Recent developments in the field of Delta Scuti stars are discussed. Considerable progress has been made in determining the multiple-period structure of individual variable stars and in identifying the excited radial and nonradial modes through a variety of methods. This allows an analysis of the change of excited modes as a function of the position in the instability strip.

Expressions for the amplitudes and phases of the light, colour and radial velocity variations are derived for a star in nonradial oscillation. For stars in the cepheid instability strip the spherical harmonic mode of the oscillation can be obtained from the phase difference between the light and colour variations. For 3 Cep stars the mode can be estimated from the amplitude ratio of the light and colour variations.

Mode identifications from the phase shift between the B-V color curves and the V light curves of Delta Scuti stars are discussed. For five Delta Scuti stars the frequency of highest amplitude is due to pulsation in a radial mode with one or more frequencies due to nonradial modes lying nearby. Thus there may be a resonance between the frequencies of radial and nonradial modes. This behavior has only been found in subgiant and giant stars so far, but this could easily be a selection effect. Theoretical predictions of frequencies for different 1-modes of the same overtone for main sequence, subgiant, and giant stars are needed to compare with these observations. Theoretical predictions of the strength of resonance coupling between radial and nonradial modes as a function of frequency separation are also needed.

Radial pulsation periods are calculated for models of variables in the lower Cepheid instability strip. Evolution tracks in several diagrams are constructed and used for comparisons with observed periods, period ratios, and effective temperatures. These comparisons are simpler and more direct than in earlier studies with separate evolution and pulsation calculations.

Recent work on Cepheids is reviewed in the areas of (1) the large-amplitude mode behavior, (2) convection, and (3) Cepheid masses. Initial-value type nonlinear calculations have not yet yielded true double-mode behavior. Yet we have the beginnings of a promising theory of modal selection. Theoretical calculations also yield reasonably located red edges to Cepheid (and Cepheid-like) instability regions.

As their name implies double-mode (or beat) cepheids form a subgroup of cepheid variables which appear to be pulsating simultaneously in two modes. From the period ratio of the two frequencies, the modes have been identified with the fundamental and first overtone modes of radial pulsation. Petersen (1973) was the first to establish that the two periods can be used to determine the masses and radii of these stars independent of any other knowledge such as luminosities, effective temperatures or gravities. The masses derived by this technique are 2 to 3 times lower than the expected evolutionary masses, given that these stars are normal population I cepheids. It is this result that has stimulated much of the subsequent research on double-mode cepheids.

The standing oscillation in an isothermal semi-infinite plane-parallel atmosphere has a critical frequency. The significance of critical frequency in the stellar pulsation is discussed briefly. The critical period is calculated for the cepheid instability strip. A star having relatively large radius compared with the mass should be examined by the criterion. The pulsational instability is reduced by the linear running wave.

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.

We have obtained photometric observations and radial velocities of the F6I-IIb star HR 7308. The spectral type, the period (1d.49), the relative range and phase of light, colour and velocity variations all suggest that the star is a small-amplitude Cepheid. The metal abundance appears to be normal. However, the light amplitude decreased slowly during 1978 from 0m.3 to 0m.1, and increased during 1979 and 1980 from 0m.05 to 0m.15. Such behaviour is unprecedented in a population I Cepheid.

HR 7308 is a F6 lb-11 star of 6th magnitude. Semi-regular photometric variations were detected by Breger (1969) , Percy et al. (1979) find that this star is a new small-amplitude Cepheid, and Burki and Mayor (1980) obtain a period of 1.49107 d. and detect a strongly variable amplitude.

The small-amplitude classical cepheid HR 7308 has the shortest period known in our Galaxy for a classical cepheid. 1966-1969 photoelectric observations together with more recent data show a period of 1d.49078 with sinusoidal light variations. Except for the presence of the beat period, no secondary period can be found in the extensive 1966 data. The lack of a secondary period near Pi/Po = 0.7 sets HR 7308 apart from many other short-period classical cepheids.

This paper contains a preliminary report on research aimed at extending the pulsational work integral to next highest order beyond the linear regime.

We begin by writing the integral in fully nonlinear form (Cox and Giuli 1968), normalized by the stellar luminosity L

Six Cepheids in the Large Magellanic Cloud have been discovered with periods less than one day. They lie at the faint, blue end of the instability strip as would be expected but form a separate Period-Luminosity relation from that for normal Cepheids. Membership in the LMC is based upon the existence of the P-L relationship. Several of the variables have uncertain periods although all apparently have periods under one day. One additional variable has tentatively been identified as a bright Anomalous Cepheid.

The distance moduli of galactic clusters containing classical Cepheids are being redetermined using the four-color and Hβ photometric system. The results for four clusters are presented here and it is found that the distance moduli are smaller than previous values. Possible reasons for this discrepancy are discussed.

A matter of great interest to variable star students concerns the mode of pulsation of Mira long period variables. In this report we first give observational evidence for the pulsation constant Q = P(M/R3)½ where P is the period and M and R are the mass and radius in solar units. We then compare the observations with calculations. Next, we review two interesting groups of papers dealing with hydrodynamic properties of long period variables. In the first, a fully dynamic nonlinear calculation maps out the Mira instability domain. In the second, special attention is paid to shock propagation beyond the photosphere which in large measure accounts for the complex spectra from this region. Finally, we review the paper by Wood-Zarro (1980) dealing with the pulsation constant Q.

Several theories seek to explain the peculiar shapes of planetary nebulae. Those of Louise, Kirkpatrick, and Phillips and Reay rely on progenitor rotation. The velocity-radius relation for the shells of well observed planetaries do not extrapolate back through the origin, but rather fall short, suggesting that the shell acquires its velocity over a significant period of time. Kirkpatrick’s theory relies heavily on long term acceleration of the nebular shell, and other theoretical studies support the idea of acceleration of the nebular shell up to the time it becomes optically thin to the ionizing radiation from the central star.

Spherical harmonics are an integral part of the study of stellar pulsations. To gain an understanding of how the star is affected by non-radial pulsations, the radial part of the oscillation is plotted, with an assumed sinusoidal time variation. The amplitude of the motion is arbitrarily set at 20% of the radius.

The RR Lyrae variables are currently believed to have masses between about 0.5 and 0.8 M⊙, effective surface temperatures between 6350 and 7500K, radii from about 4.0 to 6.0 R⊙ and luminosities between log L/L⊙ of 1.5 and 2.0. Since they are found in population II locations, they generally have Y = 0.3 and Z = 10−3 , but there are exceptions for both higher Z like the sun and lower Z like 0.0002. In globular clusters the periods range from 0.25 - 0.45 day for the first overtone pulsators and 0.40 - 0.80 day for those in the fundamental mode, depending on their luminosity. At transition lines, to be discussed in detail below, the switch from fundamental to first overtone, or maybe vice versa, involves a period change factor of about 0.74 - 0.75.

The evolution of an 0.6 M⊙ stellar model during core helium burning is presented. Following the off-center ignition of helium in the “core” flash, the star remains on the red giant branch for > 106 years, undergoing twelve additional flashes. After leaving the giant branch, the star evolves on the horizontal branch for 8.15×107 years before returning to the giant branch and undergoing strong helium-shell flashes. The implications for horizontal branch and RR Lyrae stars are discussed.

The role of convection in the core helium flash is simulated by two-dimensional eddies interacting with the thermonuclear runaway. These eddies are followed by the explicit solution of the 2D conservation laws with a 2D finite difference hydrodynamics code. Thus, no phenomenological theory of convection such as the local mixing length theory is required.