where
is the rest mass density,
K
is a constant, and
is the polytropic exponent. Instead of
, one often uses the polytropic index
N, defined through
For this equation of state, the quantity
has units of length. In gravitational units (c
=
G
=1), one can thus use
as a fundamental length scale to define dimensionless
quantities. Equilibrium models are then characterized by the
polytropic index
N
and their properties can be scaled to different values, using an
appropriate value for
K
. For
N
<1.0 (N
>1.0), one obtains stiff (soft) models, while for
N
=0.5 - 1.0, one obtains models with bulk properties that are
comparable to those of observed neutron stars.
Note that for the above polytropic EOS, the polytropic index
coincides with the adiabatic index of a relativistic isentropic
fluid
This is not the case for the polytropic equation of state,
, that has been used by other authors, which satisfies (12
) only in the Newtonian limit.
The true equation of state that describes the interior of
compact stars is largely unknown. This results from the inability
to verify experimentally the different theories that describe the
strong interactions between baryons and the many-body theories of
dense matter at densities larger than about twice the nuclear
density (i.e. at densities larger than about
).
To date, many different realistic EOSs have been proposed
which produce neutron stars that satisfy the currently available
observational constraints (Currently, the two main constraints
are that the EOS must admit nonrotating neutron stars with
gravitational mass of at least
and allow rotational periods at least as small as 1.56 ms, see [6
,
7
].). The proposed EOSs are qualitatively and quantitatively very
different from each other. Some are based on relativistic
many-body theories, while others use nonrelativistic theories
with baryon-baryon interaction potentials. A classic collection
of early proposed EOSs was compiled by Arnett and Bowers [8
], while recent EOSs are described in Salgado et al. [9
].
High density equations of state with pion condensation have
been proposed by Migdal [10] and Sawyer and Scalapino [11]. The possibility of Kaon condensation is discussed by Brown and
Bethe [12] and questioned by Pandharipande et al. [13]. Many authors have examined the possibility of stars composed
of strange quark matter, and a recent review can be found in [14].
The realistic EOSs are supplied in the form of an energy
density vs. pressure table, and intermediate values are
interpolated. This results in some loss of accuracy because the
usual interpolation methods do not preserve thermodynamical
consistency. Recently however, Swesty [15] devised a cubic Hermite interpolation scheme that does preserve
thermodynamical consistency; the scheme has been shown to indeed
produce higher accuracy neutron star models in Nozawa et al. [16].
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Rotating Stars in Relativity
Nikolaos Stergioulas http://www.livingreviews.org/lrr-1998-8 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |