Observar com sentido: uma competencia importante na vida profissional do professor de Matemática

Este artigo apresenta um experimento com sete estudantes de Licenciatura em Matemática da Universidade Luterana do Brasil, Canoas, Rio Grande do Sul, com o objetivo de desenvolver a competência de “observar com sentido”. Para isso foi desenvolvido um ambiente de investigação composto por um vídeo de uma aula de Matemática, dois textos de suporte às discussões, um fórum de discussão e uma wiki sintetizando o debate realizado no fórum. Os resultados apontam que os estudantes conseguem analisar uma aula e identificar a metodologia utilizada e que com o experimento foi possível ampliar a compreensão do ambiente profissional.

Chandra and Suzaku observations of the Be/X-ray star HD110432

We present an analysis of a pointed 141 ks Chandra high-resolution transmission gratings observation of the Be X-ray emitting star HD110432, a prominent member of the γ Cas analogs. This observation represents the first high-resolution spectrum taken for this source as well as the longest uninterrupted observation of any γ Cas analog. The Chandra light curve shows a high variability but its analysis fails to detect any coherent periodicity up to a frequency of 0.05 Hz. Hardness ratio versus intensity analyses demonstrate that the relative contributions of the [1.5-3] Å, [3-6] Å, and [6-16] Å energy bands to the total flux change rapidly in the short term. The analysis of the Chandra High Energy Transmission Grating (HETG) spectrum shows that, to correctly describe the spectrum, three model components are needed. Two of those components are optically thin thermal plasmas of different temperatures (kT ≈ 8-9 and 0.2-0.3 keV, respectively) described by the models vmekal or bvapec. The Fe abundance in each of these two components appears equal within the errors and is slightly subsolar with Z ≈ 0.75 Z ☉. The bvapec model better describes the Fe L transitions, although it cannot fit well the Na XI Lyα line at 10.02 Å, which appears to be overabundant. Two different models seem to describe well the third component. One possibility is a third hot optically thin thermal plasma at kT = 16-21 keV with an Fe abundance Z ≈ 0.3 Z ☉, definitely smaller than for the other two thermal components. Furthermore, the bvapec model describes well the Fe K shell transitions because it accounts for the turbulence broadening of the Fe XXV and Fe XXVI lines with a v turb ≈ 1200 km s–1. These two lines, contributed mainly by the hot thermal plasma, are significantly wider than the Fe Kα line whose FWHM < 5 mÅ is not resolved by Chandra. Alternatively, the third component can be described by a power law with a photon index of Γ = 1.56. In either case, the Chandra HETG spectrum establishes that each one of these components must be modified by distinct absorption columns. The analysis of a noncontemporaneous 25 ks Suzaku observation shows the presence of a hard tail extending up to at least 33 keV. The Suzaku spectrum is described with the sum of two components: an optically thin thermal plasma at kT ≈ 9 keV and Z ≈ 0.74 Z ☉, and a very hot second plasma with kT ≈ 33 keV or, alternatively, a power law with photon index of Γ = 1.58. In either case, each one of the two components must be affected by different absorption columns. Therefore, the kT = 8-9 keV component is definitely needed while the nature of the harder emission cannot be unambiguously established with the present data sets. The analysis of the Si XIII and S XV He-like triplets present in the Chandra spectrum points to a very dense (ne ~ 1013 cm–3) plasma located either close to the stellar surface (r < 3R *) of the Be star or, alternatively, very close (r ~ 1.5R WD) to the surface of a (hypothetical) white dwarf companion. We argue, however, that the available data support the first scenario.

An XMM-Newton view of FeKα in high-mass X-ray binaries

We present a comprehensive analysis of the whole sample of available XMM-Newton observations of high-mass X-ray binaries (HMXBs) until August 2013, focusing on the FeKα emission line. This line is key to better understanding the physical properties of the material surrounding the X-ray source within a few stellar radii (the circumstellar medium). We collected observations from 46 HMXBs and detected FeKα in 21 of them. We used the standard classification of HMXBs to divide the sample into different groups. We find that (1) different classes of HMXBs display different qualitative behaviours in the FeKα spectral region. This is visible especially in SGXBs (showing ubiquitous Fe fluorescence but not recombination Fe lines) and in γ Cass analogues (showing both fluorescent and recombination Fe lines). (2) FeKα is centred at a mean value of 6.42 keV. Considering the instrumental and fits uncertainties, this value is compatible with ionization states that are lower than Fe xviii. (3) The flux of the continuum is well correlated with the flux of the line, as expected. Eclipse observations show that the Fe fluorescence emission comes from an extended region surrounding the X-ray source. (4) We observe an inverse correlation between the X-ray luminosity and the equivalent width of FeKα (EW). This phenomenon is known as the X-ray Baldwin effect. (5) FeKα is narrow (σline< 0.15 keV), reflecting that the reprocessing material does not move at high speeds. We attempt to explain the broadness of the line in terms of three possible broadening phenomena: line blending, Compton scattering, and Doppler shifts (with velocities of the reprocessing material V ~ 1000 km s-1). (6) The equivalent hydrogen column (NH) directly correlates to the EW of FeKα, displaying clear similarities to numerical simulations. It highlights the strong link between the absorbing and the fluorescent matter. (7) The observed NH in supergiant X-ray binaries (SGXBs) is in general higher than in supergiant fast X-ray transients (SFXTs). We suggest two possible explanations: different orbital configurations or a different interaction compact object – wind. (8) Finally, we analysed the sources IGR J16320-4751 and 4U 1700-37 in more detail, covering several orbital phases. The observed variation in NH between phases is compatible with the absorption produced by the wind of their optical companions. The results clearly point to a very important contribution of the donor’s wind in the FeKα emission and the absorption when the donor is a supergiant massive star.

The emergence of classical behaviour in magnetic adatoms

A wide class of nanomagnets shows striking quantum behaviour, known as quantum spin tunnelling (QST): instead of two degenerate ground states with opposite magnetizations, a bonding-antibonding pair forms, resulting in a splitting of the ground-state doublet with wave functions linear combination of two classically opposite magnetic states, leading to the quenching of their magnetic moment. Here we study how QST is destroyed and classical behaviour emerges in the case of magnetic adatoms, where, contrary to larger nanomagnets, the QST splitting is in some instances bigger than temperature and broadening. We analyze two different mechanisms for the renormalization of the QST splitting: Heisenberg exchange between different atoms, and Kondo exchange interaction with the substrate electrons. Sufficiently strong spin-substrate and spin-spin coupling renormalize the QST splitting to zero allowing the environmental decoherence to eliminate superpositions between classical states, leading to the emergence of spontaneous magnetization. Importantly, we extract the strength of the Kondo exchange for various experiments on individual adatoms and construct a phase diagram for the classical to quantum transition.

Highly localized accelerating beams using nano-scale metallic gratings

Spatially accelerating beams are non-diffracting beams whose intensity is localized along curvilinear trajectories, also incomplete circular trajectories, before diffraction broadening governs their propagation. In this paper we report on numerical simulations showing the conversion of a high-numerical-aperture focused beam into a nonparaxial shape-preserving accelerating beam having a beam-width near the diffraction limit. Beam shaping is induced near the focal region by a diffractive optical element that consists of a non-planar subwavelength grating enabling a Bessel signature.