Convection in Astrophysics, Session E, Invited Talk 1 (Wed, Aug. 23)
P.R. Wood: The Relation of Convection to Pulsation and Mass Loss in Red Giants
Concerning pulsations in red giants, the good news is that there have been one or two attempts of global modelling of convection in red giants. One is Woodward et al., where the star pulsates and shows a dipolar structure. The other is Freytag et al. (1999).
The bad news is that studies of pulsation in red giants use convection theories that belong in the past. They use spherically symmetric models and mixing length theory.
This introduction was followed by a discussion of the relation of convection and pulsational stability. In the red giant envelope, almost 100% of the energy flux is transported by convection. The driving of pulsation depends on the energy transport into and out of mass zones, hence it depends on convection. It follows that one has to know how convection varies throughout the pulsational cycle. The work integral shows that most work is done in the convective region.
The linear pulsation models by Xiong et al. (1998) show that turbulent pressure and turbulent viscosity introduce damping.
Pulsation in the presence of turbulent convection: Turbulent eddies transport momentum in a medium with a pulsation velocity gradient. This gives rise to turbulent viscosity.Wood mentioned that this can be seen as the macroscopic analogy of molecular viscosity, but in the discussion after the talk, Stein noted that turbulent viscosity is very different from molecular viscosity.
Nonlinear pulsation models show that work dissipated by turbulent viscosity is the major damping factor. How good are these models? Not very good. In general, pulsation models (linear and nonlinear) with current convective treatments are too unstable. Nonlinear models give large luminosity spikes that are not observed - the convection is too efficient (Olivier & Wood 2005).
On the observational side, microlensing surveys have given enough data that one can begin to do asteroseismology on red giants (MACHO, OGLE). Sample MACHO light curves were shown. They are often semiregular, multimode, and show a large amplitude range.
Next, the period-luminosity diagram (Wood et al. 1999) was discussed. Can one see different modes of oscillation? The periods and period ratios fit only approximately, which indicates that the envelope structure is inadequate. What is the cause of closely-spaced periods? Are they stochastic excitation by convection, or structural changes resulting from convective irregularities, or nonradial modes?
The closely-spaced periods were also discussed using O-C diagrams for red giants (O ... date of observed maximum, C ... predicted date). A straight line in these diagrams means that the period is constant. It was shown that red giant periods vary abruptly by a few percent.
Another way to look at closely-spaced periods are the so-called Peterson diagrams, which show period ratios vs. log(period). In these diagrams, the models do not fit well the observed ratios.
Period-luminosity relations by Lebzelter and Wood (2005) were also discussed. The importance of mass loss was stressed. But - what causes the mass loss?
For an ideal study of pulsations in red giants, one needs to follow the pulsation for 50 to 100 years.
As a final curiosity, red giants with long secondary periods were mentioned. The light amplitudes are up to 0.8 mag, the velocity amplitudes only a few km/s. Are they associated with the chromosphere?