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Register a new userInference for Stellar Opacities from Seismic Studies of the Hybrid $beta$ Cep/SPB pulsators
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Przemys{\\l}aw Walczak dr
Publication date
2017
fields
Physics
and research's language is
English
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We present a comprehensive seismic study of the three pulsating stars of $beta$ Cep/SPB type: $ u$ Eridani, 12 Lacertae and $gamma$ Pegasi. Models with the modified mean opacity profile are constructed in order to account for both the observed frequency range and the values of some individual frequencies. To decrease the number of possible solutions, we make use of the non-adiabatic parameter $f$, whose value is very sensitive to subphotospheric layers where pulsations are driven. This complex seismic modelling show the need for a significant modification of the opacity profile.
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We undertake another attempt towards seismic modelling of the most intensive studied main sequence pulsators of the early B spectral type, $ u$ Eridani. Our analysis is extended by a requirement of fitting not only pulsational frequencies but also the complex amplitude of the bolometric flux variation, $f$, related to each mode frequency. This approach, called {it complex asteroseismology}, provides a unique test of stellar parameters, atmospheres and opacities. In particular, the concordance of the empirical and theoretical values of $f$ we obtained for the high-order g mode opens a new gate in seismic studies of the main-sequence hybrid pulsators. The most intriguing and challenging result is that whereas an agreement of the theoretical and empirical values of $f$ for the radial mode can be achieved only with the OPAL data, a preference for the OP tables is derived from the analysis of the high-order gravity mode.
Results of mode identification and seismic modelling of the $beta$ Cep/SBP star 12 Lacertae are presented. Using data on the multi-colour photometry and radial velocity variations, we determine or constrain the mode degree, $ell$, for all pulsational frequencies. Including the effects of rotation, we show that the dominant frequency, $ u_1$, is most likely a pure $ell=1$ mode and the low frequency, $ u_A$, is a dipole retrograde mode. We construct a set of seismic models which fit two pulsational frequencies corresponding to the modes $ell= 0,$ p$_1$ and $ell= 1,$ g$_1$ and reproduce also the complex amplitude of the bolometric flux variations, $f$, for both frequencies simultaneously. Some of these seismic models reproduce also the frequency $ u_A$, as a mode $ell= 1,$ g$_{13}$ or g$_{14}$, and its empirical values of $f$. Moreover, it was possible to find a model fitting the six 12 Lac frequencies (the first five and $ u_A$), only if the rotational splitting was calculated for a velocity of $V_{rm rot}approx 75$ km/s. In the next step, we check the effects of model atmospheres, opacity data, chemical mixture and opacity enhancement. Our results show that the OP tables are preferred and an increase of opacities in the $Z-$bump spoils the concordance of the empirical and theoretical values of $f$.
We determine the fundamental parameters of SPB and Beta Cep candidate stars observed by the Kepler satellite mission and estimate the expected types of non-radial pulsators by comparing newly obtained high-resolution spectra with synthetic spectra computed on a grid of stellar parameters assuming LTE and check for NLTE effects for the hottest stars. For comparison, we determine Teff independently from fitting the spectral energy distribution of the stars obtained from the available photometry. We determine Teff, log(g), micro-turbulent velocity, vsin(i), metallicity, and elemental abundance for 14 of the 16 candidate stars, two of the stars are spectroscopic binaries. No significant influence of NLTE effects on the results could be found. For hot stars, we find systematic deviations of the determined effective temperatures from those given in the Kepler Input Catalogue. The deviations are confirmed by the results obtained from ground-based photometry. Five stars show reduced metallicity, two stars are He-strong, one is He-weak, and one is Si-strong. Two of the stars could be Beta Cep/SPB hybrid pulsators, four SPB pulsators, and five more stars are located close to the borders of the SPB instability region.
We present results of a {bf comprehensive} asteroseismic modelling of the $beta$ Cephei variable $theta$ Ophiuchi. {bf We call these studies {it complex asteroseismology} because our goal is to reproduce both pulsational frequencies as well as corresponding values of a complex, nonadiabatic parameter, $f$, defined by the radiative flux perturbation.} To this end, we apply the method of simultaneous determination of the spherical harmonic degree, $ell$, of excited pulsational mode and the corresponding nonadiabatic $f$ parameter from combined multicolour photometry and radial velocity data. Using both the OP and OPAL opacity data, we find a family of seismic models which reproduce the radial and dipole centroid mode frequencies, as well as the $f$ parameter associated with the radial mode. Adding the nonadiabatic parameter to seismic modelling of the B-type main sequence pulsators yields very strong constraints on stellar opacities. In particular, only with one source of opacities it is possible to agree the empirical values of $f$ with their theoretical counterparts. Our results for $theta$ Oph point substantially to preference for the OPAL data.
Aims: We develop a method that provides a comprehensive analysis of the oscillation spectra of solar-like pulsators. We define new seismic indicators that should be as uncorrelated and as precise as possible and should hold detailed information about stellar interiors. This is essential to improve the quality of the results obtained from asteroseismology as it will provide better stellar models which in turn can be used to refine inferences made in exoplanetology and galactic archaeology. Methods: The presented method - WhoSGlAd - relies on Gram-Schmidts orthogonalisation process. A Euclidean vector subspace of functions is defined and the oscillation frequencies are projected over an orthonormal basis in a specific order. This allows the obtention of independent coefficients that we combine to define independent seismic indicators. Results: The developed method has been shown to be stable and to converge efficiently for solar-like pulsators. Thus, detailed and precise inferences can be obtained on the mass, the age, the chemical composition and the undershooting in the interior of the studied stars. However, attention has to be paid when studying the helium glitch as there seems to be a degeneracy between the influence of the helium abundance and that of the heavy elements on the glitch amplitude. As an example, we analyse the 16CygA (HD 186408) oscillation spectrum to provide an illustration of the capabilities of the method.
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