The subnuclear density layer of supernova cores shows many similarities with that of neutron star crusts. In both cases, the matter is formed of nuclear clusters embedded in a sea of leptons and hadrons. Nevertheless, the conditions are very different since supernova cores are lepton rich (contain many electrons, positrons as well as trapped neutrinos and antineutrinos) with lepton fraction
and very hot with temperatures typicallyOf particular importance for supernova simulations is the adiabatic index defined by
where The striking differences between the adiabatic index of supernova matter, , and that for cold
catalyzed matter in neutron stars,
, deserves additional explanation. In the core collapse,
compression of the matter becomes adiabatic as soon as
, so that the entropy per nucleon
Simultaneously, due to neutrino trapping, the electron-lepton fraction is frozen,
The condition
blocks evaporation of nucleons from the nuclei; the motion of nucleons
have to remain ordered. Therefore, the fraction of free nucleons stays small and they do not
contribute significantly to the pressure, which is supplied by the electrons, until the density reaches
1014 g cm–3.
At , nuclei coalesce forming uniform nuclear matter. Thus, there are two density
regimes for
. For
, pressure is supplied by the electrons, while nucleons are
confined to the nuclei, so that
. Then, for
nuclei coalesce into uniform
nuclear matter, and the supernova matter stiffens violently, with the adiabatic index jumping by a factor of
about two, to
. This stiffening is actually responsible for the bounce of infalling matter. An
additional factor stabilizing nuclei at
in spite of a high
, is a large lepton
fraction,
, enforcing a relatively large proton fraction,
, to be compared with
for neutron stars.
Finally, for supernova matter we notice the absence of a neutron-drip softening, so well pronounced in
, Figure 31
. This is because neutron gas is present in supernova matter also at
,
and the increase of the free neutron fraction at higher density is prevented by strong neutron binding in the
nuclei (large
), and low
.
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