Engineering topics

Chin, Chao-Wen

Publications and source records attributed to Chin, Chao-Wen.

13 records

NASA NTRS1995

Tests of two convection theories for red giant and red supergiant envelopes

Two theories of stellar envelope convection are considered here in the context of red giants and red supergiants of intermediate to high mass: Boehm-Vitense's standard mixing-length theory (MLT) and Canuto & Mazzitelli's new theory incorporating the full spectrum of turbulence (FST). Both theories assume incompressible convection. Two formulations of the convective mixing length are also evaluated: l proportional to the local pressure scale height (H(sub P)) and l proportional to the distance from the upper boundary of the convection zone (z). Applications to test both theories are made by calculating stellar evolutionary sequences into the red zone (z). Applications to test both theories are made by calculating stellar evolutionary sequences into the red phase of core helium burning. Since the theoretically predicted effective temperatures for cool stars are known to be sensitive to the assigned value of the mixing length, this quantity has been individually calibrated for each evolutionary sequence. The calibration is done in a composite Hertzsprung-Russell diagram for the red giant and red supergiant members of well-observed Galactic open clusters. The MLT model requires the constant of proportionality for the convective mixing length to vary by a small but statistically significant amount with stellar mass, whereas the FST model succeeds in all cases with the mixing lenghth simply set equal to z. The structure of the deep stellar interior, however, remains very nearly unaffected by the choices of convection theory and mixing lenghth. Inside the convective envelope itself, a density inversion always occurs, but is somewhat smaller for the convectively more efficient MLT model. On physical grounds the FST model is preferable, and seems to alleviate the problem of finding the proper mixing length.

Stothers, Richard B.↗

NASA NTRS1994

Galactic stars applied to tests of the criterion for convection and semiconvection in an inhomogeneous star

The question of the effective criterion for convection and semiconvection to use in the inhomogeneous layers of models of massive stars is addressed here in terms of a choice between the Schwarzschild (temperature-gradient) criterion and the Ledoux (density-gradient) criterion. These two extremes give rise to and suppress, respectively, a fully convective zone (FCZ) in the layers immediately above the hydrogen-burning shell, if the star's mass is neither too low nor too high. Specifically, the existence of a large FCZ delays or prevents the star during core helium burning from becoming a red supergiant. The applicable range of initial stellar masses for a solar metallicity is approximately 13 to 30 solar mass. Nine different tests for the effective criterion for convection and semiconvection in Galactic supergiants, as well as a test using SN 1987A of the Large Magellanic Cloud, are performed, or reexamined, by using both old and new theoretical data, while three of the Galactic tests are repeated for association supergiants separately from cluster supergiants. Although eight of the 13 tests yield inconclusive results, five do support the Ledoux criterion, and three do so strongly.

Stothers, Richard B.↗

NASA NTRS1994

Luminous blue variables at quiescence: The zone of avoidance in the Hertzsprung-Russell diagram

Two phases of dynamical instability are theoretically predicted to exist during the evolution of supergiants of normal metallicity that are initially more massive than approximately 60 solar mass. One phase occurs briefly in the yellow or red region of the Hertzsprung-Russell diagram for stars in the early stages of core helium burning, and the other phase occurs for a longer time in the blue or blue-white region for stars exhausting their core helium. Probably only the second phase exists in the case of supergiants with initial masses between approximately 60 solar mass and approximately 30 solar mass or with low metallicities The cause of instability is the partial ionization of hydrogen and helium in a quasi-isolated outer region of the stellar envelope, above the layer where the iron opacity attains a large local maximum. Predicted luminosities, effective temperatures, ejected nebular masses, remnant masses, eruption recurrence times, and lifetimes, though very approximate, are generally consistent with available observational data for the important class of unstable supergiants known as luminous blue variables.

Stothers, Richard B.↗

NASA NTRS1994

More missing stellar opacity?

