Neutrino production mechanisms in strongly magnetized quark matter: Current status and open questions

TL;DR

The paper investigates neutrino emission mechanisms in strongly magnetized, unpaired two-flavor quark matter relevant to compact-star cores. It develops a Kadanoff–Baym transport framework to derive direct Urca and neutrino–antineutrino synchrotron rates, incorporating Landau-level quantization for electrons and high-density approximations for quarks. Key findings show oscillatory and mildly suppressed direct Urca rates with magnetic field, a small anisotropic momentum emission leading to negligible pulsar kicks, and subdominant $\nu\bar{\nu}$ synchrotron emission that scales as $|eB|^2 T^5$ with a universal function $F(b)$; overall, magnetic fields influence cooling and dynamics but do not radically change the cooling picture for typical magnetar cores. The work lays groundwork for extensions to color-superconducting phases and to lepton-rich regimes with neutrino trapping, which are essential for a complete understanding of early neutron-star evolution. The results have implications for magnetar cooling and the interpretation of potential anisotropic neutrino signals from dense quark matter.

Abstract

We review the main neutrino emission mechanisms operating in dense quark matter under strong magnetic fields, with particular emphasis on conditions expected in the interiors of compact stars. We discuss the direct Urca and neutrino synchrotron processes in unpaired quark matter, incorporating the effects of Landau-level quantization. For the direct Urca process, the quantization of the electron energy spectrum plays a critical role, whereas quark quantization can often be neglected at sufficiently high baryon densities. The resulting field-dependent neutrino emissivity is anisotropic and exhibits an oscillatory behavior as a function of magnetic-field strength. We explore the implications of these effects for magnetar cooling and for possible anisotropic neutrino emission that could contribute to pulsar kicks. In addition, we review the $ν\barν$ synchrotron emission process, which, although subdominant, provides valuable insights into the interplay between magnetic fields and weak interactions in dense quark matter. Overall, our analysis highlights the nontrivial influence of strong magnetic fields on neutrino production in magnetized quark cores, with potential consequences for the thermal and dynamical evolution of compact stars.

Figures (6)

• Figure S1: Feynman diagrams for (a) direct Urca (anti)neutrino emission and (b) neutrino-antineutrino synchrotron emission in magnetized quark matter.
• Figure S2: Neutrino self-energy diagram used in the Kadanoff-Baym formalism to compute the direct Urca neutrino emission rate in dense quark matter.
• Figure S3: The neutrino energy emission rates for three fixed temperatures: $T=0.5~\hbox{MeV}$, $T=1~\hbox{MeV}$, and $T=2~\hbox{MeV}$. The rates in the LLL approximation are represented by dotted lines. The inset shows a close-up view of the region with the magnetic field strength below $5\times 10^{16}~\hbox{G}$.
• Figure S4: The neutrino net momentum emission rates for three fixed temperatures: $T=0.5~\hbox{MeV}$, $T=1~\hbox{MeV}$, and $T=2~\hbox{MeV}$. The rates in the LLL approximation are represented by dotted lines. The inset shows a close-up view of the region with the magnetic field strength below $5\times 10^{16}~\hbox{G}$.
• Figure S5: Neutrino self-energy diagram used in the Kadanoff-Baym formalism to compute the neutrino-antineutrino synchrotron emission rate in dense quark matter.