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D. K. Galloway and L. Keek
5.2.1 Thin-Shell Instability and Electron Degeneracy
The typical response of a star to heating is expansion, which reduces the pressure
and thereby the temperature. For runaway nuclear burning to occur, this cooling
mechanism must be circumvented, via a combination of the thin-shell instability and
electron degeneracy. Some past reviews highlight the latter [115], whereas others
present the former [171]. Here we review the two mechanisms.
X-ray bursts are an example of nuclear burning that happens in a thin shell [162,
205]. If the radial extent of the burning layer is small with respect to the stellar
radius, expansion of the thin shell does not result in a sufficient change in pressure to
reduce the temperature. This allows for the temperature to continue to increase, and
is known as the thin-shell instability. For X-ray bursts and superbursts the ignition
layer has a depth of a few meters up to ∼100 m, which is very thin compared to the
≈10 km neutron star radius. Therefore, the thin-shell instability allows for a growing
temperature increase due to burning, which leads to the ignition of bursts.
Electron degeneracy, identified as the primary mechanism for the ignition of
novae on white dwarfs [57], also plays a role in bursts on neutron stars. In degenerate
material, the pressure is independent of the temperature, such that a reduction in
pressure does not counter a temperature increase. On neutron stars, however, the
electrons are only mildly degenerate near y 10 8 g cm −2 : the ratio of the electron
Fermi energy and thermal energy prior to a burst is η 3. A small amount of
heating at the burst onset lifts the degeneracy, but the runaway continues.
A simple numerical experiment elucidates the relative importance of the two
mechanisms. Employ a one-zone model to simulate the burning behaviour with
and without a pressure term for degenerate electrons. 4 When ignoring the pressure
term from electron degeneracy, bursts are still produced. Of course, electrons do
contribute to the pressure, and ignoring that term leads to a slightly larger ignition
depth. Therefore, the primary mechanism for the thermal instability of bursts is
the thin-shell instability, while the electron degeneracy is important for obtaining
accurate ignition conditions.
Intermediate duration bursts and superbursts ignite deeper in the envelope
(Table 5.2), where the electron degeneracy is larger, up to η 10 2 . Nevertheless,
their fuel layer is a thin shell, which implies that long duration bursts would also
occur without the degeneracy effect.
5.2.2 Reignition After a Short Recurrence Time
In the classical picture, a burst burns nearly all hydrogen and helium in the neutron
star envelope, and a completely new fuel layer must be accreted before the next burst
4 For example, the one-zone helium ignition model available at https://github.com/
andrewcumming/onezone.
D. K. Galloway and L. Keek
5.2.1 Thin-Shell Instability and Electron Degeneracy
The typical response of a star to heating is expansion, which reduces the pressure
and thereby the temperature. For runaway nuclear burning to occur, this cooling
mechanism must be circumvented, via a combination of the thin-shell instability and
electron degeneracy. Some past reviews highlight the latter [115], whereas others
present the former [171]. Here we review the two mechanisms.
X-ray bursts are an example of nuclear burning that happens in a thin shell [162,
205]. If the radial extent of the burning layer is small with respect to the stellar
radius, expansion of the thin shell does not result in a sufficient change in pressure to
reduce the temperature. This allows for the temperature to continue to increase, and
is known as the thin-shell instability. For X-ray bursts and superbursts the ignition
layer has a depth of a few meters up to ∼100 m, which is very thin compared to the
≈10 km neutron star radius. Therefore, the thin-shell instability allows for a growing
temperature increase due to burning, which leads to the ignition of bursts.
Electron degeneracy, identified as the primary mechanism for the ignition of
novae on white dwarfs [57], also plays a role in bursts on neutron stars. In degenerate
material, the pressure is independent of the temperature, such that a reduction in
pressure does not counter a temperature increase. On neutron stars, however, the
electrons are only mildly degenerate near y 10 8 g cm −2 : the ratio of the electron
Fermi energy and thermal energy prior to a burst is η 3. A small amount of
heating at the burst onset lifts the degeneracy, but the runaway continues.
A simple numerical experiment elucidates the relative importance of the two
mechanisms. Employ a one-zone model to simulate the burning behaviour with
and without a pressure term for degenerate electrons. 4 When ignoring the pressure
term from electron degeneracy, bursts are still produced. Of course, electrons do
contribute to the pressure, and ignoring that term leads to a slightly larger ignition
depth. Therefore, the primary mechanism for the thermal instability of bursts is
the thin-shell instability, while the electron degeneracy is important for obtaining
accurate ignition conditions.
Intermediate duration bursts and superbursts ignite deeper in the envelope
(Table 5.2), where the electron degeneracy is larger, up to η 10 2 . Nevertheless,
their fuel layer is a thin shell, which implies that long duration bursts would also
occur without the degeneracy effect.
5.2.2 Reignition After a Short Recurrence Time
In the classical picture, a burst burns nearly all hydrogen and helium in the neutron
star envelope, and a completely new fuel layer must be accreted before the next burst
4 For example, the one-zone helium ignition model available at https://github.com/
andrewcumming/onezone.