Arthur N. Cox

Driving the Gravity-Mode Pulsations in γ Doradus Variables

The γ Doradus stars are a newly discovered class of gravity-mode pulsators that lie just at or beyond the red edge of the δ Scuti instability strip. We present the results of calculations that the predict pulsation instability of high-order g-modes with periods between 0.4 and 3 days, as observed in these stars. The pulsations are driven by the modulation of the radiative flux by convection at the base of a deep envelope convection zone. Pulsation instability is predicted only for models with temperatures at the convection zone base between ~200,000 and ~480,000 K. The estimated shear dissipation that is due to turbulent viscosity within the convection zone or in an overshoot region below the convection zone can be comparable to or even exceed the predicted driving and is likely to reduce the number of unstable modes or possibly quench the instability. Additional refinements in the pulsation modeling are required to determine the outcome. At least one γ Doradus star has been observed that also pulsates in δ Scuti-type p-modes, and others have been identified as chemically peculiar. Since our calculated driving region is relatively deep, γ Doradus pulsations are not necessarily incompatible with surface abundance peculiarities or with δ Scuti p-mode pulsations driven by the H and He ionization κ-effect. Such stars will provide useful observational constraints on the proposed γ Doradus pulsation mechanism.

Oscillations of solar models with internal element diffusion

Data on the evolution of a solar model are presented which include the effects of diffusive processes that lead to a partial sorting of the elements with depth. The two models are with and without the effects of diffusion. The diffusion process of gravitational settling, composition gradient diffusion, and thermal diffusion are based on the method of Iben and MacDonald (1985). It is found that a high original helium content is required to match the observed global oscillation data, and that the total neutrino flux detectable by the chlorine detector accordingly is increased to over 10 SNU. 111 refs.

Can enhanced diffusion improve helioseismic agreement for solar models with revised abundances

Recent solar photospheric abundance analyses (by Asplund et al. and Lodders) revise the C, N, O, Ne, and Ar abundances downward by 0.15-0.2 dex compared to previous determinations by Grevesse & Sauval. The abundances of Fe and other elements are reduced by smaller amounts, 0.05-0.1 dex. With these revisions, the photospheric Z/X decreases to 0.0165 (or 0.0177, according to Lodders), and Z decreases to ~0.0122 (or 0.0133, according to Lodders). A number of papers (by, e.g., Basu & Antia, Montalban et al., Bahcall & Pinsonneault, Turck-Chieze et al., and Antia & Basu) report that solar models evolved with standard opacities and diffusion treatment using these new abundances give poor agreement with helioseismic inferences for sound-speed and density profile, convection-zone helium abundance, and convection-zone depth. These authors also considered a limited set of models with increased opacities, enhanced diffusion, or abundance variations to improve agreement, finding no entirely satisfactory solution. Here we explore evolved solar models with varying diffusion treatments, including enhanced diffusion with separate multipliers for helium and other elements, to reduce the photospheric abundances, while keeping the interior abundances about the same as earlier standard models. While enhanced diffusion improves agreement with some helioseismic constraints compared to a solar model evolved with the new abundances using nominal input physics, the required increases in thermal diffusion rates are unphysically large, and none of the variations tried completely restores the good agreement attained using the earlier abundances. A combination of modest opacity increases, diffusion enhancements, and abundance increases near the level of the uncertainties, while somewhat contrived, remains the most physically plausible means to restore agreement with helioseismology. The case for enhanced diffusion would be improved if the inferred convection-zone helium abundance could be reduced; we recommend reconsidering this derivation in light of new equations of state with modified abundances and other improvements. We also recommend considering, as a last resort, diluting the convection zone, which contains only 2.5% of the Suns mass, by accretion of material depleted in the more volatile elements C, N, O, Ne, and Ar after the Sun arrived on the main sequence.

Using solar p-modes to determine the convection zone depth and constrain diffusion-produced composition gradients

Low- and intermediate-degree (1=5-60) solar p-mode frequencies, which are sensitive to the solar structure near the bottom of the convection zone, are used to find the convection zone depth and to constrain the size and shape of composition gradients produced by diffusive settling of helium and heavier elements. We have calculated the evolution and nonadiabatic oscillation frequencies of solar models incorporating the latest Mihalas, Dappen, Hummer, and Mihalas (MHD) equation of state, OPAL opacities, and diffusion of hydrogen, helium, and several heavier elements

The discovery of nonradial instability strips for hot, evolved stars

We have performed radial and nonradial, linear, nonadiabatic pulsation analyses of model stellar envelopes in the effective temperature range from 8 x 10/sup 4/ K to 1.5 x 10/sup 5/ K. These models have total masses of 0.6 M/sub sun/ and radii chosen so that they line up along a pre-white dwarf cooling curve computed by Schoenberner. We use three different interior compositions: (1) 100% carbon: (2) 50% /sup 12/C and 50% /sup 16/O (by mass); and (3) 10% /sup 12/C and 90% /sup 16/O (by mass). We find nonradial and radial instability strips for each composition caused by the partial ionization of carbon or oxygen or both. Our objective is to find the cause of the observed pulsations of PG 1159-035, a hot, evolved star with T/sub e/> or =10/sup 5/ K. While this star may be too hot to lie within any of our new instability strips, the closest agreement comes from models with significant amounts of /sup 16/O near the stellar surface. If correct, this result implies that helium burning in envolved stars produces much more /sup 16/O than heretofore believed.

Masses of RRd variables using Livermore opal capacities

The new Livermore opacities are used to construct 27 new stellar envelope models in order to determine if the discrepancy between the masses of the double-mode RR Lyrae variables using pulsation and evolution theories can be reconciled. For these extreme Population II variables, the large opacity increases found from the extensive line absorptions of iron around 250,000 K seen in Population I compositions are not realized. It is discovered that the opacity decreases below a temperature of 10{sup 5} K, due to more narrow lines of hydrogen than those used in the Los Alamos opacities, can also decrease theoretical period ratios. This opacity decrease, as with the higher temperature increases, produces steeper temperature increases and more shallow density gradients in the regions where the pulsation eigenvectors can feel the stellar structure. Small opacity increases at about 250,000 K can increase the more-metal-content RRd variables in the Oosterhoff I clusters by 0.1 solar mass. This essentially eliminates the inconsistency between masses from the two globular cluster types and between those determined from pulsation and evolution theories. 28 refs.

Modal selection in pulsating stars

Initial-value and periodic nonlinear pulsation integrations are carried out for a series of double-mode Cepheid models (P/sub 1//P/sub 0/approx.0.7) in the vicinity of the resonance ..omega../sub 1/+..omega../sub 0/=..omega../sub 3/. None of the models tested shows persistent double-mode behavior. A new, semiquantitative description of modal selection, based upon the iterative theory of Simon, is introduced to analyze the nonlinear results. In the simplest version of this description, modal section categories emerge which are identical to those of Stellingwerf. Our hydrodynamic results also agree at least partially with Stellingwerfs in that we find a region in the red where the models approach (though never reach) simultaneous instability of both limit cycles. Analysis of resonant effects on modal selection in our calculations leads to the conclusion that models lying between the resonances ..omega../sub 1/+..omega../sub 0/=..omega../sub 3/ and P/sub 2//P/sub 0/=0.5 may yet be viable candidates for double-mode pulsation.

Theoretical Period Changes in Yellow Giant Pulsators

Period changes in RR Lyrae variables and Cepheids, known for more than 60 years, can possibly be explained by small changes in a helium composition gradient below the hydrogen and helium convection zones. The particular cases for the globular cluster M15 double-mode RR Lyrae variable V53 and the Cepheid Polaris are studied. For the last 80 years, the fundamental mode period of V53 has been decreasing while the overtone mode period in this same star has been increasing. The rather steady overtone mode period increase for Polaris stopped very recently, and the period now seems constant. Diffusive settling of helium in these kinds of stars has been known to be slight because of the two convection zones and the long diffusion timescale below them. But a small amount of helium settling, even before the star begins to pulsate, and then a dredge-up of just a little helium by an occasional overshooting can change surface layer structures and periods. This dredge-up can have a timescale as short as the convection turnover time, i.e., a few days. A slight helium dredge-up episode may now have temporarily stopped the decaying pulsations and period increase of Polaris. Such an episode cannot explain the double-mode V53 case, but possibly the helium composition gradient is deepened enough by matter accretion in only 80 years to explain its observed opposite period changes. Another mechanism that might be important for period changes is tidal mixing of the small composition gradients caused by occasional close encounters of stars in clusters. Significant stellar rotation would keep the surface layer composition homogeneous and not allow the anomalous period changes discussed here.

On the sensitivity of high-degree p-mode frequencies to the solar convection zone helium abundance

Nonadiabatic frequencies for modes of degree l = 200-1000 for the MHD equation of state model described in Guzik and Cox (1991) with a convection zone Y = 0.27 are compared with a model with Y = 0.24, corresponding to the decrease expected due to diffusion. The frequencies of the l = 300-600 modes, which sample best the helium ionization region, show the greatest sensitivity to this helium abundance change. The frequency sensitivity to helium abundances is not affected by changes in the mixing-length/pressure scale height ratio or the inclusion of the turbulent pressure, although these effects can alter considerably the upper convection zone structure and the calculated frequencies. The observed minus calculated frequency differences for these high-degree low-order modes are discussed. The O - C differences for the accurately observed modes favor a reduction in the convection zone helium mass fraction of about 0.3, consistent with that expected due to diffusion. 32 refs.

Post-asymptotic giant branch nonradial instability strips

Stability analyses are performed for nonradial g(+)-mode pulsations of postasymptotic AGB stellar models to determine the location of their pulsational instability strips in the Hertzsprung-Russell diagram. Stellar models are analyzed that are assumed to have undergone a major mass loss event either near the tip of the AGB or shortly thereafter and, therefore, consist of a 50-percent carbon 50-percent oxygen core. Their mass is 0.6 solar mass, which is in good agreement with the peak of the observed distribution of white dwarf masses. The results are compared both to the observed planetary nebula nuclei variables and the hot pulsating DO variables. An analysis is also presented of the stability of DB white dwarfs, which have much deeper and stronger convection zones, and an instability strip is found between about 18,000 and 26,000 K approximately as observed for the known variable stars. 51 refs.