3D radiative transfer: Continuum and line scattering in non-spherical winds from OB stars

Context: State of the art quantitative spectroscopy of OB-stars compares synthetic spectra (calculated by means of 1D, spherically symmetric computer codes) with observations. Certain stellar atmospheres, however, show strong deviations from spherical symmetry, and need to be treated in 3D. Aims: We present a newly developed 3D radiative transfer code, tailored to the solution of the radiation field in rapidly expanding stellar atmospheres. We apply our code to the continuum transfer in wind-ablation models, and to the UV resonance line formation in magnetic winds. Methods: We have used a 3D finite-volume method for the solution of the equation of radiative transfer, to study continuum- and line-scattering problems. Convergence has been accelerated by a non-local approximate Lambda-iteration scheme. Particular emphasis has been put on careful (spherically symmetric) test cases. Results: Typical errors of the source functions, when compared to 1D solutions, are of the order of 10-20 %, and increase for optically thick continua. In circumstellar discs, the radiation temperatures in the (optically thin) transition region from wind to disc are quite similar to corresponding values in the wind. For MHD simulations of dynamical magnetospheres, the line profiles, calculated with our 3D code, agree well with previous solutions using a 3D-SEI method. When compared with profiles resulting from the `analytic dynamical magnetosphere' (ADM) model, significant differences become apparent. Conclusions: Due to similar radiation temperatures in the wind and the transition region to the disc, the same line-strength distribution can be applied within radiation hydrodynamic calculations for circumstellar discs in `accreting high-mass stars'. To properly describe the UV line formation in dynamical magnetospheres, the ADM model needs to be further developed, at least in a large part of the outer wind

Refinement in hybridised institutions

Hybrid logics, which add to the modal description of transition structures the ability to refer to specific states, offer a generic framework to approach the specification and design of reconfigurable systems, i.e., systems with reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response to both external stimuli or internal performance measures. A formal representation of such systems is through transition structures whose states correspond to the different configurations they may adopt. Therefore, each node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics of the services provided in the corresponding configuration. This paper characterises equivalence and refinement for these sorts of models in a way which is independent of (or parametric on) whatever logic (propositional, equational, fuzzy, etc) is found appropriate to describe the local configurations. A Hennessy–Milner like theorem is proved for hybridised logics.This work is funded by ERDF-European Regional Development Fund, through the COMPETE Programme, and by National Funds through FCT within project FCOMP-01-0124-FEDER-028923 and by project NORTE-07-0124-FEDER-000060, co-financed by the North Portugal Regional Operational Programme (ON.2), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF). The work had also partial financial assistance by the project PEst-OE/MAT/UI4106/2014 at CIDMA, FCOMP-01-0124-FEDER-037281 at INESC TEC and the Marie Curie project FP7-PEOPLE-2012-IRSES (GetFun)

Dynamic logic with binders and its application to the development of reactive systems

Publicado em "Theoretical aspects of computing - ICTAC 2016: 13th International Colloquium, Taipei, Taiwan, ROC, October 24–31, 2016, Proceedings". ISBN 978-3-319-46749-8This paper introduces a logic to support the specification and development of reactive systems on various levels of abstraction, from property specifications, concerning e.g. safety and liveness requirements, to constructive specifications representing concrete processes. This is achieved by combining binders of hybrid logic with regular modalities of dynamic logics in the same formalism, which we call D↓-logic. The semantics of our logic focuses on effective processes and is therefore given in terms of reachable transition systems with initial states. The second part of the paper resorts to this logic to frame stepwise development of reactive systems within the software development methodology proposed by Sannella and Tarlecki. In particular, we instantiate the generic concepts of constructor and abstractor implementations by using standard operators on reactive components, like relabelling and parallel composition, as constructors, and bisimulation for abstraction. We also study vertical composition of implementations which relies on the preservation of bisimularity by the constructions on labeleld transition systems.FCT individual grants SFRH/BPD/103004/2014 and SFRH/BSAB/113890/2015ERDF European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Cência e a Tecnologia within project POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013 at CIDM

A 3D short-characteristics method for continuum and line scattering problems in the winds of hot stars

