Stars as Laboratories for Fundamental Physics - MPP Theory Group

40 Chapter 2
detailed structure of the star.
When these oscillations are damped, stars are found in their equilibrium
configurations with constant color and brightness. However, it
is possible that a small deviation from equilibrium is amplified, leading
to a growing oscillation amplitude. Throughout a star there can be regions
which try to excite oscillations, and others which damp them. If
the driving mechanism is strong enough the star is found in a continuing
oscillation which manifests itself in an oscillating lightcurve.
Of particular interest are the Cepheid-type variables. Their oscillations
are excited by the “κ mechanism” where the driving force is the
heat valve provided by the opacity of the stellar matter near the surface.
There, hydrogen and helium are only partially ionized so that a
temperature increase leads to increased ionization which increases the
opacity because the Thomson cross section on free electrons is much
larger than the Rayleigh one on neutral atoms. Therefore, the temperature
increase caused by compression makes it more difficult for energy
to escape: the valve shuts. In most regions of the star the opposite happens.
Increased temperature makes it easier for energy to leak out from
the compressed region, the valve opens, and oscillations are damped.
Because the operation of the κ mechanism is determined by conditions
near the stellar surface which is characterized by its temperature
and luminosity, Cepheid-type variables are found on a certain locus of
color and brightness. This “instability strip” extends throughout the
Hertzsprung-Russell diagram (hatched band in Fig. 2.9); it applies to
stars of radically different internal structure. Variable stars are found
wherever the instability strip overlaps with an actual stellar population.
At the bright end of the strip which is close and nearly parallel to the
red-giant Hayashi line one finds the classical Cepheids (δ Cepheids) with
luminosities 300−30,000 L ⊙ and periods 1−50 days. The brightness
variation can be up to 1 mag (visual), or a luminosity which changes
by up to a factor of 3. Classical Cepheids are massive stars which cross
the otherwise unpopulated Hertzsprung gap from the main-sequence
to the red-giant region, and red giants and supergiants which execute
blue loops and so temporarily move to the blue of the Hayashi line.
The linear relationship between period and brightness of Cepheids as
well as their large intrinsic luminosities are the key for their prominent
role as standard candles and thus as astronomical distance indicators.
The crossing of the instability strip with the HB is the domain of
the RR Lyrae stars. Their luminosities are around 50−100 L ⊙ , their
periods 1.5−24 h. Their color coincides with the MS turnoff in globular
clusters (Fig. 2.3). RR Lyrae stars play an important role in the ongoing