Testing stellar evolution models with the retired A star HD 185351
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When the internal temperature of a star exceeds 1 BK (109 °K) the evolution is very rapid. The time scale is around 3000 years. Energy dissipated by emission of neutrinos is several orders of magnitude higher than that by optical radiation. Neutrinos have exceedingly long mean free path (∼10(exp 20) gram/cm(exp 2)) and they will escape as soon as they are produced. The star will contract to release gravitational energy to make up the energy lost to neutrinos and the internal temperature will rise to comply with the virial theorem. It is possible in this fast evolutionary phase, to neglect optical radiations all together as compared with the neutrino radiation. A set of structural equations is thus obtained. The envelope is replaced by boundary conditions. A simple model is constructed to illustrate our approach.
Hertzsprung-Russell diagram calibration in terms of age and mass for main-sequence B and A stars
Metal-rich star evolution from main sequence to red giant, examining mass, nuclear reactions and theoretical models
The discrepancy between the masses of Cepheid variables deduced from evolution theory and pulsation theory is examined. The effect of input physics on evolutionary tracks is first discussed; in particular, changes in the opacity are considered. The sensitivity of pulsation masses to opacity changes and to the ascribed values of luminosity and effective temperature are then analyzed. The Cepheid mass discrepancy is discussed in the light of the results already obtained. Other astronomical evidence, including the mass-luminosity relation for main sequence stars, the solar neutrino flux, and cluster ages are also considered in an attempt to determine the most likely source of error in the event that substantial mass loss has not occurred.
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Theoretical evolutionary sequences of models for stars of 15 and 30 solar masses were computed from the zero-age main sequence to the end of core helium burning. During the earliest stages of core helium depletion, the envelope rapidly expands into the red-supergiant configuration. At 15 solar mass, a blue loop on the H-R diagram ensues if the initial metals abundance, initial helium abundance, or C-12 + alpha particle reaction rate is sufficiently large, or if the 3-alpha reaction rate is sufficiently small. These quantities affect the opacity of the base of the outer convection zone, the mass of the core, and the thermal properties of the core. The blue loop occurs abruptly and fully developed when the critical value of any of these quantities is exceeded, and the effective temperature range and fraction of the lifetime of core helium burning during the slow phase of the blue loop vary surprisingly little. At 30 solar mass no blue loop occurs for any reasonable set of input parameters.
It has been found that pulsars are rotating magnetic neutron stars, which are created during catastrophic collapses of old stars whose nuclear fuel has long since been used up. The maximum size of pulsars, based on the fastest rotation period of 33 msec, cannot exceed 100 km. The densest star the theory predicts is the neutron star. Its diameter is only 10 km. The processes producing radiation from pulsars are discussed, giving attention to a process similar to that by which a klystron operates and to a process based on a maser mechanism.
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The effects of semiconvective mixing are investigated in evolutionary sequences of models for stars of 10, 15, and 30 solar masses with four different initial chemical compositions. The models are constructed using the Ledoux criterion for both the definition of convective instability and the state of convective neutrality assumed to be attained in regions with a gradient of mean molecular weight. It is shown that semiconvection is nonexistent at 10 solar masses, of minor importance at 15 solar masses, but covers most of the intermediate zone at 30 solar masses, developing into full convection if the initial hydrogen and metals abundances are high. The effects of low initial hydrogen and metals abundances are examined, and the critical importance is demonstrated of the depths of the semiconvective zone and the outer convective envelope in promoting a blue loop and determining the maximum effective temperature on the loop. The extent of the thermally stable stages of the blue-loop phase is determined.
A consistent set of 247 evolutionary sequences extending from the ZAMS to the red-giant branch is presented for Y from 0.10 to 0.40, Z from 0.00001 to 0.10, and masses of 0.55 to 6.90 solar masses. Each sequence is started from a homogeneous ZAMS model, and almost all are evolved to the base of the red-giant branch. It is shown that: (1) the relative position of the main sequence can be determined as a function of composition; (2) theoretical luminosity functions can be derived from the relative evolutionary time scales; (3) a dip in luminosity sometimes occurs at the base of the red-giant branch and is most pronounced at larger Z values; (4) metal-poor stars evolve farther up along the main sequence before turning off toward the red-giant branch; and (5) the onset of helium burning halts the evolution across the Hertzsprung gap for the most massive and most metal-poor models, so that the star remains blue during its phase of core-helium burning.
