An analysis of the linear, adiabatic oscillations of a star in terms of potential fields

Aizenman, M. L.; Smeyers, Paul

doi:10.1007/bf00643044

Cited by 151 publications

(179 citation statements)

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“…From Eq. (21), and approximating the specific heat of ions in the Debye regime by C ion V ∼ 3.2π 4 (T c /θ D ) 3 ℜ/A, to a first approximation we obtain: Table 1 Onset of Debye cooling. …”

Section: Coulomb Interactions and Debye Coolingmentioning

confidence: 99%

“…In addition, the mass and chemical composition of the core and outer layers -which, as we saw, have a marked influence on the white dwarf evolution -are specified by the evolutionary history of the progenitor star. Thus, an accurate treatment of white dwarf evolution requires the use of complete stellar evolutionary codes to calculate the evolutionary history of the progenitor 4 He, 12 C, and 16 O distribution within a typical DA white dwarf in terms of the outer mass fraction…”

Section: Detailed Models Of White Dwarf Evolutionmentioning

confidence: 99%

“…21 that when T eff < 176 600 K, the low-order periods (Π k ∼ < 200 s) exhibit a behavior reminiscent of the well-known "avoided crossing". When a pair of modes experiences avoided crossing, the modes exchange their intrinsic properties (Aizenman et al 1977). These are modes with a mixed character, that is, modes that behave as g-modes in certain zones of the star and as p-modes in other regions.…”

Section: The Rate Of Period Changes: Clues To the Core Chemical Compomentioning

confidence: 99%

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Evolutionary and pulsational properties of white dwarf stars

Althaus

Córsico

Isern

et al. 2010

Astron Astrophys Rev

380

372

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White dwarf stars are the final evolutionary stage of the vast majority of stars, including our Sun. Since the coolest white dwarfs are very old objects, the present population of white dwarfs contains a wealth of information on the evolution of stars from birth to death, and on the star formation rate throughout the history of our Galaxy. Thus, the study of white dwarfs has potential applications to different fields of astrophysics. In particular, white dwarfs can be used as independent reliable cosmic clocks, and can also provide valuable information about the fundamental parameters of a wide variety of stellar populations, like our Galaxy and open and globular clusters. In addition, the high densities and temperatures characterizing white dwarfs allow to use these stars as cosmic laboratories for studying physical processes under extreme conditions that cannot be achieved in terrestrial laboratories. Last but not least, since many white dwarf stars undergo pulsational instabilities, the study of their properties constitutes a powerful tool for applications beyond stellar astrophysics. In particular, white dwarfs can be used to constrain fundamental properties of elementary particles such as axions and neutrinos, and to study problems related to the variation of fundamental constants.These potential applications of white dwarfs have led to a renewed interest in the calculation of very detailed evolutionary and pulsational models for these stars. In this work, we review the essentials of the physics of white dwarf stars. We enumerate the reasons that make these stars excellent chronometers and we describe why white dwarfs provide tools for a wide variety of applications. Special emphasis is placed on the physical processes that lead to the formation of white dwarfs as well as on the different energy sources and processes responsible for chemical abundance changes that occur along their evolution. Moreover, in the course of their lives, white dwarfs cross different pulsational instability strips. The existence of these instability strips provides astronomers with an unique opportunity to peer into their internal structure that would otherwise remain hidden from observers. We will show that this allows to measure with unprecedented precision the stellar masses and to infer their envelope thicknesses, to probe the core chemical stratification, and to detect rotation rates and magnetic fields. Consequently, in this work, we also review the pulsational properties of white dwarfs and the most recent applications of white dwarf asteroseismology.

