Gravitational wave observations can potentially measure properties of neutron star equations of state by measuring departures from the point-particle limit of the gravitational waveform produced in the late inspiral of a neutron star binary. Numerical simulations of inspiraling neutron star binaries computed for equations of state with varying stiffness are compared. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly if the neutron stars are more compact. This suggests that gravitational wave observations at frequencies around 1 kHz will be able to measure a compactness parameter and place stringent bounds on possible neutron star equations of state. Advanced laser interferometric gravitational wave observatories will be able to tune their frequency band to optimize sensitivity in the required frequency range to make sensitive measures of the late-inspiral phase of the coalescence.
In numerical simulations of the late inspiral and merger of binary neutron-star systems, one commonly specifies an equation of state for the matter, perform a numerical simulation and extract the gravitational waveforms produced in the inspiral. The scope of this talk is to report work on the inverse problem: if gravitational radiation from an inspiraling binary system is detected, can one use it to infer the bulk properties of neutron star matter and, if so, with what accuracy? To answer this question, a number of simulations with systematic variation of the equation of state (EOS) is performed. The simulations use the evolution and initial-data codes of Shibata and Uryū to compute the last several orbits and the merger of neutron stars, with matter described by a parameterized equation of state, previously obtained in [1]. Our analysis uses waveforms from these simulations to examine the accuracy with which detectors with the sensitivity of Advanced LIGO can extract from inspiral waveforms an EOS parameter associated with the stiffness of the neutron star EOS above nuclear density.
One might expect that gravitational wave observations can potentially measure properties of neutron star EOS by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral of a binary system. A way to quantify this departure is to make use of the fact that the gravitational wave phase near the end of inspiral accumulates more rapidly for smaller values of the neutron star compactness (the ratio of the mass of a neutron star to its radius). In this way, greater accuracy may be obtained compared to previous work that suggested the use of an effective cutoff frequency to place constraints on the equation of state. Our results based on this approach suggest that realistic equations of state will lead to gravitational waveforms that are distinguishable from point arXiv:1110.3759v2 [gr-qc] 18 Oct 2011 particle inspirals at a distance 100 Mpc for an optimally oriented system, using Advanced LIGO in a broadband or narrowband configuration. Waveform analysis, that uses the sensitivity curves of commissioned and proposed gravitational wave detectors, allows us to also estimate the accuracy with which neutron star radii, closely linked to the EOS parameter varied, can be extracted. The choice of EOS parameter varied in this work is motivated by the fact that, as Lattimer and Prakash observed [3], neutron-star radius is closely tied to the pressure at density not far above nuclear. Analysis of the numerical waveforms also indicates that optimizing the sensitivity of gravitational wave detectors to frequencies above 700 Hz can lead to improved constraints on the radius and EOS of neutron stars.
Difficulties inherent in astrophysically constraining the EOS of neutron star matter are the wide range of different microphysical models, implying the lack of a model-independent set of fundamental observables, and the fact that models often have more free parameters than the number of astrophysical observables. Therefore, an effort to systematize such constraints necessitates a form of EOS (i) parameterized in a model independent way, with a number of EOS parameters (ii) large enough to accurately model the universe of candidate EOS, but (iii) smaller than the number of neutron star observables that have been measured or will have been measured in the next several years.
In the past, for different purposes, Müller and Eriguchi [4] have used non-relativistic piecewise polytropes, with a large number (20-100) of segments, to accurately approximate realistic EOS, in order to construct Newtonian models of differentially rotating stars. More recently, with conditions (i), (ii) and especially (iii) in mind, Read et al [1,2] have developed a relativistic piecewise polytropic approximation, which reproduces the features of most realistic neutron star EOS with rms error 4%, using only 3-4 segments (or 3-4 free parameters), as described below.
The EOS pressure p is specified as a function of rest mass density ρ (rest mass density ρ = m b n is proportional to number density n, where m b = 1.66 × 10 -24 g is the mean baryon rest mass). The relativistic piecewise polytropic EOS proposed in [1,2] has the form
in a set of intervals ρ i-1 ≤ ρ ≤ ρ i in rest mass density, with the constants K i determined by requiring continuity on each dividing density ρ i :
The energy density as a function of ρ is then determined by the first law of thermodynamics,
which is integrated, to give
(for Γ i = 1), where we used the condition /ρ → c 2 as ρ → 0. This condition implies a 0 = 0 and the other constants a i are fixed by continuity of (ρ) at each ρ i . In the above equations, ρ is measured in g cm -3 , and p have units of erg cm -3 = dyn cm -2 and c is the speed of light. The specific enthalpy, h, is dimensionless and is given by
The crust EOS is considered to be known and, for the purposes of this work, can be mo
This content is AI-processed based on open access ArXiv data.
