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1.
Pulsation period changes in Mira type variables are investigated using the stellar evolution and nonlinear stellar pulsation calculations. We considered the evolutionary sequence of stellar models with initial mass \({M_{ZAMS}} = \;3{M_ \odot }\) and population I composition. Pulsations of stars in the early stage of the asymptotic giant branch are shown to be due to instability of the fundamental mode. In the later stage of evolution when the helium shell source becomes thermally unstable the stellar oscillations occur in either the fundamental mode (for the stellar luminosuty \(L < 5.4 \times {10^3}{L_ \odot }\)) or the first overtone (\(L > 7 \times {10^3}{L_ \odot }\)). Excitation of pulsations is due to the κ-mechanism in the hydrogen ionization zone. Stars with intermediate luminosities \(5.4 \times {10^3}{L_ \odot } < L < 7 \times {10^3}{L_ \odot }\) were found to be stable against radial oscillations. The pulsation period was determined as a function of evolutionary time and period change rates \(\dot \Pi \) were evaluated for the first ten helium flashes. The period change rate becomes the largest in absolute value \((\dot \Pi /\Pi \approx - {10^{ - 2}}y{r^{ - 1}})\) between the helium flash and the maximum of the stellar luminosity. Period changes with rate \(\left| {\dot \Pi /\Pi } \right| \geqslant - {10^{ - 3}}y{r^{ - 1}}\) take place during ≈500 yr, that is nearly one hundredth of the interval between helium flashes.  相似文献   

2.
Phenomena of bifurcation in hydrodynamic stellar models of radial pulsation are reviewed. By changing control parameters of models, we can see qualitatively different pulsation behaviors in hydrodynamic models with transitions due to various types of bifurcation.In weakly dissipative models (classical Cepheids), the bifurcation is induced by modal resonances. Two types of the modal resonances found in models are discussed: The higherharmonic resonances of the second overtone mode in the fundamental mode pulsator and of the fourth overtone mode in the first overtone pulsator are relevant to observations. The subharmonic resonance between the fundamental and first overtone modes is confirmed in classical Cepheid models.In strongly dissipative models (less-massive supergiant stars), the bifurcation of nonlinear pulsation is induced by the hydrodynamics of ionization zones as well as modal resonances. The sequence of the bifurcation sometimes leads to chaotic behaviors in nonlinear pulsation. The transition routes from regular to the chaotic pulsations found in models are discussed with respect to the theory of chaos in simple dynamical systems: The cascade of period-doubling bifurcation is confirmed to cause chaotic pulsation in W Virginis models. For models of higher luminosity, the tangent bifurcation is found to lead intermittent chaos.Finally, hydrodynamic models for chaotic pulsation with small amplitudes observed in the post-AGB stars are briefly discussed.  相似文献   

3.
We discuss visual observations spanning nearly 70 years of the nearby semiregular variable R Doradus. Using wavelet analysis, we show that the star switches back and forth between two pulsation modes having periods of 332 d and about 175 d, the latter with much smaller amplitude. Comparison with model calculations suggests that the two modes are the first and third radial overtone, with the physical diameter of the star making fundamental-mode pulsation unlikely. The mode changes occur on a time-scale of about 1000 d, which is too rapid to be related to a change in the overall thermal structure of the star and may instead be related to weak chaos.   The Hipparcos distance to R Dor is 62.4 ± 2.8 pc which, taken with its dominant 332-d period, places it exactly on the period–luminosity (P–L) relation of Miras in the Large Magellanic Cloud. Our results imply first-overtone pulsation for all Miras which fall on the P–L relation. We argue that semiregular variables with long periods may largely be a subset of Miras and should be included in studies of Mira behaviour. The semiregulars may contain the immediate evolutionary Mira progenitors, or stars may alternate between periods of semiregular and Mira behaviour.  相似文献   

4.
Using our non-local time-dependent theory of convection, the linear non-adiabatic oscillations of 10 evolutionary model series with masses of  1–3 M⊙  are calculated. The results show that there is a red giant instability strip in the lower temperature side of the Hertzsprung–Russell diagram which goes along the sequences of the red giant branch and the asymptotic giant branch. For red giants of lower luminosities, pulsation instability is found at high order overtones; the lower order modes from the fundamental to the second overtone are stable. Towards higher luminosity and lower effective temperature, instability moves to lower order modes, and the amplitude growth rate of oscillations also grows. At the high luminosity end of the strip, the fundamental and the first overtone become unstable, while all the modes above the fourth order become stable. The excitation mechanisms have been studied in detail. It is found that turbulent pressure plays a key role for excitation of red variables. The frozen convection approximation is unavailable for the low temperature stars with extended convective envelopes. In any case, this approximation can explain neither the red edge of the Cepheid instability strip, nor the blue edge of the pulsating red giant instability strip. An analytic expression of a pulsation constant as a function of stellar mass, luminosity and effective temperature is presented from this work.  相似文献   

