Table 3 - uploaded by J. Telting
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The numbering of the different sets of theoretically generated line profiles, as a function of angles i and β.
Source publication
We investigate the optical line-profile variability of the prototype of
the β Cephei stars. From more than 600 spectra, with a typical
signal to noise ratio of over 200 and high spectral resolution, we
deduce that the variations show periodicity with at least five different
frequencies. We find variability at the previously known frequencies
f_1_=5...
Contexts in source publication
Context 1
... have generated 16 sets of 250 line profiles with observation times that are randomly spread in the time interval of our β Cep data. The different sets are numbered according to the values for the geometric angles i and β as given in Table 3. We then performed an IPS frequency analysis on sets 1,...,16 to see if our simple temperature model can reproduce the observed frequency splitting around the main pulsation frequency. ...
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This paper concentrates on the roles of the port limiters and Test Blanket Modules (TBMs) on the heat load to the Plasma FacingComponents (PFCs). The TBMs create toroidally and poloidally localized perturbations to
the magnetic field, removing the remaining toroidal periodicity. The TBMs have been modeled in detail, and we use this model in our ASC...
Citations
... This method had not yet been applied to β Cru's complex line-profile variability. It can handle more modes than the moment method because it is based on the periodic variability in each of the wavelength bins belonging to the spectral lines, rather than using integrated quantities across the profiles as is the case for the moment method 54 . We fixed the frequencies found in the space photometry according to Table 1 to test which of those have significant amplitude A λ and phase ϕ λ across each of the three Si iii lines. ...
... Together with the predicted polarimetric amplitudes, the final solutions are given in Supplementary Table 7, listed in order of highest probability in complying with all constraints from spectroscopy and polarimetry together. Notably, the mode with frequency f 5 must be a zonal mode (m 5 = 0) from its zero amplitude in the line centre and its step function in phase 54 , as shown in the lower right panel of Fig. 5. The best solution (solution A in Supplementary Table 7) identifies f 2 as a (3, −3) mode and f 1 as (1, −1), for an inclination angle of 46° ± 2° and vsini 16 ± 2 km s −1 . ...
Here we report the detection of polarization variations due to non-radial modes in the β Cephei star β Crucis. In so doing we confirm 40-year-old predictions of pulsation-induced polarization variability and its utility in asteroseismology for mode identification. In an approach suited to other β Cephei stars, we combine polarimetry with space-based photometry and archival spectroscopy to identify the dominant non-radial mode in polarimetry, f2, as mode degree ℓ = 3, azimuthal order m = −3 (in the m-convention of Dziembowski) and determine the stellar axis position angle as 25 (or 205) ± 8°. The rotation axis inclination to the line of sight was derived as ~46° from combined polarimetry and spectroscopy, facilitating identification of additional modes and allowing for asteroseismic modelling. This reveals a star of 14.5 ± 0.5 M⊙ and a convective core containing ~28% of its mass—making β Crucis the most massive star with an asteroseismic age.
... Therefore, we discuss the results of our line-profile modelling from visual inspection of the amplitude and phase distributions across the line profiles as it has been done previously in the literature, see e.g. Telting et al. (1997) and Briquet et al. (2005) for β Cephei, θ Ophiuchi and HD180642, respectively. ...
