Z. Kollath
University of Florida
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Featured researches published by Z. Kollath.
Astronomy and Astrophysics | 2002
Z. Kollath; J. R. Buchler; R. Szabó; Z. Csubry
The numerical hydrodynamic modelling of beat Cepheid behavior has been a long-standing quest in which purely radiative models have failed consistently. We find that beat pulsations occur quite naturally when turbulent convection is accounted for in our hydrodynamics code. The developments of a relaxation code and of a Floquet stability analysis greatly facilitate the search for and the analysis of beat Cepheid models. The conditions for the occurrence of beat behavior can be understood easily and at a fundamental level with the help of amplitude equations.
Astronomy and Astrophysics | 2004
R. Szabó; Z. Kollath; J. R. Buchler
We describe a methodology that allows us to follow the pulsational behavior of an RR Lyrae model consistently and automatically along its evolutionary track throughout the whole instability strip. It is based on the powerful amplitude equation formalism, and resorts to a judicious combination of numerical hydrodynamical simulations, the analytical signal time-series analysis, and amplitude equations. A large-scale survey of the nonlinear pulsations in RR Lyr instability strip is then presented, and the mode selection mechanism is delineated throughout the relevant regions of parameter space. We obtain and examine two regions with hysteresis, where the pulsational state depends on the direction of the evolutionary tracks, namely a region with either fundamental (RRab) or first overtone (RRc) pulsations and a region with either fundamental (RRab) or double-mode (RRd) pulsations. The regions where stable double-mode (DM, or RRd) pulsations occur are very narrow and hard to find in astrophysical parameter (L, M, Teff, X, Z) space with hydrodynamic simulations, but our systematic and efficient methodology allows us to investigate them with unprecedented detail. It is shown that by simultaneously considering the effects of mode selection and of horizontal branch evolution we can naturally solve one of the extant puzzles involving the topologies of the theoretical and observed instability strips, namely the slope of the fundamental blue edge. The importance of the interplay between mode selection and stellar evolutionary effects is also demonstrated for the properties of double-mode RR Lyr. Finally, the Petersen diagram of double-mode RR Lyr models is discussed for the first time.
Astrophysics and Space Science | 1997
J. Robert Buchler; Z. Kollath; Ariel Marom
We describe an implicit 1–D adaptive mesh hydrodynamics code that is specially tailored for radial stellar pulsations. In the Lagrangian limit the code reduces to the well tested Fraley scheme. The code has the useful feature that unwanted, long lasting transients can be avoided by smoothly switching on the adaptive mesh features starting from the Lagrangean code. Thus, a limit cycle pulsation that can readily be computed with the relaxation method of Stellingwerf will converge in a few tens of pulsation cycles when put into the adaptive mesh code. The code has been checked with two shock problems, viz. Noh and Sedov, for which analytical solutions are known, and it has been found to be both accurate and stable. Superior results were obtained through the solution of the total energy (gravitational + kinetic + internal) equation rather than that of the internal energy only.
Annals of the New York Academy of Sciences | 1995
J. Robert Buchler; Z. Kollath; Thierry Serre
It was Eddington who first explained stellar variability as the excitation of normal modes of oscillation in the star.’ In fact, to phrase it simply, the stellar pulsations are self-excited standing waves in a spherical quarter-wavelength “tube.” In the region of the Hertzsprung-Russell diagram, called the instability strip, where the radially pulsating stars are located, the physical conditions are suitable for the modes or waves to be energized by the interaction of the pulsations with the outward heat flow. In modern thermodynamical parlance the star acts as a natural heat engine2 in which the temperature dependence of the opacity behavior provides the driving.’ Observations and theory have shown that in the classical variable stars, such as the Cepheids and RR Lyrae stars, the pulsations are often periodic to good accuracy, or when they are multiperiodic they involve just a couple of frequencies, and thus of standing waves. In contrast, the pulsations of many of their more luminous and metal poor, Population I1 (Pop. 11) cousins are irregular for pulsation “periods” in excess of 15 days. This was already known observationally at least as far back as the beginning of the ~ e n t u r y . ~ For a long time, however, the nature of this irregularity remained a mystery, even though some early numerical hydrodynamical modeling managed to reproduce irregular pulsation^.^ It is only in the last decade that a systematical numerical hydrodynamical survey of W Virginis models5s6 has shown that the pulsations of these Pop. I1 objects are in fact chaotic in the dynamical systems sense of the word.’.’ The dominant clue as to the chaotic nature of these pulsations comes from the fact that, as a control parameter, namely the equilibrium effective temperature of the models is varied, the pulsations display a perioddoubling cascade that is a clear signature of a chaotic dynamics (for a review, see reference 9).
Astronomy and Astrophysics | 2004
J. R. Buchler; Z. Kollath; J. P. Beaulieu
The pulsational properties of the Cepheid models along the evolutionary tracks from the Padova group (Girardi et al.), as calculated with our turbulent convective pulsation code, are in good agreement with the resonance constraints imposed by the observational OGLE-2 data of the Small and Large Magellanic Clouds. Our study suggests that the P4/P1 = 1/2 resonance for the overtone Cepheids occurs for periods clustering around 4.2 d, in disagreement with the suggestion of Antonello & Poretti based on the observations of light curves, but in agreement with Kienzle et al. and Feuchtinger et al. For the fundamen- tal Cepheids the lowest order Fourier decomposition coefficients from the light curves, viz. R21 and φ21 can be used to locate the resonance region, but not so for the first overtone Cepheids. Here, the radial velocity curves can be used to locate the overtone resonance region, or in their absence, one needs to resort to numerical hydrodynamic modelling.
arXiv: Astrophysics | 2002
J. Robert Buchler; Z. Kollath; Robert Cadmus
The light curves (time series of the radiated energy) of most large amplitude, pulsating stars such as the well known Cepheid stars are regular. However, a smaller group of variable stars that are located next to them in the Hertzsprung‐Russell diagram undergoes irregular light variations and exhibits irregular radial velocities as well. The mechanism behind this irregular behavior was a long standing mystery. A flow reconstruction technique based on the observed lightcurves of six separate stars shows that their underlying dynamics is chaotic and low dimensional (d = 4). Furthermore, we present evidence that the physical mechanism behind the behavior is the nonlinear interaction of just two pulsation eigenmodes. In a generalized Shil’nikov scenario, the pulsation energy alternates continuously, but irregularly between a lower frequency mode that is linearly unstable and thus growing, and a stable overtone that gets entrained through a low order resonance (2:1), but that wants to decay. The flow reconstru...
International Astronomical Union Colloquium | 2002
Z. Csubry; R. Szabó; Z. Kollath; J. R. Buchler
The radial pulsations of variable stars at specified points along their evolution are accurately described with numerical hydrodynamics. The behavior of the pulsations along evolutionary tracks can then be modeled with amplitude equations, whose coefficients are obtained from fits to these hydrodynamical models. To simulate stellar evolution we make the stellar core’s properties time-dependent and can investigate directly the effects on pulsation despite the very different time-scales (dynamical, thermal, evolutionary).
Physical Review Letters | 1995
J. Robert Buchler; Thierry Serre; Z. Kollath; Janet Akyuz Mattei
Astronomy and Astrophysics | 1996
T. Serre; Z. Kollath; J. R. Buchler
Astronomy and Astrophysics | 1998
P. A. Yecko; Z. Kollath; J. R. Buchler