Structure and Evolution of Stars

Schwarzschild, M.

doi:10.1515/9781400879175

Cited by 949 publications

(441 citation statements)

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“…However, later on when central helium burning was computed, it was found that the convective core expands and builds up a discontinuity in chemical composition. The mistake, which had important consequences on the models structure, was noticed and corrected by Castellani et al (1971a,b) who rediscovered the justification given earlier by Schwarzschild (1958). The correction of that mistake also led them to discover that the mass of the convective core increases much more than with the incorrect boundary condition.…”

Section: With the Schwarzschild Criterionmentioning

confidence: 99%

Proper use of Schwarzschild Ledoux criteria in stellar evolution computations

Gabriel

Noels

Montalbán

et al. 2014

A&A

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The era of detailed asteroseismic analyses opened by space missions such as CoRoT and Kepler has highlighted the need for stellar models devoid of numerical inaccuracies, in order to be able to diagnose which physical aspects are being ignored or poorly treated in standard stellar modeling. We tackle here the important problem of fixing convective zone boundaries in the frame of the local mixing length theory. First we show that the only correct way to locate a convective zone boundary is to find, at each iteration step, through interpolations or extrapolations from points within the convective zone, the mass where the radiative luminosity is equal to the total luminosity. We then discuss two misuses of the boundary condition and the ways they affect stellar modeling and stellar evolution. The first consists in applying the neutrality condition for convective instability on the radiative side of the convective boundary. The second way of misusing the boundary condition comes from the process of fixing the convective boundary through the search for a change of sign of a possibly discontinuous function. We show that these misuses can lead to completely wrong estimates of convective core sizes with important consequences for the following evolutionary phases. We point out the advantages of using a double mesh point at each convective zone boundary. The specific problem of a convective shell is discussed and some remarks concerning overshooting are given.

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Section: With the Schwarzschild Criterionmentioning

confidence: 99%

Proper use of Schwarzschild Ledoux criteria in stellar evolution computations

Gabriel

Noels

Montalbán

et al. 2014

A&A

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“…The growth time of both the oscillatory and non-oscillatory instabilities is relatively short, and instabilities are likely to operate operate in a non-linear regime. We can estimate the saturation velocity using the mixing-length model (e.g., Schwarzschild 1958) that assumes that the turnover time of turbulence generated by instability is on the order of the growth time of this instability. Consider, for example, the saturation regime of oscillatory modes.…”

Section: Discussionmentioning

confidence: 99%

Instabilities, turbulence, and mixing in the ocean of accreting neutron stars

Урпин¹

2005

A&A

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Abstract.We consider the stability properties of the ocean of accreting magnetic neutron stars. It turns out that the ocean is always unstable due to the combined influence of the temperature and chemical composition gradients along the surface and of the Hall effect. Both the oscillatory and non-oscillatory modes can be unstable in accreting stars. The oscillatory instability grows on a short timescale ∼0.1−10 s depending on the lengthscale of a surface inhomogeneity and the wavelength of perturbations. The instability of non-oscillatory modes is typically much slower and can develop on a timescale of hours or days. Instability generates a weak turbulence that can be responsible for mixing between the surface and deep ocean layers and for spreading the accreted material over the stellar surface. Spectral features of heavy elements can be detected in the atmospheres of accreting stars due to mixing, and these features should be different in neutron stars with both stable and unstable burning. Motions caused by instability can also be the reason for slow variations in the luminosity.

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“…In a typical stellar interior, this series converges extremely rapidly (see §75 in [96], or §II.6 in [234]), with a typical convergence rate given by…”

Section: Radiative Transportmentioning

confidence: 99%

Structure and Evolution of Low-Mass Stars: An Overview and Some Open Problems

Catelan¹

2007

AIP Conference Proceedings

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Abstract.A review is presented of some of the ingredients, assumptions and techniques that are used in the computation of the structure and evolution of low-mass stars. Emphasis is placed on several ingredients which are still subject to considerable uncertainty. An overview of the evolution of low-mass stars is also presented, from the cloud collapse phase all the way to the white dwarf cooling curve. Keywords DEFINITION OF "LOW-MASS STARS"Low-mass stars are self-gravitating gaseous (or, rather, plasmatic) bodies that develop electron-degenerate cores (meaning that all low-lying energy states are filled and electron pressure is accordingly dominated by the Pauli exclusion principle) soon after leaving the main sequence (MS) phase, and hence undergo the so-called "helium flash" (i.e., ignition of the triple-α process, whereby three alpha particles are converted into a 12 C nucleus, under degenerate conditions) at the end of their evolution on the red giant branch (RGB). Evolutionary calculations indicate that this corresponds to an upper mass limit M ≈ 2 − 2.5 M ⊙ (e.g., [258,259,109]). Exceptionally, and as a consequence of extreme mass loss on the RGB, some such stars may directly become helium white dwarfs (WD's) before they are ever able to ignite helium in their degenerate cores (e.g., [16] and references therein). At the low-mass end, on the other hand, one finds that objects below M ≃ 0.08 M ⊙ are incapable of quiescent hydrogen burning. This corresponds to the commonly adopted "dividing line" between low-mass stars and the so-called brown dwarfs (see, e.g., [58], and references therein). Empirically, the latter have recently been associated to the new spectral classes L ([156]) and T ([31]). ASTROPHYSICAL IMPORTANCELow-mass stars are of great astrophysical importance for a variety of reasons, which include the following:• Due to the shape of the so-called "Initial Mass Function" ([227]; see also [163] for a recent review), which gives the number of stars that are born in a given

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Structure and Evolution of Stars

Cited by 949 publications

References 0 publications

Proper use of Schwarzschild Ledoux criteria in stellar evolution computations

Proper use of Schwarzschild Ledoux criteria in stellar evolution computations

Instabilities, turbulence, and mixing in the ocean of accreting neutron stars

Structure and Evolution of Low-Mass Stars: An Overview and Some Open Problems

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