J. Robert Buchler
Professor Emeritus
Education
PhD University of California, San Diego (1969)Research Group
Theoretical AstrophysicsResearch Interest
Theoretical Astrophysics
(Stellar Structure and Evolution, Variable Stars): Cepheids, RR Lyrae and other variable stars play an important role in determining the scale of the Universe. At a more basic level an explanation of their pulsational properties and the satisfaction of the multitude of new observational constraints also provide an interesting physical challenge. We have developed a number of mathematical tools, from numerical hydrodynamical simulations that generate accurate state-of-the-art models and their stability properties, to analytical approaches, such as bifurcation theory and normal forms, provide a framework within which one can understand the systematics of the variety of observed behavior. Our inclusion of a simple one dimensional model equation for time-dependent turbulent convection has led to two notable successes. First, the modelling of the commonly observed phenonmenon beat Cepheid and beat RR Lyrae pulsations, steady pulsations in which two modes are simultaneously excited to large amplitudes, was an unsurmountable challenge to radiative models, i.e. models that only considered energy transport by radiation. Double-mode pulsations are now found quite naturally with turbulent convective models. Second, radiative models had been incapable of reproducing the light-curves of Cepheids that are pulsating in their first overtone. Our recent modelling predicts a new class of very low amplitude Cepheids and RR Lyrae on the edge of the usual instability strip. Work is now underway to make 2D/3D simulations of convection in pulsating envelopes.
Nonlinear Dynamics
(Chaos, Time Series Analysis, Dynamics Reconstruction, Application to Irregular Variable Stars): The physical properties of a dynamical system can be inferred from the observations of a single irregularly fluctuating quantity. In the case of variable stars we can thus extract novel physical properties of the underlying pulsation mechanism from the mere knowledge of the observed lightcurves of irregular variable stars. These properties provide powerful novel constraints that allow us to obtain a better understanding and make better models of these intriguing stars. It appears that in a number of these stars the chaotic pulsations are the result of the nonlinear interaction of two highly nonadiabatic pulsation modes, one of them linearly unstable, and the other one linearly stable, but entrained through a 2:1 resonance.
Selected Publications
Buchler, J. R., Kolláth, Zoltan and Cadmus, R. Evidence for Low-Dimensional Chaos in Semiregular Variable Stars, Astrophysical Journal, Volume 613, pp. 532-547.http://xxx.lanl.gov/abs/astro-ph/0406109
Szabó, R., Kolláth, Z. and Buchler, J.R., 2004, Automated nonlinear stellar pulsation calculations: Applications to RR Lyrae stars. The slope of the fundamental blue edge and the first RRd model survey, Astronomy and Astrophysics, Vol. 425, p. 627-639. http://xxx.lanl.gov/abs/astro-ph/0406373
Buchler, J. R. & Kolláth, Z., 2001, Strange Cepheids and RR Lyrae, Astrophysical Journal, Vol. 255, p. 961-966; http://xxx.lanl.gov/abs/astro-ph/0101392
Kolláth, Z., Beaulieu, J.P., Buchler, J. R., Yecko, P., 1998, Nonlinear Beat Cepheid Models, Astrophysical Journal Letters 502, L55-L58 astro-ph/9804111 , ApJ
Buchler, J.R., 1996, Search for Low-Dimensional Chaos in Observational Data, International School of Physics Enrico Fermi, Course CXXXIII, Past and Present Variability of the Solar-Terrestrial System, Eds. G. Cini Castagnoli & A. Provenzale, p. 275-288, Societa Italiana de Fisica, Bologna, Italy. source