Australia Telescope National Facility

Variable Red Giants in the LMC: Pulsating Stars and Binaries?
P.R. Wood, PASA, 17 (1), 18.

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Interpreting the non-pulsation sequences

Adiabatic pulsation theory tells us that there is no mode of radial pulsation with a period longer that that of the fundamental mode. In Fig. 1, it can be seen that the stars on sequence D have periods approximately 3-4 times longer than those of sequence C. Clearly, if it is accepted that sequence C corresponds to the fundamental radial pulsation mode, then the variability on sequence D can not be attributed to radial pulsation.

Some examples of light curves of stars on sequence D are given in Wood et al. (1999). The oscillation period that fits sequence D is always a long secondary period (LSP), where the primary period usually falls on sequence B. The LSP amplitudes can be large, up to a factor of 2 in light output in the two MACHO bandpasses. The large amplitudes suggest that an explanation in terms of non-radial pulsation is unlikely (g modes could, in principle, have periods of the observed length). Similarly, although episodic dust formation of the type found by Winters et al. (1994) and Höfner et al. (1995) could cause the variability observed on sequence D, most of the stars on this sequence are of relatively low luminosity and are not expected to have the high mass loss rates and dust-laden winds required for this process to occur. A third possible cause of the LSPs is rotation of red giants with a giant star spot. Once again, it seems difficult to image a spot sufficiently large to cause light variation by a factor of 2, and it is not clear why the rotation period should be such as to cause the observed period-luminosity law.

At this stage, there are two seemingly plausible explanations for the LSPs on sequence D: binarity and strange pulsation modes. In the binary scenario, Wood et al. (1999) have shown that an orbiting companion at about two stellar radii from the red giant will have a period very similar to that observed in these stars. In order to produce the observed variability, the orbiting companion would need to carry along with it a large, loosely-bound, comet-like cloud which would partially obscure the red giant once per orbital period. The observational test of this scenario is to look for orbital radial velocity variations of the stars with LSPs. This is currently being done with 2dF on the AAT and it is estimated that companions with masses down to a few tenths of a solar mass should be detectable with these data. The results of this search for orbital velocity variations should be known by the end of this (second) millennium!

The second plausible mechanism for the production of the LSPs is stellar oscillation caused by a newly-discovered interaction of convection and pulsation. A study of the linear, non-adiabatic pulsation of red giants has shown the existence of a family of modes with just the periods observed on sequence D (Wood 1999). An investigation of the origin of these modes showed that they are a completely new type of oscillatory thermal mode caused by convection-pulsation interaction. The position of the eigenvalues $\omega$ of these convection-induced oscillatory thermal (COT) modes in the complex plane is shown in Fig. 2, where a time dependence $\exp \omega t$ has been assumed. Clearly, the frequencies of the COT modes (given by the imaginary part of $\omega$ ) are similar to those required to explain the LSPs. However, the extremely large damping of the modes (given by the real part of $\omega$ ) means that the COT modes found in these models will never be seen.

The treatment of convection-pulsation interaction used in the current models is very simplistic (it is based on mixing-length theory). It is not inconceivable that a proper treatment of convection-pulsation interaction could lead to unstable modes that could explain the LSPs. Why such modes should be seen in only 25% of AGB stars would then need to be answered. (Note: 25% is the percentage of LMC AGB variables that show LSPs; the LSPs also occur in local semi-regular variables (Houck 1963) but the percentage of local semi-regulars that show LSPs is not known because extended and high quality light curves are needed to find LSPs).

**Figure 2:** Eigenvalues in the complex $\omega$ plane for an AGB star with the parameters given on the figure. The linear, non-adiabatic, normal modes of pulsation for the fundamental ( $\omega _{0}$ ) and first overtone ( $\omega _{1}$ ) lie near the vertical axis. The eigenvalues of the first five COT modes are shown as starred symbols, starting near $\omega$ = (-0.6,0.3). All eigenvalues are normalized to the frequency
$\sqrt (GM/R^{3})$ .
$\begin{figure} \begin{center} \centerline{\psfig{file=fig2.pasa99.ps,width=7.5cm}}\end{center}\end{figure}$

The final sequence of stars in Fig. 1 is sequence E. The stars on this sequence belong to the first giant branch (FGB) rather than the AGB. They can be picked out from a sample of LPVs by the regularity of their light curves, which are also of small amplitude (mostly less than a few tenths of a magnitude). Some examples are shown in Wood et al. (1999). A clue to the cause of the variability of these objects is provided by the fact that a few of them have light curves very similar to those of close eclipsing binaries or contact binaries. In addition, the periods are consistent with the orbital periods expected for contact binaries at the tip of the FGB. Once again, the 2dF observations of radial velocity variations should be able to confirm or refute this explanation for the origin of the variability of stars on sequence E.

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Contents Page: Volume 17, Number 1

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