5.
A. N. Cox recently showed that a 20% opacity decrease in the 20,000-30,000 K region as indicated by the new Livermore OPAL opacities reconciles the discrepancy between pulsation and evolution masses of double-mode RR Lyrae variables. Nonlinear hydrodynamic calculations were performed for RR Lyrae models of mass 0.75M , 51L , andZ = 0.0001 (Osterhoff II type) including this opacity decrease. The Stellingwerf periodic relaxation method was used to converge the models to a limit cycle, and the Floquet matrix eigenvalues calculated to search for a tendency of the fundamental mode to grow from the full-amplitude overtone solution, and the overtone mode to grow from the full-amplitude fundamental solution, thereby predicting double-mode behavior. Models ofT eff < 7000 K with the opacity decrease have positive fundamental-mode growth rates in the overtone solution, in contrast to earlier results by Hodson and Cox (1982), and models withT eff > 7000 have positive 1st overtone growth rates in the fundamental-mode solution, but double-mode behavior was not found.  相似文献   

6.
Some theoretical calculations of linear non-adiabatic pulsations of intermediate- and low- luminosity red giants in globular clusters have been carried out using a time-dependent theory of nonlocal stellar convection. As shown by the results, for all models with temperatures higher than 5400 K the modes up to the fourth overtone are pulsationally stable. With the increase of stellar luminosity, the low-order overtones also become pulsationally unstable. For red giants of intermediate and low luminosities, the pulsational stability is exceedingly low and is close to neutral stability. Therefore, they will be either non-variables or short-period variables (P < 2 days) with extremely small amplitudes.  相似文献   

7.
Stellar evolution calculations were carried out from the main sequence to the final stage of the asymptotic giant branch for stars with initial masses 1 M⊙ ≤ MZAMS ≤ 2 M⊙ and metallicity Z = 0.01. Selected models of evolutionary sequences were used as initial conditions for solution of the equations of radiation hydrodynamics and time–dependent convection describing radial stellar pulsations. The study was aimed to construct the hydrodynamic models of Mira–type stars that show the secular decrease in the pulsation period Π commenced in 1970th at Π = 315 day. We show that such a condition for the period change is satisfied with evolutionary sequences 1 M⊙ ≤ MZAMS ≤ 1.2 M⊙ and the best agreement with observations is obtained for MZAMS = 1.2 M⊙. The pulsation period reduction is due to both the stellar radius decrease during the thermal pulse of the helium burning shell and mode switch from the fundamental mode to the first overtone. Theoretical estimates of the fundament parameters of the star at the onset of pulsation period reduction are as follows: the mass is M = 0.93 M⊙, the luminosity is L = 4080 L⊙, and the radius is R = 220 R⊙. The mode switch occurs 35 years after the onset of period reduction.  相似文献   

8.
We analyse the periods of theoretical radial pulsators, covering the range of total masses, luminosities, effective temperatures and chemical compositions expected for RR Lyrae variables in both galactic fields and globular clusters.
We show that for fixed values of the structural parameters (mass, luminosity and effective temperature), the period of fundamental and first-overtone pulsators is independent of the helium content ( Y ), whereas it slightly increases as the amount of metals ( Z ) increases. Furthermore, we find that the period along the blue edge for first-overtone pulsation is a function of mass, luminosity and helium content, with a marginal dependence on Z .
On these grounds, new linear relations connecting the periods to stellar parameters are derived. Such new relations should allow a more accurate interpretation of the RR Lyrae observed periods and, in particular, they should help in ascertaining the calibration of the mean absolute magnitude of RR Lyrae stars in terms of metal content.  相似文献   

9.
Employing recent TP-AGB synthesis, we have carried out a detailed study on pulsation mode and period-luminosity relation of Mira variables by means of a population synthesis code. The theoretical criterion for selecting Mira variables has a great effect on the periods distribution. Compared with the observations, the distributions of the periods and the period-luminosity relations support that Mira variables are the fundamental mode pulsators.  相似文献   

