Poretti and Antonello (1988), and Antonello, Poretti, and Stellingwerf (1988) proposed, based on analysis of one-zone models, that the unusual light curves of the large-amplitude Delta Scuti stars V1719 Cyg, V798 Cyg, and V974 Oph can be explained by helium diffusion. The light curves of these stars have descending branches that are steeper than the rising branch.
Delta Scuti stars have shallow surface convection zones, and thus rather short diffusion timescales compared to their main-sequence lifetimes (Guzik and Cox 1991). Stellar evolution calculations including diffusion show that helium (and heavier elements, unless radiative levitation is included) diffuses from the upper 10-4 solar masses (T < 300,000 K) in about 108 years. This implies that mixing, or mass loss at a rate of ~10-12 solar masses/year would be required to restore a normal Pop I (Y ~ 0.28) envelope composition. If the mass loss rate is an order of magnitude less, an envelope helium abundance Y ~ 0.10 could be maintained.
Hydrodynamic calculations were performed for 60-zone radiative Delta Scuti models with and without reduced upper envelope helium abundances. The models have mass 1.8 solar masses, luminosity 32 solar luminosities, effective temperature 6800 K, near the red edge of the instability strip, and fundamental mode period ~ 0.19 d, near that of V974 Oph and V798 Cyg. The Stellingwerf (1974) periodic relaxation method was used to quickly reach limiting amplitude.
Reducing the envelope helium abundance from Y = 0.28 to Y = 0.10 for temperatures <100,000 K decreases the radial velocity amplitude from 40 km/sec to nearer the observed value of ~ 10 km/sec, but the light curves are still steeper on the rising branch. This is illustrated in the figure shown on the cover of this Newsletter. This figure shows bolometric magnitudes of limiting amplitude solutions for d Scuti models with envelope helium abundance decreased to Y = 0.10 for T < 100,000 K (dotted line); and to Y = 0.12 for T < 300,000 K (solid line). These curves show how helium diffusion could alter the light curve shapes of Delta Scuti stars. When the helium depletion is extended to ~ 200,000 K, the light curve becames less steep on the rising branch, and steeper on the descending branch.
Extending the helium depletion to ~ 300,000 K further enhances this effect (see figure on the cover). If the envelope helium abundance is reduced too much (to Y < 0.10), or over too large a portion of the envelope, the helium-ionization driving is weakened and the models stop pulsating.
The calculated light curve shapes including helium diffusion do not quite match those observed for V1719 Cyg, V798 Cyg, and V974 Oph, but the approach appears promising. Calculations are in progress to study the effects of the shape of the helium composition gradient, and possible enhanced metal abundance due to radiative levitation.
Acknowledgement: The author would like to thank Dr. Elio Antonello for suggesting these calculations, and for encouragement and useful discussions.