Chaos in cosmological Hamiltonians

This paper summarises a numerical investigation which aimed to identify and characterise regular and chaotic behaviour in time-dependent Hamiltonians H(r,p,t) = p^2/2 + U(r,t), with U=R(t)V(r) or U=V[R(t)r], where V(r) is a polynomial in x, y, and/or z, and R = const * t^p is a time-dependent scale factor. When p is not too negative, one can distinguish between regular and chaotic behaviour by determining whether an orbit segment exhibits a sensitive dependence on initial conditions. However, chaotic segments in these potentials differ from chaotic segments in time-independent potentials in that a small initial perturbation will usually exhibit a sub- or super-exponential growth in time. Although not periodic, regular segments typically exhibit simpler shapes, topologies, and Fourier spectra than do chaotic segments. This distinction between regular and chaotic behaviour is not absolute since a single orbit segment can seemingly change from regular to chaotic and visa versa. All these observed phenomena can be understood in terms of a simple theoretical model.Comment: 16 pages LaTeX, including 5 figures, no macros require

Uncovering hidden modes in RR Lyrae stars

The Kepler space telescope revealed new, unexpected phenomena in RR Lyrae stars: period doubling and the possible presence of additional modes. Identifying these modes is complicated because they blend in the rich features of the Fourier-spectrum. Our hydrodynamic calculations uncovered that a 'hidden' mode, the 9th overtone is involved in the period doubling phenomenon. The period of the overtone changes by up to 10 per cent compared to the linear value, indicating a very significant nonlinear period shift caused by its resonance with the fundamental mode. The observations also revealed weak peaks that may correspond to the first or second overtones. These additional modes are often coupled with period doubling. We investigated the possibilities and occurrences of mutual resonances between the fundamental mode and multiple overtones in our models. These theoretical findings can help interpreting the origin and nature of the 'hidden' modes may be found in the high quality light curves of space observatories.Comment: In proceedings of "20th Stellar Pulsation Conference Series: Impact of new instrumentation & new insights in stellar pulsations", 5-9 September 2011, Granada, Spai

Multi-Periodic Oscillations in Cepheids and RR Lyrae-Type Stars

Classical Cepheids and RR Lyrae-type stars are usually considered to be textbook examples of purely radial, strictly periodic pulsators. Not all the variables, however, conform to this simple picture. In this review I discuss different forms of multi-periodicity observed in Cepheids and RR Lyrae stars, including Blazhko effect and various types of radial and nonradial multi-mode oscillations.Comment: Proceedings of the 20th Stellar Pulsation Conference Series: "Impact of new instrumentation & new insights in stellar pulsations", 5-9 September 2011, Granada, Spai

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc

Mode Identification with Cepheid Phase-lag

A large model survey with the Florida-Budapest hydrodynamical code has revisited the Cepheid phase-lag problem. A good agreement between the models and the available observational data has been found for normal amplitude Cepheids. The phase-lag is a method for mode identification that is complementary to that of Fourier decomposition coefficients. In this contribution we exploit its potential in identifying the pulsational mode of Cepheids. The possible application of the phase lag as a test for ultra-low amplitude pulsation is discussed as well

Beat Cepheids as Galactic Metallicity Tracers

We give a brief overview of Cepheids and of their modeling, with particular emphasis on F/O1 Beat Cepheids. Then we revisit the use of Period Ratio vs. Period diagram (Petersen diagram) for fundamental/first overtone Beat Cepheids, because they allow one to put very tight constraints on their metallicity Z. The Petersen diagram is shown to be largely independent of the helium content Y, of the mass-luminosity relation that is used in their construction, and of stellar rotation rates. However, it shows sensitivity to the chemical makeup of the elements that are lumped into the metallicity parameter Z. The Petersen diagram for the new Asplund, M., Grevesse, N., & Sauval, A.J. (2005, ASP Conf. Ser., 336, 25) solar mix is compared to that for for the older, “standard” solar mix of Grevesse, N., & Noels, A., (1993)

THE AFTERCLAP OF DEGENERATE CARBON IGNITION REVISITED

L'ignition du carbone et le mode de propagation de la combustion décident de manière critique du sort des étoiles qui développent des coeurs de carbone/oxygène, c'est-à-dire explosion ou implosion. Le processus le plus rapide (détonation, conduction ou convection) détermine la vitesse de propagation du front de combustion. On peut probablement éliminer la formation d'une détonation à cause de la petitesse de la surpression générée par la combustion à haute densité. Nous démontrons qu'après une courte durée de combustion par conduction, un régime de convection s'établit. Nous en tirons la conclusion que si l'ignition a lieu à densité suffisamment grande (ρ>5 x 109 g/cc) les captures d'électrons et les pertes de neutrino concomitantes causent la réimplosion du coeur de l'étoile.Whether the degenerate C-O cores, with develop in the heart of 4-8 Mθ stars, get fully disrupted or implode into neutron stars depends critically on the results of carbon ignition and on the nature of the propagation of the burning front. The velocity of this front is determined by the fastest of several processes, namely (1) detonation, (2) conductive burning, and (3) convective burning. Detonation can probably be excluded because of the small overpressures resulting from burning at high density. Since conductive burning is estimated to be very slow, the burning front is shown to propagate by convection. We conclude that if ignition occurs at sufficiently high density (ρ > 5 x 109 g/cm3), electron captures and concomitant neutrino losses will then offset the effects of burning and cause the implosion of the core

Chaos in variable stars: Topological analysis of W Vir model pulsations

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