Observational data for Population I stars have shown that blue loops on the Hertzsprung-Russell (H-R) diagram form for stellar masses as low as approximately 4 solar mass. However, current state-of-the-art stellar models, unlike the older ones that were based on smaller opacities, fail to loop out of the red-giant region during core helium burning for masses less than 7 solar mass. A possible explanation is that the currently used Livermore opacities need to be further increased, by at least 70%, at temperatures characteristic of the base of the outer convection zone, around 1 x 10(exp 6) K. Indeed, no other suggested remedy seems to yield a blue loop at the lowest observed loop luminosities.

Stothers, Richard B.↗

NASA NTRS1993

Iron and molecular opacities and the evolution of Population I stars

Effects of recent opacity revisions on the evolution of Population I stars are explored over the range 1.5-60 solar masses. Opacity parameters considered include the angular momentum coupling scheme for iron, the relative iron abundance, the total metal abundance, and diatomic and triatomic molecular sources. Only the total metal abundance exerts an important control over the evolutionary tracks. Blue loops on the H-R diagram during core helium burning can be very sensitive to opacity, but only insofar as the simple formation or suppression of a blue loop is concerned. The blue loops are most robust for stellar masses around 10 solar masses. We confirm, from a comparison of stellar models with observational data, that the total metal abundance is close to solar and that convective core overshooting is likely to be very slight. The new models predict the existence of an iron convection zone in the envelope and a great widening of the main-sequence band in the H-R diagram at luminosities brighter than 100,000 solar luminosities.

Stothers, Richard B.↗

NASA NTRS1993

Dynamical instability as the cause of the massive outbursts in Eta Carinae and other luminous blue variables

A new type of stellar envelope structure has been computationally discovered at very high stellar masses. The outer part of the envelope resembles a nearly detached, diffusely filled shell overlying an ultrahot surface of small radius. This structural anomaly is caused by a large iron bump occurring in the new opacities of Iglesias et al. (1992). The new stellar models with normal metallicity encounter a strong ionization-induced dynamical instability in the outer envelope as they rapidly transit the H-R diagram after the end of central hydrogen burning. Preliminary evolutionary and hydrodynamical calculations successfully mimic the most basic observed properties of Eta Carinae and other very luminous blue variables. The Humphreys-Davidson sloped line in the H-R diagram, however, seems to be unrelated to these variables, and is instead the observed terminus of the main-sequence phase of evolution if convective core overshooting is insignificant.

Stothers, Richard B.↗

NASA NTRS1992

Stellar evolution in blue populous clusters of the Small Magellanic Cloud and the problems of envelope semiconvection and convective core overshooting

New theoretical evolutionary sequences of models for stars with low metallicities, appropriate to the Small Magellanic Cloud, are derived with both standard Cox-Stewart opacities and the new Rogers-Iglesias opacities. Only those sequences with little or no convective core overshooting are found to be capable of reproducing the two most critical observations: the maximum effective temperature displayed by the hot evolved stars and the difference between the average bolometric magnitudes of the hot and cool evolved stars. An upper limit to the ratio of the mean overshoot distance beyond the classical Schwarzschild core boundary to the local pressure scale height is set at 0.2. It is inferred from the frequency of cool supergiants in NGC 330 that the Ledoux criterion, rather than the Schwarzschild criterion, for convection and semiconvection in the envelopes of massive stars is strongly favored. Residuals from the fitting for NGC 330 suggest the possibility of fast interior rotation in the stars of this cluster. NGC 330 and NGC 458 have ages of about 3 x 10 exp 7 and about 1 x 10 exp 8 yr, respectively.

Stothers, Richard B.↗

NASA NTRS1992

Criterion for convection in an inhomogeneous star

To resolve the question of whether the Schwarzschild criterion or the Ledoux criterion should be used to test for convective instability in a star, a well-observed cluster of chemically inhomogeneous massive stars, in which the choice of the criterion for convection makes a crucial and easily observable difference, is required. NGC 330, a metal-poor cluster in the Small Magellanic Cloud, is ideal for this test. Its large evolved stellar population contains both blue and red supergiants, of which its many red supergiants should be absent if a gradient of mean molecular weight did not choke off rapid convective motions in the inhomogeneous region connecting the envelope and core. Thus the Ledoux criterion for convection is strongly indicated as being correct.

