected, ii) a graphical user interface that synchronously shows the robot movements in a map and the evolution of the Hellinger distance components, allowing a quick investigation of the causes of the detected anomalies. The tools are applied to a real-world dataset allowing to discover that an anomalous movement of the Kairos robot is caused by a wrong reading of the lidar from a window in the environment

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation

The Weight of Time: Time influences on overweight and obesity in women

We know that adults’ weight increases with age, at least until around the age of 55 years or older. Recent National Australian surveys show that men and women of all age groups were heavier in 2000 than in 1995 or 1990. These studies also found that a greater proportion of people of all ages were overweight or obese in 2000 than in the previous surveys. These studies also suggested that different generations, also known as ‘birth cohorts’, had different patterns of weight gain. These birth cohort influences mean that the year a person is born and the unique set of experiences people born at that time experience, have an effect on weight gain patterns. People born at other times experience different conditions and have different weight gain patterns. Some birth cohorts or ‘generations’ are well-known, such as the ‘baby boomer’ generation, or pre-war generation. For example, Australians born in the first three decades of the twentieth century experienced World War I and II and the Great Depression during their childhood and early adult life. During these times food was scarce and everyday life required high levels of physical activity. This group overall had lower body weights than more recent generations, meaning they were less at risk of becoming obese. Australians born after 1980 were born into an advanced technological society with greater availability of food, a vastly increased range of food products and increasing serving sizes. At the same time, levels of physical activity in everyday life have been decreasing. Together these factors produce an obesogenic environment. The three National Health surveys, conducted by the Australian Bureau of Statistics for the Australian Institute of Health and Welfare in 1990, 1995 and 2000, produced data which the NSW Centre for Overweight and Obesity has analyzed to find out what effects three time factors -- ageing, the time of the surveys and birth cohort, have on body mass index (BMI) and the prevalence of overweight and obesity. [Note – BMI used as the indicator of weight status, where BMI = weight (kg)/height2 (M2)] This report provides an overview of key findings of the analyses of the effects of these three time factors on female weight patterns. The complete findings have been published in a comprehensive technical report. The results from the analysis of the effect of birth cohorts have been used to predict the mean body mass index of women in NSW in 2010. The graphs in this report show the results for women, and the results for men are available in a separate document. The overall patterns and implications for men are generally similar to those for women. NS

The Weight of Time: Time influences on overweight and obesity in men

We know that adults’ weight increases with age, at least until around the age of 55 years or older. Recent National Australian surveys show that men and women of all age groups were heavier in 2000 than in 1995 or 1990. These studies also found that a greater proportion of people of all ages were overweight or obese in 2000 than in the previous surveys. These studies also suggested that different generations, also known as ‘birth cohorts’, had different patterns of weight gain. These birth cohort influences mean that the year a person is born and the unique set of experiences people born at that time experience, have an effect on weight gain patterns. People born at other times experience different conditions and have different weight gain patterns. Some birth cohorts or ‘generations’ are well-known, such as the ‘baby boomer’ generation, or pre-war generation. For example, Australians born in the first three decades of the twentieth century experienced World War I and II and the Great Depression during their childhood and early adult life. During these times food was scarce and everyday life required high levels of physical activity. This group overall had lower body weights than more recent generations, meaning they were less at risk of becoming obese. Australians born after 1980 were born into an advanced technological society with greater availability of food, a vastly increased range of food products and increasing serving sizes. At the same time, levels of physical activity in everyday life have been decreasing. Together these factors produce an obesogenic environment. The three National Health surveys, conducted by the Australian Bureau of Statistics for the Australian Institute of Health and Welfare in 1990, 1995 and 2000, produced data which the NSW Centre for Overweight and Obesity has analyzed to find out what effects three time factors -- ageing, the time of the surveys and birth cohort -- have on body mass index (BMI) and the prevalence of overweight and obesity. [Note – BMI used as the indicator of weight status, where BMI = weight (kg)/height2 (M2)] This report provides an overview of key findings of the analyses of the effects of these three time factors on male weight patterns. The complete findings have been published in a comprehensive technical report. The results from the analysis of the effect of birth cohorts have been used to predict the mean body mass index of men in NSW in 2010. The graphs in this report show the results for men but the results for women are available. The overall patterns and implications for women are generally similar to those for men