11.8 Other neutrino emission mechanisms
There are many other mechanisms of neutrino emission. For example, there is the possibility of
pair Bremsstrahlung emission accompanying
scattering of dripped neutrons, and scattering
of neutrons on nuclear clusters,
. Moreover, in a newly-born neutron
star beta processes involving electrons, positrons and nuclei, e.g.,
,
, etc., are a source of neutrino emission. These are the famous Urca processes,
proposed in the early 1940s; their intriguing history is described, e.g., in Section 3.3.5 of Yakovlev et
al. [428
]. One can also contemplate a photo-emission from nuclei,
. Finally, we
should also mention the interesting possibility of a very efficient neutrino emission by the direct Urca
process in some “pasta layers” (see Section 3.3) near the bottom of the crust [274, 259
, 260
, 179
]. As this
mechanism, restricted to a bottom layer of the neutron star crust, could be a very efficient neutrino
emission channel, we will describe it in more detail.
11.8.1 Direct Urca process in the pasta phase of the crust
It is well known that the direct Urca process is the most efficient mechanism of neutrino emission [254].
The direct Urca reactions in a dense degenerate plasma composed mainly of neutrons, with an admixture of
protons and electrons, are the neutron beta decay and the inverse reaction of electron capture on a proton,
These reactions are allowed by momentum conservation, if the Fermi momenta of neutrons,
protons, and electrons satisfy the triangle condition
. The triangle condition
implies that the proton fraction in the
plasma should be greater than
. For
the time being, we ignore whether this condition is satisfied in the cores of the most massive
neutron stars. If the direct Urca (dUrca) process is forbidden, then the main neutrino emission
mechanism from the nonsuperfluid neutron star core is the modified Urca (mUrca) process,
where
or
is an additional “spectator” nucleon needed for momentum conservation. By
strong (nuclear) interaction with
or
,
absorbs (supplies) the excessive (missing) momentum of
the nucleons participating in the processes (275), without changing its own nucleon state. The difference in
emissivities from the dUrca and mUrca processes is huge. For nonsuperfluid neutron star cores,
, where
[255
].
If the “pasta mantle” of the crust exists (see Section 3.3), it allows for a partial opening of the dUrca
process in those phases, in which the
matter component fills most of the space. This happens in the
phases with tubes or bubbles filled with a neutron gas. However, because of the periodicity of the lattice
of tubes or bubbles, neutrons and protons in the
plasma move in a periodic nuclear
single-particle potential. This means that the nucleon single particle wave functions are no longer the
eigenfunctions of momentum (plane waves), but have to be replaced by Bloch wave functions (see
Section 3.2.4). All in all, the dUrca process becomes “slightly open” in the relevant pasta layers of the
crust [259, 260, 179
]. The emissivities calculated by Gusakov et al. [179
] can be presented as
where
is the dUrca emissivity for a homogeneous
plasma, calculated using plane waves
and ignoring momentum conservation, and
is the reduction factor, resulting from momentum and
energy constraints in the presence of a periodic lattice of tubes or bubbles filled with a neutron gas. The
calculation performed for the bubble phase shows that
, but even this strong reduction still
allows
to be much larger than that from any other process of neutrino emission in the
neutron star crust [179
]. However, it should be stressed that
acts in a rather thin
bottom layer of the crust. In the model developed by Gusakov et al. [179], it was localized in the
“Swiss-cheese” layer in the density range (1014.14 – 1014.16) g cm–3. Within this layer, and at
temperature
,
exceeds all other crust emissivities by a factor of at least
104.