Context: Knowledge about hot, massive stars is usually inferred from quantitative spectroscopy. To analyse non-spherical phenomena, the existing 1D codes must be extended to higher dimensions, and corresponding tools need to be developed. Aims: We present a 3D radiative transfer code that is capable of calculating continuum and line scattering problems in the winds of hot stars. By considering spherically symmetric test models, we discuss potential error sources, and indicate advantages and disadvantages by comparing different solution methods. Further, we analyse the UV resonance line formation in the winds of rapidly rotating O stars. Methods: We consider both a (simplified) continuum model including scattering and thermal sources, and a UV resonance line transition approximated by a two-level-atom. We applied the short-characteristics (SC) method, using linear or monotonic B\'ezier interpolations, to solve the equation of radiative transfer on a non-uniform Cartesian grid. To calculate scattering dominated problems, our solution method is supplemented by an accelerated $\Lambda$-iteration scheme. Results: For the spherical test models, the mean relative error of the source function is on the $5-20\,\%$ level, depending on the applied interpolation technique and the complexity of the considered model. All calculated line profiles are in excellent agreement with corresponding 1D solutions. The predicted line profiles from fast rotating stars show a distinct behaviour as a function of rotational speed and inclination. This behaviour is tightly coupled to the wind structure and the description of gravity darkening and stellar surface distortion. Conclusions: Our SC methods are ready to be used for quantitative analyses of UV resonance line profiles. When calculating optically thick continua, both SC methods give reliable results, in contrast to the alternative finite-volume method

Binary-object spectral-synthesis in 3D (BOSS-3D) -- Modelling H-alpha emission in the enigmatic multiple system LB-1

Context: To quantitatively decode the information stored within an observed spectrum, detailed modelling of the physical state and accurate radiative transfer solution schemes are required. In the analysis of stellar spectra, the numerical model often needs to account for binary companions and 3D structures in the stellar envelopes. The enigmatic binary (or multiple) system LB-1 constitutes a perfect example of such a complex multi-D problem. Aims: To improve our understanding of the LB-1 system, we directly modelled the phase-dependent H-alpha line profiles of this system. To this end, we developed a multi-purpose binary-object spectral-synthesis code in 3D (BOSS-3D). Methods: BOSS-3D calculates synthetic line profiles for a given state of the circumstellar material. The standard pz-geometry commonly used for single stars is extended by defining individual coordinate systems for each involved object and by accounting for the appropriate coordinate transformations. The code is then applied to the LB-1 system, considering two main hypotheses, a binary containing a stripped star and Be star, or a B star and a black hole with a disc. Results: Comparing these two scenarios, neither model can reproduce the detailed phase-dependent shape of the H-alpha line profiles. A satisfactory match with the observations, however, is obtained by invoking a disc around the primary object in addition to the Be-star disc or the black-hole accretion disc. Conclusions: The developed code can be used to model synthetic line profiles for a wide variety of binary systems, ranging from transit spectra of planetary atmospheres, to post-asymptotic giant branch binaries including circumstellar and circumbinary discs and massive-star binaries with stellar winds and disc systems. For the LB-1 system, our modelling provides strong evidence that each object in the system contains a disc-like structure

Ultraviolet Line Profiles of Slowly Rotating Massive Star Winds Using the "Analytic Dynamical Magnetosphere" Formalism

Recent large-scale spectropolarimetric surveys have established that a small but significant percentage of massive stars host stable, surface dipolar magnetic fields with strengths on the order of kG. These fields channel the dense, radiatively driven stellar wind into circumstellar magnetospheres, whose density and velocity structure can be probed using ultraviolet (UV) spectroscopy of wind-sensitive resonance lines. Coupled with appropriate magnetosphere models, UV spectroscopy provides a valuable way to investigate the wind-field interaction, and can yield quantitative estimates of the wind parameters of magnetic massive stars. We report a systematic investigation of the formation of UV resonance lines in slowly rotating magnetic massive stars with dynamical magnetospheres. We pair the Analytic Dynamical Magnetosphere (ADM) formalism with a simplified radiative transfer technique to produce synthetic UV line profiles. Using a grid of models, we examine the effect of magnetosphere size, the line strength parameter, and the cooling parameter on the structure and modulation of the line profile. We find that magnetic massive stars uniquely exhibit redshifted absorption at most viewing angles and magnetosphere sizes, and that significant changes to the shape and variation of the line profile with varying line strengths can be explained by examining the individual wind components described in the ADM formalism. Finally, we show that the cooling parameter has a negligible effect on the line profiles.Comment: 16 pages, 15 figures, accepted to MNRA

