the evolution of low-mass stars
Stars of mass less than 1.1
M fuse hydrogen
As this has a comparatively weak temperature
dependence, energy generation is not sufficiently concentrated at
the centre of the star to induce
convection, and the core of
the star is
radiative. This means that the
core of the star is not mixed and nuclear reactions can therefore
draw only on the
fuel that is available locally. The temperature is highest at the
centre and so the rate of burning is highest there, forming a
concentration gradient with smallest hydrogen content in the centre
of the star. Eventually, the centre of the star becomes completely
devoid of hydrogen. Immediately outside the centre,
however, the temperature is only a little lower and there is still
hydrogen left to burn. Nuclear reactions therefore continue, but now
in a thick shell rather than throughout a sphere, as shown
in figure 14.
The structure of a low-mass star
on the sub-giant and red-giant branches of the HR diagram.
The continuation of nuclear burning in a shell means that there
is no need for the whole star to contract. Only in the central
regions, where there is no longer any energy production but energy
is still leaking outwards in
to the rest of the star, is there a
need for an additional energy source. The core thus begins to contract,
releasing gravitational potential energy
and therefore getting hotter. Because the core gets hotter, the
temperature of the hydrogen-fusing shell outside the core also
increases, increasing the rate of fusion. This heats up the
intermediate layers of the star, causing them to expand. The
expansion increases the total radius of the star. Recalling
Ls = 4rs2
and given that the luminosity a radiative envelope can carry
is nearly constant for a star of given mass,
there must be a decrease in the effective temperature of the star,
causing the star to appear red. The immediate post-main-sequence
evolution of a radiative star therefore
moves the star's position more-or-less horizontally to the right
in to the sub-giant branch of the
HR diagram, as shown
in figure 15.
The complete evolution of a low-mass star
from the main sequence to a white dwarf, depicted
schematically on an HR diagram.
As the star expands, however, the effective temperature cannot continue
to fall indefinitely. When the temperature of the outer layers of the
star fall below a certain level, they become fully convective. This
enables a greater luminosity to be carried by the outer layers and hence
abruptly forces the evolutionary tracks of low-mass stars in the HR
diagram to travel almost vertically upwards to the giant
branch (see figure 15).
The effective temperature at which this
upward excursion in luminosity on the HR diagram occurs is known as
the Hayashi line.
Meanwhile, the helium core continues to contract until
it becomes degenerate.
The increased gravity at the border of the core and the
shell which results from the core contraction raises the
density of the hydrogen in the shell. This increases
the rate of hydrogen burning in the shell, sending the star
quickly up the red giant branch.
The hotter hydrogen-burning shell heats up the degenerate core
until it reaches the point where helium fusion to carbon through the
is possible. The onset of this fusion process
and the consequent heating of the core would normally increase the
core pressure, causing it to expand and cool in response, keeping the
temperature just high enough for the nuclear reactions to continue;
helium burning would therefore start in a stable fashion.
Because the core is degenerate, however,
its pressure is independent of the temperature and hence it cannot
expand and cool in response to the nuclear energy generation.
Hence the core heats up, which increases
the rate of helium fusion, which in turn increases the core
temperature still further,
leading to a thermonuclear runaway reaction
know as the helium flash (see
The helium flash ends
when the temperature has risen sufficiently to make
higher-energy electron states available for electrons to move into,
lifting the core degeneracy and allowing the core to expand.
The expansion of the core following the helium flash reduces the
gravity at the core/shell boundary, which weakens the
hydrogen shell-source. Thus, although the star now has two
nuclear energy sources - the helium burning core and the
hydrogen-burning shell - the
prodigious shell source is now so
weakened that the star produces less luminosity than before.
The lower total luminosity is too little to keep the star in its
distended red-giant state and the star shrinks in size, dims and
settles on the horizontal branch (see figure
The structure of a low-mass star
on the asymptotic giant branch of the HR diagram.
The history of the helium burning stage is much like the earlier
hydrogen burning stage. When the core helium is exhausted, a helium
burning shell is established between the inert carbon-oxygen core and
the hydrogen-burning shell (see
and the star evolves up the
asymptotic giant branch, as shown in
This stage of stellar evolution is not well understood,
involving complex interactions between the helium
and hydrogen burning shells.
The star becomes increasingly unstable and begins to lose mass in an
intense stellar wind, which eventually consumes the whole outer
envelope. This lost mass forms an expanding cloud around the star
known as a planetary nebula, an example of which is shown
in figure 17.
The Helix nebula (©Anglo-Australian Observatory).
The extremely hot, degenerate, carbon-oxygen
core of the original star, no longer generating energy, remains
as the central star of the planetary nebula and cools slowly as it
radiates away its stored heat. When the core has finally burnt its
hydrogen and helium shells, lost its extended envelope and descended
the HR diagram, it is known as a
white dwarf. The final approach to a white dwarf
from an asymptotic giant star is shown as a dashed line in
because the theory is incomplete for these late stages of stellar
summarises the complete evolution of a low-mass star
1.1 M) from
the main sequence to a carbon-oxygen white dwarf in pictorial
Pictorial representation of the complete life-cycle of a solar-mass
©Vik Dhillon, 27th September 2010