10.
Six ways for obtaining approximate period-luminosity (P-L) relations for classical cepheids and Delta Scuti variables are presented. Three out of these ways were earlier schematically considered by J.P. Cox (1980, 1985). It was proceeded from certain results derived from the study of stellar pulsation and evolution, by using some simple considerations and simplifying assumptions. The expressions obtained for the coefficients of these approximate P-L relations, were used to estimate the slopes and the zero-points. In addition, it was evaluated the influence of both different modes of radial pulsations and variations of Population I chemical composition on the zero-points. The results satisfactorily agree with those derived from observations or accurate theoretical calculations.  相似文献   

11.
The short-period limiting pulsation found by Fadeyev and Fokin (1985) in a short-period, Population II Cepheid model is examined by means of the Baker-von Sengbush-Stellingwerf (BSS) algorithm of limit cycles.It is shown that the model has a stable limit cycle of the fundamental mode and an unstable limit cycle of the first overtone mode. When the method is applied for pulsations spanning the time interval of twice the period of the fundamental mode, we find only the fundamental cycle repeated doubly or the first overtone limit cycle repeated three times, depending on initial conditions of the integration.We thus conclude that the period-doubling limiting pulsation found by Fadeyev and Fokin (1985) is a transient feature of the model.  相似文献   

12.
Some results of linear adiabatic and nonlinear pulsation models of first overtone mode Cepheids are discussed. New and augmented opacities and a nonstandard mass-luminosity relation have been taken into account. The models indicate the possible importance of the resonanceP1/P4 = 2 nearP1 = 3 days. The resonance could explain the observed characteristics of the light curve shape of first overtone mode Cepheids.  相似文献   

13.
We study the possibility of the excitation of non-radial oscillations in classical pulsating stars. The stability of an RR Lyrae model is examined through non-adiabatic non-radial calculations. We also explore stability in the presence of non-linear coupling between radial and non-radial modes of nearly identical frequency.   In our model, a large number of unstable low-degree (ℓ = 1,2) modes have frequencies in the vicinity of unstable radial mode frequencies. The growth rates of such modes, however, are considerably smaller than those of the radial modes. We also recover an earlier result that at higher degrees (ℓ = 6–12) there are modes trapped in the envelope with growth rates similar to those of radial modes.   Subsequently, monomode radial pulsation of this model is considered. The destabilizing effect of the 1:1 resonance between the radial mode and nearby non-radial modes of low degrees is studied, with the assumption that the excited radial mode saturates the linear instability of all other modes. The instability depends on the radial mode amplitude, the frequency difference, the damping rate of the non-radial mode, and the strength of the non-linear coupling between the modes considered. At the pulsation amplitudes typical for RR Lyrae stars, the instability of the monomode radial pulsation and the concomitant resonant excitation of some non-radial oscillation modes is found to be very likely.  相似文献   

14.
We have performed a detailed systematic search for multiperiodicity in the Population I Cepheids of the Large Magellanic Cloud. In this process, we have identified for the first time several new types of Cepheid pulsational behaviour. We have found two triple-mode Cepheids pulsating simultaneously in the first three radial overtones. In 9 per cent of the first overtone (FO) Cepheids, we have detected weak but well-resolved secondary periodicities. They appear either very close to the primary pulsation frequency or at a much higher frequency with a characteristic period ratio of 0.60–0.64. In either case, the secondary periodicities must correspond to non-radial modes of oscillation. This result presents a major challenge to the theory of stellar pulsations, which predicts that such modes should not be excited in Cepheid variables. Non-radial modes have also been found in three of the fundamental first overtone (FU/FO) double-mode Cepheids, but no such oscillations have been detected in single-mode Cepheids pulsating in the FU mode.
In 19 per cent of double-mode Cepheids pulsating in the first two radial overtones (FO/SO type), we have detected a Blazhko-type periodic modulation of amplitudes and phases. Both modes are modulated with a common period, which is always longer than 700 d. Variations of the two amplitudes are anticorrelated, and maximum of one amplitude always coincides with minimum of the other. We have compared observations of modulated FO/SO Cepheids with predictions of theoretical models of the Blazhko effect, showing that the currently most popular models cannot account for properties of these stars. We propose that the Blazhko effect in FO/SO Cepheids can be explained by a non-stationary resonant interaction of one of the radial modes with another, perhaps non-radial, mode of oscillations.  相似文献   

