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Leonard E Parker

Center for Gravitation, Cosmology & Astrophysics

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Leonard E Parker Center for Gravitation, Cosmology and Astrophysics

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Acknowledgement

The Leonard E Parker Center for Gravitation, Cosmology and Astrophysics is supported by NASA, the National Science Foundation, UW-Milwaukee College of Letters and Science, and UW-Milwaukee Graduate School. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of these organizations.

Systematic and statistical errors in a bayesian approach to the estimation of the neutron-star equation of state using advanced gravitational wave detectors

Systematic and statistical errors in a bayesian approach to the estimation of the neutron-star equation of state using advanced gravitational wave detectors Leslie Wade, Jolien D. E. Creighton, Evan Ochsner, Benjamin D. Lackey, Benjamin F. Farr, Tyson B. Littenberg, Vivien Raymond (Paper)
NS EOS

The probability density of the tidal deformability parameter for the simulated binary neutron star system. The vertical dashed line is the injected value for the tidal deformability of the system, and the shaded region marks the 90% confidence intervals for this parameter estimation measurement. Credit: L. Wade.

Advanced ground-based gravitational-wave detectors currently under construction are expected to begin operating in the next few years. They are expected to achieve their design sensitivity c. 2019, at which time the detection rate of coalescing binary neutron-star systems is expected to be roughly 40 per year in a single detector.

Theoretical models of the gravitational waveform of a binary neutron-star system depend on the properties of the system. Some of these properties, or source parameters, include the masses and spins of each neutron star, the binary's location in the sky, the distance to the binary, and the binary’s orientation relative to the Earth. By adjusting the values of the source parameters in the theoretical model, the form of the modeled gravitational wave will change. It is therefore possible to estimate the properties of a binary neutron star system by comparing its measured gravitational-wave signal to many versions of a theoretically modeled waveform with different values for its source parameters. This process is known as parameter estimation.

Neutron stars in merging binary systems will be tidally deformed by the gravitational gradient of their companion across their finite diameter. This effect is insignificant at large separations but becomes increasingly significant as the neutron stars near each other. The internal structure of a neutron star, which is characterized by its unknown equation of state, determines how much each star will deform. The amount that a neutron star deforms will affect how fast the neutron stars spiral towards each other, which is encoded in the observed gravitational waveform. Therefore, if a gravitational wave signal from a binary neutron star system is detected, then such a detection could provide insight into the neutron star equation of state, and therefore its internal structure, through parameter estimation.

The amount that a binary neutron star will deform under tidal influences can be parameterized by a single parameter, which we call the tidal deformability. In this work, we demonstrate that the tidal deformability of a coalescing binary neutron star system will likely be measurable using advanced gravitational wave detectors. Since gravitational waves have not yet been detected, we simulate a gravitational wave detection by injecting a theoretical gravitational waveform into synthetic noise. We then attempt to extract the properties of this simulated system using parameter estimation techniques. In the figure on the right, we plot the probability density of the tidal deformability parameter for the simulated binary neutron star system. The vertical dashed line is the injected value for the tidal deformability of the system, and the shaded region marks the 90% confidence intervals for this parameter estimation measurement. We show how tidal deformability measurements such as this from real gravitational wave detections of binary neutron stars can be used to constrain the highly coveted neutron star equation of state.

We also report on the anticipated uncertainties in measuring tidal deformability in binary neutron star systems. We notably find that error resulting from measuring tidal effects using the current, incomplete, theoretical waveform models can significantly bias the estimation of tidal deformability measured from a real gravitational wave. The way that we test this without a real gravitational wave signal is by injecting the gravitational waveform given by one theoretical model and using another theoretical model in the parameter estimation process. Since each theoretical model is slightly different, this process simulates the real gravitational wave being slightly different from the theoretical waveform that we use to model it. In the figure below, we demonstrate how much the measurement of tidal deformability can be biased by waveform uncertainties. This result motivates the continued development of more reliable waveform models.

Gravitational-wave observatories will almost certainly be making many binary neutron star detections in the near future. Through the parameter estimation of tidal deformability, the highly coveted neutron star equation of state can be tightly constrained with such detections. However, in order to make accurate tidal deformability measurements, better theoretical gravitational waveform models need to be developed.

parameter estimation with theoretical waveforms

Parameter estimation was performed five times using different theoretical waveforms, which are labeled in the legend, as the injected signal. In each case, vastly different measurements of the tidal deformability parameter were made. This result motivates the continued development of more reliable waveform models. Credit: L. Wade.


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