Now that detection of gravitational wave signals from the coalescence of extra-galactic compact binary star mergers has become nearly routine, it is intriguing to consider other potential gravitational wave signatures. Here we examine the prospects for discovery of continuous gravitational waves from fast-spinning neutron stars in our own galaxy and from more exotic sources. Potential continuous-wave sources are reviewed, search methodologies and results presented and prospects for imminent discovery discussed. 

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Searches for continuous-wave gravitational radiation

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Primordial black hole constraints with Hawking radiation—A review

Non-axisymmetrical deformations of the crust on rapidly rotating neutron stars are one of the main targets of searches for continuous gravitational waves. The maximum ellipticity, or fractional diﬀerence in moments of inertia, that can be supported by deformations of the crust (known as “mountains”) provides an important upper limit on the strength of these continuous gravitational wave sources. We use the formalism developed by Gittins and Andersson, along with a deforming force that acts mainly in the transverse direction, to obtain a maximum ellipticity of 7.4 × 10 − 6 . This is larger than the original results that Gittins and Andersson obtained but consistent with earlier calculations by Ushomirsky, Cutler and Bildsten. This suggests that rotating neutron stars could be strong sources of continuous gravitational waves.

Neutron Star Crust Can Support A Large Ellipticity


 Pulsars are rotating neutron stars that emit periodic electromagnetic radiation. While pulsars generally slow down as they lose energy, some also experience glitches: spontaneous increases of their rotational frequency. According to several models, these glitches can also lead to the emission of long-duration transient gravitational waves (GWs). We present detection prospects for such signals by comparing indirect energy upper limits on GW strain for known glitches with the sensitivity of current and future ground-based GW detectors. We first consider the optimistic case of generic constraints based on the glitch size and find that realistic matched-filter searches in the fourth LIGO–Virgo–KAGRA observing run (O4) could make a detection, or set constraints below these indirect upper limits, for equivalents of 36 out of 726 previously observed glitches, and 74 in the O5 run. With the third-generation Einstein Telescope or Cosmic Explorer, 35–40% of glitches would be accessible. When specialising to a scenario where transient mountains produce the post-glitch GW emission, following the Yim & Jones model, the indirect upper limits are stricter. Out of the smaller set of 119 glitches with measured healing parameter, as needed for predictions under that model, only 6 glitches would have been within reach for O4 and 14 for O5, with a similar percentage as before with third generation detectors. We also discuss how this model matches the observed glitch population.

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Prospects for detecting transient quasi-monochromatic gravitational waves from glitching pulsars with current and future detectors


 Detection of continuous gravitational waves from rapidly-spinning neutron stars opens up the possibility of examining their internal physics. We develop a framework that leverages a future continuous gravitational wave detection to infer a neutron star’s moment of inertia, equatorial ellipticity, and the component of the magnetic dipole moment perpendicular to its rotation axis. We assume that the neutron star loses rotational kinetic energy through both gravitational wave and electromagnetic radiation, and that the distance to the neutron star can be measured, but do not assume electromagnetic pulsations are observable or a particular neutron star equation of state. We use the Fisher information matrix and Monte Carlo simulations to estimate errors in the inferred parameters, assuming a population of gravitational-wave-emitting neutron stars consistent with the typical parameter domains of continuous gravitational wave searches. After an observation time of one year, the inferred errors for many neutron stars are limited chiefly by the error in the distance to the star. The techniques developed here will be useful if continuous gravitational waves are detected from a radio, X-ray, or gamma-ray pulsar, or else from a compact object with known distance, such as a supernova remnant.

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Inferring neutron star properties with continuous gravitational waves

We present a targeted search for continuous gravitational waves (GWs) from 236 pulsars using data from the third observing run of LIGO and Virgo (O3) combined with data from the second observing run (O2). Searches were for emission from the $l=m=2$ mass quadrupole mode with a frequency at only twice the pulsar rotation frequency (single harmonic) and the $l=2, m=1,2$ modes with a frequency of both once and twice the rotation frequency (dual harmonic). No evidence of GWs was found so we present 95\% credible upper limits on the strain amplitudes $h_0$ for the single harmonic search along with limits on the pulsars' mass quadrupole moments $Q_{22}$ and ellipticities $\varepsilon$. Of the pulsars studied, 23 have strain amplitudes that are lower than the limits calculated from their electromagnetically measured spin-down rates. These pulsars include the millisecond pulsars J0437\textminus4715 and J0711\textminus6830 which have spin-down ratios of 0.87 and 0.57 respectively. For nine pulsars, their spin-down limits have been surpassed for the first time. For the Crab and Vela pulsars our limits are factors of $\sim 100$ and $\sim 20$ more constraining than their spin-down limits, respectively. For the dual harmonic searches, new limits are placed on the strain amplitudes $C_{21}$ and $C_{22}$. For 23 pulsars we also present limits on the emission amplitude assuming dipole radiation as predicted by Brans-Dicke theory. 

https://iopscience.iop.org/article/10.3847/1538-4357/ac6acf/pdf

Searches for Gravitational Waves from Known Pulsars at Two Harmonics in the Second and Third LIGO-Virgo Observing Runs

ABSTRACT The problem of the gravitational radiation damping of neutron star fundamental (f) mode oscillations has received considerable attention. Many studies have looked at the stability of such oscillations in rapidly rotating stars, calculating the growth or decay rate of the mode amplitude. In this paper, we look at the relatively neglected problem of the radiation reaction on the spin of the star. We specialize greatly to the so-called Kelvin modes: the modes of oscillation of (initially) non-rotating incompressible stars. We find the unexpected result that the excitation of a mode of angular momentum δJ on an initially non-rotating star ends up radiating an angular momentum 2δJ to infinity, leaving the star itself with a bulk angular momentum of −δJ. This result is interesting in itself, and also will have implications for the angular momentum budgets of spinning down neutron stars, should such modes be excited. 

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Tat-Tai Truong

Papers

Searches for Gravitational Waves from Known Pulsars at Two Harmonics in the Second and Third LIGO-Virgo Observing Runs

Gravitational radiation back-reaction from f-modes on neutron stars