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Register a new userNeutrino emission due to Cooper-pair recombination in neutron stars revisited
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Neutrino emission in processes of breaking and formation of neutron and proton Cooper pairs is calculated within the Larkin-Migdal-Leggett approach for a superfluid Fermi liquid. We demonstrate explicitly that the Fermi-liquid renormalization respects the Ward identity and assures the weak vector current conservation. The systematic expansion of the emissivities for small temperatures and nucleon Fermi velocity, v_{F,i}, i=n,p, is performed. Both neutron and proton processes are mainly controlled by the axial-vector current contributions, which are not strongly changed in the superfluid matter. Thus, compared to earlier calculations the total emissivity of processes on neutrons paired in the 1S_0 state is suppressed by a factor ~(0.9-1.2) v_{F,n}^2. A similar suppression factor (~v_{F,p}^2) arises for processes on protons.
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Neutrino emissivities in a neutron star are computed for the neutrino bremsstrahlung process. In the first part the electro-weak nucleon-nucleon bremsstrahlung is calculated in free space in terms of a on-shell $T$-matrix using a generalized Low energy theorem. In the second part the emissivities are calculated in terms of the hadronic polarization at the two-loop level. Various medium effects, such as finite particle width, Pauli blocking in the $T$-matrix are considered. Compared to the pioneering work of Friman and Maxwell in terms of (anti-symmetrized) one-pion exchange the resulting emissivity is about a factor 4 smaller at saturation density.
Magnetars are a subclass of neutron stars whose intense soft-gamma-ray bursts and quiescent X-ray emission are believed to be powered by the decay of a strong internal magnetic field. We reanalyze neutrino emission in such stars in the plausibly relevant regime in which the Landau band spacing of both protons and electrons is much larger than kT (where k is the Boltzmann constant and T is the temperature), but still much smaller than the Fermi energies. Focusing on the direct Urca process, we find that the emissivity oscillates as a function of density or magnetic field, peaking when the Fermi level of the protons or electrons lies about 3kT above the bottom of any of their Landau bands. The oscillation amplitude is comparable to the average emissivity when the Landau band spacing mentioned above is roughly the geometric mean of kT and the Fermi energy (excluding mass), i. e., at fields much weaker than required to confine all particles to the lowest Landau band. Since the density and magnetic field strength vary continuously inside the neutron star, there will be alternating surfaces of high and low emissivity. Globally, these oscillations tend to average out, making it unclear whether there will be any observable effects.
We simulate cooling of superfluid neutron stars with nucleon cores where direct Urca process is forbidden. We adopt density dependent critical temperatures $T_{cp}(rho)$ and $T_{cn}(rho)$ of singlet-state proton and triplet-state neutron pairing in a stellar core and consider a strong proton pairing (with maximum $T_{cp}^{max} ga 5 times 10^9$ K) and a moderate neutron pairing ($T_{cn}^{max} sim 6 times 10^8$ K). When the internal stellar temperature $T$ falls below $T_{cn}^{max}$, the neutrino luminosity $L_{CP}$ due to Cooper pairing of neutrons behaves $propto T^8$, just as that produced by modified Urca process (in a non-superfluid star) but is higher by about two orders of magnitude. In this case the Cooper-pairing neutrino emission acts like an enhanced cooling agent. By tuning the density dependence $T_{cn}(rho)$ we can explain observations of cooling isolated neutron stars in the scenario in which direct Urca process or similar process in kaon/pion condensed or quark matter are absent.
The minimal cooling paradigm for neutron star cooling assumes that enhanced cooling due to neutrino emission from any direct Urca process, due either to nucleons or to exotica such as hyperons, Bose condensates, or deconfined quarks, does not occur. This scenario was developed to replace and extend the so-called standard cooling scenario to include neutrino emission from the Cooper pair breaking and formation processes that occur near the critical temperature for superfluid/superconductor pairing. Recently, it has been found that Cooper-pair neutrino emission from the vector channel is suppressed by a large factor compared to the original estimates that violated vector current conservation. We show that Cooper-pair neutrino emission remains, nevertheless, an efficient cooling mechanism through the axial channel. As a result, the elimination of neutrino emission from Cooper-paired nucleons through the vector channel has only minor effects on the long-term cooling of neutron stars within the minimal cooling paradigm. We further quantify precisely the effect of the size of the neutron 3P2 gap and demonstrate that consistency between observations and the minimal cooling paradigm requires that the critical temperature T_c for this gap covers a range of values between T_c^min < 0.2 x 10^9 K up to T_c^max > 0.5 times 10^9 K in the core of the star. In addition, it is required that young neutron stars have heterogenous envelope compositions: some must have light-element compositions and others must have heavy-element compositions. Unless these two conditions are fulfilled, about half of the observed young cooling neutron stars are inconsistent with the minimal cooling paradigm and provide evidence for the existence of enhanced cooling.
We investigate the nonlocal thermoelectric transport in a Cooper-pair splitter based on a double-quantum-dot-superconductor three-terminal hybrid structure. We find that the nonlocal coupling between the superconductor and the quantum dots gives rise to nonlocal thermoelectric effects which originate from the nonlocal particle-hole breaking of the system. We show that Cooper-pair splitting induces the generation of a thermo-current in the superconducting lead without any transfer of charge between the two normal metal leads. Conversely, we show that a nonlocal heat exchange between the normal leads is mediated by non-local Andreev reflection. We discuss the influence of finite Coulomb interaction and study under which conditions nonlocal power generation becomes possible, and when the Cooper-pair splitter can be employed as a cooling device.
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