Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 33
2.1.3 Helium Ignition
The core of a red giant reaches its limiting mass when it has become
so hot and dense that helium ignites. Because the nucleus 8 Be which
consist of two α particles (He nuclei) is not stable, He burning proceeds
directly to carbon, 3α → 12 C (“triple-α reaction”), via an intermediate
8 Be state. Because it is essentially a three-body reaction its rate depends
sensitively on ρ and T . In a red-giant core helium ignites when
M c ≈ 0.5 M ⊙ with central conditions of ρ ≈ 10 6 g cm −3 and T ≈ 10 8 K
where the triple-α energy generation rate per unit mass, ϵ 3α , varies approximately
as ρ 2 T 40 . This steep temperature dependence allows one
to speak of a sharp ignition point even though there is some helium
burning at any temperature and density.
The helium core of a red giant is like a powder keg waiting for a
spark. When the critical temperature is reached where ϵ 3α exceeds
the neutrino losses a nuclear runaway occurs. Because the pressure
is mainly due to degenerate electrons the energy production at first
does not lead to structural changes. Therefore, the rise in temperature
is unchecked and feeds positively on the energy generation rate. As
this process continues the core expands nearly explosively to a point
where it becomes nondegenerate and the familiar self-regulation by the
gravitational negative specific heat kicks in (Chapter 1). The “explosion
energy” is absorbed by the work necessary to expand the core from
about 10 6 g cm −3 to about 10 4 g cm −3 . The core temperature of the final
configuration remains at about 10 8 K because of the steep temperature
dependence of ϵ 3α which allows only for a narrow range of stationary
burning conditions.
The final configuration with a helium-burning core and a hydrogenburning
shell (Fig. 2.5) is known as a horizontal-branch (HB) star, a
term which is justified by the location of these objects in the colormagnitude
diagram Fig. 2.3. Note that the overall luminosity has decreased
by the process of helium ignition (Fig. 2.6) because of the core
expansion which lowers the gravitational potential at the core edge and
thus the temperature in the hydrogen-burning shell which continues to
be regulated by the core mass and radius. The total luminosity of an
HB star is given to about 1/3 by He burning and 2/3 by hydrogen shell
burning (Fig. 2.4, right panels).
Because helium ignition is an almost explosive process on dynamical
time scales it is known as the “helium flash.” For the same reason, a
realistic numerical treatment does not seem to exist (for a review, see
Iben and Renzini 1984). There are two main problems. First, normal