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Slowly rotating superfluid Newtonian neutron star model with entrainment

Slowly rotating superfluid Newtonian neutron star model with entrainment
Slowly rotating superfluid Newtonian neutron star model with entrainment
We develop a formalism that can be used to model slowly rotating superfluid Newtonian neutron stars. A simple two-fluid model is used to describe the matter, where one fluid consists of the superfluid neutrons that are believed to exist in the inner crust and core of mature neutron stars, while the other fluid is a charge neutral conglomerate of the remaining constituents (crust nuclei, core superconducting protons, electrons, etc.). We include the entrainment effect, which is a non-dissipative interaction between the two fluids whereby a momentum induced in one of the fluids will cause part of the mass of the other fluid to be carried along. The equations that describe rotational equilibria (i.e. axisymmetric and stationary configurations) are approximated using the slow-rotation approximation; an expansion in terms of the rotation rates of the two fluids where only terms up to second-order are kept. Our formalism allows the neutrons to rotate at a rate different from that of the charged constituents. For a particular equation of state that is quadratic in the two mass-densities and relative velocities of the fluids, we find an analytic solution to the slow-rotation equations. This result provides an elegant generalisation to the two-fluid problem of the standard expressions for the one-fluid polytrope . The model equation of state includes entrainment and is general enough to allow for realistic values for, say, mass and radius of the star. It also includes a mixed term in the mass densities that can be related to "symmetry energy" terms that appear in more realistic equations of state. We use the analytic solution to explore how relative rotation between the two fluids, the "symmetry energy" term, and entrainment affect the neutron star's local distribution of particles, as well as global quantities as the Kepler limit, ellipticity, and moments of inertia.
neutron stars, rotation, hydrodynamics
0004-6361
178-196
Prix, R.
96ea3047-4071-44f4-9a9f-e9e331c61421
Comer, G.L.
f2c1746c-8638-4268-94f0-e5d4375f0358
Andersson, N.
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Prix, R.
96ea3047-4071-44f4-9a9f-e9e331c61421
Comer, G.L.
f2c1746c-8638-4268-94f0-e5d4375f0358
Andersson, N.
2dd6d1ee-cefd-478a-b1ac-e6feedafe304

Prix, R., Comer, G.L. and Andersson, N. (2002) Slowly rotating superfluid Newtonian neutron star model with entrainment. Astronomy & Astrophysics, 381, 178-196. (doi:10.1051/0004-6361:20011499).

Record type: Article

Abstract

We develop a formalism that can be used to model slowly rotating superfluid Newtonian neutron stars. A simple two-fluid model is used to describe the matter, where one fluid consists of the superfluid neutrons that are believed to exist in the inner crust and core of mature neutron stars, while the other fluid is a charge neutral conglomerate of the remaining constituents (crust nuclei, core superconducting protons, electrons, etc.). We include the entrainment effect, which is a non-dissipative interaction between the two fluids whereby a momentum induced in one of the fluids will cause part of the mass of the other fluid to be carried along. The equations that describe rotational equilibria (i.e. axisymmetric and stationary configurations) are approximated using the slow-rotation approximation; an expansion in terms of the rotation rates of the two fluids where only terms up to second-order are kept. Our formalism allows the neutrons to rotate at a rate different from that of the charged constituents. For a particular equation of state that is quadratic in the two mass-densities and relative velocities of the fluids, we find an analytic solution to the slow-rotation equations. This result provides an elegant generalisation to the two-fluid problem of the standard expressions for the one-fluid polytrope . The model equation of state includes entrainment and is general enough to allow for realistic values for, say, mass and radius of the star. It also includes a mixed term in the mass densities that can be related to "symmetry energy" terms that appear in more realistic equations of state. We use the analytic solution to explore how relative rotation between the two fluids, the "symmetry energy" term, and entrainment affect the neutron star's local distribution of particles, as well as global quantities as the Kepler limit, ellipticity, and moments of inertia.

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More information

Published date: 2002
Keywords: neutron stars, rotation, hydrodynamics

Identifiers

Local EPrints ID: 29445
URI: http://eprints.soton.ac.uk/id/eprint/29445
ISSN: 0004-6361
PURE UUID: 89c8b52d-027f-45cf-8765-9c5ecd6dab23
ORCID for N. Andersson: ORCID iD orcid.org/0000-0001-8550-3843

Catalogue record

Date deposited: 11 May 2006
Last modified: 09 Jan 2022 02:57

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Contributors

Author: R. Prix
Author: G.L. Comer
Author: N. Andersson ORCID iD

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