D. S. King

Revised masses for the double-mode and bump Cepheids. [Rotation, helium- or metal-rich-layer]

We consider Population I Cepheids with two pulsation modes and those with a bump in the light and velocity curves. Model envelopes for these Cepheids have been altered in several ways in an attempt in remove the discrepancy between masses predicted from the evolution theory mass-luminosity relation an th masses predicted from pulsation theory. One of these ways, the inclusion of rotation, does not change the period ratio of the first overtone mode to the fundamental mode enough to resolve this mass discrepancy. Another way, the inclusion of a helium- (or metal-) rich layer mixed by convection and pulsation between the stellar surface and 70,000 K decreases this period ratio appreciably. The ratio of the second overtone period to the fundamental period is also reduced with this structure. The masses of the double-mode Cepheids U TrA and V367 Sct and the bump Cepheids U Sgr and ..beta.. Dor are found to be much closer to the masses derived from stellar evolution theory.

Nonpulsating Stars and the Populations i and II Instability Strips

With specially computed detailed tables of equations of state and opacities, the instability strips for delta Scuti stars and Cepheids of Population I and RR Lyrae and W Virginis stars of Population II have been computed. Uncertainties in the observed strip locations and sometimes in the mode of the observed pulsations do not allow high accuracy in fixing helium contents or the variables masses. Nevertheless, if masses close to those given by evolutionary theory are used, the helium content in Population II objects is likely less than Y=0.25. For Population I, Y can be more than 0.3; but if a given star has Y less than abeut 0.25, it can appear in the dwarf and classical Cepheid strips as nonpulsating.

Theoretical period ratios for RR Lyrae variables and AQ Leonis

The ratio of the overtone to fundamental periods has been calculated for models of RR Lyrae variables by using the linear nonadiabatic theory. Both homogeneous envelope and helium-enriched surface-layer models have been considered in order to predict the observed period ratio for the only known Population II double-mode RR Lyrae variable AQ Leonis. It is shown that the period ratio for homogeneous models in the radial pulsation instability strip depends only on the fundamental mode period at 0.58 M/sub sun/ and 0.65 M/sub sun/ and does not depend on the luminosity or surface effective temperature. The AQ Leo period of 0/sup d/.55 and the period ratio of 0.746 can be explained with a homogeneous composition model with a mass of 0.65 M/sub sun/. No surface helium enrichment is necessary for this variable even though such enrichment seems to be necessary for the more luminous double- and triple-mode Cepheids. It appears that the double-mode behavior of AQ Leo can be explained by mode switching in its blueward or redward horizontal branch evolution. This mode switching is rapid compared with its lifetime as an RR Lyrae variable.

Linear theory period ratios for surface helium enhanced double-mode Cepheids. [Periods between 1 and 7 days]

Linear nonadiabatic theory period ratios for models of double-mode Cepheids with their two periods between 1 and 7 days have been computed, assuming differing amounts and depths of surface helium enhancement. Evolution theory masses and luminosities are found to be consistent with the observed periods. All models give Pi/sub 1//Pi/sub 0/approx. =0.70 as observed for the 11 known variables, contrary to previous theoretical conclusions. The composition structure that best fits the period ratios has the helium mass fraction in the outer 10/sup -3/ of the stellar mass (T< or =250,000 K) as 0.65, similar to a previous model for the triple-mode pulsator AC And. This enrichment can be established by a Cepheid wind and downward inverted ..mu.. gradient instability mixing in the lifetime of these low-mass classical Cepheids.

Pulsations of the R Coronae Borealis stars

The radial pulsations of very luminous, low-mass models (L/M ∼ 104, solar units), which are possible representatives of the R CrB stars, have been examined. These pulsations are extremely nonadiabatic. We find that there are in some cases at least one extra (“strange”) mode which makes interpretation difficult. The blue instability edges are also peculiar, in that there is an abrupt excursion of the blue edge to the blue for L/M sufficiently large. The range of periods of the model encompasses observed periods of the Cepheid-like pulsations of actual R CrB stars.

Full amplitude models of 15 day Cepheids

Numerical models of Cepheids have been computed with a range of effective temperatures and compositions. The amplitudes increase if the helium abundance increases or if the effective temperature decreases. The latter effect is contrary to observational data. The models also exhibit velocity amplitudes which are much lower than those observed.

Nonlinear calculations for BL Her stars

From the linear and nonlinear calculations it is evident that bumps occur in the velocity and light curves when there is a near resonance between ..pi../sub 0/ and ..pi../sub 2/. In addition, these resonance bumps do not seem to depend on the limit cycle amplitude, and cannot be attributed to the surface shock encountered when models are driven to excessively high amplitudes.

Pulsations of the R Coronae Borealis Stars

The radial pulsations of very luminous, low-mass models (L/M ˜ 10 4 , solar units), which are possible representatives of the R CrB stars, have been examined. These pulsations are extremely nonadia – batic. We find that there are in some cases at least one extra (“strange”) mode which makes interpretation difficult. The blue instability edges are also peculiar, in that there is an abrupt excursion of the blue edge to the blue for L/M sufficiently large. The range of periods of the model encompasses observed periods of the Cepheid-like pulsations of actual R CrB stars.

Full Amplitude Models of 15 Day Cepheids

Numerical models of Cepheids have been computed with a range of effective temperatures and compositions. The amplitudes increase if the helium abundance increases or if the effective temperature decreases. The latter effect is contrary to observational data. The models also exhibit velocity amplitudes which are much lower than those observed.