The Size, Structure, and Variability of Late-Type Stars Measured ...

77
Chapter 4
Time Variability in o Cet
The regularity observed in the periods of Miras’ light curves implies that there
must be a resonant feedback mechanism responsible for generating the pulsation in Mira
variables. The current view holds that a temporary increase in density and temperature in
the stellar core triggers an increase in the energy generation and a resulting pressure which
drives an expansion travelling outward to the surface of the star and then collapsing back on
itself due to gravity. This contraction, when it reaches the core, increases the temperature
and density thereby triggering another cycle.
A fundamental mode resonance will be established having a period equal to the
transit time for the acoustic wave to travel to the surface, be mostly reflected, and return
to the core. The star becomes a resonant cavity holding a density standing wave. For
fundamental mode pulsation, each layer will be radially displaced in the same direction
except for the node at the center of the star which is stationary. Higher radial modes will
have one or more additional nodes (layers which remain stationary) at radii other than the
center (Schwarzschild, 1941 [92]). Non-radial modes may also be present provided that the
resonance condition is satisfied. The first overtone mode, for instance, will have a node
at the center and an additional node at some radius so that the core of the star will be
contracting at the same time that the envelope is expanding. The period of the first overtone
mode will be shorter than the period of the fundamental mode because the density wave
travels a smaller distance in one cycle. Worded another way, a star with a given period
must have a larger radius if it is oscillating in an overtone mode.