Evidence for Low-Dimensional Chaos in Semiregular Variable Stars

An analysis of the photometric observations of the light curves of the five large amplitude, irregularly pulsating stars R UMi, RS Cyg, V CVn, UX Dra and SX Her is presented. First, multi-periodicity is eliminated for these pulsations, i.e. they are not caused by the excitation of a small number of pulsation modes with constant amplitudes. Next, on the basis of energetics we also eliminate stochasticity as a cause, leaving low dimensional chaos as the only alternative. We then use a global flow reconstruction technique in an attempt to extract quantitative information from the light curves, and to uncover common physical features in this class of irregular variable stars that straddle the RV Tau to the Mira variables. Evidence is presented that the pulsational behavior of R UMi, RS Cyg, V CVn and UX Dra takes place in a 4-dimensional dynamical phase space, suggesting that two vibrational modes are involved in the pulsation. A linear stability analysis of the fixed points of the maps further indicates the existence of a two-mode resonance, similar to the one we had uncovered earlier in R Sct: The irregular pulsations are the result of a continual energy exchange between two strongly nonadiabatic modes, a lower frequency pulsation mode and an overtone that are in a close 2:1 resonance. The evidence is particularly convincing for R UMi, RS Cyg and V CVn, but much weaker for UX Dra. In contrast, the pulsations of SX Her appear to be more complex and may require a 6D space.Comment: 20 pages, 14 figures, accepted in ApJ - paper with clearer figures is available at http://www.phys.ufl.edu/~buchler/publications/u12.ps.gz (1Mb

Spectrum of a magnetized strong-leg quantum spin ladder

Inelastic neutron scattering is used to measure the spin excitation spectrum of the Heisenberg $S=1/2$ ladder material (C$_7$H$_10$N)$_2$CuBr$_4$ in its entirety, both in the gapped spin-liquid and the magnetic field induced Tomonaga-Luttinger spin liquid regimes. A fundamental change of the spin dynamics is observed between these two regimes. DMRG calculations quantitatively reproduce and help understand the observed commensurate and incommensurate excitations. The results validate long-standing quantum field theoretical predictions, but also test the limits of that approach

Modulations in Multi-Periodic Blue Variables in the LMC

As shown by Mennickent, et al(2003), a subset of the blue variable stars in the Large Magellanic Cloud exhibit brightness variability of small amplitude in the period range 2.4 to 16 days as well as larger amplitude variability with periods of 140 to 600 days, with a remarkably tight relation between the long and the short periods. Our re-examination of these objects has led to the discovery of additional variability. The Fourier spectra of 11 of their 30 objects have 3 or 4 peaks above the noise level and a linear relation of the form f_a = 2(f_b - f_L) among three of the frequencies. An explanation of this relation requires an interplay between the binary motion and that of a third object. The two frequency relations together with the Fourier amplitude ratios pose a challenging modeling problem.Comment: 4 pages, 3 figures, Astrophysical Journal (in press

Strange Cepheids and RR Lyrae

Strange modes can occur in radiative classical Cepheids and RR Lyrae models. These are vibrational modes that are trapped near the surface as a result of a 'potential barrier' caused by the sharp hydrogen partial ionization region. Typically the modal number of the strange mode falls between the 7th and 12th overtone, depending on the astrophysical parameters of the equilibrium stellar models (L, M, \Teff, X, Z). Interestingly these modes can be linearly unstable outside the usual instability strip, in which case they should be observable as new kinds of variable stars, 'strange Cepheids' or 'strange RR Lyrae' stars. The present paper reexamines the linear stability properties of the strange modes by taking into account the effects of an isothermal atmosphere, and of turbulent convection. It is found that the linear vibrational instability of the strange modes is resistant to both of these effects. Nonlinear hydrodynamic calculations indicate that the pulsation amplitude of these modes is likely to saturate at the millimagnitude level. These modes should therefore be detectable albeit not without effort.Comment: 6 pages, 7 figures, submitted to Ap