238
D. K. Galloway and L. Keek
common theoretical interpretation, but it remains unclear whether it signals a failing
of the theory or is the result of the limited quality of the data.
The behaviour that we described was found for all mentioned sources, except
Terzan 5 X-2. The behaviour of the bursts and mHz QPOs of this source has been
unique among the known bursters. This transient source went into a month-long
outburst in 2011, in which the accretion rate steadily increased and subsequently
decreased until the source was once again quiescent. During the outburst rise, the
burst rate steadily increased until the recurrence time was a mere 3 min, and the
light curve exhibited oscillations. This interval was followed by an absence of
bursts or oscillations at the highest persistent flux. As the flux gradually returned to
quiescence, the reverse was observed: oscillations reappeared, followed by bursts,
whose recurrence time increased as the flux decreased. The behaviour of Terzan 5 X2 is different from the other four sources, in which bursts and QPOs alternated while
the persistent flux remained approximately constant at a value corresponding to a
much lower accretion rate. Furthermore, for those sources there is a large difference
between the burst recurrence time of several hours and the oscillation period of a
few minutes. For Terzan 5 X-2 there was no clear transition at which bursts ceased
and mHz QPOs appeared.
5.6.2 Theoretical Interpretation: Marginally Stable Burning
From the apparent interaction between the mHz QPOs and Type I bursts, as well as
from the energetics of the observed oscillations compared to the persistent flux, it
was argued that the mHz QPOs could be produced by a nuclear burning mode [2,
155]. Oscillatory burning modes are predicted to be present at the transition of stable
and unstable burning [144], because of competition between heating and cooling
processes. Stable burning results from an equilibrium between cooling processes
and heating by nuclear burning, taking into account the rate at which fresh fuel is
accreted. Conversely, bursts appear after a period of accretion during which cooling
was sufficiently efficient to prevent most nuclear burning. Once the bottom of the
fuel column is compressed to reach a sufficiently high temperature and density, the
nuclear burning rate runs away unstably, quickly overtaking the cooling rate and
producing a burst. At the transition between the stable and unstable burning modes,
nuclear burning is “marginally” stable: the nuclear burning rate starts to rise, but the
cooling rate quickly catches up and prevents a runaway. This alternates to produce
an oscillatory burning mode with a period, P , that is the geometric mean of the
cooling (thermal) timescale, t therm , and the accretion timescale (time to replenish
the burned fuel), t acc : P
√
t therm t acc [72]. This picture is confirmed by multizone numerical simulations. The marginally stable burning mode is reproduced in a
narrow range of mass accretion rates at the stability transition. For current standard
theory, this transition takes place at the Eddington limit, whereas mHz QPOs are
typically observed at a ten times lower mass accretion rate.
D. K. Galloway and L. Keek
common theoretical interpretation, but it remains unclear whether it signals a failing
of the theory or is the result of the limited quality of the data.
The behaviour that we described was found for all mentioned sources, except
Terzan 5 X-2. The behaviour of the bursts and mHz QPOs of this source has been
unique among the known bursters. This transient source went into a month-long
outburst in 2011, in which the accretion rate steadily increased and subsequently
decreased until the source was once again quiescent. During the outburst rise, the
burst rate steadily increased until the recurrence time was a mere 3 min, and the
light curve exhibited oscillations. This interval was followed by an absence of
bursts or oscillations at the highest persistent flux. As the flux gradually returned to
quiescence, the reverse was observed: oscillations reappeared, followed by bursts,
whose recurrence time increased as the flux decreased. The behaviour of Terzan 5 X2 is different from the other four sources, in which bursts and QPOs alternated while
the persistent flux remained approximately constant at a value corresponding to a
much lower accretion rate. Furthermore, for those sources there is a large difference
between the burst recurrence time of several hours and the oscillation period of a
few minutes. For Terzan 5 X-2 there was no clear transition at which bursts ceased
and mHz QPOs appeared.
5.6.2 Theoretical Interpretation: Marginally Stable Burning
From the apparent interaction between the mHz QPOs and Type I bursts, as well as
from the energetics of the observed oscillations compared to the persistent flux, it
was argued that the mHz QPOs could be produced by a nuclear burning mode [2,
155]. Oscillatory burning modes are predicted to be present at the transition of stable
and unstable burning [144], because of competition between heating and cooling
processes. Stable burning results from an equilibrium between cooling processes
and heating by nuclear burning, taking into account the rate at which fresh fuel is
accreted. Conversely, bursts appear after a period of accretion during which cooling
was sufficiently efficient to prevent most nuclear burning. Once the bottom of the
fuel column is compressed to reach a sufficiently high temperature and density, the
nuclear burning rate runs away unstably, quickly overtaking the cooling rate and
producing a burst. At the transition between the stable and unstable burning modes,
nuclear burning is “marginally” stable: the nuclear burning rate starts to rise, but the
cooling rate quickly catches up and prevents a runaway. This alternates to produce
an oscillatory burning mode with a period, P , that is the geometric mean of the
cooling (thermal) timescale, t therm , and the accretion timescale (time to replenish
the burned fuel), t acc : P
√
t therm t acc [72]. This picture is confirmed by multizone numerical simulations. The marginally stable burning mode is reproduced in a
narrow range of mass accretion rates at the stability transition. For current standard
theory, this transition takes place at the Eddington limit, whereas mHz QPOs are
typically observed at a ten times lower mass accretion rate.