Stars as Laboratories for Fundamental Physics - MPP Theory Group

32 Chapter 2
shell-burning phase the luminosity is determined almost entirely by the
core mass. On the MS it was determined by the total mass, a parameter
which now hardly matters.
The red-giant branch (RGB) ascension is a fast process compared
with the main-sequence (MS) evolution (Fig. 2.6). Therefore, the red
giants in the observational color-magnitude diagram of Fig. 2.3 differ
only by very small amounts of their initial mass. The stars beyond
the MS have nearly identical properties while those on the MS differ
by their total mass. Therefore, the evolved stars in Fig. 2.3 essentially
trace out the evolutionary path of a single star with an approximate
mass corresponding to the MS turnoff (TO). For example, the stars on
the RGB in Fig. 2.3 essentially constitute snapshots of the single-star
evolutionary track shown in the upper panel of Fig. 2.6.
A red giant is a star with a compact energy source at the center and
a large convective envelope. In the present case we have a degenerate
helium core with shell hydrogen burning, but other configurations are
possible. The core is a star unto itself with near to negligible feedback
from the envelope. The envelope, on the other side, is strongly
influenced by the nontrivial central boundary conditions provided by
the core. Convective configurations with a fixed mass and a prescribed
luminosity from a central point source occupy the “Hayashi line” in
the Hertzsprung-Russell diagram. A low-mass red giant ascends the
Hayashi line corresponding to its envelope mass.
The inflation of a star to red-giant dimensions is a remarkable phenomenon
which defies an intuitive explanation, except that the stellar
structure equations allow for such solutions. Another conceivable structure
is a much smaller envelope with radiative rather than convective
energy transfer—upper MS stars are of that nature. Prescribing a core
with a given luminosity one can imagine these two extreme configurations.
Indeed, bright stars (L > ∼ 10 2 L ⊙ ) are usually found either near
the MS or near the RGB which together form a V-shaped pattern in
the Hertzsprung-Russell diagram (Fig. 2.9). The empty space in the
V is known as the “Hertzsprung gap”—the few stars found there are
thought to be on the move from one arm of the V to the other, i.e.
from a radiative to a convective envelope structure. Massive stars after
completing hydrogen burning move almost horizontally across the
Hertzsprung gap and inflate to red-giant dimensions. Remarkably, they
can deflate and move horizontally back, executing a “blue loop.”