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 (one-component
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 de-excite,
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.
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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 heat-per-nucleon 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
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
108 g cm–3 to
1013.6 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 electro-neutrality,
, 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
.
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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
])
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