Stothers, Richard B.↗

NASA NTRS1991

Metal opacities and convective core overshooting in Population I stars

New stellar opacities computed by Rogers and Iglesias are found to lead to revised evolutionary models for stars of intermediate-to-high mass that show remarkably close agreement with observed stars, under otherwise standard physical assumptions. Most or all of the earlier discrepancies, except for the problem of predicted apsidal motion constants that are perhaps still too large, appear to have been resolved by using these new opacities with their increased metal line contribution. Thus, the implied interior metallicity of massive stars in the solar neighborhood now becomes 'normal'. Furthermore, the effective distance of convective overshooting beyond the classical convective core boundary is confirmed to be small and probably less than 0.2 times the local pressure scale height.

Stothers, Richard B.↗

NASA NTRS1991

Evolutionary sequences of stellar models of intermediate and high mass including convective core overshooting

Stellar evolution with parameterized overshooting from the convective core has been studied for the stellar mass range M/M(solar) = 3-30 and for the initial chemical composition range Xe = 0.650-0.739 (hydrogen) and Ze = 0.021-0.044 (metals). Evolutionary sequences run from the zero-age main sequence to the end of core helium burning, but emphasis is placed here on the core helium-burning phase. Convective core overshooting during the previous main-sequence phase leads, in most cases, to a shortening of the blue loop on the H-R diagram that forms when helium is being depleted in the core. On the other hand, convective overshooting from the helium-burning core has the opposite effect. A larger initial metals abundance also tends to shorten the blue loop. In an extreme case the blue loop can be fully suppressed, but in a marginal case the normal trend can be reversed.

Chin, Chao-Wen↗

NASA NTRS1991

Blue loops during core helium burning as the consequence of moderate convective envelope overshooting in stars of intermediate to high mass

New calculations of stellar evolutionary sequences without semiconvection in any phase have unexpectedly turned up, for stars in the mass range 3-30 solar masses, an irregular pattern of blue loops on the H-R diagram during the core helium-burning phase. Blue loops occur for 3 and 10 solar masses, but not for 5, 7, 15, and 30 solar masses. It is found, however, that the models near the bottom of the red supergiant branch are only marginallly stable against small inward displacements of the former base of the outer convection zone when it was deepest, for the stellar mass range 5-15 solar masses. As a consequence, convective envelope overshooting need only penetrate a distance of about 0.3 of a local pressure scale height to promote a delayed blue loop in these particular sequences. In conformity with previous work, the triggering mechanism for the blue loop appears to be proximity of the hydrogen-burning shell to the hydrogen discontinuity at the former base of the outer convection zone.

Stothers, Richard B.↗

NASA NTRS1990

Tables and intercomparisons of evolutionary sequences of models for massive stars

Tables of evolutionary sequences of models for massive stars have been prepared for a variety of physical input parameters that are normally treated as free. These parameters include the interior convective mixing scheme, the mixing length in the outer convective envelope, the rate of stellar-wind mass loss, the initial stellar mass, and the initial chemical composition. Ranges of specified initial mass and initial chemical composition are M = 10-120 solar masses, Xe = 0.602-0.739, and Ze = 0.021-0.044. The tables cover evolution of the star from the ZAMS to either the end of core H burning or the end of core He burning. Differences among the evolutionary tracks are illustrated primarily in terms of the interior mixing scheme, since the amount and timing of stellar wind mass loss are still very uncertain for initial masses above about 30 solar masses.

Chin, Chao-Wen↗

NASA NTRS1990

Limit on overshooting from the convective core in upper main-sequence stars

Overshooting of convective elements far beyond the classical Schwarzschild convective core boundary in theoretical models of massive ZAMS stars is found to lead to significant reductions of stellar luminosity and radius, provided that the temperature gradient in the overshoot region can be approximated by the adiabatic gradient. Comparison of these theoretical models with binary star data for the range of 5-15 solar masses indicates that the ratio of overshoot distance to pressure scale height is probably less than 1.5. This result apparently excludes any overshooting theories that predict very extended adiabatic convective cores.

Stothers, Richard B.↗