In this paper we describe our convective hydrocodes for radial stellar pulsation. We adopt the Kuhfuss (1986) model of convection, reformulated for the use in stellar pulsation hydrocodes. Physical as well as numerical assumptions of the code are described in detail. Described tests show, that our models are numerically robust and reproduce basic observational constraints.
We discuss the effects of different treatment of some quantities in other pulsation hydrocodes. Our most important finding concerns the treatment of the turbulent source function in convectively stable regions. In our code we allow for negative values of source function in convectively stable zones, which reflects negative buoyancy. However, some authors restrict the source term to non-negative values. We show that this assumption leads to very high turbulent energies in convectively stable regions. The effect looks like overshooting, but it is not, because turbulence is generated by pulsations. Also, turbulent elements do not carry kinetic nor thermal energy, into convectively stable layers. The range of this artificial overshooting (as we shall call it) is as large as 6 local pressure scale heights, leading to unphysical internal damping through the eddy-viscous forces, in deep, convectively stable parts of the star.
The longstanding problem of modeling double-mode behaviour of classical pulsators was solved with the incorporation of turbulent convection into pulsation hydrocodes. However, the reasons for the computed double-mode behaviour were never clearly identified. In our recent papers (Smolec & Moskalik 2008a,b) we showed that the double-mode behaviour results from the neglect of negative buoyancy effects in some of the hydrocodes. If these effects are taken into account, no stable non-resonant double-mode behaviour can be found. In these proceedings we focus our attention on the role of negative buo…
For many years modeling of double-mode pulsation of classical pulsators was a challenging problem. Inclusion of turbulent convection into pulsation hydrocodes finally led to stable double-mode models. However, it was never analysed, which factor of turbulent convection is crucial. We show that the double-mode behaviour displayed in the computed models results from incorrect assumptions adopted in some of the pulsation hydrocodes, namely from the neglect of buoyant forces in convectively stable layers. This leads to significant turbulent energies and consequently to strong eddy-viscous damping …
We review the numerical modelling of the nonlinear pulsations of classical variable stars with hydrocodes that include the effects of turbulent convection. Despite their simplicity these turbulent convective recipes appear to remove many of the difficulties that radiative codes faced. In particular, the numerical modelling of double mode pulsations has become possible.
Results of nonradial, nonadiabatic pulsation calculations on hydrogen-rich white dwarf models are presented. In contrast to earlier attempts, the modeling builds on hydrodynamically simulated convective surface layers supplemented with standard interior models. Based on our stellar models and despite of various simple attempts to couple convection and pulsation we could not reproduce theoretically the presently adopted location of the observed blue edge of the ZZ Ceti variables. When the convective efficiency is high enough we found a sensitive dependence of the stability properties of the g-m…
We present the results of a detailed set of one-zone models that account for the coupling between pulsation and convection following the original prescriptions of Stellingwerf (1986). Motivated by the arbitrary nature of the input parameters adopted in this theoretical framework, we computed several sequences of models that cover a substantial fraction of the parameter space and a longer integration time. We also included a turbulent pressure term and found that this physical mechanism plays a crucial role in the pulsation characteristics of the models by removing the sharp discontinuities alo…
A one-dimensional turbulent convection model in the form of a time-dependent diffusion equation for the turbulent energy is incorporated into our numerical pulsation code. The effect of turbulent convection on the structural rearrangement of the static equilibrium star is taken into account, and the linear eigenvalues (periods and growth-rates) for the complete turbulent convective nonadiabatic pulsations of the equilibrium models are calculated. The linearized code allows us to perform efficiently a systematic survey of the stability of Cepheid models for a wide range of astrophysical paramet…
We use high precision multiband photometric data of the first overtone RR Lyrae U Com to investigate the predictive capability of full amplitude, nonlinear, convective hydrodynamical models. The main outcome of this investigation is that theoretical predictions properly account for the luminosity variations along a full pulsation cycle. Moreover, we find that this approach, due to the strong dependence of this observable and of the pulsation period on stellar parameters, supply tight constraints on stellar mass, effective temperature, and distance modulus. Pulsational estimates of these parame…
We investigate dynamical interactions between turbulent convection and g-mode pulsations in ZZ Ceti variables (DAVs). Since our understanding of turbulence is rudimentary, we are compelled to settle for order of magnitude results. A key feature of these interactions is that convective response times are much shorter than pulsation periods. Thus the dynamical interactions enforce near uniform horizontal velocity inside the convection zone. They also give rise to a narrow shear layer in the region of convective overshoot at the top of the radiative interior. Turbulent damping inside the convecti…
The identification of pulsation modes in delta Scuti stars is mandatory to constrain the theoretical stellar models. The non-adiabatic observables used in the photometric identification methods depend, however,on convection modeling in the external layers. Our aim is to determine how the treatment of convection in the atmospheric and sub-atmospheric layers affects the mode identification, and what information about the thermal structure of the external layers can be obtained from amplitude ratios and phase lags in Strömgren photometric bands. We derive non-adiabatic parameters for delta Scuti …
We give a status report of convective Cepheid and RR Lyrae model pulsations. Some striking successes can be reported, despite the use of a rather simple treatment of turbulent convection with a 1D time-dependent diffusion equation for the turbulent energy. It is now possible to obtain stable double-mode (beat) pulsations in both Cepheid and RR Lyrae models with astrophysical parameters, i.e. periods and amplitude ratios, that are in agreement with observations. The turbulent convective models, however, have difficulties giving global agreement with the observations. In particular, the Magellan…