15.
We present new multicolour photometry and simultaneous high-dispersion spectroscopy for the δ Scuti star 1 Mon. The two main periodicities in the star are still present, but the third known period is not directly detected in the new radial velocities or light variations. However, it is detected in the periodogram of the second moment of the line profile variations. We use the cross-correlation function as an approximation for the line profile variations. By computing theoretical profiles for a given mode and comparing them with phased cross-correlation profiles, we are able to determine a goodness-of-fit criterion and estimate the most probable spherical harmonic degree,     the azimuthal order, m , of the pulsation and also the angle of inclination. We then compare the relative amplitudes and phases of the photometric variations in five wavebands and obtain the best estimates of     for the two visible periodicities. We confirm the earlier determinations that the main periodicity is a radial mode and that the other periodicity is probably         We show that the line profile variations and light variations give consistent results. We point out the importance of a long wavelength range when using the photometric mode identification technique. Finally, we attempt to match the two periods with unstable modes from linear, non-adiabatic calculations. We are able to show that the principal period is well matched by either the fundamental or first overtone radial mode, but could not find a satisfactory fit to the     mode. We discuss implications for mode identification of δ Scuti stars based on what we have learned from this star.  相似文献   

16.
本文采用恒星演化计算与恒星振动计算相结合的方法，对中等质量富金属恒星演化到渐近巨星分支时的振动性质进行了分析研究，从理论上得出这类恒星的振动方式是处于一阶谐频振动，而振动的激发则是在氢电离区和氦的二次电离区由多种机制共同作用造成的，同时提出很长周期的ＡＧＢ长周期变星只能是由中等质量恒星演化到ＡＧＢ阶段形成的。我们的理论计算结果还比较支持在ＡＧＢ顶端存在巨大星风物质损失的观点，且这种星风物质损失很可能与恒星振动有关。  相似文献   

17.
Linear and nonlinear pulsation computations for the modelsM=0.8M ⊙,L=10000 and 20000L ⊙ were carried out in order to understand FG Sge's pulsation. The results may be summarized as follows:
  1. In the modelsL=10000L ⊙, the fundamental blue edge is nearT e =5700 K. The models show that instability of the third overtone extends to 7400 K and still has large positive growth rates. A nonlinear model of 7000 K shows a small amplitude ΔV=10 km s?1, ΔM bol=0.03 with a period of around 18 days, nearly equal to that of the third overtone.
  2. In the linear models ofL=20000L ⊙, the fundamental blue edge is shifted to 7000 K but the damping of this mode is so small that it is marginally stable to 7700 K. The third overtone has large positive growth rates of this region. The nonlinear model at 7700 K, however, shows no indication of third overtone pulsation.
We also examine the possibility, suggested by Whitney (1978), that the mass of FG Sge is 0.4M ⊙.  相似文献   

18.
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   

19.
If one is only interested in the behaviour of a few longlived modes, the simplest model for the evolution to steady nonlinear stellar pulsation is nonresonant interaction. As the coupled-mode equations are generically not dependent upon a particular stellar model, qualitative ideas about the eventual evolution of mode energies give scenarios that depend mainly upon nonlinear coupling constants and linear growth rates. Two linearly unstable modes are considered in the presence of a representative stable or slave mode. One scenario models a double-mode pulsator, without it being necessary that all coupling constants be negative, if only the model is well behaved enough in excluding unbounded solutions and in avoiding finite amplitudes for the slave modes. The influence of driving on slave modes is then such that all slave modes ultimately decay away. Other scenarios show evolution to classic pulsators. A discussion is given of the modelling of a classic Cepheid in a mode which is not the linearly most unstable one. Findings of the present paper show the need for additional theoretical and numerical modelling and a cautious discussion thereof.  相似文献   

20.
This paper presents observations of SiO maser emission from 161 Mira variables distributed over a wide range of intrinsic parameters like spectral type, bolometric magnitude and amplitude of pulsation. The observations were made at 86.243 GHz, using the 10-4 m millimeter-wave telescope of the Raman Research Institute at Bangalore, India. These are the first observations made using this telescope. From these observations, we have established that the maser emission is restricted to Miras having mean spectral types between M6 and M10. The infrared period-luminosity relation for Mira variables is used to calculate their distances and hence estimate their maser luminosities from the observed fluxes. The maser luminosity is found to be correlated with the bolometric magnitude of the Mira variable. On an H-R diagram, the masing Mira variables are shown to lie in a region distinct from that for the non-masing ones.  相似文献   

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