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Section: Coulomb Interactions and Debye Coolingmentioning

confidence: 99%

Section: Detailed Models Of White Dwarf Evolutionmentioning

confidence: 99%

Section: The Rate Of Period Changes: Clues To the Core Chemical Compomentioning

confidence: 99%

See 1 more Smart Citation

Evolutionary and pulsational properties of white dwarf stars

Althaus

Córsico

Isern

et al. 2010

Astron Astrophys Rev

380

372

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“…In particular questions connected with the unfolding of multiple eigenvalues receive an elegant solution in this context (Arnold, 1976 ;Poston and Stewart, 1978). The recently stressed phenomenon of "avoided crossing" of g-modes (Aizenman et al, 1977 ;Christensen-Dalsgaard, 1979) emerges from CT as a mere effect of the structural instability of the crossing : What requires an explanation is not the avoided crossing but the possible occurrence of actual crossings ! The latter always stem from a special invariance group ("symmetry") of the underlying stellar model, as flows directly from an application of the von Neumann-Wigner (1929) perturbation scheme.…”

Section: (+) Chercheur Qualifie Du Fnrsmentioning

confidence: 99%

Dynamic Catastrophes in Stars

Perdang¹

1980

Highlights astron.

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(+) Chercheur Qualifie du FNRSThe invariance of the equations of linear stability of a physical system under a change of sign of the dependent variables implies that we cannot foresee, once an instability is detected, in which direction the system will evolve. In the context of radial dynamical stability this means that the linear analysis does not allow us to discriminate between a subsequent contraction or expansion. To fix up the arrow of the evolution beyond the onset of the instability, a nonlinear analysis is required.Recently mathematicians have developed a broad framework currently known as "catastrophe theory" (CT) which can be typified as a systematically precise equivalent to the analysis of a singular point of a vector field. Therefore we are entitled to expect that CT offers an ideal context for a nonlinear description of stellar stability. To take full advantage of CT however, we have to meet two conditions for our system : (a) it is a "gradient system", i.e. stable equilibrium states correspond to the minima of a potential ; (b) the total number of "effective" dependent variables ("behaviour variables" in Zeeman's 1977 terminology) must not exceed 2. At first sight these requirements seem so stringent that one might rightly wonder whether Nature has any such systems in store. To our surprise the problem of radial dynamical stability can actually be reformulated to obey both requirements. Under conservation of entropy the equilibrium states of a star satisfy a minimum energy theorem. The total energy which plays the part of the potential of CT (condition a) is given in standard notations by(V is here the specific volume, X stands for the composition profiles and r is the derivative of the radial position with respect to mass). The explicit form of V in terms of r and r flows from the conservation of mass. Any distribution r(m) that renders the functional E{r} minimum specifies a dynamically stable equilibrium state. Since r(m) stands in fact for an infinity of behaviour variables, namely the radial location at any mass point m, one has to devise a method to drastically reduce this number of variables to << 2 in order to -conform to condition (b). 501

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“…An outstanding importance of this fiducial model, whose extended discussion can be found in Refs. [2][3][4][5][6][7], is that it sets the standard for analytic study of non-radial pulsations of the main-sequence stars and serves as an example, according to Chandrasekhar 3 , of "at least one problem for which analytic solution can be found" and which illustrates "the type of difficulties one must confront in the other problem", because "in most instances, the problems become of such complexity and involve so many parameters that elementary methods of solution seem impracticable". It is this model from which the very notion of fundamental vibrational mode has come into the theory of stellar pulsations ?…”

Section: Introductionmentioning

confidence: 99%

Self-Gravitating Astrophysical Mass With Singular Central Density Vibrating in Fundamental Mode

Баструков

Chang

et al. 2009

Mod. Phys. Lett. A

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The fluid-dynamical model of a self-gravitating mass of viscous liquid with singular density at the center vibrating in fundamental mode is considered in juxtaposition with that for Kelvin fundamental mode in a homogeneous heavy mass of incompressible inviscid liquid. Particular attention is given to the difference between spectral formulae for the frequency and lifetime of f -mode in the singular and homogeneous models. The newly obtained results are discussed in the context of theoretical asteroseismology of pre-white dwarf stage of red giants and stellar cocoons -spherical gas-dust clouds with dense star-forming core at the center.

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An analysis of the linear, adiabatic oscillations of a star in terms of potential fields

Cited by 151 publications

References 7 publications

Evolutionary and pulsational properties of white dwarf stars

Evolutionary and pulsational properties of white dwarf stars

Dynamic Catastrophes in Stars

Self-Gravitating Astrophysical Mass With Singular Central Density Vibrating in Fundamental Mode

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