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1.
The effect of slow uniform rotation on the radial and nonradial modes of partially degenerate standard models has been investigated. For the case of the radial mode, it is shown that the destabilizing effect of slow uniform rotation reduces with increased central condensation of the model. However, it is found that the models with a strongly degenerate interior, become more unstable dynamically as a result of slow uniform rotation. Further, it is noted that the frequency of the nonradial modes of oscillation (Kelvin mode) increases due to the presence of rotation. Thus the period of radial modes of oscillation of a slowly uniformly rotating partially degenerate standard model are much larger than the corresponding periods of nonradial (Kelvin) modes.  相似文献   

2.
Carl A. Rouse 《Solar physics》1986,106(2):205-216
The high-Z core (HZC) model of the Sun, supported in Rouse (1985) by superior agreements of nonradial g-mode periods of oscillation with long period observations, is used to calculate frequencies of oscillation in the five-minute band (5MB). Allowing for the fact that the present HZC model profile does not include an upper photosphere and self-consistent chromosphere, the HZC model of the Sun is also supported by the very good agreements of the 5MB nonradial frequencies of oscillation with observations for HZC l degrees 0 to 19 and orders n 20, and the good agreement of the HZC purely radial frequencies of oscillation with about the same n-orders with observations previously identified as l = 0 oscillations. Two important aspects of these agreements are (1) the nonradial frequencies were calculated with the equations that neglect the gravitational perturbation (the Cowling approximation), and (2) the radial frequencies were calculated with the equation that includes the gravitational perturbation. The present agreements suggest that for solar-type stars, the gravitational perturbation may not affect the nonradial p-modes of oscillation as much as it affects the radial modes and the nonradial g-modes. More research will be performed.  相似文献   

3.
Linearized nonradial expressions for light, colour and radial velocity changes are employed to examine the Baade-Wesselink method as applied to the problem of nonradial mode identification in variable stars. It is demonstrated that the usual assumption of a single-valued relation between surface brightness changes and colour variations fails for spherical harmonics withl>1. A Baade-Wesselink expression taking this into account is then given. Using test models for different variable star regimes it is shown that discrimination betweenl=0, 1, and 2 is currently feasible provided adequate attention is paid to pressure effects and to the procedure used to obtain radial velocity data. For higherl, mode discrimination, while possible in principle, is constrained by the stringent requirements on radial velocity measurements and by cases of confusion with lowerl. A review of related but less observationally demanding possible mode discriminators is given. This demonstrates that techniques based on amplitude and phase information in light and colour data may provide reliable discrimination betweenl=0, 1, and 2 when pressure effects are allowed for. For these techniques discrimination of higherl is limited by inadequate model atmosphere limbdarkening information and by confusion with lowerl.  相似文献   

4.
In this study V2109 Cyg (a pulsating δ Scuti star) has been modelled. In treating the oscillation equations perturbation in gravitational potential energy has been taken into account. Both radial and nonradial oscillations are treated with adiabatic approximation. The so called radial fundamental frequency (5.3745 c/d) and the nonradial frequency (5.8332 c/d) were obtained within a satisfactory precision. It was found that the Cowling approximation introduced more error as one went from low overtones to high overtones in radial oscillations. A similar trend was observed in nonradial case with low values of l. By keeping the effective temperatures almost the same as with V2109 Cyg two more models with different masses have also been calculated to see the effect of inclusion of perturbation in gravitational potential energy on oscillation frequencies in different masses. Conclusion arrived is that one must be careful to employ the Cowling approximation especially for high nonradial oscillation frequencies. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

