While a newly born neutron star is made of hot matter in nuclear equilibrium, its subsequent evolution can lead to the formation of regions, where the matter is out of nuclear equilibrium. This may happen in a neutron star crust, where reshuffling of nucleons necessary for the formation of large nuclei (present in the cold catalyzed matter) may be prohibited by high Coulomb barriers. This is the case of an old accreting neutron star. For an accretion rate — 10"10 Mq yr"1, the typical temperature in the neutron star interior is — 108K (Fujimoto et al. 1984; Miralda-Escude et al. 1990).
Let us consider a standard scenario of the evolution of accreted matter. Explosive burning of the helium layer leads to the formation of matter consisting mainly of 56Ni, which transforms into 56Fe by electron captures. The growing layer of the processed accreted matter pushes down the original crust. The original catalyzed (ground-state) outer crust is replaced by a new, noncatalyzed one in — 105 years. In view of low temperature (T < 108 K), the only processes which can take place when the accreted matter sinks inwards are electron captures and beta decays, neutron emission or absorption and, at sufficiently high densities, pycnonuclear fusion. A detailed study of these processes was done by Sato (1979), who considered several scenarios with different initial compositions of the matter, and by Haensel & Zdunik (1990a) (also see Bisnovatyi-Kogan & Chechetkin 1979 and references therein).
A noncatalyzed crust represents a reservoir of energy. The energy release takes place owing to the nonequilibrium processes. Some aspects of this problem were first considered by Vartanyan & Ovakimova (1976). Later nonequi-librium processes and resulting crustal heating were studied in detail by Haensel & Zdunik (1990a). These processes lead to the appearance of very thin layers where heat is produced at a rate proportional to the accretion rate. As shown by Haensel & Zdunik (1990a), the associated total heat release - deep crustal heating - in the crust can be larger than the original inward heat flow resulting from the steady hydrogen burning between the helium flashes (Fujimoto et al., 1984). The total heat release per one accreted nucleon, — 1.5 MeV, depends rather weakly on the initial composition of ashes produced by X-ray bursts (Haensel & Zdunik, 2003).
In the scenario of Haensel & Zdunik (1990a), nuclei in the inner crust have Z < 20, to be compared with Z & 40—50 in the catalyzed matter. The nuclei in the inner accreted crust appear to be much lighter than in the catalyzed matter. Very recently Jones (2005) argued that the deviation of the inner accreted crust from nuclear equilibrium could be much smaller than in the scenarios of Sato (1979) and Haensel & Zdunik (1990a), which would result in a much weaker deep crustal heating. Clearly, the problem requires further studies.
Many neutron stars in close X-ray binaries are transient accretors (transients); § 1.4.6. They exhibit X-ray bursts separated by long periods (months or even years) of quiescence. It is believed that the quiescence corresponds to a low-level, or even halted, accretion onto the neutron star. During high-state accretion episodes, the heat is deposited by nonequilibrium processes in the deep layers (1012 — 1013 g cm-3) of the crust. This deep crustal heating can maintain the temperature of the neutron star interior at a sufficiently high level to explain a persistent thermal X-ray radiation in quiescence (Brown et al., 1998).
The problem of the detailed outcome of time-dependent nucleosynthesis during X-ray bursts is very complicated and is not completely solved (see, e.g., Rembges et al. 1997; Schatz et al. 1999, 2001). The nature of the unstable thermonuclear burning at higher accretion rates 10-8 Mq yr-1 < M < 10-9 Mq yr-1, is not well understood. The ashes from such a burning might contain some admixture of nuclei beyond the iron group, with A ~ 60 —100 (Schatz etal., 1999,2001).
The case of thermally stable burning of hydrogen and helium at sufficiently high accretion rates should be considered separately. This regime corresponds to most of the X-ray pulsars - magnetized accreting neutron stars (surface magnetic field B > 1012 G), where the local accretion rate in the polar cap region is thought to be large enough for a stable burning. A similar situation is encountered at very high rates of accretion (M > 10-8 Mq yr-1) on weakly magnetized (B ^ 1011 G) neutron stars. At high temperatures, corresponding to the high accretion rates, the hydrogen burns via the rapid proton capture producing a mix of elements beyond the iron group. It is expected that the compression of this heterogeneous matter will produce an impure solid crust.
If the starting composition is a mix with significant fractions of different nuclides, its further evolution may keep heterogeneity of the matter. The thermal and electrical conductivities of such a crust could be lower than in a perfect crystal. The distribution of nuclides would be rather smooth, in contrast to the extreme case of a one-nucleus model with noticeable density jumps. The average values of Z and A will still be lower than in the cold catalyzed matter.
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