5 Thermonuclear X-ray Bursts
239
The mass accretion rate of the stability transition ( ˙
M st ) depends on the conditions
in the neutron star atmosphere and potentially the burning latitude. These conditions
include the effective gravity in the neutron star envelope and the composition of
the accreted material [72, 103]. Equally important are the details of the processes
that take place in the atmosphere. In particular, an increased heat flux into the
atmosphere substantially lowers ˙
M st [98]. Similarly, turbulent mixing induced by
rotation or a magnetic field lowers ˙
M st by reducing the time it takes to bring fresh
fuel to the burning depth [98, 151]. Furthermore, several nuclear reactions have been
identified that play a key role in setting the stability of the burning processes. The
CNO breakout reaction 15 O(α, γ ) 19 Ne is one of the most important in this respect
[35, 44, 45], but its reaction rate is poorly constrained by nuclear experiments,
leading to a substantial uncertainty in ˙
M st [103]. Competition of this reaction with
another breakout reaction, 18 Ne(α, p) 21 Na, has been shown to increase the range of
˙
M where burning is marginally stable [103].
The oscillation period depends on t acc , and is therefore expected to be a function
of ˙
M st . Similarly, the waveform and the amplitude of the oscillations depend on
˙
M st . Additionally, changes are expected as a function of the “distance” from the
stability transition. For example, at a mass accretion rate close to ˙
M st , the amplitude
is smaller, the waveform is more symmetric, and the frequency is higher [103].
Marginally stable burning is an elegant explanation for mHz QPOs, as it is
expected to occur in a narrow range of mass accretion rate, broadly matching
observations. The predicted periods are consistent with the observed values of
a few minutes. However, if the observed accretion timescale is considered, the
predictions for the period are actually larger. Furthermore, marginally stable burning
takes place at the transition from bursts to stable burning; this appears to be
the behaviour observed from Terzan 5 X-2, but not for the other sources, where
bursts and mHz QPOs alternate, and the transition to stable burning takes place at
higher persistent flux [97]. Instead, these sources more closely resemble models
that include a slowly decreasing heat flux into the neutron star envelope. Those
simulations display oscillations with an evolving frequency up to the ignition of a
burst [98]. This suggests that the observed mHz QPOs are indicative of cooling of
the atmosphere, possibly heated by a preceding burst [120]. However, multi-zone
models that self-consistently include the heating and cooling of deeper layers, do
not exhibit alternating oscillations and bursts. Therefore, while marginally stable
burning is the most likely process to power mHz QPOs, the circumstances under
which it is observed are challenging to explain with current theory.
5.7 Burst Duration and Fuel Composition
The majority of observed bursts have durations of ∼10–100 s. A typical burst ignites
at a depth of y 10 8 g cm −2 , where the thermal timescale is of the order of 10 s. If
all fuel burns quickly after ignition, this cooling timescale sets the burst duration. If
239
The mass accretion rate of the stability transition ( ˙
M st ) depends on the conditions
in the neutron star atmosphere and potentially the burning latitude. These conditions
include the effective gravity in the neutron star envelope and the composition of
the accreted material [72, 103]. Equally important are the details of the processes
that take place in the atmosphere. In particular, an increased heat flux into the
atmosphere substantially lowers ˙
M st [98]. Similarly, turbulent mixing induced by
rotation or a magnetic field lowers ˙
M st by reducing the time it takes to bring fresh
fuel to the burning depth [98, 151]. Furthermore, several nuclear reactions have been
identified that play a key role in setting the stability of the burning processes. The
CNO breakout reaction 15 O(α, γ ) 19 Ne is one of the most important in this respect
[35, 44, 45], but its reaction rate is poorly constrained by nuclear experiments,
leading to a substantial uncertainty in ˙
M st [103]. Competition of this reaction with
another breakout reaction, 18 Ne(α, p) 21 Na, has been shown to increase the range of
˙
M where burning is marginally stable [103].
The oscillation period depends on t acc , and is therefore expected to be a function
of ˙
M st . Similarly, the waveform and the amplitude of the oscillations depend on
˙
M st . Additionally, changes are expected as a function of the “distance” from the
stability transition. For example, at a mass accretion rate close to ˙
M st , the amplitude
is smaller, the waveform is more symmetric, and the frequency is higher [103].
Marginally stable burning is an elegant explanation for mHz QPOs, as it is
expected to occur in a narrow range of mass accretion rate, broadly matching
observations. The predicted periods are consistent with the observed values of
a few minutes. However, if the observed accretion timescale is considered, the
predictions for the period are actually larger. Furthermore, marginally stable burning
takes place at the transition from bursts to stable burning; this appears to be
the behaviour observed from Terzan 5 X-2, but not for the other sources, where
bursts and mHz QPOs alternate, and the transition to stable burning takes place at
higher persistent flux [97]. Instead, these sources more closely resemble models
that include a slowly decreasing heat flux into the neutron star envelope. Those
simulations display oscillations with an evolving frequency up to the ignition of a
burst [98]. This suggests that the observed mHz QPOs are indicative of cooling of
the atmosphere, possibly heated by a preceding burst [120]. However, multi-zone
models that self-consistently include the heating and cooling of deeper layers, do
not exhibit alternating oscillations and bursts. Therefore, while marginally stable
burning is the most likely process to power mHz QPOs, the circumstances under
which it is observed are challenging to explain with current theory.
5.7 Burst Duration and Fuel Composition
The majority of observed bursts have durations of ∼10–100 s. A typical burst ignites
at a depth of y 10 8 g cm −2 , where the thermal timescale is of the order of 10 s. If
all fuel burns quickly after ignition, this cooling timescale sets the burst duration. If