J. P. Cox

On Second Helium Ionization as a Cause of Pulsational Instability in Stars.

This investigation was to test the hypothesis that He+ ionization in the envelope is the source of the instability in cepheid variables and possibly also in other types of pulsating stars. Numerical solutions of the complete set of linearized, nonadiabatic pulsation equations were obtained for a large number of simplified stellar envelope models in radiative equilibrium. The solutions were used to compute the (negative) dissipation in the envelopes and to estimate the (positive) dissipation in the interiors. The parameter values were chosen so that the envelopes correspond approximately to classical cepheids, RR Lyrae variables, W Virginis variables, and zero-age mainsequence stars in the middle and late As. (auth)

The quasi-adiabatic analysis of nonradial modes of stellar oscillation in the presence of slow rotation

We have computed the vibrational stability of nonradial modes of oscillation in the quasi-adiabatic approximation for slowly, uniformly rotating stars, in the Cowling approximation. Only first-order effects are taken into account in the ratio of rotation angular frequency to oscillation angular frequency. We have applied the theory to iron white dwarf models and to zero-age main-sequence modesl. We find that slow rotation renders prograde traveling waves of nonradial oscillation (m<0) slightly more unstable than retrograde modes, essentially independently of the stability of the model in a given mode in the nonrotating state.

Adiabatic oscillations of accretion disks

We have used a variational principle to derive an integral expression for the frequencies of adiabatic oscillations of an accretion disk and have applied this expression to vertical oscillations. A number of examples show that this expression generally gives fairly good results with a simple trial function. In particular, the oscillatory periods of vertical oscillations in some of the low modes are found to be of the order of the corresponding Keplerian periods (or less, if self-gravity is taken into account), regardless of the detailed structure of the disk model. These times are of the order of those observed in the quasi-periodic oscillations of dwarf novae or in variable quasars. Physical arguments, based mostly on the virial theorem, make these results plausible. We have also obtained the differential equation for the vertical, adiabatic oscillations of an accretion disk. This equation embraces the equations derived by two other groups as special cases. Exact solutions are found in a number of cases. These solutions agree with results based on the variational principle.

Vibrational stability of differentially rotating stars

The formal solution, in linear, nonadiabatic theory, has been obtained of the problem of the vibrational stability of a system possesing arbitrary, but steady, inviscid flows in its unperturbed (nonoscillating) state. The unperturbed system may have any geometry, but no large-scale magnetic fields are assumed. A special case is a (steadily) rotating star, where the rotation may be uniform or differential, slow or fast. This formulation may ultimately provide a new approach to the problem of the interaction (in linear theory) between stellar convection and pulsations. The formal solution is expressed in terms of certain integrals over the volume of the system. These integrals involve the nonadiabatic eigenfunctions for the oscillating system, but they may be approximated by suitable trial functions. This solution is surprisingly simple, bears considerable resemblance to previously derived formal solutions, and has a straightforward physical interpretation. (AIP)

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.

Pulsation of high luminosity helium stars

A discussion of the long period R Coronae Borealis stars is presented. The constraints on theoretical models imposed by their age, kinematics and distribution led to difficulties in formulating an evolutionary sequence to the formation of this type of star. Several types of models are investigated and the results given.

Recent work on Cepheid variables

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.Recent observational results have led to increased values of the “pulsation mass,” so that this mass is now in fair agreement with evolution theory. The “Wesselink mass” is also satisfactory. Thus now only “bump” and “beat” masses are possibly discrepant. Some possible ways which have been suggested to alleviate these discrepancies are reviewed. The proposal of helium enrichment in the outer stellar layers can apparently satisfactorily resolve the beat (and perhaps also the bump) mass anomaly. A recent suggestion that part of the pressure in the envelope is due to a tangled magnetic field (not unusually strong) resolves the above mass anomaly about as well as the helium-enrichment idea does.Recent results regarding duplicity and period changes in Cepheids are reviewed.

Linear, nonadiabatic pulsation calculations for models of upper main sequence and β cephei stars

Equations for linear nonadiabatic pulsation and the method of their solution are discussed in some detail. The numerical results presented concern mainly 7 Mδ stellar models in early evolutionary phase. A driving zone at a temperature of 1.5 x 105 K was found to be present for both radial and nonradial modes, but no net pulsational instability was observed. Effects of rotation on pulsation frequencies and on stability are also discussed.

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.

Recent Work on Cepheid Variables

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.