12.7 Low mass X-ray binaries
As reviewed in Section 4, the accretion of matter (mainly hydrogen and helium) onto the surface of
neutron stars triggers thermonuclear fusion reactions. Under certain circumstances, these reactions can
become explosive, giving rise to X-ray bursts. The unstable burning of helium ash produced by the fusion of
accreted hydrogen, is thought to be at the origin of type I X-ray bursts. A new type of X-ray burst has been
recently discovered. These superbursts are a thousand times more energetic than normal bursts
and last several hours compared to a few tens of seconds, but occur much more rarely. These
superbursts could be due to the unstable burning of 12C accumulated from He burning. The
mass of 12C fuel has to be as high as
to get
. It can be seen from
Figure 39 that 12C ignition has to occur at
at a depth of
30 m. At the
accretion rates characteristic of typical superbursters (
), this would
correspond to recurrence times of a few years. It also seems that crustal heating might be quite
important to getting such a relatively low ignition density of 12C [178]. The ignition conditions
are very sensitive to the thermal properties of the crust and core [104]. X-ray observations of
low-mass X-ray binaries thus provide another way of probing the interior of neutron stars,
both during thermonuclear bursting episodes and during periods of quiescence as discussed
below.
12.7.1 Burst oscillations
During the past ten years, millisecond oscillations have been discovered in X-ray bursts in low mass X-ray
binaries as illustrated in Figure 81 (see, for instance, [392] and references therein for a recent review).
Such oscillations have been observed during the rise time of bursts, as well as at later times in
the decay phase. The observations of burst oscillations in the accreting millisecond pulsars
SAX J1808.4–3658 [213, 279, 89] and XTE J1814–338 [395] firmly established that burst
oscillations occur close to the spin frequency of the neutron star. This conclusion was further
supported by the discovery of about 500,000 highly coherent pulsation cycles at 582 Hz during
a superburst from the low mass X-ray binary 4U 1636–356 [394]. This suggests that burst
oscillations arise from some nonuniformities on the neutron star surface. In the burst rise, the
oscillations are likely to be caused by the presence of hot spots induced by the ignition of nuclear
burning. This interpretation naturally explains why oscillation amplitudes decrease with time as
the burning region spreads over the entire surface [398], as shown in Figure 82. Nevertheless,
this model cannot explain the oscillations detected in the burst tail, since the duration of the
burst (of the order 10 – 30 seconds) is much larger than the spreading time of thermonuclear
burning (typically less than 1 second). Surface inhomogeneities during the cooling phase could be
produced by the dynamic formation of vortices driven by the Coriolis force [386
] and by nonradial
surface oscillations [196]. The outer envelope of an accreting neutron star is formed of three
distinct regions: a hot bursting shell, an ocean and the solid outer crust, so that many different
oscillation modes could be excited during a burst. The observed frequencies and positive frequency
drifts are consistent with shallow surface waves excited in the hot bursting layer changing into
crustal interface waves in the ocean as the surface cools [330]. This model can also explain
the energy dependence of the burst oscillation amplitude [331]. The interface waves resemble
shallow surface waves, but with a large radial displacement at the ocean/crust boundary due to
the elasticity of the crust [329]. The frequency of the interface wave is reduced by a factor
, where
is the shear modulus and
the pressure, as compared to a rigid surface.
The frequencies of these modes depend on the composition of the neutron star surface layers.
This raises the exciting possibility of probing accreting neutron star crusts with X-ray burst
oscillations. Very recently evidence has come forth for burst oscillations at a frequency of 1122 Hz
in the X-ray transient XTE J1739–285 [227]. If confirmed, it would imply that this system
contains the fastest spinning neutron star ever discovered. Since the spinning rate is limited by the
mass shedding limit, these observations would thus put constraints on the gravitational mass
and circumferential equatorial radius
of the neutron star in XTE J1739–285 [45]
12.7.2 Soft X-ray transients in quiescence
The phenomenon of deep crustal heating appears to be relevant for the understanding of the thermal
radiation observed in soft X-ray transients (SXTs) in quiescence, when the accretion from a disk is switched
off or strongly suppressed. Typically, the quiescent emission is much higher than it would be in an old
cooling neutron star. It has been suggested that this is because the interiors of neutron stars in SXTs
are heated up during relatively short periods of accretion and bursting by the nonequilibrium
processes associated with nuclear reactions taking place in the deep layers of the crust ([60], see
also Section 4.3). The deep crustal heating model, combined with appropriate models of the
neutron star atmosphere and interior, is used to explain measured luminosities of SXTs in
quiescence. The luminosity in quiescence depends on the structure of neutron star cores, and
particularly on the rate of neutrino cooling. This opens up the new possibility of exploring the
internal structure and equation of state of neutron stars (see [102, 358
, 429, 430] and references
therein).
Let us denote the duration of the accretion stage, with accretion rate
, by
, and the duration
of quiescence between two active periods by
, with
. After a few thousands of
accretion-quiescence cycles, an SXT reaches a steady thermal state with the well-defined thermal structure
of quiescence. This thermal structure is fully determined by the time-averaged accretion rate
. A steady state in quiescence satisfies the global energy balance “on average”. The
heat associated with nuclear H and He burning and X-ray bursting during
is nearly completely
radiated away, and therefore does not contribute to the steady-state energy balance. Therefore, to a good
approximation, the sum of the total average cooling rates (photon surface and neutrino volume
emission) is balanced by deep crustal heating during an accretion period. Except for a thin
blanketing envelope, the interior of an SXT in quiescence is isothermal, with temperature
. A
blanketing envelope separates the isothermal interior from the surface, where the photons are
emitted with a spectrum formed in a photosphere of effective temperature
. Therefore,
where the total time-averaged deep-crustal heating rate is
and
is the total heat released per accreted nucleon.
As can be seen in Figure 83,
/nucleon is consistent with SXTs observations. However,
different sources require different neutron star masses
. This is because the core neutrino cooling rate
depends on the mass of the inner core, where the direct Urca process is possible. As shown in Figure 84,
/nucleon (and a fortiori
) would contradict observations of Aql X–1,
RX 1709–2639 and 4U 1608–52 in quiescence.
12.7.3 Initial cooling in quasi-persistent SXTs
Quasi-persistent SXTs, with accretion periods lasting for years – decades, might be particularly useful for
studying the structure of neutron star crusts. This is because one can observe their thermal
relaxation between the accreting and quiescent stages. For standard SXTs, with accretion lasting
days – weeks, such relaxation cannot be detected, because crustal heating due to accretion is
too small. On the contrary, thermal relaxation toward the quiescent state for KS 1731–260
(after accreting over 12.5 y) and for MXB 1659–29 (after accreting over 2.5 y), called “initial
cooling”, was observed [66
]. Let us consider the thermal relaxation of KS 1731–260. After 12.5 y
of accretion and deep crustal heating, the crust and the surface became significantly hotter
than in the quiescent state. The cooling curve depends on crust properties, such as thermal
conductivity (Section 9), thickness (Section 6), distribution of heat sources (Section 4), and neutrino
emissivity (Section 11). Some of these properties depend strongly on the crust structure, as
illustrated in Figure 85. Modeling of the initial cooling curve can hopefully constrain the crust
physics [358, 66, 379
]. An example of such modeling is shown in Figure 86. The cooling curve is much
more sensitive to the crust physics than to that of the dense core. For example, an amorphous crust,
with its low thermal conductivity (see Figure 85), yields a too slow relaxation (see Figure 86
). Moreover, the star has to be massive to have a sufficiently thin crust to relax sufficiently
rapidly.