Relativistic finite temperature multifluid hydrodynamics in a neutron star from a variational principle. (arXiv:2004.07468v5 [astro-ph.HE] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Rau_P/0/1/0/all/0/1">Peter B. Rau</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Wasserman_I/0/1/0/all/0/1">Ira Wasserman</a>
We develop a relativistic multifluid dynamics appropriate for describing
neutron star cores at finite temperatures based on Carter’s convective
variational procedure. The model includes seven fluids, accounting for both
normal and superfluid/superconducting neutrons and protons, leptons (electrons
and muons) and entropy. The formulation is compared to the non-variational
relativistic multifluid hydrodynamics of Gusakov and collaborators and shown to
be equivalent. Vortex lines and flux tubes, mutual friction, vortex pinning,
heat conduction and viscosity are incorporated into the model in steps after
the basic hydrodynamics is described. The multifluid system is then considered
at the mesoscopic scale where the currents around individual vortex lines and
flux tubes are important, and this mesoscopic theory is averaged to determine
the detailed vortex line/flux tube contributions to the macroscopic “effective”
theory. This matching procedure is partially successful, though obtaining full
agreement between the averaged mesoscopic and macroscopic effective theory
requires discarding subdominant terms. The matching procedure allow us to
interpret the magnetic $H$-field inside a neutron star in a way that is
consistent with condensed matter physics literature, and to clarify the
difference between this interpretation and that in previous astrophysical
works.
We develop a relativistic multifluid dynamics appropriate for describing
neutron star cores at finite temperatures based on Carter’s convective
variational procedure. The model includes seven fluids, accounting for both
normal and superfluid/superconducting neutrons and protons, leptons (electrons
and muons) and entropy. The formulation is compared to the non-variational
relativistic multifluid hydrodynamics of Gusakov and collaborators and shown to
be equivalent. Vortex lines and flux tubes, mutual friction, vortex pinning,
heat conduction and viscosity are incorporated into the model in steps after
the basic hydrodynamics is described. The multifluid system is then considered
at the mesoscopic scale where the currents around individual vortex lines and
flux tubes are important, and this mesoscopic theory is averaged to determine
the detailed vortex line/flux tube contributions to the macroscopic “effective”
theory. This matching procedure is partially successful, though obtaining full
agreement between the averaged mesoscopic and macroscopic effective theory
requires discarding subdominant terms. The matching procedure allow us to
interpret the magnetic $H$-field inside a neutron star in a way that is
consistent with condensed matter physics literature, and to clarify the
difference between this interpretation and that in previous astrophysical
works.
http://arxiv.org/icons/sfx.gif
