Stellar structure theory
Stellar structure theory, examining particle aggregates gravitational and pressure forces, energy flow, generation and opacity and equations of state
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Stellar structure theory, examining particle aggregates gravitational and pressure forces, energy flow, generation and opacity and equations of state
Natural expansion parameter for outward integration from center of stellar structure
Relativity theory and astrophysics, Volume 3, Stellar structure
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. A general relativistic version of the mixing-length formalism for convection is presented. It is argued that in work on spherical systems, general relativity theorists have identified the wrong quantity as total mass-energy inside radius r.
Instability of stellar structures intermediate between white dwarfs and neutron stars shown by stellar models, discussing pulsar signals periodicities
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."
The general-relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general-relativistic version of the mixing-length formalism for convection is presented.
Instability of stellar structures intermediate between dwarfs and neutron stars
A scale covariant kinetic theory for particles and photons is developed. The mathematical framework of the theory is given by the tangent bundle of a Weyl manifold. The Liouville equation is derived, and solutions to corresponding equilibrium distributions are presented and shown to yield thermodynamic results identical to the ones obtained previously. The scale covariant theory is then used to derive results of interest to stellar structure and evolution. A radiative transfer equation is derived that can be used to study stellar evolution with a variable gravitational constant. In addition, it is shown that the sun's absolute luminosity scales as L approximately equal to GM/kappa, where kappa is the stellar opacity. Finally, a formula is derived for the age of globular clusters as a function of the gravitational constant using a previously derived expression for the absolute luminosity.
The problem of treating convective energy transport without MLT approximations is approached here by formulating the results of numerical simulations of convection in terms of energy fluxes. This revised treatment of convective transport can be easily incorporated within existing stellar structure codes. As an example, the technique is applied to the sun. The treatment does not include any free parameters, making the models extremely sensitive to the accuracy of the treatments of opacities, chemical abundances, treatments of the solar atmosphere, and the equation of state.
We discuss the importance of Population II Li-6 as a diagnostic for models of primordial nucleosynthesis, cosmic-ray nucleosyntheses in the early Galaxy, and the structure and evolution of metal-poor solar-type stars. The observation of Li-6 in the subdwarf HD 84937 is shown to be consistent with the existing Population II LiBeB data within the context of a simple three-component model: (1) standard big bang nucleosynthesis, (2) Population II cosmic-ray nucleosynthesis, (3) standard (nonrotating) stellar LiBeB depletion. If this interpretation is correct, we predict a potentially detectable boron abundance for this star: about 2 x 10 exp -12. Subsequent Population II LiBeB observations, and in particular further observations of Population II Li-6, are shown to be crucial to our understanding of the primordial and early galactic creation and destruction mechanisms for light elements.
We have constructed a series of models of Alpha Centauri A and Alpha Centauri B for the purposes of testing the effects of convection modeling both by means of the mixing-length theory (MLT), and by means of parameterization of energy fluxes based upon numerical simulations of turbulent compressible convection. We demonstrate that while MLT, through its adjustable parameter alpha, can be used to match any given values of luminosities and radii, our treatment of convection, which lacks any adjustable parameters, makes specific predictions of stellar radii. Since the predicted radii of the Alpha Centauri system fall within the errors of the observed radii, our treatment of convection is applicable to other stars in the H-R diagram in addition to the sun. A second set of models is constructed using MLT, adjusting alpha to yield not the 'measured' radii but, instead, the radii predictions of our revised treatment of convection. We conclude by assessing the appropriateness of using a single value of alpha to model a wide variety of stars.
A physical mechanism is proposed that couples the Sun's dynamo magnetic field to its gravitational potential energy. The mechanism involves the isotropic field pressure resulting in a lifting force on the convective envelope, thereby raising its potential energy. Decay of the field due to solar activity allows the envelop to subside and releases this energy, which can augment the otherwise steady solar luminosity. Equations are developed and applied to the Sun for several field configurations. The best estimate model suggests that uniform luminosity variations as large as 0.02% for half a sunspot cycle may occur. Brief temporal variations or the rotation of spatial structures could allow larger excursions in the energy released.
We have updated a previous attempt to incorporate within a solar model a treatment of convection based upon numerical simulations of convection rather than mixing-length theory (MLT). We have modified our formulation of convection for a better treatment of the kinetic energy flux. Our solar model has been updated to include a complete range of OPAL opacities, the Debye-Hueckel correction to the equation of state, helium diffusion due to gravitational settling, and atmospheres by Kurucz. We construct a series of models using both MLT and our revised formulation of convection and the compared results to measurements of the solar radius, the solar luminosity, and the depth of the solar convection zone as inferred from helioseismology. We find X(solar) = 0.702 +/- 0.005, Y(solar) = 0.278 +/- 0.005, and Z(solar) = 0.0193 +/- 0.0005.
Stellar statistics and determination of galactic structure
Stellar isolated disks spiral structure, examining large numbers of point masses self consistent motion in galactic plane
Satellite measurement of atmospheric structure by stellar refraction, starlight transmission through atmosphere, and background sky brightness
The thermodynamics of stellar atmospheres is discussed. Particular attention is given to the relation between theoretical modeling and empirical evidence. The characteristics of distinctive atmospheric regions and their radical structures are discussed.