This project studies neutron stars for the eventual purpose of relating both electromagnetic and gravitational wave observations to the properties of the neutron star interior. The neutron star matter will be described in terms of a multi-fluid model, where one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of cold neutron stars, another is a conglomerate of all other electromagnetically charged constituents (crust nuclei, superconducting protons, and electrons), the third is the entropy, and the last consists of massless neutrinos. A properly formulated set of dissipative equations for Newtonian superfluid neutron stars will be developed and their linearized form will be used to determine the time rate of change of the canonical energy. Local dispersion relations for the mode frequencies and a decomposition of the space of zero-frequency modes will be employed in the analysis of the mode spectrum. Realistic equations of state will be used that incorporate the entrainment effect (i.e. a momentum induced in the neutrons, say, causes some of the mass of the protons to be carried along) and symmetry energy (which tends to force nuclei to have as many neutrons as protons). Estimates for gravitational wave detector signal-to-noise will be obtained, as well as a basic understanding of how the potentially observable mode frequencies depend on superfluidity/superconductivity at the equation of state and dynamical levels.
The project has the potential to answer the following specific questions: 1. What are the generic features of multi-fluid, dynamical instabilities that have no counterparts for systems consisting of only a single fluid? What are the astrophysical consequences of such instabilities? 2. How do superfluidity and superconductivity, and their unique forms of dissipation, affect gravitational wave emission from neutron stars? Do they leave distinctive and detectable signatures in the gravitational waves themselves? With the advent of gravitational wave astronomy, there is an accompanying need to push the limits of modelling of astrophysical objects like neutron stars, so as to maximize the insights that result from analyses of gravitational wave data. In this way neutron stars can be maximally utilized as astrophysical laboratories for the study of large-scale superfluidity, truely high-temperature superconductivity, and the supra-nuclear equation of state. Undergraduates will participate in this research.
