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1.
Weight functions for the non-adiabatic radial pulsations are introduced. It is shown from behavior of these functions that the pulsation periods in classical Cepheids are determined essentially in the adiabatic region of stellar envelopes and, on the other hand, those of low surface-gravity models are strongly affected in the region where the acoustic waves are strongly coupled with the radiation fields. The fact is important for understanding basic difference of the pulsation properties between classical Cepheids and low surfacegravity models.The non-adiabatic weight functions deviate from adiabatic ones in two ways in the stellar envelope layers. In the region where the acoustic waves are tightly coupled with radiation fields, the non-adiabatic weight functions have larger values than the corresponding adiabatic ones. On the contrary, the functions are smaller in the outer isothermal region.These results are discussed from the viewpoint on the propagation of the acoustic waves in radiation nelds.  相似文献   

2.
We present a finite difference code intended for computing linear, adiabatic, non radial pulsations of spherical stars. This code is based on a slight modification of the general Newton-Raphson technique in order to handle the relaxation of the eigenvalue(square of the eigenfrequency) of the modes and their corresponding eigenfunctions. This code has been tested computing the pulsation spectra of polytropic spheres finding a good agreement with previous work. Then, we have coupled this code to our evolutionary code and applied it to the computation of the pulsation spectrum of a low mass, pure-helium white dwarf of 0.3 M ⊙ for a wide range of effective temperatures. In making this calculation we have taken an evolutionary time step short enough such that eigenmodes corresponding to a given model are used as initial approximation to those of the next one. Specifically, we have computed periods, period spacing, eigenfunctions, weight functions, kinetic energies and variational periods for a wide range of modes. To our notice this is the first effort in studying the pulsation properties of helium white dwarfs. The solution we have found working with these realistic white dwarf models are in good accord with the predictions of the asymptotic theory of Tassoul (1980) for high order modes. This indicates that the code presented here is able to work adequately also with realistic stellar models. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

3.
Modal coupling oscillation models for the stellar radial pulsation and coupled-oscillators are reviewed. Coupled-oscillators with the second-order and third-order terms seemed to behave non-systematically. Using the equation by Schwarzschild and Savedoff (1949) with the dissipation term of van del Pol's type which is third-order, we demonstrate the effect of each term. The effects can be understood by the terms of the nonlinear dynamics, which is recently developing, that is. phase-locking, quasi-periodicity, period doubling, and chaos. As the problem of stellar pulsation, especially of double-mode cepheids on the period-ratio, we examine the dependence on the stellar structure from which the coupling constants in the second-order terms are derived. Eigen functions for adiabatic pulsations had been used for the calculation of the constants. It is noted that only two set of the constants are available, that is, for the polytrope model withn = 3 and a cepheid model without convection. Some examples of nonlinear dynamical effects will be shown.It is shown that if the constants were suitable values, the period-ratio of double-mode cepheids is probably realized. The possibility is briefly suggested.  相似文献   

4.
The second order theory of coupling is discussed regarding the radial pulsation of stellar models which are constructed ignoring convection. The formula including the nonadiabatic effect is presented. Numerical values given for model classical cepheids are considerably greater than the adiabatic values.  相似文献   

5.
We describe an implicit 1–D adaptive mesh hydrodynamics code that is specially tailored for radial stellar pulsations. In the Lagrangian limit the code reduces to the well tested Fraley scheme. The code has the useful feature that unwanted, long lasting transients can be avoided by smoothly switching on the adaptive mesh features starting from the Lagrangean code. Thus, a limit cycle pulsation that can readily be computed with the relaxation method of Stellingwerf will converge in a few tens of pulsation cycles when put into the adaptive mesh code. The code has been checked with two shock problems, viz. Noh and Sedov, for which analytical solutions are known, and it has been found to be both accurate and stable. Superior results were obtained through the solution of the total energy (gravitational + kinetic + internal) equation rather than that of the internal energy only. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

6.
The unrestricted second-order virial tensor formalism has been used to calculate the characteristic frequencies of linear adiabatic oscillations of a composite stellar model having an isothermal core and a polytropic envelope in presence of a weak poloidal magnetic field. The frequencies of the transverse shear mode and the nonradial pulsation mode for both a radiative and a convective envelope (corresponding to polytropic index 3 and 1.5, respectively) alongwith that of the toroidal mode for the radiative envelope get increased in presence of the magnetic field. However, the frequency of the toroidal mode for the convective envelope registers a decrease in presence of the field. The corrections to the various frequencies decrease with increasing values of the parameter characterizing the lowering of the core temperature in presence of the magnetic field.  相似文献   