Population II pulsatingvariables play a relevant role both as distance indicators and as tracers of the properties of old stellar populations. In this paper we present an update and homogeneous pulsational scenario for a wide range of stellar parameters typical of BL Her stars i.e., Population II Cepheids with periods shorter than 8 days. To this purpose, we adopt a nonlinear convective hydrodinamical code evaluate the stability and full amplitude behaviour of an extensive set of BL Her pulsation models. Various assumptions of mass, luminosity and metallicity consistent with the most recent ev…
Despite all advances in multi-dimensional hydrodynamics, investigations of stellar evolution and stellar pulsations still depend on one-dimensional computations. The present work devises an alternative to the mixing length theory or turbulence models usually adopted for the modelling of convective transport in such studies. Assuming that the largest convective patterns generate the majority of convective transport, the convective velocity field is described using two parallel radial columns to represent up- and downstream flows. Horizontal exchange in the form of fluid flow and radiation over …
This paper examines the mode identification and presents pulsation models for FG Vir, for which 24 frequencies have been detected. Histograms of the frequency spacings show peaks which are identified with adjacent radial orders and rotational splitting. Pulsational $\ell$ values are deduced for eight modes by comparing the observed photometric phase lags between $v$ and $y$ variations with calculated values. The dominant pulsation mode at 12.72 c/d can be identified with $\ell$ = 1, while the 12.15 c/d mode is the radial fundamental. These results are in agreement with identifications publishe…
A grid of stellar evolution models for Procyon A has been calculated. These models include the best physics available to us (including the latest opacities and equation of state) and are based on the revised astrometric mass of Girard et al (1996). Models were calculated with helium diffusion and with the combined effects of helium and heavy element diffusion. Oscillation frequencies for l=0,1,2 and 3 p-modes and the characteristic period spacing for the g-modes were calculated for these models. We find that g-modes are sensitive to model parameters which effect the structure of the core, such…
We investigate a selected sample of Galactic classical Cepheids with available distance and reddening estimates in the framework of the theoretical scenario provided by pulsation models, computed with metal abundance Z=0.02, helium content in the range of Y=0.25 to 0.31, and various choices of the stellar mass and luminosity. After transforming the bolometric light curve of the fundamental models into BVRIJK magnitudes, we derived analytical relations connecting the pulsation period with the stellar mass, the mean (intensity-averaged) absolute magnitude, and the color of the pulsators. These r…
We have derived new orbits for zeta Aur, 32 Cyg, and 31 Cyg with observations from the TSU Automatic Spectroscopic Telescope and used them to identify non-orbital velocities of the cool supergiant components of these systems. We measure periods in those deviations, identify unexpected long-period changes in the radial velocities, and place upper limits on the rotation of these stars. These radial-velocity variations are not obviously consistent with radial pulsation theory, given what we know about the masses and sizes of the components. Our concurrent photometry detected the non-radial pulsat…
The current understanding of the turbulent dissipation in stellar convective zones is based on the assumption that the turbulence follows Kolmogorov scaling. This assumption is valid for some cases in which the time frequency of the external shear is high (e.g., solar p modes). However, for many cases of astrophysical interest (e.g., binary orbits, stellar pulsations, etc.), the timescales of interest lie outside the regime of applicability of Kolmogorov scaling. We present direct calculations of the dissipation efficiency of the turbulent convective flow in this regime, using simulations of a…
An adiabatic, nonradial pulsation study of GW Vir stars is presented. The pulsation calculations are based on PG1159 evolutionary sequences with different stellar massess artificially derived from a full evolutionary sequence of 0.5895 Mo that has been computed taking into account the evolutionary history of the progenitor star. The artificial sequences were constructed by appropriately scaling the stellar mass of the 0.5895 Mo sequence well before the models reach the low-luminosity, high-gravity stage of the GW Vir domain. We compute g-mode pulsation periods appropriate to GW Vir variable st…
The results of a multisite photometric campaign of Theta2 Tau are reported. This binary system consists of evolved and main-sequence A stars inside the instability strip. The 12th Delta Scuti Network campaign included 152 hours of high-precision photometry obtained at four observatories. This leads to the derivation of 11 frequencies of pulsation in the 10.8 to 14.6 c/d range. These frequencies confirm the results from previous Earth-based (1982-1986) as well as satellite (2000) photometry,although amplitude variability on a time scale of several years is present. We show that at least two hig…
Direct measurements of Cepheid radii are a key for understanding the physical structure of these variables, and in turn for constraining their pulsation properties. In this paper we discuss the numerical experiments we performed for testing the accuracy of Cepheid radii obtained by adopting both the pure Baade-Wesselink (BW) method and the revised CORS method, as well as the consistency of the physical assumptions on which these methods are based. We applied both the BW and the revised CORS methods to the synthetic light, color and radial velocity curves predicted by Cepheid full amplitude, no…
We present an analysis of the response of a radiative region to waves generated by a convective region of the star; this wave treatment of the classical problem of ``overshooting'' gives extra mixing relative to the treatment traditionally used in stellar evolutionary codes. The interface between convectively stable and unstable regions is dynamic and nonspherical, so that the nonturbulent material is driven into motion, even in the absence of ``penetrative overshoot.'' These motions may be described by the theory of nonspherical stellar pulsations, and are related to motion measured by helios…
