Fundamental Astronomy

Fig. 11.4a–c. Energy transport in the main sequence phase.
(a) The least massive stars (M < 0.26 M⊙) are convective
throughout. (b) For0.26 M⊙ < M < 1.5 M⊙ the core
is radiative and the envelope convective. (c) Massive stars
(M > 1.5 M⊙) have a convective core and a radiative
envelope
that their entire hydrogen content is available as fuel.
These stars evolve very slowly toward the upper left
in the HR diagram. Finally, when all their hydrogen
has burned to helium, they contract to become white
dwarfs.
11.4 The Giant Phase
The main-sequence phase of stellar evolution ends when
hydrogen is exhausted at the centre. The star then settles
in a state in which hydrogen is burning in a shell
surrounding a helium core. As we have seen, the transition
takes place gradually in lower main-sequence stars,
giving rise to the Subgiant Branch in the HR diagram,
while the upper main-sequence stars make a rapid jump
at this point.
The mass of the helium core is increased by the hydrogen
burning in the shell. This leads to the expansion
of the envelope of the star, which moves almost horizontally
to the right in the HR diagram. As the convective
envelope becomes more extensive, the star approaches
the Hayashi track. Since it cannot pass further to the
right, and since its radius continues to grow, the star has
to move upwards along the Hayashi track towards larger
luminosities (Fig. 11.3). The star has become a red giant.
In low-mass stars (M ≤ 2.3 M⊙), as the mass of the
core grows, its density will eventually become so high
that it becomes degenerate. The central temperature will
continue to rise. The whole helium core will have a uniform
temperature because of the high conductivity of
the degenerate gas. If the mass of the star is larger than
0.26 M⊙ the central temperature will eventually reach
11.4 The Giant Phase
about 100 million degrees, which is enough for helium
to burn to carbon in the triple alpha process.
Helium burning will set in simultaneously in the
whole central region and will suddenly raise its temperature.
Unlike a normal gas, the degenerate core
cannot expand, although the temperature increases
(c. f. (10.16)), and therefore the increase in temperature
will only lead to a further acceleration of the rate of
the nuclear reactions. When the temperature increases
further, the degeneracy of the gas is removed and the
core will begin to expand violently. Only a few seconds
after the ignition of helium, there is an explosion, the
helium flash.
The energy from the helium flash is absorbed by the
outer layers, and thus it does not lead to the complete
disruption of the star. In fact the luminosity of the star
drops in the flash, because when the centre expands,
the outer layers contract. The energy released in the
flash is turned into potential energy of the expanded
core. Thus after the helium flash, the star settles into
a new state, where helium is steadily burning to carbon
in a nondegenerate core.
After the helium flash the star finds itself on the
horizontal giant branch in the HR diagram. The exact
position of a star on the horizontal branch after the helium
flash is a sensitive function of its envelope mass.
This in turn depends on the amount of mass lost by the
star in the helium flash, which can vary randomly from
star to star. While the luminosity does not vary much
along the horizontal branch, the effective temperatures
are higher for stars with less mass in the envelope. The
horizontal branch is divided into a blue and a red part
by a gap corresponding to the pulsational instability
leading to RR Lyrae variables (see Section 13.2). The
form of the horizontal branch for a collection of stars
depends on their metal-abundance, in the sense that
a lower metal abundance is related to a more prominent
blue horizontal branch. Thus the blue horizontal
branch in globular clusters with low metal-abundances
is strong and prominent (Section 16.3). For stars with
solar element abundances the horizontal branch is reduced
to a short stump, the red clump, where it joins the
red giant branch.
In intermediate-mass stars (2.3 M⊙ ≤ M ≤ 8 M⊙),
the central temperature is higher and the central density
lower, and the core will therefore not be degenerate.
Thus helium burning can set in non-catastrophically as
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