7.
Within the framework of a non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial influence on pulsation stability of g modes and low-order(radial order n_r 5) p modes.The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most high-order(n r 5) p modes of all low-temperature stars become unstable. Fortunately,within a wide range of the anisotropic parameter c_3, stellar pulsation stability is not sensitive to the specific value of c_3. Therefore it is safe to say that calibration errors of the convective parameter c_3 do not cause any uncertainty in the calculation of stellar pulsation stability.  相似文献   

8.
This paper describes the OSCROX stellar oscillation code for the calculation of the adiabatic oscillations of low degree ? of a spherical star. There are two principal versions: one in Lagrangian variables (oscroxL), the second in Eulerian variables (oscroxE). The Lagrangian code does not require values of the Brunt Väisälä frequency or equivalently the density gradient. For ?=1 the oscillation equations have both an exact integral and an exact partial wave solution, and codes oscroxL1 and oscroxE1 incorporate these exact solutions. The difference in the frequencies obtained with the various codes gives some estimate of the uncertainty in the results due both to limited accuracy of hydrostatic support of the stellar model, and the limited accuracy of the integration of the oscillation equations. We compare the results of the different methods by calculating the frequencies in the range 20–2500 μHz of a model of a 1.5 M⊙ main-sequence star (ModelJC) kindly provided by J. Christensen-Dalsgaard for the purposes of cross comparison of codes, a modified version of this model (ModelJCA) with improved hydrostatic support, and of a highly accurate n=3 polytropic model of a star with the same mass and radius. For the polytropic model the frequencies as calculated by all codes agree to within 0.001 μHz, whereas for the 1.5 M⊙ main sequence model the frequency differences reach a maximum of 0.04 μHz, due primarily to the limited accuracy of hydrostatic support in the model; this is reduced to 0.01 μHz for ModelJCA.  相似文献   

9.
We briefly discuss the current status of our radiation-hydrodynamical models of pulsation in various stellar objects and of dust-driven mass loss in LPVs. We emphasize the importance of a future combined modelling of pulsation and mass loss in AGB stars which has to be based on reliable physical and numerical methods.  相似文献   

10.
Development of the Aarhus adiabatic pulsation code started around 1978. Although the main features have been stable for more than a decade, development of the code is continuing, concerning numerical properties and output. The code has been provided as a generally available package and has seen substantial use at a number of installations. Further development of the package, including bringing the documentation closer to being up to date, is planned as part of the HELAS Coordination Action.  相似文献   

11.
The Fourier coefficients of the hydrodynamic variables are calculated for the limit-cycle models of classical Cepheids having periods from 7.2 to 10.9 days. In adiabatically pulsating layers of the stellar envelope, each Fourier harmonic of orderk 8 is shown to be identified with a corresponding standing wave, so that the pulsation motions of the adiabatic layers may be represented as a superposition of standing waves. Each Fourier harmonic of orderk may also be identified with the eigenfunction of orderl of the linear adiabatic wave equation when the resonance condition l /0 =k is fulfilled. The spectra of the oscillatory moment of inertia and the spectra of kinetic energy obey the power law for the Fourier harmonics of orderk 15, the spectrum slope being steeper for shorter pulsation periods. In the helium and hydrogen ionizing regions all of the Fourier harmonics drive the pulsation instability, whereas in the radiative damping region the mechanical work done by each Fourier harmonic is negative. In classical Cepheids having periods shorter than 10 days the period dependence of the secondary bump is due to phase changes of the second order Fourier harmonic in the outer nonadiabatic layers of the stellar envelope. At a pulsation period of II 9.7 days the second order Fourier harmonic is identified with the second overtone. At periods II > 10 days the second order Fourier harmonic tends to be attracted by the fundamental mode in such a way that their phases coincide in the outer layers of the stellar envelope.  相似文献   

