scholarly journals Some Insights into Stellar Structure from Nonlinear Pulsations

1993 ◽  
Vol 134 ◽  
pp. 231-233
Author(s):  
M. J. Goupil
Keyword(s):  
Amplitude Equation ◽  
Second Order ◽  
Stellar Structure ◽  
Static Structure ◽  
Stellar Radius ◽  
Stellar Pulsation ◽  
Oscillation Frequencies ◽  
Mass Level ◽  
Marginal Mode ◽  
Second Order Of Approximation

Efficient tools of investigation of stellar pulsation are the integral relations which link oscillation frequencies to the static structure of stellar models, as provided by the linear theory of pulsation (for a review, see Saio, this conference).Similarly, oscillation amplitudes and phases, which arise from nonlinear processes, can be related to the stellar structure by means of amplitude equation formalisms (for a review, see Buchler, this conference).For the simple case of a monoperiodic oscillation, involving only one unstable marginal mode, such a formalism shows that the (limit cycle) radius variations, at time t and mass level m, can be approximated, up to second order of approximation, (Buchler and Goupil, 1984; Buchler and Kovàca, 1986) by:where A, R, Ω, ĸ, £r(m) respectively are the amplitude, stellar radius, linear nonadiabatic frequency, growth rate, radius eigenfunction. Second order nonlinearities generated first harmonic oscillations and change in equilibrium radius about which the star oscillates, as represented by the last two terms in (la) respectively. Analogous expressions are obtained for velocity and light variations, that can be compared with observations.

scholarly journals Pulsation and Evolution. An observer’s viewpoint

1995 ◽  
Vol 155 ◽  
pp. 23-30
Author(s):  
C. Waelkens
Keyword(s):  
Mass Loss ◽  
Observational Evidence ◽  
Stellar Structure ◽  
Forced Oscillations ◽  
Agb Stars ◽  
Pulsating Stars ◽  
Stellar Pulsation

AbstractWe review observational evidence on the interaction between stellar pulsation and evolution. We discuss to what extent observations of pulsating stars with variable amplitudes and pulsation periods have implications on our understanding of stellar structure and evolution. The probable link between mass loss and pulsation in AGB stars and in hot luminous stars appears to be the strongest way in which pulsations affect evolution. We point out the possibility that forced oscillations in the components of binaries may have important consequences on evolution, that could offer an explanation for some classes of peculiar evolved objects.

scholarly journals On The Seismic Signature of the HeII Ionization Zone in Stellar Envelopes

1998 ◽  
Vol 185 ◽  
pp. 317-318
Author(s):  
Mário J.P.F.G. Monteiro ◽  
Michael J. Thompson
Keyword(s):  
Equation Of State ◽  
Stellar Structure ◽  
Ionization Zone ◽  
Characteristic Signal ◽  
Oscillation Frequencies ◽  
Stellar Envelopes ◽  
Seismic Signature ◽  
Better Than

Sharp variations of the structure of the star create a characteristic signal in its frequencies of oscillation (e.g. [3]). The zone of the second ionization of helium is such a localized feature of the structure whose properties depend mainly on the abundance of helium and the equation of state. Considering that such a signal should easily be detectable provided the frequencies are measured to rather better than 1μHz accuracy (the COROT project should measure oscillation frequencies with an accuracy of 0.1μHz), we present here a tool to study this aspect of stellar structure.

scholarly journals Modeling the global oscillations of Epsilon Eridani

1988 ◽  
Vol 123 ◽  
pp. 281-284
Author(s):  
David R. Soderblom ◽  
Werner Däppen
Keyword(s):  
Observational Data ◽  
Stellar Structure ◽  
Global Oscillation ◽  
Oscillation Frequencies ◽  
Best Estimates

