One of the largest uncertainties in the input physics of NS-NS merger simulations is the true behavior of the
nuclear matter EOS. To date, EM observations have yielded relatively weak constraints on the NS
mass-radius relation, with the most precise simultaneous measurement of both as of now resulting from
observations of Type 1 X-ray bursts from accreting NSs in three different sources [220]. In each case, the
NS mass was found to lie in the range and the radius
,
implying a NS compactness
Given the large theoretical uncertainties in describing the proper physical NS EOS, many groups have
chosen the simplest possible parameterization: a polytrope (see Eq. 12). Under this choice, the enthalpy
takes the particularly simple form
Since the temperatures of NSs typically yield thermal energies per baryon substantially below the
Fermi energy, one may treat nearly all NSs as effectively cold, except for the most recently
born ones. During the merger process for NS-NS binaries, the matter will remain cold until
the two NSs are tidally disrupted and a disk forms, at which point the thermal energy input
and substantially reduced fluid densities require a temperature evolution model to properly
model the underlying physics. In light of these results, some groups adopt a two-phase model for
the NS EOS (see, e.g., [286]), where a cold, zero-temperature EOS, evaluated as a function of
the density only, encodes as much information about as we possess about the NS EOS, and
the hot phase depends on both the density and internal energy, typically in a polytropic way,
There are a number of physically motivated EOS models that have been implemented for merger
simulations, whose exact properties vary depending on the assumptions of the underlying model. These
include models for which the pressure is tabulated as a function of the density only: FPS [222], SLy [83],
and APR [3
]; as well as models including a temperature dependence: Shen [268
, 267
] and
Lattimer–Swesty [162]. A variety of models have been used to study the effects of quarks, kaons, and other
condensates, which typically serve to soften the EOS, leading to reduced maximum masses and more
compact NSs [223, 119, 230, 120, 23, 5].
Given the variance among even the physically motivated EOS models, it has proven useful to
parameterize known EOS models with a much more restricted set of parameters. In a series of works, a
Milwaukee/Tokyo collaboration determined that essentially all current EOS models could be fit using four
parameters, so that their imprint on GW signal properties could be easily analyzed [237, 238, 184]. Their
method assumes that the SLy EOS describes NS matter at low densities, and that the EOS at higher
densities can be described by a piecewise polytropic fit with breaks at and
. The
four resulting parameters are
, the pressure at the first breakpoint density, which
normalizes the overall density scale, as well as
, the adiabatic exponents in the three regions.
Their results indicate that advanced LIGO should be able to determine the NS radius to approximately
1 km at an effective distance of 100 Mpc, which would place tight constraints on the value of
in
particular.
http://www.livingreviews.org/lrr-2012-8 |
Living Rev. Relativity 15, (2012), 8
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