5.
On short time-scales of under a year, the vast majority of Scuti stars studied in detail show completely regular multiperiodic pulsation. Nonradial pulsation is characterized by the excitation of a large number of modes with small amplitudes. Reports of short-term irregularity or nonperiodicity in the literature need to be examined carefully, since insufficient observational data can lead to an incorrect impression of irregularity. Some interesting cases of reported irregularities are examined.A few Scuti stars, such as 21 Mon, have shown stable variations with sudden mode switching to a new frequency spectrum. This situation might be an indication of deterministic chaos. However, the observational evidence for mode switching is still weak.One the other hand, the case for the existence of long-term amplitude and period changes is becoming quite convincing. Recently found examples of nonradial pulsators with long-term changes are 4 CVn, 44 Tau, Peg and HD 2724. (We note that other Scuti pulsators such as X Cae and 2 Tau, have shown no evidence for amplitude variations over the years.) Neither the amplitude nor the period changes are periodic, although irregular cycles with time scales between a few and twenty years can be seen. While the amplitude changes can be very large, the period changes are quite small. This property is common in nonlinear systems which lead to chaotic behavior. There exists observational evidence for relatively sudden period jumps changing the period by about 10–5 and/or slow period changes near dP/dt 10–9. These period changes are an order of magnitude larger than those expected from stellar evolution.The nonperiodic long-term changes are interpreted in terms of resonances between different nonradial modes. It is shown that a large number of the nonradial acoustic modes can be in resonance with other modes once the mode interaction terms, different radial orders and rotationalm-mode splitting are considered. These resonances are illustrated numerically by the use of pulsation model. Observational evidence is presented that these interaction modes exist in the low-frequency domain.  相似文献   

6.
The averaging technique of Kippenhahn and Thomas (1970) has been used in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials to determine the effects of rotation and tidal distortions on the periods of small adiabatic radial and nonradial modes of oscillations of polytropic models of the stars.  相似文献   

7.
A number of white dwarf models have been calculated which correspond to various radial and nonradial modes of vibration with eigenfrequencies in agreement with the observed pulsation frequencies of the X-ray sources Hercules X-1 and Centaurus X-3. Most of the white dwarf models have hot interiors, but for calculational purposes these were simplified so that the bulk of the interior was isothermal, and the surface layers were designed to produce an energy generation rate of 1037 erg s?1 and to transport this energy continuously to the surface by radiative transfer. Cold white dwarfs have a fairly large spread of masses corresponding to the different overtone modes with the given eigenfrequencies, but in the hot models this spread of masses is greatly reduced, for both radial and nonradial modes. It is concluded that if the pulsating X-ray sources are hot white dwarfs, the mass of Cen X-3 probably lies in the range 0.7–1.2M ⊙, and the mass of Her X-1 probably lies in the range 1.1–1.25M ⊙ (in accord with observation).  相似文献   

8.
In the present paper we have studied the eigenfrequencies of small adiabatic barotropic pseudo-radial and nonradial modes of oscillations of the white dwarf models of rotating stars in binary systems. In this work the methodology of Mohan and Saxena (in Astrophys. Space Sci. 113:155, 1985) has been used that utilizes the averaging technique of Kippenhahn and Thomas (in Proc. IAU Colloq., vol. 4, p. 20, 1970) and certain results on Roche equipotential as that given by Kopal (in Advances in Astronomy and Astrophysics, Academic Press, 1972). The objective of this study is to investigate the effects of rotation and/or tidal distortion on the periods of oscillations of rotationally and/or tidally distorted white dwarf models of stars assuming it to be the primary component of the binary system and rotating uniformly. The results of present study show that the eigenfrequencies (both radial and nonradial modes) of the rotationally distorted and rotationally and tidally distorted white dwarf model of stars in binary systems tend to decrease under the influence of rotational distortions and rotational and tidal distortions, respectively. However, results are contrary for tidally distorted white dwarf model of stars.  相似文献   

9.
We show that in evolved stars, even at relatively low surfaceamplitudes, nonradial modes become strongly nonlinear in thehydrogen shell source, where the Brunt-Väisälä frequency hasits absolute maximum. The measure of nonlinearity is the productof horizontal displacement times the radial wavenumber, . It becomes large already in evolved -Scuti stars.This nonlinearity presents a major problem for interpretations ofamplitude modulation in RR Lyrae stars in terms of nonradial modeexcitation.  相似文献   

10.
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   

11.
The existence proof of continuous spectra of eigenvaluess developed in the framework of the function space ofq-regularizations (Perdang, 1976) is extended in this paper by relaxing the severe restrictions previously imposed o the mathematical structure of the stellar stability equations. It is stressed that these local modes depend on the variable system in terms of which the linearized stellar structure equations are set up. We therefore search for a systematic procedure to select the most satisfactory system to analyze Local Stability. Our procedure is illustrated in great detail in the case of nonradial adiabatic stability. Moreover when applied to nonadiabatic perturbations it reveals the existence of two new types of local instability which seem to prevail in the majority of stars in a thermonuclear burning phase: (a) a nonrdial local secular instability; (b) a radial local nuclear instability. Numerical test calculations exhibit that the latter helps us to understand certain evolutionary features of stars, in particular it provides an interpretation of Hayashiet al.'s (1962) rule.  相似文献   

