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Pulsations

Most RCB stars are small-amplitude variables at maximum light. Light variations are typically a few tenths of a magnitude with periods between 40 and 100 days. In well-studied cases, radial-velocity variations have been found with amplitudes proportional to the light variations. The visual light curve of RYSgr (period $\sim38$ days, amplitude 0.2-0.3 mag.) correlates well with the radial velocity curve (amplitude $40\,{\rm km\,s^{-1}}$) and indicates that RCBs are radially pulsating stars ([Alexander et al. 1972]).

The light curves of RCB stars are not strictly periodic. Some authors suggest that this is due to interference between a number of radial modes with different periods ([Marraco & Milesi 1982], [Kilkenny 1982], [Lawson & Cottrell 1988], 1990). Since pulsation periods are directly related to the mean density of a star, evidence for period changes were thought to imply secular changes in RCB radii ([Kilkenny 1982]). More recent work suggests that the changes in period are random ([Lombard & Koen 1993]). The author believes that this is likely because the extreme non-adiabacity in the stellar envelope can lead to chaotic behaviour in the pulsation cycle length (cf. [Jeffery 2000]). More detailed models are needed to test this (cf. [Saio & Wheeler 1985]).

The driving mechanism for pulsations in RCB stars is not the classical $\kappa$ mechanism found in CEPHEID VARIABLES; RCB stars do not lie in any of the classical instability strips. Their pulsations are due to `strange-mode' oscillations ([Saio et al. 1984]). Such pulsation modes are also seen in other high luminosity stars, such as luminous blue variables and $\alpha$Cyg variables. Their properties are summarized in the accompanying article on extreme helium stars ([Jeffery 2000]).

A consequence of the high $L/M$ ratios of RCB stars is that densities in their atmospheres are low. The action of the pulsations on the photosphere resembles that of a piston imparting an outward impulse at regular intervals. In between these impulses the photosphere is virtually in free-fall. During the impulse, highly non-linear processes can generate shock waves within the photosphere. Evidence for such non-linearity has been observed in RYSgr where, at minimum radius, absorption lines are seen to double. A red-shifted component is due to infalling material and a blue-shifted component is due to lower-lying plasma that has already being accelerated outwards ([Danziger 1963], [Lawson et al. 1991]). Strong shock waves are expected from theoretical models of pulsations in RCB stars ([Saio & Wheeler 1985]).