Stellar model

Stars are suns of varying masses, at different stages in their evolution, as our models will show. Some like to design protoype cars or aeroplanes, others wedding dresses, whilst we astral physicists make evolutionary models of stars. 

We are thus able to reconstruct the Sun s whole career, from its nebulous birth, through its first nuclear reaction, right up to its last breath as a red giant. We may watch it swell up proudly as it burns its first helium, then throw its envelope off a hot, dense core, before the latter grows rigid, becoming a white dwarf, frozen in crystal. Wonders But let us recall the vast effort that went into this undertaking. 

The mathematical architecture of the model had to be built up from scratch. The structure equations were put together like the timbers of a house and filled out with physical data describing the behaviour of matter at high temperatures, where atomic and nuclear physics come into play. 

Finally, the numerical model had to converge, no mean achievement from the computing point of view. It is with obvious satisfaction that one sees the results emerge at the end of the day, neatly arranged on the computer printout. 

The model Sun tells all. We may read off its temperature, density, chemical composition, luminosity and nuclear reaction rates at any depth and any stage of its evolution, from the youthful Sun, to its current middle age and forthcoming old age. The day-star has become limpid and with it every other star. 

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Our multi-level carbon model atom is adapted from D. Kiselman (private communication), with improved atomic data and better sampling of some absorption lines. The statistical equilibrium code MULTI (Carlsson 1986), together with ID MARCS stellar model atmospheres for a grid of 168 late-type stars with varying Tefj, log g, [Fe/H] and [C/Fe], were used in all Cl non-LTE spectral line formation calculations, to solve radiative-transfer and rate equations and to find the non-LTE solution for the multi-level atom. We put particular attention in the study of the permitted Cl lines around 9100 A, used by Akerman et al. (2004). 

For the WC phase, the milder composition gradients, when revealed at the surface, make smoother transitions. This produces on the average lower C/He ratios, in very good agreement with observations [1]. The abundances in WC stars are not equilibrium values, but are products of the partial He-burning, thus they are model dependent and offer a most interesting test on the quality of stellar models. 

We compare the evolutions of 3 stellar models with initial mass 5Mq for a metallicity typical of those GCs like M3, M13, whose stars exhibit the quoted anomalies, i.e. Z = 0.001. 

Simple stellar models - black body radiation... 

SIMPLE STELLAR MODELS - BLACK BODY RADIATION... 

A useful insight into the structure of nearly homogeneous stars or parts thereof can be gained from the study of so-called polytropic stellar models which depend on a combination of the principle of hydrostatic equilibrium with an assumed equation of state of the form... 

Mishustin et al. (2003). The results of calculation of hadronic (H) and quark stellar models (SS, QC and MC) in Hard-Dense-Loop approach are represented in Fig. 9 from Thoma et al. (2003), where one of the model parameters is changing. The free quarks exist in the state of deconfined quarks, and the density when deconfined quarks become energetically preferable is also rather indefinite (Berezhiani et al., 2003). 

By coupling the nuclear reaction network to stellar models, we may calculate the compositions resulting from these nuclear processes, under any imaginable... 

Theoretical modeling provides strong evidence that most presolar silicon carbide grains come from 1.5 to 3 M stars. As discussed in Chapter 3, stellar modeling of the evolution of the CNO isotopes in the envelopes of these stars makes clear predictions about the 12C/13C, 14N/15N, 170/160,180/160 ratios as a star evolves. For example, in the envelopes of low- to intermediate-mass stars of solar composition, the 12C/13C ratio drops to 40 (from a starting value of 89), and 14N/15N increases by a factor of six as carbon and nitrogen processed by... 

A systematic study of stellar models for C/O-rich Wolf-Rayet stars... 

Three different structures are found for stellar models with identical luminosity, total mass, core mass, and core radius as the effective temperature is varied. Two of these solutions can correspond to effective temperatures in the range pertinent to SK -69 202. This implies that models for the progenitor of SN 1987A will prove very sensitive to physical assumptions and numerical treatment in structural and evolutionary calculations. 

Another major and as yet unresolved issue centers upon precisely why SK-202-69 was a blue supergiant, and not a red one. This issue has been recently reviewed by Woosley (1987) and will be briefly summarized here. The essential problem is that there exist multiple solutions to the structure equations for the stellar atmosphere (see also Wheeler, this volume). Two stars having the same helium core mass and only slightly different luminosities, for example, can have radically different envelope structures, either a convective red supergiant or one that is radiative and blue (Woosley, Pinto, and Ensman 1987). There are several physical parameters that may break this symmetry and cause the star to chose one solution and not the other. Among them axe metallicity, (extreme) mass loss, and the theory of convection used in calculating the stellar model. 

The star that exploded, SK-202-69, was, as theory required, a massive star. When it lived on the main sequence, it had a mass of 19 3 M . At the time it exploded it had a helium core mass of 6 1 M , a radius 3 1 xlO12 cm, a luminosity 3 to 6 xlO38 erg s 1, and an effective temperature 15,000 to 18,000 K. Further consideration of the stellar models (Woosley 1987 Nomoto, this volume) suggests that the iron core mass at the time of collapse was 1.45 0.15 M0. Adding 0.15 M0 for matter between the iron core and the entropy jump... 

A Systematic Study of Stellar Models for C/O-Rich Wolf-Rayet Stars... 

Explosive astrophysical environments invariably lead to the production of nuclei away from stability. An understanding of the dynamics and nucleosynthesis in such environments is inextricably coupled to an understanding of the properties of the synthesized nuclei. In this talk a review is presented of the basic explosive nucleosynthesis mechanisms (s-process, r-process, n-process, p-process, and rp-process). Specific stellar model calculations are discussed and a summary of the pertinent nuclear data is presented. Possible experiments and nuclear-model calculations are suggested that could facilitate a better understanding of the astrophysical scenarios. 

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