We have reviewed the observational data for ∊ Eri to derive our best estimates of luminosity, radius, temperature, composition, and age, as well as the uncertainties associated with each of these. These quantities are then used in stellar structure models to try to reproduce the global oscillation frequencies observed by Noyes et al. We find that we can reproduce the observed frequencies and splittings at least as well as the computations of Guenther and Demarque, yet for significantly different stellar parameters, most notably the age.

scholarly journals Coupled-Oscillators

1993 ◽  
Vol 134 ◽  
pp. 333-341
Author(s):  
Y. Tanaka
Keyword(s):  
Coupled Oscillators ◽  
Phase Locking ◽  
Period Doubling ◽  
Second Order ◽  
Coupling Constants ◽  
Stellar Structure ◽  
Radial Pulsation ◽  
Third Order ◽  
Period Ratio ◽  
Dissipation Term

AbstractModal 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 with n = 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.

Second order rotational effect on the oscillation frequencies of V1162 Ori

2007 ◽  
Vol 310 (3-4) ◽  
pp. 189-193
Author(s):  
Ziyad Matalgah ◽  
H. Kırbıyık ◽  
R. Civelek ◽  
N. Kızıloğlu
Keyword(s):  
Second Order ◽  
Rotational Effect ◽  
Oscillation Frequencies

scholarly journals Continuum-driven versus line-driven mass loss and the Eddington limit

2006 ◽  
Vol 2 (14) ◽  
pp. 202-203
Author(s):  
Stanley P. Owocki
Keyword(s):  
Mass Loss ◽  
Radiation Pressure ◽  
Stellar Structure ◽  
High Mass ◽  
Mass Limit ◽  
Static Structure ◽  
Eta Carinae ◽  
The Masses ◽  
Eddington Limit ◽  
Sharp Cutoff

AbstractBasic stellar structure dictates that stars of ∼ 100 M⊙ or more will be close to the Eddington limit, with luminosities in excess of 106 L⊙, and radiation pressure contributing prominently to the support against gravity. Although it is formally possible to generate static structure models of even more massive stars, recent studies of dense clusters show there is a sharp cutoff at masses above ∼ 150 M⊙. This talk examines the role of extreme mass loss is limiting the masses of stars, emphasizing in particular that continuum driving, possibly associated with structural instabilities of radiation dominated envelope, can lead to much stronger mass loss than is possible by the usual line-scattering mechanism of steady stellar winds.However, population studies of very young, dense stellar clusters now suggest quite strongly that there is a sharp cutoff at masses above ca. 150 M⊙ (see, e.g., the talk by Sally Oey, in this JD 05, p. 206). This is sometimes attributed to a mass limit on star formation by accretion processes, though there are competing formation scenarios by binary or cluster merging that would seem likely to lead to formation of even higher mass stars (see talks in JD14 and S237).So given the above rough coincidence of the observational upper mass limit with the Eddington-limit domain of radiation-pressure dominance, it seems associated instabilities in stellar structure might actually be a more important factor in this upper mass limit, leading to extreme mass loss in LBV and/or giant eruption events, much as inferred from circumstellar nebulae observed around high mass stars like eta Carinae and the Pistol star.

MONOTONE AND CONSERVATIVE DIFFERENCE SCHEMES FOR ELLIPTIC EQUATIONS WITH MIXED DERIVATIVES

2005 ◽  
Vol 9 (2) ◽  
pp. 169-178 ◽  
Author(s):  
I.V. Rybak
Keyword(s):  
Maximum Principle ◽  
Elliptic Equations ◽  
Second Order ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Order Of Approximation ◽  
Conservative Difference Schemes ◽  
Mixed Derivatives ◽  
Conservative Difference ◽  
Second Order Of Approximation

In the paper elliptic equations with alternating‐sign coefficients at mixed derivatives are considered. For such equations new difference schemes of the second order of approximation are developed. The proposed schemes are conservative and monotone. The constructed algorithms satisfy the grid maximum principle not only for coefficients of constant signs but also for alternating‐sign coefficients at mixed derivatives. The a prioriestimates of stability and convergence in the grid norm C are obtained.

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