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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 −9 10 M ⊙ to get 42 Eburst ∼ 10 erg. It can be seen from Figure 39View Image that 12C ignition has to occur at 9 −3 ρ ∼ 10 g cm at a depth of ∼ 30 m. At the accretion rates characteristic of typical superbursters (M˙ ∼ (1 –3) × 10− 9M ⊙∕y), 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 12[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 81View Image (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 [21327989] 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 82View Image. 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 [386Jump To The Next Citation Point] 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 ----- ∘ μ∕P ∼ 0.1, where μ is the shear modulus and P 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 M and circumferential equatorial radius R of the neutron star in XTE J1739–285 [45]

( )1∕3 --M---- R < 15.52 1.4M ⊙ km . (304 )
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Figure 81: Oscillations detected in an X-ray burst from 4U 1728–34 at frequency ∼ 363 Hz [399].
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Figure 82: Spreading of a thermonuclear burning hotspot on the surface of a rotating neutron star simulated by Spitkovsky [386] (from External Linkhttp://www.astro.princeton.edu/~anatoly/).

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 [102358Jump To The Next Citation Point429430] and references therein).

Let us denote the duration of the accretion stage, with accretion rate M˙a, by ta, and the duration of quiescence between two active periods by t q, with t ≫ t q a. 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 ⟨M˙ ⟩ = taM˙a ∕(ta + tq). 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 ta 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 Tint. 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 Teff. Therefore,

L γ(Teff) + L ν(Tint) = Ldh(⟨M˙ ⟩), (305 )
where the total time-averaged deep-crustal heating rate is
˙ ˙ 33 ˙ -----Qtot---- Ldh(⟨M ⟩) = Qtot ⟨M ⟩∕mu ≈ 6.03 × 10 ⟨M − 10⟩MeV erg s−1 , (306 )
and Qtot is the total heat released per accreted nucleon.
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Figure 83: X-ray luminosities of SXTs in quiescence vs. time-averaged accretion rates. The heating curves correspond to different neutron star masses, increasing from the top to the bottom, with a step of ΔM = 0.02M ⊙. The EoS of the core is moderately stiff, with Mmax = 1.977 M ⊙ [340]. The model of a strong proton and a weak neutron superfluidity is assumed [261Jump To The Next Citation Point]. The highest curve (hottest stars) corresponds to M = M ⊙, and the lowest one (coldest stars) to M = Mmax. The upper bundle of coalescing curves corresponds to masses M ⊙ ≤ M ≤ MD, where a star of mass M D has a central density equal to the threshold for the direct Urca process. The red dotted line represents thermal states of a “basic model” (nonsuperfluid core, slow cooling via a modified Urca process). Total deep heat released per accreted nucleon is Qtot = 1.5 MeV. Figure made by K.P. Levenfish. For a further description of neutron star models and observational data see Levenfish & Haensel [261].
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Figure 84: Same as Figure 83View Image but assuming ten times smaller Qtot = 0.15 MeV. Such a low crustal heating is contradicted by the measured luminosities of three SXTs: Aql X–1, RXJ1709–2639, and 4U 1608–52. Figure made by K.P. Levenfish.

As can be seen in Figure 83View Image, Qtot = 1.5 MeV/nucleon is consistent with SXTs observations. However, different sources require different neutron star masses M. 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 84View Image, Qtot = 0.15 MeV/nucleon (and a fortiori Qtot = 0) 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 [66Jump To The Next Citation Point]. 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 85View Image. Modeling of the initial cooling curve can hopefully constrain the crust physics [35866379Jump To The Next Citation Point]. An example of such modeling is shown in Figure 86View Image. 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 85View Image), yields a too slow relaxation (see Figure 86View Image ). Moreover, the star has to be massive to have a sufficiently thin crust to relax sufficiently rapidly.

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Figure 85: Left vertical axis: thermal conductivity of neutron star crust vs. density, at log10(T)[K ] = 7 and 8. GS – pure ground state crust. A – pure accreted crust. GS (low κ) – amorphous ground state crust. Right vertical axis – deep crustal heating per accreted nucleon in a thin heating shell, vs. density, according to A = 56 i model of Haensel & Zdunik [188]. From Shternin et al. [379Jump To The Next Citation Point]. Figure made by P.S. Shternin.
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Figure 86: Theoretical cooling curves for KS 1731–260 relaxing toward a quiescent state; observations expressed in terms of effective surface temperature as measured by a distant observer, T ∞ s. Curves 1 and 4 were obtained for pure crystal accreted crust with two different models of superfluidity of neutrons in the inner crust (strong and weak). Curves 1 and 4 give best fit to data points. Line 5 – amorphous ground state crust; line 2 – ground state crust without neutron superfluidity: both are ruled out by observations. From Shternin et al. [379]. Figure made by P.S. Shternin.

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