Extended ML: Past, present and future

An overview of past, present and future work on the Extended ML formal program development framework is given, with emphasis on two topics of current active research: the semantics of the Extended ML specification language, and tools to support formal program development

Ultraviolet line profiles of slowly rotating massive star winds using the 'analytic dynamical magnetosphere' formalism

peer reviewedRecent large-scale spectropolarimetric surveys have established that a small but significant percentage of massive stars host stable, surface dipolar magnetic fields with strengths on the order of kG. These fields channel the dense, radiatively driven stellar wind into circumstellar magnetospheres, whose density and velocity structure can be probed using ultraviolet (UV) spectroscopy of wind-sensitive resonance lines. Coupled with appropriate magnetosphere models, UV spectroscopy provides a valuable way to investigate the wind-field interaction, and can yield quantitative estimates of the wind parameters of magnetic massive stars. We report a systematic investigation of the formation of UV resonance lines in slowly rotating magnetic massive stars with dynamical magnetospheres. We pair the analytic dynamical magnetosphere (ADM) formalism with a simplified radiative transfer technique to produce synthetic UV line profiles. Using a grid of models, we examine the effect of magnetosphere size, the line strength parameter, and the cooling parameter on the structure and modulation of the line profile. We find that magnetic massive stars uniquely exhibit redshifted absorption at most viewing angles and magnetosphere sizes, and that significant changes to the shape and variation of the line profile with varying line strengths can be explained by examining the individual wind components described in the ADM formalism. Finally, we show that the cooling parameter has a negligible effect on the line profiles

Testing data types implementations from algebraic specifications

Algebraic specifications of data types provide a natural basis for testing data types implementations. In this framework, the conformance relation is based on the satisfaction of axioms. This makes it possible to formally state the fundamental concepts of testing: exhaustive test set, testability hypotheses, oracle. Various criteria for selecting finite test sets have been proposed. They depend on the form of the axioms, and on the possibilities of observation of the implementation under test. This last point is related to the well-known oracle problem. As the main interest of algebraic specifications is data type abstraction, testing a concrete implementation raises the issue of the gap between the abstract description and the concrete representation. The observational semantics of algebraic specifications bring solutions on the basis of the so-called observable contexts. After a description of testing methods based on algebraic specifications, the chapter gives a brief presentation of some tools and case studies, and presents some applications to other formal methods involving datatypes

A modern guide to quantitative spectroscopy of massive OB stars

Quantitative spectroscopy is a powerful technique from which we can extract information about the physical properties and surface chemical composition of stars. In this chapter, I guide the reader through the main ideas required to get initiated in the learning process to become an expert in the application of state-of-the-art quantitative spectroscopic techniques to the study of massive OB stars. NB: This chapter is intended to serve to young students as a first approach to a field which has attracted my attention during the last 20 years. I should note that, despite its importance, at present, the number of real experts in the field around the world is limited to less than 50 people, and about one third of them are close to retirement. Hence, I consider that this is a good moment to write a summary text on the subject to serve as guideline for the next generations of students interested in joining the massive star crew. If you are one of them, please, use this chapter as a first working notebook. Do not stop here. Dig also, for further details, into the literature I quote along the text. And, once there, dig even deeper to find all the original sources explaining in more detail the physical and technical concepts that are presently incorporated into our modern (almost) automatized tools.Comment: Accepted for publication in the book "Reviews in Frontiers of Modern Astrophysics: From Space Debris to Cosmology" (eds Kabath, Jones and Skarka; publisher Springer Nature) funded by the European Union Erasmus+ Strategic Partnership grant "Per Aspera Ad Astra Simul" 2017-1-CZ01-KA203-03556