Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-18T11:21:52.378Z Has data issue: false hasContentIssue false

CA Simulations of 2D Stellar Atmosphere Pulsations

Published online by Cambridge University Press:  15 August 2009

J. Perdang*
Affiliation:
Institute of Astronomy, Madingley Road, Cambridge, CB3 OHA, UK Astrophysique B5c, Allée du 6 Août, Sart Tilman, 4000 Liège, Belgium
Get access

Abstract

We develop a new version of a Cellular Automaton (CA) for the simulation of the dynamics of a stellar atmosphere sitting on top of an inert core, and specified by the following physical input parameters: mass, radius and luminosity of core, and mass of atmosphere. The CA incorporates various parametrised simulation schemes of the instability mechanism (essentially ionisation). The initial state in all of our numerical experiments is a radially symmetric atmosphere of exponential density run and uniform temperature (input parameters: density scale– height and temperature of atmosphere). The initial atmosphere is not in hydrostatic and thermal equilibrium. After a transient stage, the system relaxes, for certain ranges of the parameters of the instability mechanism, towards a state of nontrivial dynamical behaviour: Local heat–driven circulations are set up which may range from nearly stationary and spatially symmetric cellular patterns to temporally and spatially irregularly fluctuating velocity fields. The traditional radial symmetry of the density pattern is broken, so that the star acquires a globally non–spherical shape. The residual non–stationary component, when integrated over the star to produce the counterpart of an observational velocity curve of a variable star, shows an irregular cyclic behaviour which does not have the signature of low–dimensional deterministic chaos.

Type
Research Article
Copyright
© EAS, EDP Sciences, 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chandrasekhar, S., 1969, Ellipsoidal Figures of Equilibrium, Yale University, New Haven
Constantinescu, D.M., et al., 1979, J. Phys. (France) 40, 147
Cragg, T.A., 1983, J. Am. Ass. Variable Star Observers, 12, 20
Dupret, M.A., et al., 2005, A&A, 435, 927
Fernie, J.D., & Demers, S., 1966, ApJ, 144, 440
Frisch, U., Hasslacher, B., & Pomeau, Y., 1986, Phys. Rev. Lett., 56, 1505 CrossRef
Frisch, U., et al., 1987, Complex Systems, 1, 649
Grigahcène, A., et al., 2005, A&A, 434, 1055
Hardy, J., de Pazzis, O., & Pomeau, Y., 1976, Phys. Rev., A13, 1949 CrossRef
Huth, H., 1966, Sterne, 42, 129
Iooss, G., & Joseph, D.D., 1990, Elementary Stability and Bifurcation Theory (Springer, Berlin)
Kolláth, Z., & Szeidl, L., 1993, A&A, 277, 62
Nordlund, A., & Stein, R.F., 2001, ApJ, 546, 576 CrossRef
Perdang, J., 1976, New Mathematical Tools in Stellar Stability. Part One, GAT–IR 51, Università degli Studi di Padova, Padua, Italy
Perdang, J., 1985, in Chaos in Astrophysics, ed. Buchler, J.R., et al. (Reidel, Dordrecht) NATO ASI C 161, 11
Perdang, J., 1993, in Cellular Automata: Prospects in Astrophysical Applications, 342, Perdang, J.M., & Lejeune, A., ed. (World Scientific, Singapore)
Perdang, J., 1993a, in Cellular Automata: Prospects in Astrophysical Applications, 3; Perdang, J.M., & Lejeune, A., ed. (World Scientific, Singapore)
Perdang, J., 1994, Ap&SS, 220, 1
Perdang, J., 2003, PASPC, 292, 346
Perdang, J., 2008, to be published in Bull. Acad. Roy. Belgique, Classe des Sciences
Perdang, J., & Serre, Th., 1998, A&A, 334, 976
Rivet, J.P., & Boon, J.P., 2001, Lattice Gas Hydrodynamics (Cambridge University Press, Cambridge)
Robert, A., 1985, Analyse non standard (Presses Polytechniques Romandes, Lausanne)
Robinson, A., 1980, Non-Standard Analysis (North-Holland, Amsterdam)
Rothman, D.H., & Zaleski, S., 1997, Lattice–Gas Cellular Automata (Cambridge University Press, Cambridge)
Succi, S., 2001, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, Oxford)
Succi, S., Karlin, I.V., & Chen, H., 2002, Rev. Mod. Phys., 74, 1203 CrossRef
Szeidl, B., et al., 1992, Communications from the Konkoly Observatory of the Hungarian Academy of Sciences, 97 (Vol. 11, Part 4) 247
Zaitseva, G.V., Lyutyi, V.M., & Efremov, Yu.N., 1973, SvA, 16, 856