Relativistic Superfluid Models for Rotating Neutron Stars

Abstract

This article starts by providing an introductory overview of the theoretical mechanics of rotating neutron stars as developped to account for the frequency variations, and particularly the discontinuous glitches, observed in pulsars. The theory suggests, and the observations seem to confirm, that an essential role is played by the interaction between the solid crust and inner layers whose superfluid nature allows them to rotate independently. However many significant details remain to be clarified, even in much studied cases such as the Crab and Vela. The second part of this article is more technical, concentrating on just one of the many physical aspects that needs further development, namely the provision of a satisfactorily relativistic (local but not microscopic) treatment of the effects of the neutron superfluidity that is involved. Long before their observational detection as pulsars, theoreticiens were well aware [1] of the special physical interest of neutron stars -whose existence was confidently predicted -as well as of the (still entirely speculative) possibility of other more exotic (e.g. strange) stars of comparable compactness, meaning a radius only a few times larger than the Schwarzschild limit value, R = 2GM/c 2 , for a mass comparable with that of our Sun. Having presumably been formed by collapse of a stellar core that marginally exceeds the Chandrasekhar limit for for a self gravitating body with insufficient thermal pressure, a typical neutron star can be expected to a have a mass rather close to this limit, which -in terms of Newton's constant G, the speed of light c, the Dirac Planck constanth, and the proton mass m p -is given very roughly by the simple formulawhose derivation is based just on the supposition that m p gives a rough estimate of the mass per cubic Fermi length, regardless whether the degenerate relativistic fermions in question are electrons (as in an ordinary white dwarf) neutrons, or even quarks. Unlike what was possible when superfluidity of the neutron matter in such compact stars was originally predicted [2] by Migdal, present day article accelerators can explore the physics of individual particle at energies that are now approaching the order of a TeV. Nevertheless, although their levels -from MeV to at most the order of GeV -are only moderate by such modern standards, the thermal energies -and particularly the Fermi energies -characteristic of matter in neutron stars remain beyond the range accessible in the laboratory for bulk matter.For a mass near the value given by (1), the condition that the stellar radius be large compared with the Schwarzschild value, R = 2GM/c 2 , places an upper boundon the mean stellar density ρ * -and hence also on the central density (since unlike what is possible other kinds of stars, a neutron star cannot have a density profile that is sharply peaked at the center). While less compact neutron star configurations (with lower mass and larger radius) can exist in principle, it is hard to see how they could be created in nature, so ...

Analogue Gravity

“…This year saw more applications of analogue-inspired ideas to cosmological inflation [179, 441, 440, 343, 459], to neutron star cores [116], and to the cosmological constant [656, 658]. …”

Analogue Gravity

“…This year saw more applications of analogue-inspired ideas to cosmological inflation [107, 263, 262, 207, 275], to neutron star cores [66], and to the cosmological constant [414, 416]. …”

Constraint on the internal structure of neutron stars from pulsar glitches

“…An elegant and generic covariant variational formalism for describing such multicomponent systems was developed by Brandon Carter and his collaborators using exterior calculus. Originally formulated in the relativistic context [45,46], it was later adapted to the Newtonian framework [41,47,48,49]. A concise presentation of this formalism can be found, e.g., in Ref.…”