The matter can be modeled to be a perfect fluid because
observations of pulsar glitches have shown that the departures
from a perfect fluid equilibrium (due to the presence of a solid
crust) are of order
(see [112
]). The temperature of a cold neutron star does not affect its
bulk properties and can be assumed to be 0 K, because its
thermal energy (
) is much smaller than Fermi energies of the interior (
). One can then use a zero-temperature,
barotropic
equation of state (EOS) to describe the matter:
where
is the energy density and
P
is the pressure. At birth, a neutron star is expected to be
rotating differentially, but as the neutron star cools, several
mechanisms can act to enforce uniform rotation. Kinematical shear
viscosity is acting against differential rotation on a timescale
that has been estimated to be [101
,
102,
78]
where
,
T
and
R
are the central density, temperature, and radius of the star. It
has also been suggested that convective and turbulent motions may
enforce uniform rotation on a timescale of the order of
days [153]. In recent work, Shapiro [267] suggests that magnetic braking of differential rotation by
Alfvén waves could be the most effective damping mechanism,
acting on short timescales of the order of minutes.
Within roughly a year after its formation, the temperature of
a neutron star becomes less than
and its outer core is expected to become superfluid (see [227] and references therein). Rotation causes superfluid neutrons to
form an array of quantized vortices, with an intervortex spacing
of
where
is the angular velocity of the star in
. On scales much larger than the intervortex spacing,
e.g.
on the order of 1 cm, the fluid motions can be averaged and
the rotation can be considered to be uniform [285]. With such an assumption, the error in computing the metric is
of order
assuming
to be a typical neutron star radius.
The above arguments show that the bulk properties of an isolated rotating relativistic star can be modeled accurately by a uniformly rotating, zero-temperature perfect fluid. Effects of differential rotation and of finite temperature need only be considered during the first year (or less) after the formation of a relativistic star.
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Rotating Stars in Relativity
Nikolaos Stergioulas http://www.livingreviews.org/lrr-2003-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei.mpg.de |