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11.8 Other neutrino emission mechanisms

There are many other mechanisms of neutrino emission. For example, there is the possibility of ν ¯ν pair Bremsstrahlung emission accompanying nn −→ nn ν¯ν scattering of dripped neutrons, and scattering of neutrons on nuclear clusters, n(A, Z) −→ n (A, Z )ν¯ν. Moreover, in a newly-born neutron star beta processes involving electrons, positrons and nuclei, e.g., e− (A, Z ) − → (A, Z − 1)ν e, − (A, Z − 1) −→ (A, Z)e ¯νe, 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. [428Jump To The Next Citation Point]. One can also contemplate a photo-emission from nuclei, γ(A, Z ) − → (A, Z )ν¯ν. 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 [274259Jump To The Next Citation Point260Jump To The Next Citation Point179Jump To The Next Citation Point]. 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,

n −→ p + e− + ¯νe, p + e− −→ n + νe . (274 )
These reactions are allowed by momentum conservation, if the Fermi momenta of neutrons, protons, and electrons satisfy the triangle condition pFn < pFp + pFe. The triangle condition implies that the proton fraction in the npe plasma should be greater than 1∕9 ≈ 11%. 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,
− − n + X −→ p + X + e + ¯νe, p + X + e − → n + X + νe, (275 )
where X = n or X = p is an additional “spectator” nucleon needed for momentum conservation. By strong (nuclear) interaction with n or p, X absorbs (supplies) the excessive (missing) momentum of the nucleons participating in the processes (275View Equation), without changing its own nucleon state. The difference in emissivities from the dUrca and mUrca processes is huge. For nonsuperfluid neutron star cores, QdUrca∕QmUrca ∼ 106 T −2 ν ν 9, where T9 ≡ T ∕(109 K ) [255Jump To The Next Citation Point].

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 npe 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 npe 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 [259260179Jump To The Next Citation Point]. The emissivities calculated by Gusakov et al. [179Jump To The Next Citation Point] can be presented as

dUrca(m) dUrca(0) Q ν = ℛ (ρ ) Q ν (ρ,T ), (276 )
where QdνUrca(0) is the dUrca emissivity for a homogeneous npe plasma, calculated using plane waves and ignoring momentum conservation, and ℛ 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 ℛ ∼ 10− 5, but even this strong reduction still allows QdUrca(m) ν to be much larger than that from any other process of neutrino emission in the neutron star crust [179Jump To The Next Citation Point]. However, it should be stressed that dUrca(m ) Qν 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 T = 3 × 108 K, QdUrca(m ) ν exceeds all other crust emissivities by a factor of at least 104.
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