Newly defined characteristics of planetary nebulae (PN) derived from analysis of a photometric survey of 57 PN are reported. The data were combined with measurements of 27 other PN made since 1918 and were found to indicate core masses ranging from 0.55-1.0 solar mass. N/O elemental abundance ratios observed were correlated with the planetary nuclei masses, and were in direct proportion. IUE data on PN that overlapped a large part of the survey indicated that the PN in the galactic disk are more massive than PN in the halo. It is suggested that PN evolve into white dwarfs, a hypothesis supported by astrometric solutions for three nearby visual binaries featuring white dwarfs with well-determined masses. It is noted, however, that PN with masses exceeding one solar mass have been sighted in the Magellanic Clouds.
The structure and evolution of a protostar forming from a cloud composed of pure hydrogen and helium gas are calculated. Using an accretion rate of 0.0044 solar mass/yr, the collapse of the cloud is followed numerically as a sequence of steady state accretion flows onto the hydrostatic core, which grows from an initial mass of 0.01 solar mass to 10.5 solar masses. The core is surrounded by an optically thick radiative precursor for most of its evolution. The core radius reaches 47 solar radii when the mass is 1 solar mass. For sufficiently massive cores, the deep interior contracts strongly, driving out a 'luminosity wave' which reaches the surface when the mass is 8 solar masses. This results in a large increase in core radius, the establishment of surface convection, and the disappearance of the radiative precursor. The dependence of core radius on the mass and accretion rate is analytically derived, and a new table or Rosseland mean opacities for metal-free gas is presented.
The quasi-static contraction of primordial stars composed of pure hydrogen and helium gas is studied by following numerically the evolution of a star of five solar masses from the end of protostellar accretion to the onset of hydrogen burning. Although the protostellar core of this mass is radiatively stable and undergoing nonhomologous contraction, its large surface area and luminosity force the star to a partially convective, homologously contracting state within only 100 yr. Deuterium later ignites at an off-center temperature maximum but fails to produce interior convection. The star follows a conventional premain sequence track in the HR diagram, reaching the ZAMS after 1.2 million yr, with a luminosity of 880 solar luminosities and a radius of 1.2 solar radii.
It is demonstrated here that the measurable properties of systems containing degenerate dwarfs can be used as a direct test of the core mass-radius relation for moderate-mass giants if the final stages of the loss of the envelope of the progenitor giant occurred via stable critical lobe overflow. This relation directly probes the internal structure of stars at a relatively advanced evolutionary state and is only modestly influenced by adjustable parameters. The measured properties of six binary systems, including such diverse systems as Sirius and Procyon and two millisecond pulsars, are utilized to derive constraints on the empirical core mass-radius relation, and the constraints are compared to the theoretical relation. The possibility that the final stages of envelope ejection of the giant progenitor of Sirius B occurred via critical lobe overflow in historical times is considered.
Models of stars of various masses and rotational parameters were developed and compared with observations of stars in open clusters of various ages in order to analyze the evolution of rotating stars from the early premain sequence to an age of 1.7 x 10 to the 9th yrs. It is shown that, for stars older than 10 to the 8th yrs and less massive than 1.1 solar mass, the surface rotation rates depend most strongly on the properties of the angular momentum loss. The trends of the currently available observations suggest that the rotation periods are a good indicator of the field-star ages.
The observed secular period changes of RR Lyrae stars in five globular clusters have been compared with those predicted by synthetic models of the horizontal branch (HB). It is shown that most of the observed number distributions of the period change rate beta could be attributed to evolutionary effects, if the random observational error is of order + or - 0.07 days/Myr in beta as suggested by the observers. The model calculations indicate that the mean rate of period change in RR Lyrae stars in globular clusters depends sensitively on their HB type, as is the case for the period shift at a given effective temperature. The distinct bias toward positive period changes in M15 and Omega Cen is evidence that most HB stars in the Oosterhoff group II clusters pass through the instability strip from blue to red toward the end of their core helium burning phase. If confirmed by future observations, this is strong support for the Lee et al. (1990) explanation of the Sandage (1957) period-shift effect.
The results of canonical theory for the evolution of horizontal-branch (HB) stars are examined. Particular attention is given to how an HB star maintains the appropriate composition distribution within the semiconvective zone and how this composition is affected by the finite time-dependence with which convective boundaries actually move. Newly developed models based on time-dependent overshooting are presented for both the core-helium-exhaustion and main HB phases.