12.
Simple models of nonlinear stellar pulsation, whose temporal behavior may reproduce some of the observed features of different classes of variable stars, have been studied. The temporal behavior of dynamical variables of these models exhibits a cascade of period doubling chaos, depending on the specific values of the various control parameters. A multifractal detrended fluctuation analysis (MFDFA) method is further used to identify the scaling behavior of such synthetic time series. The MFDFA of the considered time series, for various models of nonlinear stellar pulsation, shows that the observed multifractal nature is due to long-range correlations. The pulsating star with increased nonadiabaticity and the star with increased convective luminosity, as represented by the simulated data, is shown to possess a strange attractor with noninteger correlation dimension that lies between 2–3. Also the problem of synchronization in coupled nonlinear pulsation models has been investigated using permutation entropy—a complexity measure of the system. The computed order parameter, Γ, representing the correlation of computed permutation entropy for different segments of the simulated time series of displacement of two nonidentical oscillators, has been further used to find the critical coupling parameter for general synchronization of the oscillators.  相似文献   

13.
The Liège Oscillation code can be used as a stand-alone program or as a library of subroutines that the user calls from a Fortran main program of his own to compute radial and nonradial adiabatic oscillations of stellar models. We describe the variables and the equations used by the program and the methods used to solve them. A brief account is given of the use and the output of the program.  相似文献   

14.
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15.
The distortion of the surface of a hot variable star undergoing nonradial pulsation produces a variable polarization. Resultant changes in the Stokes parameters are here calculated analytically in the linear regime as a function of both the pulsation mode (l, m) and the orientation of the stellar rotation axis. It is shown that all of the necessary stellar atmosphere information may be condensed into one simple integral. The analytic form permits a systematic appraisal of the mode-discriminating ability of polarization observations. A suitable systematic approach is outlined and illustrated with reference to the data for BW Vul.  相似文献   

16.
Combination frequencies are observed in the Fourier spectra of pulsating DA and DB white dwarfs, along with frequencies that are associated with stellar gravity modes. They appear at the sum and difference frequencies of the stellar modes. Brickhill proposed that the combination frequencies result from mixing of the eigenmode signals by a depth-varying surface convection zone when undergoing pulsation. The depth changes cause time-dependent thermal impedance.
Following Brickhill's proposal, we developed analytical expressions for the amplitudes and phases of these combination frequencies. The parameters that appear in these expressions are the depth of the stellar convection zone when at rest, the sensitivity of this depth towards changes in the stellar effective temperature, the inclination angle of the stellar pulsation axis with respect to the line of sight, and lastly the spherical degrees of the eigenmodes involved in the mixing. Adopting credible values for these parameters, we apply our expressions to DA and DB variable white dwarfs. We find reasonable agreement between theory and observation, although some discrepancies remain unexplained. It is possible to identify the spherical degrees of the pulsation modes using the combination frequencies.  相似文献   

17.
Fadeyev  Yu. A. 《Astronomy Letters》2020,46(8):550-554
Astronomy Letters - On the basis of consistent stellar evolution and nonlinear stellar pulsation calculations, the Cepheid V1033 Cyg is shown to be the post-main sequence star at the first crossing...  相似文献   

18.
The atmospheres and circumstellar envelopes of AGB stars are characterized by complex physical phenomena like shock waves caused by stellar pulsation or formation of molecules and dust which often lead to a heavy mass loss and have a strong influence on IR properties as observed by ISO. To allow a physical interpretation of various observations we have constructed improved dynamical model atmospheres of long-period variables. In this contribution we mainly investigate the dependence of the atmospheric structure and its variability on stellar pulsation, molecular opacities and time-dependent dust formation. IR spectra resulting from our models are discussed in detail by Loidl et al. (1997b) and compared to ISO-SWS spectra obtained by Hron et al. (1997). This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

19.
Techniques for deriving amplitude equations for stellar pulsation are outlined. For the simplest such equations with multiple instabilities, the derivation of a map for the patterns of pulsation phases is described. This map gives the time between two successive maxima of pulsation in terms of the time between the previous pair, under suitable conditions. The phase differences can be regular, chaotic or hyperchaotic.  相似文献   

20.
We use high-precision multiband photometric data of the first-overtone RR Lyrae star U Comae 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, because of the strong dependence of this observable and of the pulsation period on stellar parameters, supplies tight constraints on stellar mass, effective temperature, and distance modulus. Pulsational estimates of these parameters appear in good agreement with empirical ones. Finally, a well-defined bump just before the luminosity maximum gave the unique opportunity to calibrate the turbulent convection model adopted for handling the coupling between pulsation and convection.  相似文献   

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