Heating due to nonequilibrium nuclear processes in the outer and inner crust of an accreting neutron star (deep crustal heating) was calculated, using different scenarios and models [186, 187, 188]. The effect of crustal heating on the thermal structure of the interior of an accreting neutron star can be seen in Figures 25 and 26. In what follows, we will describe the most recent calculations of crustal heating by Haensel & Zdunik [188]. In spite of the model’s simplicity (onecomponent plasma, approximation), the heating in the accreted outer crust obtained by Haensel & Zdunik [188] agrees nicely with extensive calculations carried out by Gupta et al. [178]. The latter authors considered a multicomponent plasma, a reaction network of many nuclides, and included the contribution from the nuclear excited states. They found that electron captures in the outer crust proceed mostly via the excited states of the daughter nuclei, which then deexcite, the excitation energy heating the matter; this strongly reduces neutrino losses, accompanying nonequilibrium electron captures. The total deep crustal heating obtained by Haensel & Zdunik [188] is equal to and per accreted nucleon for and , respectively.

In Figure 22, we show the heat deposited in the matter, per accreted nucleon, in the thin shells where nonequilibrium nuclear processes occur. Actually, reactions proceed at a constant pressure, and there is a density jump within a thin “reaction shell”. The vertical lines, whose height gives the heat deposited in matter, are drawn at the density of the bottom of the reaction shell. The number of heat sources and the heating power of a single source depend on the assumed . In the case of the number of sources is smaller, and their heatpernucleon values are larger, than for .
An important quantity is the integrated heat deposited in the crust in the outer layer with bottom density . It is given by
where labels the crustal heating model (specific , etc.). The quantity for two models of compressional evolution is plotted in Figure 23. The second model illustrates the effect of switching off pycnonuclear reactions. This was done by artificially blocking pycnonuclear fusion until the nuclear charge went down to , which occurred at . And yet, for is very similar to that obtained in the first scenario, which was the most advantageous, as far as crust heating was concerned. Heating by pycnonuclear fusion at is insignificant. Heat from pycnonuclear fusions at is to a large extent replaced by an additional heat release associated with electron captures and neutron emissions within the density range 10^{12} – 10^{13} g cm^{–3}. The values of and saturate above 10^{13.6} g cm^{–3}, where 80% of nucleons are in neutron gas phase. All in all, for two scenarios with , the total deep crustal heat release is 1.8 – 1.9 MeV/nucleon. For , these numbers are lowered by about 0.5 MeV/nucleon.

The quite remarkable weak dependence of the total heat release in the crust, , on the nuclear history of an element of matter undergoing compression from 10^{8} g cm^{–3} to 10^{13.6} g cm^{–3} deserves an explanation [188]. One has to study the most relevant thermodynamic quantity, the Gibbs free energy per nucleon (baryon chemical potential). Its minimum determines the state of thermodynamic equilibrium. Moreover, its drop at reaction surface yields the total energy release per one nucleon [341]. In the approximation, we have = enthalpy per nucleon. Minimizing , at a fixed , with respect to the independent thermodynamic variables (, mean free neutron density , mean baryon density , size of the Wigner–Seitz cell, etc.), under the constraint of electroneutrality, , we get the ground state of the crust at a given . This “cold catalyzed matter” (Section 3) corresponds to . All other curves displaying discontinuous drops due to nonequilibrium reactions included in a given evolutionary model lie above the ; see Figure 24.

This makes visual the fact that noncatalyzed matter is a reservoir of energy, released in nonequilibrium processes that move the matter closer to the absolute ground state. In spite of dramatic differences between different in the region where the bulk of the heating occurs, , the functions tend to for . The general structure of different is similar. At the same , their continuous segments have nearly the same slope. What differs between s are discontinuous drops, by , at reaction thresholds . The functions can therefore be expressed as (see Haensel & Zdunik [188])
where is a smooth function of , independent of . For the values of are negligibly small, and all come quite close to the ground state line. This implies that the sum must be essentially independent of .http://www.livingreviews.org/lrr200810 
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