Theory of Amplitude Modulation II. The Resonant Mode Interaction Model

With about one fourth of the RRab stars showing the Blazhko effect, amplitude modulation on long time scales is a common phenomenon in stellar pulsation. The role of nonradial oscillation modes is studied here, and it is proposed that the amplitude modulation is a result of a dynamical, nonlinear resonance between the observed radial mode and a low-degree nonradial mode. In this scenario, a nonradial mode is resonantly excited in Blazhko-type RR Lyrae stars. Degree one modes are found to have the highest probability of being excited and a crucial test of the model would be the observational determination of the degree of the proposed nonradial mode.

AH Cam: An RR Lyr (Double Mode?) Star with Blazhko Effect

We report here the discovery of a new frequency not belonging to the Blazhko series and suggest an interpretation based on coupling between a radial and a nonradial mode from multicolor observations.

Nonradial Modes in the Galactic Bulge RR Lyrae Stars

OGLE-1 photometry of RR Lyrae stars has been analyzed in search of multiperiodic pulsations. A second periodicity corresponding to a nonradial mode has been found in 11 RRab and 2 RRc variables.

Nonradial Modes in RR Lyrae Stars

We surveyed nonradial mode properties in evolutionary sequences of RR Lyrae star models, focusing attention on modes that may be driven by the opacity mechanism and on those that may be excited as a consequence of the 1:1 resonance with the radial pulsation. Our survey shows that all RR Lyrae star models share all qualitative properties of the nonradial modes. There is always a large number of unstable low degree modes with frequencies close to unstable radial modes. However, owing to higher mode inertia, for most of nonradial modes the driving rates are much lower than those for radial modes. The exceptions are the strongly trapped (STU) modes which begin with ℓ degrees 7 to 10 (depending on the model) at frequencies somewhat above the fundamental radial mode, and with ℓ = 5 or 6 at frequencies somewhat above the radial mode overtones. We argued that these modes are not likely candidates for identification of oscillations recently detected in some RR Lyrae stars. More likely candidates seem, in spite of their lower driving rates, the ℓ = 1 modes.We found also that parameters which determine the chances of the excitation of nonradial modes through the 1:1 resonance do not vary much over the range of RR Lyrae star parameters. According to our estimate the excitation has a high probability. In fact, some nonradial modes should be excited in the majority of the RRab pulsators and in a significant fraction of (~ 30%) of RRc pulsators. The actual number is likely greater because we ignored the effect of rotation, which increases the probability of resonant excitation. The instability may lead to a periodic light curve modulation, that is to the Blazkho effect, if the nonlinear interaction results in a periodic energy exchange between the radial and the nonradial modes. A light curve modulation may also take place in the case of a constant amplitude limit cycle if the nonradial mode is of low degree and it is not symmetric about the rotation axis.See Dziembowski & Cassisi (1999) for the full paper.

Velocity Variations of the roAp Star γ Equulei: Probing a puzzling pulsator

We present a pulsational RV curve for γ Equ whose amplitude is about 200 m/s and period is roughly 11 minutes. These data, combined with rapid photometry and line-profile variations, are being used to identify the nonradial mode(s) and study mode growth/decay in this unusual star.

The Periods of RR Lyrae

RR Lyrae (0.566 day period) exhibits the Blasko effect that suggests another natural mode with almost the same period as the accepted fundamental radial mode. This mode might be nonradial, but no one has done an extensive evaluation of this idea. An investigation requires a model that includes the deep composition structure where g-modes of low angular (observable) degree have weight and amplitude. An RR Lyrae model including the outer half of the mass and more than 99% of the radius, based on an asymptotic giant branch model from Hollowell (private communication), see below, was used for this study. It includes composition gradient ramps between the primordial surface hydrogen and helium and the almost pure helium shell and the one between this helium shell and the convective core that is burning helium.Nonradial mode periods almost resonant with the radial fundamental mode period seem to occur for all low ℓ values. In addition to significant pulsation amplitudes in the composition gradient regions where the Brunt Väisälä frequency is large, these low degree and low radial order modes have near-surface amplitudes very similar to the low order radial modes. These modes are evanescent in the convective core. Classical K and γ effects give enough driving in the very low mass surface layers, so that important deep radiative damping for these modes does not completely stabilize nonradial g-mode pulsations. The g4, ℓ=1 mode gives a. double-mode RR Lyrae with Blasko effect.A nonradial mode may not always be visible, depending on how rotation presents the nonspherical pulsations to the observer. Thus the Blasko effect might come and go, as observed for maybe 20% of all RR Lyrae variables. For many, the Blasko effect may not be observable, even when a nonradial mode is there.

28 And: Simultaneous Strömgren Photometry

We have carried out simultaneous uvby photometry of the low amplitude δ Set star 28 And. Analysis of the data, using the Fourier Transform method, establishes 28 And as a monoperiodic pulsator. Using the classical O-C method, it is found that the pulsation of this star can be well described by means of a linear ephemeris with a period of P=0.d069304118 over the last twenty-four years. Amplitude variations are also shown to be present from season to season. The physical parameters of this star are determined and the nature of radial or nonradial pulsation is discussed on the basis on the derived phase shifts and amplitude ratios between Strömgren colours. The results indicate that 28 And pulsates in a nonradial mode with ℓ = 2.

Radial and Nonradial Mode Instability in B-Type Stars

Recently three independent groups(Cox et al. 1992; Kiriakidis et al. 1992; Moskalik and Dziembowski, 1992), using opacity tables published by Iglesias and Rogers (1991), demonstrated that β Cep star models are pulsationally unstable. The instability is driven by the classical к- mechanism acting in the layer with temperatures near 2 × 105K where there is a bump in metal opacity. The groups reported results of calculations made for rather narrow ranges of stellar parameters and oscillation modes. We conducted an extensive search for unstable modes in complete evolutionary models of B-type stars of luminosity classes III - V. Our aim was to determine the domain of instability and examine its role not only in β Cep stars but also in variable stars located in the nearby areas of the H-R diagram.An unexpected new aspect of our calculations is the use of the improved opacity data. In a very recent work Iglesias, Rogers and Wilson (1992) showed that effects of spin-orbit interactions significantly enhance opacity in the critical region for driving the pulsations in β Cep stars. These effects and improved information about the solar metal mixture have been included in the updated opacity tables kindly provided to us via electronic mail by Dr. Rogers. The consequences of this change in opacity for stability of B-type star models are indeed quite important. Contrary to previously announced results, that only the fundamental mode is unstable, we now find the first two radial overtones to be unstable, as well. Thus, the discrepancy between the theoretical prediction and the mode identification suggested by observers has been removed. Furthermore, no longer is a high metal abundance (Z > 0.03) required to explain the occurrence of pulsation in most of the objects. In fact, the theoretical instability domain in the H-R diagram, based on the models calculated with Z = 0.02, agrees better with the observational β Cep domain than that based on the models Z = 0.03.