Neutron stars are extremely dense objects, second only to black holes. A teaspoon of neutron star matter weighs as much as Mt. Everest. Under such high densities, neutron stars possess exotic physics that cannot be reproduced on Earth.

We have been studying a subgroup of neutron stars, namely pulsars, that release their energies mainly through electromagnetic radiation. But these stars are only a fraction of the total neutron star population in the Milky Way Galaxy. We are missing out on other types of neutron stars that may not produce much electromagnetic radiation.

As a neutron star rotates, any mountains on its surface – even if they are just a few millimetres tall – will create ripples in the four-dimensional fabric of space- time. Such ripples are known as continuous gravitational waves, or continuous waves for short. Compared to the gravitational waves that have been detected, continuous waves are fainter but constant – similar to the humming of a fridge, as opposed to a loud bang.

Observing neutron stars through continuous waves provides us with information that is complementary to what can be learnt from pulsars, so that we can paint a more complete picture of the unknown physics that lies within. However, continuous waves from neutron stars are still undetected. To know whether they are detectable, and what we can learn from them, we need to perform simulations to see if our current and future gravitational wave detectors can detect continuous waves.

In this study, we looked at the capabilities of two detectors: LIGO, the first to detect gravitational waves in 2015; and the Einstein Telescope, a next- generation detector that is expected to be constructed in the 2030s. The first step to detecting continuous waves is to make sure that we are looking at the right place. The current catalogue of neutron stars contains only pulsars that may not emit any continuous waves. To get a full picture of the neutron star population in the Galaxy, we also need neutron stars that emit continuous waves. We simulated the entire neutron star population in the Galaxy, which includes continuous wave-emitting neutron stars. These stars have different energies and release different amounts of electromagnetic and continuous waves.

From this population of neutron stars, we then estimated the continuous waves produced by these stars, and how the two detectors respond to them. Using a technique called Bayesian inference, we performed searches on the faint “hums” amidst all the additional noise from the detectors. Being a next- generation detector, the Einstein Telescope is larger and more sensitive than LIGO, so the weak continuous wave signals can be more easily identified – just like how you can hear fainter sounds when you are in a quieter room.

The factor that determines the amount of continuous waves generated, known as the ellipticity, could be measured by the Einstein Telescope with an error of between 5 and 50% with 5 years of observation. This property of the neutron star cannot be determined by other methods. The limiting factor, we found, is the preciseness of our measurement of a quantity called the braking index. This number determines the fraction of a neutron star’s energy that is released as continuous waves. The ability to measure this number directly affects our measurement of ellipticity.

Our study demonstrated that future detectors, such as the Einstein Telescope, can detect continuous waves. Neutron star properties such as ellipticity, which previously could not be determined, can then be measured through the detected continuous waves. Our work provides a new way to probe the physics of neutron stars, and additional motivation to construct the next generation of gravitational wave detectors.

Reference: “Population Synthesis and Parameter Estimation of Neutron Stars with Continuous Gravitational Waves and Third-Generation Detectors”

Yuhan Hua, Karl Wette, Susan M. Scott, Matthew D. Pitkin.

Published on arXiv.