12.
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   

13.
熊大闰  邓李才 《天文学报》2011,52(2):115-125
根据非局部和非定常恒星对流理论,计算了质量3～30 M_⊙恒星演化模型低球谐阶(l=1～4)p4～g39非径向模的线性非绝热脉动,研究了对流对非径向脉动的影响.结果表明,对流对恒星非径向脉动稳定性有不可忽略的影响.然而假若不关注单个恒星和单个振动模的细节,从总体上粗略地看,理论的脉动不稳定区的大致位置和范围并未受到对流的明显影响.  相似文献   

14.
The traditional linearized stellar-structure equations, which provide information on the global stability of a stellar equilibrium state, are shown to engender a class of continuous modes, if the eigenfunctions are sought in a generalized function space. To endow the intuitive concept of Local Stellar Statility with a precise mathematical meaning, we endeavour to link this notion to the family of continuous spectra. We indicate a simple numerical method to compute the eigenfunctions associated with these modes, and we illustrate our approach by briefly analysing the continuous spectra connected with the radial and nonradial dynamical stability problem.  相似文献   

15.
Mohan and Saxena's approach of using the averaging technique of Kippenhahn and Thomas in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials has been used to compute the effects of rotation and tidal distortions on the periods of small adiabatic radial and nonradial modes of oscillations of a series of composite models of stars. In these stars the density decreases slowly in the core from the centre to the interface and then falls of rapidly in the envelope from the interface to the outer surface.  相似文献   

16.
The linearized analytic representation of observed flux changes due to nonradial pulsations is examined under conditions applicable to a variety of pulsating star types. Histograms are presented as a function ofl, documenting the relative importance of local temperature, geometry, pressure, and limb-darkening variations, which are all contributing factors to the predicted flux changes. The most favourable situation for light and colour data to assist in mode discrimination for lowl requires, amongst other things, that the geometry-related factor be significant. This is noted to occur only if theQ value of the pulsation is not grossly different from theQ value of a radial fundamental pulsation. Published light and colour data for Cephei, 53 Persei, Scuti, rapidly oscillating Ap, Cepheid, and ZZ Ceti variables are compared with model predictions on an amplitude ratio versus phase difference plane . With the notable exception of the rapidly oscillating Ap stars, these comparisons suggest consistency of the nonradial flux change model with other known constraints on the different variable star groups.  相似文献   

17.
An attempt has been made towards explaining the observed frequencies in 63 Her. The evolution of rotating stars of 1.96, 1.98, 2.00, 2.05 and 2.10 M⊙ have been studied up to a point where stellar parameters match the observed luminosity and effective temperature of 63 Her. Radial and nonradial adiabatic oscillation frequencies were obtained in low harmonic degrees ( l = 0,1,2,3 ). One radial and three nonradial frequency values that match with the observed values were found for the model of mass 2.00 M⊙.  相似文献   

18.
Nonradial oscillations of a partially degenerate standard model, approximating a class of low-mass stars, have been studied in the presence of a weak poloidal magnetic field. The magnetic field in the interior of the configuration is taken to be continuous across the equilibrium surface and is matched with an external dipole field. Using a variational formulation, corrections to the oscillation frequencies of the Kelvin mode have been found for different values of the central degeneracy. It has been noted that the effect of the magnetic field is to increase the frequency of nonradial (l=2) mode of pulsation.  相似文献   

19.
Walraven, Walraven and Balona recently discovered several new periodicities in addition to the well-known fundamental and first overtone periods of the high-amplitude Scuti star AI Velorum. Linear nonadiabatic pulsation calculations were performed for an AI Velorum model of mass 1.96M , 24.05L , andT eff 7566 K for the radial and low-degree nonradial modes to help verify the tentative identifications made by Walraven, et al. Comparison of the calculated periods with the observations suggests some alternatives to the identifications proposed by Walraven, et al.  相似文献   

20.
介绍了恒星非径向脉动的一般特性和可观测特征．着重评述早型恒星非径向脉动研究的最新进展以及非径向脉动模式证认的各种方法．  相似文献   

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