[Paper Review] Nuclear constraints on gravitational waves from deformed pulsars

Plamen Krastev, Bao-An Li|arXiv (Cornell University)|Jul 19, 2016

Pulsars and Gravitational Waves Research3 references3 citations

TL;DR

This paper estimates the maximum gravitational wave strain amplitude from 15 elliptically deformed millisecond pulsars using nuclear equation of state (EOS) constraints from terrestrial experiments. It finds strain amplitudes in the range of $[0.2-31.1] \times 10^{-24}$, suggesting detectability by LIGO/VIRGO under optimistic crustal breaking strain assumptions, but highlights significant uncertainties in EOS, crust strength, and pulsar parameters.

ABSTRACT

The recent direct detection of gravitational waves (GWs) from binary black hole mergers (2016, Phys. Rev. Lett. 116, no. 6, 061102; no. 24, 241103) opens up an entirely new non-electromagnetic window into the Universe making it possible to probe physics that has been hidden or dark to electromagnetic observations. In addition to cataclysmic events involving black holes, GWs can be triggered by physical processes and systems involving neutron stars. Properties of neutron stars are largely determined by the equation of state (EOS) of neutron-rich matter, which is the major ingredient in calculating the stellar structure and properties of related phenomena, such as gravitational wave emission from elliptically deformed pulsars and neutron star binaries. Although the EOS of neutron-rich matter is still rather uncertain mainly due to the poorly known density dependence of nuclear symmetry energy at high densities, significant progress has been made recently in constraining the symmetry energy using data from terrestrial nuclear laboratories. These constraints could provide useful information on the limits of GWs expected from neutron stars. Here after briefly reviewing our previous work on constraining gravitational radiation from elliptically deformed pulsars with terrestrial nuclear laboratory data in light of the recent gravitational wave detection, we estimate the maximum gravitational wave strain amplitude, using an optimistic value for the breaking strain of the neutron star crust, for 15 pulsars at distances 0.16 kpc to 0.91 kpc from Earth, and find it to be in the range of $\sim[0.2-31.1] imes 10^{-24}$, depending on the details of the EOS used to compute the neutron star properties. Implications are discussed.

Motivation & Objective

• To assess the detectability of continuous gravitational waves from elliptically deformed pulsars using current LIGO/VIRGO sensitivity.
• To constrain gravitational wave emission based on nuclear laboratory data, particularly the density dependence of nuclear symmetry energy.
• To evaluate how uncertainties in neutron star crust strength, equation of state, and pulsar parameters affect predicted strain amplitudes.
• To compare theoretical strain upper limits with current detector sensitivity and explain the absence of detections despite theoretical prospects.

Proposed method

• Used the MDI (Modified Dirac-Brueckner-Hartree) equation of state constrained by terrestrial nuclear data to model neutron star structure.
• Calculated the maximum quadrupole moment and gravitational wave strain amplitude using the approximate formula $ h_0 \sim \Phi_{22} \nu^2 / r $, where $ \Phi_{22} $ is the mass quadrupole moment.
• Applied an optimistic crust breaking strain of $ \sigma = 0.1 $ to estimate the maximum possible deformation and thus maximum strain.
• Evaluated 15 pulsars at distances from 0.16 to 0.91 kpc with rotational frequencies below 300 Hz.
• Compared predicted strain amplitudes with the current sensitivity of LIGO and VIRGO detectors.
• Explored the sensitivity of results to variations in neutron star mass, EOS details, and distance uncertainties.

Experimental results

Research questions

• RQ1 What is the maximum gravitational wave strain amplitude expected from elliptically deformed millisecond pulsars based on nuclear EOS constraints?
• RQ2 How do uncertainties in the neutron star crust breaking strain affect the predicted detectability of gravitational waves?
• RQ3 To what extent do variations in the equation of state and neutron star mass influence the predicted strain amplitudes?
• RQ4 Why have no gravitational wave signals been detected from these pulsars despite theoretical predictions of detectable strain levels?
• RQ5 How do current detector sensitivities compare with the upper limits of predicted strain amplitudes for these sources?

Key findings

• The maximum gravitational wave strain amplitude from the 15 pulsars is estimated to be in the range of $[0.2-31.1] \times 10^{-24}$, depending on the equation of state used.
• The highest strain estimate of $31.1 \times 10^{-24}$ occurs under the most optimistic assumptions, particularly the maximum crust breaking strain of $ \sigma = 0.1 $.
• Strain amplitudes decrease with increasing neutron star mass, indicating that heavier pulsars emit weaker gravitational waves.
• The lack of detection by LIGO/VIRGO is likely due to overly optimistic assumptions about crust strength, as theoretical estimates of $ \sigma $ vary by up to four orders of magnitude.
• Distance uncertainties of up to a factor of 2–3 and simplified modeling of the quadrupole moment further reduce the likelihood of detection with current assumptions.
• Improving the accuracy of the mass quadrupole moment through full numerical solutions of Einstein’s equations is essential for more reliable predictions.