Since solar-like oscillations were first detected in red-giant stars, the presence of non-radial oscillation modes has been debated. Spectroscopic line-profile analysis was used in the first attempt to perform mode identification, which revealed that non-radial modes are observable. Despite the fact that the presence of non-radial modes could be confirmed, the degree or azimuthal order could not be uniquely identified. Here we present an improvement to this first spectroscopic line-profile analysis. Aims: We aim to study line-profile variations of stochastically excited solar-like oscillations in four evolved stars to derive the azimuthal order of the observed mode and the surface rotational frequency. Methods: Spectroscopic line-profile analysis is applied to cross-correlation functions, using the Fourier Parameter Fit method on the amplitude and phase distributions across the profiles. Results: For four evolved stars, beta Hydri (G2IV), epsilon Ophiuchi (G9.5III), eta Serpentis (K0III) and delta Eridani (K0IV) the line-profile variations reveal the azimuthal order of the oscillations with an accuracy of ~1. Furthermore, our analysis reveals the projected rotational velocity and the inclination angle. From these parameters we obtain the surface rotational frequency. Conclusions: We conclude that line-profile variations of cross-correlation functions behave differently for different frequencies and that they provide additional information in terms of the surface rotational frequency and azimuthal order. Comment: Accepted for publication in Astronomy and Astrophysics, 9 pages, 10 figures and 3 tables. A version with figure 1 in full resolution can be obtained upon request from first author
Massive stars are important metal factories in the Universe. They have short and energetic lives, and many of them inevitably explode as a supernova and become a neutron star or black hole. In turn, the formation, evolution and explosive deaths of massive stars impact the surrounding interstellar medium and shape the evolution of their host galaxies. Yet the chemical and dynamical evolution of a massive star, including the chemical yield of the ultimate supernova and the remnant mass of the compact object, strongly depend on the interior physics of the progenitor star. We currently lack empirically calibrated prescriptions for various physical processes at work within massive stars, but this is now being remedied by asteroseismology. The study of stellar structure and evolution using stellar oscillations—asteroseismology—has undergone a revolution in the last two decades thanks to high-precision time series photometry from space telescopes. In particular, the long-term light curves provided by the MOST, CoRoT, BRITE, Kepler/K2, and TESS missions provided invaluable data sets in terms of photometric precision, duration and frequency resolution to successfully apply asteroseismology to massive stars and probe their interior physics. The observation and subsequent modeling of stellar pulsations in massive stars has revealed key missing ingredients in stellar structure and evolution models of these stars. Thus, asteroseismology has opened a new window into calibrating stellar physics within a highly degenerate part of the Hertzsprung–Russell diagram. In this review, I provide a historical overview of the progress made using ground-based and early space missions, and discuss more recent advances and breakthroughs in our understanding of massive star interiors by means of asteroseismology with modern space telescopes.
Massive stars are important metal factories in the Universe. They have short and energetic lives, and many of them inevitably explode as a supernova and become a neutron star or black hole. In turn, the formation, evolution and explosive deaths of massive stars impact the surrounding interstellar medium and shape the evolution of their host galaxies. Yet the chemical and dynamical evolution of a massive star, including the chemical yield of the ultimate supernova and the remnant mass of the compact object, strongly depend on the interior physics of the progenitor star. We currently lack empirically calibrated prescriptions for various physical processes at work within massive stars, but this is now being remedied by asteroseismology. The study of stellar structure and evolution using stellar oscillations - asteroseismology - has undergone a revolution in the last two decades thanks to high-precision time series photometry from space telescopes. In particular, the long-term light curves provided by the MOST, CoRoT, BRITE, Kepler/K2 and TESS missions provided invaluable data sets in terms of photometric precision, duration and frequency resolution to successfully apply asteroseismology to massive stars and probe their interior physics. The observation and subsequent modelling of stellar pulsations in massive stars has revealed key missing ingredients in stellar structure and evolution models of these stars. Thus asteroseismology has opened a new window into calibrating stellar physics within a highly degenerate part of the Hertzsprung-Russell diagram. In this review, I provide a historical overview of the progress made using ground-based and early space missions, and discuss more recent advances and breakthroughs in our understanding of massive star interiors by means of asteroseismology with modern space telescopes.
Pythagoras of Samos (c. 569 − 475 BC) is best-known now for the Pythagorean Theorem relating the sides of a right triangle: \({a}^{2} + {b}^{2} = {c}^{2}\), but his accomplishments go far beyond this. When Pythagoras was a young man (c. 530 BC) he emigrated to Kroton in southern Italy where he founded the Pythagorean Brotherhood who soon held secular power over not just Kroton, but more extended parts of Magna Grecia. He and his followers were natural philosophers (they invented the term “philosophy”) trying to understand the world around them; in the modern sense we would call them scientists. They believed that there was a natural harmony to everything, that music, mathematics and what we now call physics were intimately related. In particular, they believed that the motions of the Sun, moon, planets and stars generated musical sounds. They imagined that the Earth is a free-floating sphere and that the daily motion of the stars and the movement through the stars of the Sun, moon and planets were the result of the spinning of crystalline spheres or wheels that carried these objects around the sky. The gods, and those who were more-than-human (such as Pythagoras), could hear the hum of the spinning crystalline spheres: they could hear the Music of the Spheres (see Koestler 1959).
As already discussed in Chapter 3, the three components of the Lagrangian displacement vector of an undamped oscillator contain a time-dependent factor exp( − i ωt), with ω = 2πν the angular frequency of the oscillation mode and \(\Pi = 2\pi /\omega = 1/\nu \) its period (see, e.g., Eq. (3.124) where it was explained that all Eulerian and Lagrangian perturbations contain a common factor). It is therefore clear that stellar oscillations give rise to periodic variations of the physical quantities. These translate into periodic variations of observables, such as the brightness, the colours, the radial velocity and the spectral line profiles. In this Chapter we describe methodology to derive the oscillation frequencies from time series of data of pulsating stars.
