5 Thermonuclear X-ray Bursts
213
5.1.1.3 Ignition Conditions and the Stability of Burning
The specific energy generation rate nuc for the three nuclear processes important for
burst ignition rises steeply at lower T and flattens at higher T (Fig. 5.1). For helium
burning through the 3α process, nuc depends weakly on T above T 3 × 10 8 K,
and stable helium burning occurs instead of a thermonuclear runaway. Similarly,
hydrogen burning through the CNO cycle becomes stable at T 0.7×10 8 K. These
temperature thresholds are set by the depth of the Coulomb barrier which nuclei
must overcome through quantum tunnelling. Because the H burning processes
involve the conversion of protons into neutrons, they include weak decays, which
delay the process overall. The timescale for burning is set by the β-decay of 14 O
and 15 O, with half-lives of 70.620 s and 122.24 s, respectively. At high temperatures
H burning is known as the “hot CNO cycle” or the “β-limited CNO cycle”, where
burning cannot run away and is, therefore, stable [192].
Nuclear burning is only efficient if it is stronger than radiative cooling, which
is described by the specific cooling rate cool = −
acT 4
3κy , with radiation constant
a, speed of light c, and opacity κ (e.g., [14, 48]). Stable burning in a steadystate takes place at a depth where nuc = cool . For thermonuclear runaways the
ignition condition is
d nuc
dT
>
d cool
dT , which means that cooling cannot moderate
small perturbations in the nuclear burning rate. Both nuc and cool depend on T
and y, such that we can use these two conditions to map out the ignition conditions
for stable and unstable burning (Fig. 5.2; e.g., [14, 48, 50, 95, 139]). For H and He,
burning is unstable at lower T , and is stable at higher values. Carbon burning is
unstable over the entire considered range of parameters. 2
5.1.1.4 Burning Regimes as a Function of Accretion Rate
Which ignition conditions are reached on a neutron star, depends for a large part on
˙
M. The amount of heating due to compression is proportional to ˙
M. Therefore, T is
higher for larger ˙
M. Furthermore, steady-state burning requires that fuel is burned
at the same rate as at which it is accreted. For stable burning, the temperature profile
of the neutron star envelope adjusts to facilitate this equilibrium.
The simple ignition conditions presented in Fig. 5.2 are determined by considering hydrogen, helium, and carbon burning separately. Most bursters accrete a
mixture of hydrogen and helium, and the (typically steady) burning of hydrogen
influences the ignition of helium, via the heat that is contributed to the fuel layer.
Steady H burning also affects the composition of the burst fuel at ignition, and
hence the overall specific energy released by the burst, Q nuc . Where H is present
in the burst fuel, the burning can proceed to heavier species via (α, p) reactions and
proton captures (the rapid-proton, or rp-process; e.g. [159]). Q nuc can be inferred
from measurements of the so-called α parameter, the ratio of the burst fluence to the
peak flux (e.g. [53]).
2 Multi-zone models find carbon burning to be stable in hot envelopes, depending on ˙
M [94].
213
5.1.1.3 Ignition Conditions and the Stability of Burning
The specific energy generation rate nuc for the three nuclear processes important for
burst ignition rises steeply at lower T and flattens at higher T (Fig. 5.1). For helium
burning through the 3α process, nuc depends weakly on T above T 3 × 10 8 K,
and stable helium burning occurs instead of a thermonuclear runaway. Similarly,
hydrogen burning through the CNO cycle becomes stable at T 0.7×10 8 K. These
temperature thresholds are set by the depth of the Coulomb barrier which nuclei
must overcome through quantum tunnelling. Because the H burning processes
involve the conversion of protons into neutrons, they include weak decays, which
delay the process overall. The timescale for burning is set by the β-decay of 14 O
and 15 O, with half-lives of 70.620 s and 122.24 s, respectively. At high temperatures
H burning is known as the “hot CNO cycle” or the “β-limited CNO cycle”, where
burning cannot run away and is, therefore, stable [192].
Nuclear burning is only efficient if it is stronger than radiative cooling, which
is described by the specific cooling rate cool = −
acT 4
3κy , with radiation constant
a, speed of light c, and opacity κ (e.g., [14, 48]). Stable burning in a steadystate takes place at a depth where nuc = cool . For thermonuclear runaways the
ignition condition is
d nuc
dT
>
d cool
dT , which means that cooling cannot moderate
small perturbations in the nuclear burning rate. Both nuc and cool depend on T
and y, such that we can use these two conditions to map out the ignition conditions
for stable and unstable burning (Fig. 5.2; e.g., [14, 48, 50, 95, 139]). For H and He,
burning is unstable at lower T , and is stable at higher values. Carbon burning is
unstable over the entire considered range of parameters. 2
5.1.1.4 Burning Regimes as a Function of Accretion Rate
Which ignition conditions are reached on a neutron star, depends for a large part on
˙
M. The amount of heating due to compression is proportional to ˙
M. Therefore, T is
higher for larger ˙
M. Furthermore, steady-state burning requires that fuel is burned
at the same rate as at which it is accreted. For stable burning, the temperature profile
of the neutron star envelope adjusts to facilitate this equilibrium.
The simple ignition conditions presented in Fig. 5.2 are determined by considering hydrogen, helium, and carbon burning separately. Most bursters accrete a
mixture of hydrogen and helium, and the (typically steady) burning of hydrogen
influences the ignition of helium, via the heat that is contributed to the fuel layer.
Steady H burning also affects the composition of the burst fuel at ignition, and
hence the overall specific energy released by the burst, Q nuc . Where H is present
in the burst fuel, the burning can proceed to heavier species via (α, p) reactions and
proton captures (the rapid-proton, or rp-process; e.g. [159]). Q nuc can be inferred
from measurements of the so-called α parameter, the ratio of the burst fluence to the
peak flux (e.g. [53]).
2 Multi-zone models find carbon burning to be stable in hot envelopes, depending on ˙
M [94].