Hydrodynamic
Models for Pulsating BL Herculis-Type Variables
Yu. A. Fadeyev
Institute of
Astronomy, Russian Academy of Sciences, Pyatnitskaya ul. 48,
Moscow, 109017 Russia
Received November
10, 1996
Abstract—A
grid of hydrodynamic limit-cycle models is computed for pulsating
BL Her variables with masses M = 0.55, 0.6, 0.65M
, luminosities 106 
Lbol /L
169, and effective temperatures 5500 Teff 7000 K. The OP tables are used to compute the
opacity 
R for the hydrogen and helium
mass fractions X = 0.7 and Y = 0.299. Irrespective
of the stellar mass, the pulsation instability in the first
overtone is typical of stars with pulsation periods 
< 1 day, while the radial
pulsations for 
> 1 day are attributable to the
instability of the fundamental mode. Approximation formulas are
derived which relate the pulsation constant Q to the
mass-to-radius ratio (M/R) of the star. It is shown
that alternating pulsations with variable amplitude may arise
from the 2
0 = 31
resonance between the fundamental mode and the first overtone at
certain mass-to-radius ratios. The pulsations of these stars are
also characterized by good repetition of the pulsation motions,
but only in an interval that covers two cycles of the fundamental
mode. The secondary bump, which is observed in the light and
radial-velocity curves of BL Her stars with periods from 1.3 to 3
days, is associated with the pressure wave generated in the
region of partial ionization of HeII at maximum compression of
the stellar envelope.
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