Current Research Interests of J. Robert Buchler

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. In our study of Cepheids and other variable stars we have developed a number of mathematical tools. On the one hand, numerical hydrodynamical simulations generate accurate state-of-the-art models and their stability properties, and on the other hand, 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 recent inclusion of a simple one dimensional model equation for time-dependent turbulent convection has led to two spectacular 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 s Cepheids, i.e. Cepheids pulsating in their first overtone. Again, the inclusion of turbulent convective models gives agreement with observations.

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.

Selected publications:

  • Buchler, J.R., Wood, P.R., Keller, S. & Soszynski, I. 2005, "Ultra-low Amplitude Cepheids in the Large Magellanic Cloud", Astrophysical Journal Letters, Vol. 631, p. L151 - L154
  • Buchler, J.R., Kollath, Z., 2001, "Strange Cepheids and RR Lyrae", Astrophysical Journal, Vol. 255, p. 961.

  • Buchler, J.R., Kollath, Zoltan and Cadmus, R. 2004, "Evidence for Low-Dimensional Chaos in Semiregular Variable Stars", Astrophysical Journal, Vol. 613, p. 532.
  • Buchler, J. R., Serre, T., Kollath, Z. & Mattei, J. 1995, "A Chaotic Pulsating Star -- The Case of R Scuti", Physical Review Letters, Vol. 74, p. 842--845.

  • Szabo, R., Kollath, 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", 2004, Astronomy & Astrophysics, Vol. 425, p. 627.
  • Kollath, Z., Beaulieu, J.P., Buchler, J. R. & Yecko, P., 1998, "Nonlinear Beat Cepheid Models", Astrophysical Journal Letters, Vol. 502, L55--L58

    Reviews:

  • Buchler, J.R., Koll\'ath, Z. 2001a, {\sl Du chaos dans la musique des \'etoiles}, Comptes Rendus du 3$^e$ Colloque sur le "Chaos temporel et chaos spatio-temporel", 24--25 sep. 2001, Le Havre, France.
  • 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: Measurement, Data Analysis and Theoretical Models", Eds. G. Cini Castagnoli & A. Provenzale, p. 275--288, Societa Italiana de Fisica, Bologna, Italy.
  • Buchler, J.R. 1998, "Nonlinear Pulsations", in "A Half Century of Stellar Pulsation Interpretations: A Tribute to Arthur N. Cox", ed. P.A. Bradley and J.A. Guzik, Astronomical Society of the Pacific Conference Series, Vol. 135, p. 220--230.

    see also for downloadable files Publications

    Current Research Support:

    National Science Foundation:
        Nonlinear Stellar Pulsations, grants AST-98 19608, AST-03 07281
        International Collaboration (US-Australia), grant OISE-0417772

    Workshops in Nonlinear Astronomy and Physics:

    The Physics Department, jointly with the Astronomy Department has been organizing annual, interdisciplinary and international workshops in topics of current interest. The proceedings of most of these workshops have been published in the Annals of the New York Academy of Sciences.

    Gottesman, S. T., Buchler, J. R. & Mahon, M. E. 2005, Nonlinear Dynamics in Astronomy and Physics: In Memory of Henry Kandrup, Annals of the New York Academy of Sciences, Vol. 1045.

    Fry, J. N., Buchler, J. R. & Kandrup, H., 2001, The Onset of Nonlinearity in Cosmology, Proceedings of the Fifteenth Annual Florida Workshop in Nonlinear Astronomy and Physics, Annals New York Academy of Sciences, Vol. 927.

    Buchler, J.R. & Kandrup, H., 2000, Astrophysical Turbulence and Convection,Proceedings of the Fourteenth Annual Florida Workshop in Nonlinear Astronomy and Physics, Annals of the New York Academy of Sciences, Vol. 898.

    Updated November 2005