We find that models of MeV-GeV dark matter in which dark matter interacts strongly can be constrained by the observation of gravitational waves from binary neutron star (BNS) mergers. Trace amounts of dark matter, either produced during the supernova or accreted later, can alter the structure of neutron stars (NS) and influence their tidal deformability. We focus on models of dark matter interacting by the exchange of light vector gauge bosons that couple to a conserved dark charge. In these models, dark matter accumulated in neutron stars can extend to large radii. Gravitational waves detected from the first observed BNS merger GW170817 places useful constraints on such not-so compact objects. Dark halos, if present, also predict a greater variability of neutron star tidal deformabilities than expected for ordinary neutron stars.
We show that the nonzero electron mass plays a critical role in determining the magnetic properties of neutron stars, making it impossible to generate the chiral charge density needed to trigger a strong chiral magnetic instability during the core collapse of supernovae. This instability has been proposed as a plausible mechanism for generating extremely large helical magnetic fields in neutron stars at their birth; the mechanism relies on the generation of a large non-equilibrium chiral charge density via electron capture reactions that selectively deplete left-handed electrons during core-collapse and the early evolution of the protoneutron star. Our calculation shows that the electron chirality violation rate induced by Rutherford scattering, despite being suppressed by the smallness of the electron mass relative to the electron chemical potential, is still fast compared to the weak interaction electron capture rate. The resulting asymmetry between right and left-handed electron densities is therefore never able to attain an astrophysically relevant magnitude.
We analyze the chiral magnetic effect in a homogeneous neutral plasma from the point of view of energy conservation, and construct an effective potential for the growth of maximally helical perturbations of the electromagnetic field. We show that a negative curvature at the origin of the potential, indicating instability of the plasma, is induced by a chiral asymmetry in electron Fermi energy, as opposed to number density, while the potential grows at large field value. It follows that the ground state for a plasma has zero magnetic helicity; a nonzero electron mass will allow an excited state of a plasma with nonzero helicity to relax to that ground state quickly. We conclude that a chiral plasma instability triggered by weak interactions is not a viable mechanism for explaining magnetic fields in stars except possibly when dynamics drives the system far from equilibrium.
Calculating the structure of white dwarf and neutron stars would be a suitable topic for an undergraduate thesis or an advanced special topics or independent study course. The subject is rich in many different areas of physics accessible to a junior or senior physics major, ranging from thermodynamics to quantum statistics to nuclear physics to special and general relativity. The computations for solving the coupled structure differential equations (both Newtonian and general relativistic) can be done using a symbolic computational package, such as Mathematica. In doing so, the student will develop computational skills and learn how to deal with dimensions. Along the way he or she will also have learned some of the physics of equations of state and of degenerate stars.
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