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New model could help find gravitational waves in binary pulsars

The model contains, for the first time, a realistic description of how neutron stars are deformed just before they collide.
Neutron star
Tidal forces deform a neutron star (left) orbiting another compact object - a second neutron star or a black hole.
© T. Hinderer/AEI
Scientists at the Max Planck Institute for Gravitational Physics in Potsdam, Germany, have developed an accurate model for the detection and interpretation of gravitational waves emitted by neutron stars in binary systems. This model contains, for the first time, a realistic description of how neutron stars are deformed just before they collide. This will enable more robust measurements leading to an improved understanding of the properties of the densest objects in our universe.

The first discovery of gravitational waves from merging black holes announced earlier this year has initiated the use of gravitational waves as unique probes of the most violent astrophysical processes. One highly anticipated source of gravitational waves is collisions of neutron stars, which are among the most fascinating objects in the universe. They have up to two times the mass of our Sun contained in a diameter of less than 10 miles (20 kilometers). The nature of such extremely dense matter has remained a mystery for decades. By probing the interiors of neutron stars, we could understand the unknown physics of these extreme celestial bodies. Gravitational wave astronomy will allow us to do so, as neutron stars in binaries emit waves in spacetime when they merge, carrying unique information about the neutron stars.

However, such signals of astrophysical origin are weak compared to the instrumental noise of current detectors. Nevertheless, the extraction of a signal from the noisy data and its analysis becomes possible with accurate theoretical models of the plausible signals that these systems emit. In particular, the Effective One Body model for binary black holes developed at the Max Planck Institute for Gravitational Physics in Potsdam and the University of Maryland was instrumental in assessing the highest detection confidence and maximizing the science gains from the recent discovery of gravitational waves with LIGO detectors.

The present work extends this Effective One Body model to include the imprint of the rich neutron star physics on the waves. When a neutron star orbits another compact object — a second neutron star or a black hole — it is deformed due to tidal forces. The present work significantly improves the modeling of tidal effects by taking into account internal oscillations in the neutron star arising when the companion’s tidal force varies at a frequency close to a characteristic frequency of the star itself. This is analogous to oscillations of a bridge excited by a band marching at a pace that matches the bridge’s characteristic frequency. The characteristic frequency of neutron stars is in the kHz range and is approached just before the neutron star and its companion merge.

In this final stage of the collision, the neutron star orbits its companion in less than a millisecond at about half of the speed of light. Both the amount of tidal deformation and the characteristic frequency of a neutron star depend sensitively on the microphysical properties of the neutron star matter. Any tidal response of the star leaves a distinct imprint on the gravitational waves emitted by the binary. Thus, gravitational waves will reveal unique information about the exotic interior of the neutron stars.

“Our detailed model more accurately predicts the waveforms and thus tells us what to look for in the data,” said Andrea Taracchini from the Astrophysical and Cosmological Relativity division at AEI. “We tested our model against results from numerical relativity simulations produced by our collaborators in the U.S. and Japan. The model shows a better agreement with the numerical results than models which neglect the characteristic frequency.”

“This means that our model is capturing genuine physical effects,” said Tanja Hinderer from the University of Maryland.

Numerical simulations provide the most realistic predictions for gravitational waves. However, they are too expensive to deliver enough waveforms for the detectors. The newly developed analytical model not only enables generating arbitrarily many waveforms, but also explains physical characteristics of the waves.

The search and analysis of gravitational waves requires detailed knowledge of an enormous number of different waveforms. Various parameter combinations must be calculated: different compositions of the binary system, different mass ratios, spins, and models of neutron star matter. The new analytical model allows calculation of thousands of waveforms in a short time. The extraction of science from the gravitational wave data is then performed using these templates.
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