4.2 Nuclear processes and formation of accreted crusts
In this section we will describe the fate of X-ray burst ashes, produced at 107 g cm–3, and
then sinking deeper and deeper under the weight of accreted plasma above them. We start at
a few tens of meters below the surface, and we will end at a depth of 1 km, where the
density 1013 g cm–3. Under conditions prevailing in accreting neutron star crusts, at
matter is strongly degenerate, and is “relatively cold” (, see
Figures 25 and 26), so that thermonuclear processes are strongly suppressed because interacting
nuclei have to overcome a large Coulomb barrier. The structure of an accreted crust is shown in
||Model of an accreting neutron star crust. The total mass of the star is .
Stable hydrogen burning takes place in the H-burning shell, and produces helium, which accumulates
in the He-shell. Helium ignites at 107 g cm–3, leading to a helium flash and explosive burning
of all matter above the bottom of the He-layer into 56Ni, which captures electrons to become 56Fe.
After 1 h, the cycle of accretion, burning of hydrogen and explosion triggered by a helium flash
repeats again and the layer of iron from the previous burst is pushed down. Based on the unpublished
results of calculations by P. Haensel and J.L. Zdunik. Accreted crust model of [186, 185]. The core
model of .
In what follows we will use a simple model of the accreted crust formation, based on the one-component
plasma approximation at [185, 187]. The (initial) X-burst ashes are approximated by a
one-component plasma with nuclei.
At densities lower than the threshold for pycnonuclear fusion (which is very uncertain, see Yakovlev et
al. ), , the number of nuclei in an element of matter does not change
during the compression resulting from the increasing weight of accreted matter. Due to nucleon
pairing, stable nuclei in dense matter have even and (even-even nuclides). In
the outer crust, in which free neutrons are absent, the electron captures proceed in two steps,
Electron captures lead to a systematic decrease in (therefore an increase in ) with
increasing density. The first capture, Equation (67), proceeds as soon as ,
in a quasi-equilibrium manner, with negligible energy release. It produces an odd-odd nucleus, which
is strongly unstable in a dense medium, and captures a second electron in a nonequilibrium
manner, Equation (68), with energy release , where is the label of the nonequilibrium
||Electron capture processes.
||Z and N of nuclei vs. matter density in an accreted crust, for different models of dense
matter. Solid line: ; dotted line: . Every change of N and Z, which takes place
at a constant pressure, is accompanied by a jump in density: it is represented by small steep (but not
perpendicular!) segments of the curves. These segments connect the top and the bottom density of a
thin reaction shell. Arrows indicate positions of the neutron drip point. From Haensel & Zdunik .
After the neutron-drip point (), electron captures trigger neutron
Due to the electron captures, the value of decreases with increasing density. In consequence, the
Coulomb barrier prohibiting the nucleus-nucleus reaction lowers. This effect, combined with the decrease of
the mean distance between the neighboring nuclei, and a simultaneous increase of energy of the quantum
zero-point vibrations around the nuclear lattice sites, opens up a possibility for the pycnonuclear fusion
associated with quantum-mechanical tunneling through the Coulomb barrier due to zero-point vibrations
(see, e.g., Section 3.7 of the book by Shapiro & Teukolsky ). The pycnonuclear fusion timescale
is a very sensitive function of . The chain of the reactions (69) and (70) leads to an
abrupt decrease of typically by 7 to 10 orders of magnitude. In the one-component plasma
approximation, the accreted crust is composed of spherical shells containing a single nuclide
. Pycnonuclear fusion switches on as soon as is smaller than the time of the travel
of a piece of matter (due to accretion) through the considered shell of mass ,
. The masses of the shells are on the order of . As a result, in the inner crust
the chain of reactions (69 and 70) in several cases is followed by the pycnonuclear reaction,
occurring on a timescale much shorter than . Introducing , we then have
where dots in Equation (73) denote an actual nonequilibrium process, usually following reaction (72). The
total heat deposition in matter, resulting from a chain of reactions involving a pycnonuclear fusion,
Equations (71), (72) and (73), is .
The composition of accreted neutron star crusts, obtained by Haensel & Zdunik , is shown
in Figure 21. These results describe crusts built of accreted and processed matter up to the
density (slightly before the crust-core interface). At a constant accretion rate
this will take . During that time, a shell of X-ray burst ashes
will be compressed from to .
Two different compositions of X-ray burst ashes at , , , were assumed. In the
first case, , , which is a “standard composition”. In the second scenario , to
imitate nuclear ashes obtained by Schatz et al. . The value of stems then from the condition
of beta equilibrium at . As we see in Figure 21, after the pycnonuclear fusion region is
reached, both curves converge (as explained in Haensel & Zdunik , this results from and in