Statistics – Computation
Scientific paper
Sep 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009phdt.......248s&link_type=abstract
PhD Thesis Nicolaus Copernicus Astronomical Center, Warsaw, September 2009
Statistics
Computation
3
Hydrodynamics, Convection, Methods: Numerical, Stars: Oscillations, Cepheids, Double-Mode Pulsation
Scientific paper
In this thesis, I present the results of my work concerning the nonlinear modeling of radial stellar pulsations. I will focus on classical Cepheids, particularly on the double-mode phenomenon.
History of nonlinear modeling of radial stellar pulsations begins in the sixties of the previous century. At the beginning convection was disregarded in model equations. Qualitatively, almost all features of the radial pulsators were successfully modeled with purely radiative hydrocodes. Among problems that remained, the most disturbing was modeling of the double-mode phenomenon. This long-standing problem seemed to be finally solved with the inclusion of turbulent convection into the model equations (Kollath et al. 1998, Feuchtinger 1998). Although dynamical aspects of the double-mode behaviour were extensively studied, its origin, particularly the specific role played by convection, remained obscure. To study this and other problems of radial stellar pulsations, I implemented the convection into pulsation hydrocodes. The codes adopt the Kuhfuss (1986) convection model. In other codes, particularly in the Florida-Budapest hydrocode (e.g. Kollath et al. 2002), used in comput!
ation of most of the published double-mode models, different approximations concerning e.g. eddy-viscous terms or treatment of convectively stable regions are adopted. Particularly the neglect of negative buoyancy effects in the Florida-Budapest code and its consequences, were never discussed in the literature. These consequences are severe. Concerning the single-mode pulsators, neglect of negative buoyancy leads to smaller pulsation amplitudes, in comparison to amplitudes computed with code including these effects. Particularly, neglect of negative buoyancy reduces the amplitude of the fundamental mode very strong. This property of the Florida-Budapest models is crucial in bringing up the stable non-resonant double-mode Cepheid pulsation involving fundamental and first overtone modes (F/1O). Such pulsation is not observed in models computed including negative buoyancy. As the neglect of negative buoyancy is physically not correct, so are the double-mode Cepheid models computed with the Florida-Budapest hydrocode.
Extensive search for F/1O double-mode Cepheid pulsation with the codes including negative buoyancy effects yielded null result. Some resonant double-mode F/1O Cepheid models were found, but their occurrence was restricted to a very narrow domain in the Hertzsprung-Russel diagram. Model computations intended to model the double-overtone (1O/2O) Cepheids in the Large Magellanic Cloud, also revealed some stable double-mode pulsations, however, restricted to a narrow period range. Resonances are most likely conductive in bringing up the double-mode behaviour observed in these models. However, majority of the double-overtone LMC Cepheids cannot be reproduced with our codes. Hence, the modeling of double-overtone Cepheids with convective hydrocodes is not satisfactory, either. Double-mode pulsation still lacks satisfactory explanation, and problem of its modeling remains open.
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