Rapidly rotating superfluid neutron stars in Newtonian dynamics.pdf

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Rapidly rotating superfluid neutron stars in Newtonian dynamics.pdf

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Rapidly rotating superfluid neutron stars in Newtonian dynamics

a r X i v : a s t r o - p h / 0 3 0 9 5 2 2 v 1 1 9 S e p 2 0 0 3 Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 2 February 2008 (MN LATEX style file v2.2) Rapidly rotating superfluid neutron stars in Newtonian dynamics Shijun Yoshida1? and Yoshiharu Eriguchi2? 1Centro Multidisciplinar de Astrof??sica – CENTRA, Departamento de F??sica, Instituto Superior Te?cnico, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal 2Department of Earth Science and Astronomy, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Meguro, Tokyo 153-8902, Japan Typeset 2 February 2008; Received / Accepted ABSTRACT We develop a formulation for constructing and examining rapidly rotating Newtonian neutron star models that contain two superfluids, taking account of the effect of the rotation velocity difference between two superfluids. We assume neutron stars to be composed of the superfluid neutrons and the mixture of the superfluid protons and the normal fluid electrons. To describe Newtonian dynamics of the two superfluids, the Newtonian version of the so-called two-fluid formalism is employed. The effect of the rotation velocity difference on the structure of equilibrium state is treated as a small perturbation to rapidly rotating superfluid stars whose angular velocities of two superfluids are assumed to be exactly the same. We derive basic equations for the perturbed structures of rapidly rotating superfluid stars due to the rotation ve- locity difference between two superfluids. Assuming the superfluids to obey a simple analytical equation of state proposed by Prix, Comer, and Andersson, we obtain nu- merical solutions for the perturbations and find that the density distributions of the superfluids are strongly dependent on the parameter σ which appears in the analyti- cal equation of state and characterizes the so-called symmetry energy. It is also found that if Prix et al.’s analytical equation of state is assumed, the perturbations can be represented in terms o