Pulsations and outbursts of luminous blue variables Page: 4 of 8
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outbursts (Guzik et al. 1997). Many details of the stellar models used in this
paper are described in these earlier presentations.
2. Massive Star Evolution Calculations
Initial main sequence masses of 50 and 80 M with Z=0.02 are followed with
the Iben (1963,1965,1975) evolution code including extensive mass loss. This
mass loss can be due to the usual hot wind or rotation as discussed by Langer
(1997). Our model masses after evolution to the LBV region are 31 and 47
Mo. Many levels in the models are close to the Eddington luminosity limit
where the radiation pressure gradient established by the radiation diffusion flow
through the model can completely support the matter against gravity. However,
Langer (1997) shows that a model cannot actually exceed this Eddington limit,
because convection can carry an almost unlimited luminosity and always keep the
radiative luminosity sub-Eddington. Further a super-Eddington model cannot
even be constructed, because it will not be able to conform to the prescribed
hydrostatic equilibrium with a non-zero mass.
The 31 MG model lies below the horizontal part of the Humphreys-Davidson
line in the Hertzsprung-Russell diagram. Even though it is located among other
stars that are LBVs, and some layers in the model are near the Eddington
limit, hydrodynamic calculations show that we cannot make this model display
outbursts. Presumably the LBVs (such as the low Z SMC star R40) seen at this
luminosity have masses even lower than 31 M0 after they have evolved to the
red and lost considerable mass as red supergiants. Then they have returned to
higher effective temperatures (like 12,000 K) with a mass near 20 MG.
Both our 47 and 31 MG evolution models have significant helium enhance-
ment at the surface over the primordial value, because the extensive mass loss
exposes material that has had hydrogen burned away. For this study various
compositions from Y=0.28 to 0.58 are used, even though, strictly, additional
evolution models should be constructed. We assume further that convection
and pulsations homogenize the entire envelope composition down to as much as
10-3 of the stellar mass at about 106 K and at less than 0.1 of the photosphere
radius of near 1013 cm. Evolution models show only a slight helium composition
gradient in the extended outer envelope anyway.
3. The Cause of Outbursts
Here are some features of the outbursts that we have found from linear and
nonlinear (see also Despain, Guzik, and Cox 1998) calculations of stellar models
with parameters near the actual observed LBVs:
1. Evolution and considerable mass loss produces models that display radial
and nonradial pulsations in normal and "strange" modes.
2. During pulsations these stars periodically exceed the Eddington luminosity
limit and should at least give enhanced mass loss.
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Cox, A.N.; Guzik, J.A.; Soukup, M.S. & Despain, K.M. Pulsations and outbursts of luminous blue variables, article, June 1, 1997; New Mexico. (digital.library.unt.edu/ark:/67531/metadc694877/m1/4/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.