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

Nonlinear Beat Cepheid Models

The numerical hydrodynamic modelling of beat Cepheid behavior has been a longstanding quest in which purely radiative models have failed miserably. We find that beat pulsations occur naturally when turbulent convection is accounted for in our hydrodynamics codes. The development of a relaxation code and of a Floquet stability analysis greatly facilitates the search for and analysis of beat Cepheid models. The conditions for the occurrence of beat behavior can be understood easily and at a fundamental level with the help of amplitude equations. Here a discriminant D arises whose sign decides whether single mode or double mode pulsations can occur in a model, and this D depends only on the values of the nonlinear coupling coefficients between the fundamental and the first overtone modes. For radiative models D is always found to be negative, but with sufficiently strong turbulent convection its sign reverses.Comment: 5 pages, incl. 4 figs - apj lett, accepted may 18, 199

Beat Cepheids as Probes of Stellar and Galactic Metallicity

The mere location of a Beat Cepheid model in a Period Ratio vs. Period diagram (Petersen diagram) puts very tight constraints on its metallicity Z. The Beat Cepheid Peterson diagrams are revisited with linear nonadiabatic turbulent convective models, and their accuracy as a probe for stellar metallicity is evaluated. They are shown to be largely independent of the helium content Y, and they are also only weakly dependent on the mass-luminosity relation that is used in their construction. However, they are found to show sensitivity to the relative abundances of the elements that are lumped into the metallicity parameter Z. Rotation is estimated to have but a small effect on the 'pulsation metallicities'. A composite Petersen diagram is presented that allows one to read off upper and lower limits on the metallicity Z from the measured period P0 and period ratio P1/P0.Comment: 9 pages, 12 color figures (black and white version available from 1st author's website). With minor revisions. to appear in Ap

The Cepheid Phase Lag Revisited

We compute the phase lags between the radial velocity curves and the light curves $\Delta \Phi_1= \phi^{V_r}_1 - \phi^{mag}_1$ for classical Cepheid model sequences both in the linear and the nonlinear regimes. The nonlinear phase lags generally fall below the linear ones except for high period models where they lie above, and of course for low pulsation amplitudes where the two merge. The calculated phase lags show good agreement with the available observational data of normal amplitude Galactic Cepheids. The metallicity has but a moderate effect on the phase lag, while the mass-luminosity relation and the parameters of the turbulent convective model (time-dependent mixing length) mainly influence the modal selection and the period, which is then reflected in the period -- $\Delta \Phi_1$ diagram. We discuss the potential application of this observable as a discriminant for pulsation modes and as a test for ultra-low amplitudes (ULA) pulsation.Comment: 11 pages, 8 figures, accepted for publication in ApJ, minor revisions in the text and figures, (black and white version available from 2nd author's website

RR Lyrae - Theory vs Observation

The luminosities, effective temperatures and metallicities that are derived empirically by Kovacs and Jurcsik from the light curves of a large number of globular cluster and field RRab and RRc stars are compared to theoretical RR Lyrae models. The strong luminosity dependence of the empirical blue and red edges (Log L vs Log Teff diagram) is in disagreement with that of both radiative and convective models. A reexamination of the theoretical uncertainties in the modelling leads us to conclude that the disagreement is irreconcilable.Comment: 6 pages, 5 figures (revised april 2000, revisions relatively minor

Hydrodynamical Survey of First Overtone Cepheids

A hydrodynamical survey of the pulsational properties of first overtone Galactic Cepheids is presented. The goal of this study is to reproduce their observed light- and radial velocity curves. The comparison between the models and the observations is made in a quantitative manner on the level of the Fourier coefficients. Purely radiative models fail to reproduce the observed features, but convective models give good agreement. It is found that the sharp features in the Fourier coefficients are indeed caused by the P1/P4 = 2 resonance, despite the very large damping of the 4th overtone. For the adopted mass-luminosity relation the resonance center lies near a period of 4.2d +/- 0.2 as indicated by the observed radial velocity data, rather than near 3.2d as the light-curves suggest.Comment: ApJ, 12 pages, (slightly) revise

Hydrodynamic stability and mode coupling in Keplerian flows: local strato-rotational analysis

Aims. Qualitative analysis of key (but yet unappreciated) linear phenomena in stratified hydrodynamic Keplerian flows: (i) the occurrence of a vortex mode, as a consequence of strato-rotational balance, with its transient dynamics; (ii) the generation of spiral-density waves (also called inertia-gravity or $g\Omega$ waves) by the vortex mode through linear mode coupling in shear flows. Methods. Non-modal analysis of linearized Boussinesq equations written in the shearing sheet approximation of accretion disk flows. Results. It is shown that the combined action of rotation and stratification introduces a new degree of freedom -- vortex mode perturbation -- which is linearly coupled with the spiral-density waves. These two modes are jointly able to extract energy from the background flow and they govern the disk dynamics in the small-scale range. The transient behavior of these modes is determined by the non-normality of the Keplerian shear flow. Tightly leading vortex mode perturbations undergo substantial transient growth, then, becoming trailing, inevitably generate trailing spiral-density waves by linear mode coupling. This course of events -- transient growth plus coupling -- is particularly pronounced for perturbation harmonics with comparable azimuthal and vertical scales and it renders the energy dynamics similar to the 3D unbounded plane Couette flow case. Conclusions. Our investigation strongly suggests that the so-called bypass concept of turbulence, which has been recently developed by the hydrodynamic community for spectrally stable shear flows, can also be applied to Keplerian disks. This conjecture may be confirmed by appropriate numerical simulations that take in account the vertical stratification and consequent mode coupling in the high Reynolds number regime.Comment: A&A (accepted

PArallel, Robust, Interface Simulator (PARIS)

Paris (PArallel, Robust, Interface Simulator) is a finite volume code for simulations of immiscible multifluid or multiphase flows. It is based on the "one-fluid" formulation of the Navier-Stokes equations where different fluids are treated as one material with variable properties, and surface tension is added as a singular interface force. The fluid equations are solved on a regular structured staggered grid using an explicit projection method with a first-order or second-order time integration scheme. The interface separating the different fluids is tracked by a Front-Tracking (FT) method, where the interface is represented by connected marker points, or by a Volume-of-Fluid (VOF) method, where the marker function is advected directly on the fixed grid. Paris is written in Fortran95/2002 and parallelized using MPI and domain decomposition. It is based on several earlier FT or VOF codes such as Ftc3D, Surfer or Gerris. These codes and similar ones, as well as Paris, have been used to simulate a wide range of multifluid and multiphase flows