Global helioseismology is a mature field of research. Some models of the Sun agree with the helioseismic observations of the sound speed to within a fraction of a percent over 90% of the solar radius – a stunning achievement. Eddington’s longed-for “appliance” to pierce the outer layers of a star and see within has been discovered; with helioseismology we see the interior of the Sun. In addition, we understand solar nuclear fusion reactions so well that we reproduce them both explosively and non-explosively here on Earth, and we even believe that we now understand solar neutrinos, with cosmic implications. Thus the standard solar model can be elevated to “understood physics” – physics that will undergo small modifications in the future, but for which a revolutionary paradigm is unlikely.
Where do we go from here? It is important to remind ourselves that the Sun is but one star. Our model of it is exceedingly good, based on the bedrock of laboratory atomic and nuclear physics, mechanics and electromagnetism. We have a self-consistent model of one “experiment”: the Sun. As with all physics experiments, we need to alter the initial conditions and run the experiment again and again, searching parameter space, probing for weaknesses in the model, probing for new physical understanding, searching for unimagined discoveries.
As per the recent study by the MiMeS collaboration, only about 10% of massive stars possess organized global magnetic fields, typically dipolar in nature. The competition between such magnetic fields and highly non-linear radiative forces that drive the stellar winds leads to a highly complex interaction. Such an interplay can lead to a number of observable phenomena, e.g. X-ray, wind confinement, rapid stellar spindown. However, due to its complexity, such an interaction cannot usually be modeled analytically, instead numerical modeling becomes a necessary tool. In this talk, I will discuss how numerical magnetohydrodynamic (MHD) simulations are employed to understand the nature of such magnetized massive star winds.
The Fourier Transform method is a popular tool to derive the rotational
velocities of stars from their spectral line profiles. However, its domain of
validity does not include line-profile variables with time-dependent profiles.
We investigate the performance of the method for such cases, by interpreting
the line-profile variations of spotted B stars, and of pulsating B tars, as if
their spectral lines were caused by uniform surface rotation along with
macroturbulence. We perform time-series analysis and harmonic least-squares
fitting of various line diagnostics and of the outcome of several
implementations of the Fourier Transform method. We find that the projected
rotational velocities derived from the Fourier Transform vary appreciably
during the pulsation cycle whenever the pulsational and rotational velocity
fields are of similar magnitude. The macroturbulent velocities derived while
ignoring the pulsations can vary with tens of km/s during the pulsation cycle.
The temporal behaviour of the deduced rotational and macroturbulent velocities
are in antiphase with each other. The rotational velocity is in phase with the
second moment of the line profiles. The application of the Fourier method to
stars with considerable pulsational line broadening may lead to an appreciable
spread in the values of the rotation velocity, and, by implication, of the
deduced value of the macroturbulence. These two quantities should therefore not
be derived from single snapshot spectra if the aim is to use them as a solid
diagnostic for the evaluation of stellar evolution models of slow to moderate
rotators.
Context: .Be stars, which are characterised by intermittent emission in
their hydrogen lines, are known to be fast rotators. This fast rotation
is a requirement for the formation of a Keplerian disk, which in turn
gives rise to the emission. However, the pulsating, magnetic B1IV star
β Cephei is a very slow rotator that still shows
Hα emission episodes like in other Be stars, contradicting current
theories. Aims: .We investigate the hypothesis that the Hα
emission stems from the spectroscopically unresolved companion of β
Cep. Methods: .Spectra of the two unresolved components have been
separated in the 6350-6850 Å range with spectro-astrometric
techniques, using 11 longslit spectra obtained with ALFOSC at the Nordic
Optical Telescope, La Palma. Results: .We find that the Hα
emission is not related to the primary in β Cep, but is due to its
3.4 mag fainter companion. This companion has been resolved by speckle
techniques, but it remains unresolved by traditional spectroscopy. The
emission extends from about -400 to +400 km s-1. The
companion star in its 90-year orbit is likely to be a classical Be star
with a spectral type around B6-8. Conclusions: .By identifying its
Be-star companion as the origin of the Hα emission behaviour, the
enigma behind the Be status of the slow rotator β Cep has been
resolved.
